tranmission planning
TRANSCRIPT
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 1/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 1
Microwave Link Planning
Training Notes
AIRCOM InternationalGrosvenor House
65-71 London road
Redhill, Surrey.
RH1 1 LQ
United Kingdom
Tel: +44 (0) 1737 775700
Email: [email protected]: www.aircom.co.uk
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 2/192
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 3/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 3
Table of Contents
1 System Description and Definitions of Terms ............................................................. 5
1.1 Introduction ........................................................................................................... 5
1.2 Definitions of terms............................................................................................... 61.3 The Block Diagram ............................................................................................... 7
1.4 Output of design process ....................................................................................... 91.5 Module 1: Self-Assessment Exercise ................................................................. 14
2 Antennas and The Link Budget.................................................................................. 15
2.1 The Microwave Antenna ..................................................................................... 15
2.2 Significant Parameters......................................................................................... 172.2.1 Beamwidth............................................................................................................................ 18 2.2.2 Gain ...................................................................................................................................... 18
2.3 Calculating the Received Power.......................................................................... 202.4 Linking Gain to Beamwidth ................................................................................ 25
2.5 Linking Gain and Antenna Diameter................................................................... 262.6 Linking Diameter and Beamwidth ...................................................................... 272.7 EIRP..................................................................................................................... 28
2.8 Feeders, Combiners and Splitters ........................................................................ 292.8.1 Splitters and Combiners........................................................................................................ 30
2.9 The Link Budget.................................................................................................. 312.10 Module 2: Self-Assessment Exercises ............................................................ 34
3 Noise Considerations.................................................................................................. 37
3.1 Introduction ......................................................................................................... 373.2 Noise Figure and Noise Temperature.................................................................. 38
3.3 Assessing the Receiver Threshold Level............................................................. 423.4 Threshold levels and the Link Budget................................................................. 43
3.5 Cascaded Systems. .............................................................................................. 453.5.1 Down Converters.................................................................................................................. 49
3.6 Shannon and Nyquist........................................................................................... 503.7 Module 3: Self-Assessment Exercises................................................................. 56
4 Fading......................................................................................................................... 59
4.1 Introduction ......................................................................................................... 594.2 Multipath Fading ................................................................................................. 59
4.2.1 Predicting the likelihood of a fade. ....................................................................................... 61 4.3 Rain Fading.......................................................................................................... 65
4.4 Accommodating Rain and Multipath Fading ...................................................... 674.5 Selective Fading in Digital Systems.................................................................... 70
4.6 Atmospheric Absorption...................................................................................... 764.7 Estimating Link Performance.............................................................................. 784.8 Conclusion. .......................................................................................................... 81
4.9 Module 4: Self-Assessment Exercises................................................................ 82
5 Diversity Techniques.................................................................................................. 855.1 Introduction ......................................................................................................... 85
5.2 The Theory Behind Diversity Systems................................................................ 86
5.3 Types of Diversity ............................................................................................... 87
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 4/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 4
5.4 Improvement Factor ............................................................................................ 89
5.5 Improvement for Other Types of Fading............................................................. 935.6 Combining Diversity Techniques........................................................................ 94
5.7 Module 5: Self-Assessment Exercises................................................................. 96
6 Interference Issues...................................................................................................... 97
6.1 Introduction ......................................................................................................... 976.2 Quantifying the effect of interference. ................................................................ 97
6.3 The Theory Behind Diversity Systems................................................................ 98
6.4 Co-channel and Adjacent Channel Interference.................................................. 986.5 Interference Scenarios ....................................................................................... 100
6.6 Reduction Techniques ....................................................................................... 103
6.7 Anomalous Propagation .................................................................................... 1046.8 Intermodulation Effects ..................................................................................... 106
6.9 Module 6: Self-Assessment Exercises............................................................... 109
7 Repeatered Systems.................................................................................................. 1137.1 Introduction ....................................................................................................... 113
7.2 Active and Passive Repeaters ............................................................................ 1147.2.1 Back-to-back antennas........................................................................................................ 116 7.2.2 Reflector repeaters.............................................................................................................. 118
7.3 Module 7: Self-Assessment Exercises............................................................... 124
8 Clearance Requirements........................................................................................... 129
8.1 Introduction ....................................................................................................... 1298.2 Earth Bulge ........................................................................................................ 130
8.3 The Fresnel Parameter ....................................................................................... 133
8.4 ITU-R Recommendations.................................................................................. 1358.5 Diffraction Loss................................................................................................. 137
8.6 Fading due to Ground Reflections..................................................................... 1408.6.1 An explanation of Reflection-induced Fading .................................................................... 140
8.6.2 The Rayleigh Criterion. ...................................................................................................... 144 8.6.3 Protection against reflection fades ...................................................................................... 145
8.7 Module 8: Self-Assessment Exercises............................................................... 154
9 Performance Objectives ........................................................................................... 1579.1 Introduction: ...................................................................................................... 157
9.2 Propagation-related Unavailability.................................................................... 158
9.3 Equipment-related Unavailability...................................................................... 1599.3.1 Hot Standby........................................................................................................................ 161
9.4 Unavailability Objectives .................................................................................. 164
9.5 Performance Standards ...................................................................................... 16510 Solutions to Self-Assessment Questions............................................................... 169
10.1 Module 1: Self-Assessment Exercise............................................................ 169
10.2 Module 2: Self-Assessment Exercise............................................................ 17010.3 Module 3: Self-Assessment Exercises ........................................................... 173
10.4 Module 4: Self-Assessment Exercises. ......................................................... 177
10.5 Module 5: Self-Assessment Exercises ........................................................... 18110.6 Module 6: Self-Assessment Exercises ........................................................... 183
10.7 Module 7: Self-Assessment Exercises ........................................................... 186
10.8 Module 8: Self-Assessment Exercises. .......................................................... 190
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 5/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 5
1 System Description and Definitions of Terms
1.1 Introduction
Aims of CourseAims of Course
• To enable you to plan the radio elements of a point to point microwave
link against a performance requirement and to be able to predict the
performance of the link that you have planned.
• This will involve gaining an understanding of
Introductory Session
• Antennas
• Link Budgets
• Noise
• Fading
• Diversity Techniques
• Interference
• Radio Propagation
• Modulation Methods
• Performance Prediction
Methods.
A microwave link will often present a convenient, economic way of providing high speed
data communications between two points. The objective of this course is to provide you
with a sufficient information and understanding to specify the radio equipment and
configuration of a microwave link for a given purpose.
The emphasis will be on performing quantitative analyses so that specific answers can be
given to the questions: “How high?”; “How big?”; “How long?”; “How far?”; “How
good?”.
Microwave equipment is readily available through a number of manufacturers. The link
designer’s job is to select and configure equipment in the most effective and economic
manner.
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 6/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 6
Why MicrowaveWhy Microwave
Microwave radio links provide high speed (2 Mbps+)communication between two points.
They are known to be:
• fast to implement
• convenient
• economic
when compared with wire-based alternatives.
1.2 Definitions of terms
Microwave frequencies are usually taken to mean frequencies between 3 GHz and 30
GHz (wavelengths of 100 mm to 10 mm). Higher frequencies (up to 40 GHz) than this,
known as “millimetric frequencies” are being used to provide point to point
communications and these will be included in the scope of this course.
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 7/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 7
What does “Microwave” meanWhat does “Microwave” mean
Microwave refers to a section of the RF spectrum lyingbetween 3 and 30 GHz. It is also referred to as “Super
High Frequency” (SHF).
LF MF HF VHF UHF SHF mm
300 GHz
30 GHz
3 GHz
300 MHz
30 MHz
3 MHz30 kHz
300 kHz
The Microwave Band
Note that frequencies up to 40 GHz are being used for
“microwave” links although the definition suggests that this
frequency is in the “millimetric” band.
A microwave link is taken to mean a fixed, permanent (or “semi-permanent”) connection
between two points. The design of “mobile microwave” or “microwave broadcast”
systems is beyond the scope of this course.
1.3 The Block Diagram
A microwave link can be thought of as consisting of a few elements that can be
purchased “off the shelf”. However, a whole variety of specifications will be available
and the link designer must select the most appropriate equipment for the job in hand. The
saying “An engineer is someone who can do something for a pound (or dollar, or euro
etc..) that any fool can do for ten pounds” is very true of microwave engineering. Buying
the “biggest, highest, most powerful and most expensive of everything and then
employing every performance-enhancing technique in existence will almost certainly
result in a system that will perform well but it will similarly result in a system that costs
far more than necessary.
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 8/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 8
System Block DiagramSystem Block Diagram
The equipment layout is essentially very simple. The job of the
link planner is to specify and configure the equipment.
Transceiver
Antenna
Feeder
The block diagram looks relatively straightforward. The two ends of the system are very
similar to each other with both consisting of: one or more antennas; a transmitter and
receiver (commonly known as a “transceiver”) and something to connect these two
together – a “feeder”.
Transceiver
Antenna
Feeder
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 9/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 9
The antenna will have to be mounted on a mast and the required height will be dependent
on the length of the link and the characteristics of the intervening terrain, amongst other
things. The focus in this course is on the radio engineering, rather than mechanical
engineering, aspects of the system design process and we will afford mast and tower
design only the most superficial of looks.
1.4 Output of design process
In its simplest form the final output of the design process will include details of:
• frequency of operation;
• antenna sizes
• antenna heights
• feeder type and length
• transmit power
• capacity
• path length
• predictions of unavailability
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 10/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 10
Answers, Please!Answers, Please!
How big must
the antenna
be?
How high
must the
antenna be?
What will the
loss of the
feeder be?
What should
the transmit
power be?
What power
level will we
receive?
What
frequency will
we use?
At what data
rate must we
send?
How good will the
performance be?
The above parameters will be the subject of individual attention but the prediction of
unavailability parameter will benefit from a mention at this point. Unlike an optical fibre
or coaxial cable transmission system, the performance of a microwave link will vary with
time. The received power level will suffer fades, mainly due to atmospheric refraction
effects and rain. Methods exist whereby the system can be predicted to be unavailable
for a (hopefully very small) percentage of the time. The percentage unavailability will
form one of the requirements specified by the customer.
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 11/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 11
Percentage OutagePercentage Outage
Unlike an optical fibre or coaxial cable system, the received
power level of a microwave system will vary significantlywith time.
This is due to atmospheric effects and “hydrometeors” suchas rain and snow.
This will inevitably lead to the system suffering an outage for a small percentage of the time.
The link planner must be able to predict the outage periodsas a percentage on a particular system.
Quantitative AnalysisQuantitative Analysis
The link planner must be able to determine numericalparameters to define the microwave system.
The course will involve methodologies, procedures andtechniques for arriving at the correct numerical solutions.
However, all solutions should fit in with the expectations of an intuitive engineer.
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 12/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 12
All the parameters in the list interact with each other and it is necessary to gain
knowledge regarding each of them before an intelligent approach can be taken to
microwave link design. Nevertheless, an intuitive engineering consideration of the
parameters can establish certain expectations formed from an engineering base. For
example we can confidently say that:
1. If the path length is increased then we should increase the transmit power
or antenna sizes.
2. If the length of feeder is reduced we can reduce the transmit power.
The two statements above are “qualitative” rather than “quantitative” in nature. It is
necessary to be able to analyse the situation quantitatively so that we can accurately
specify the equipment required. The following sections provide information, analyses
and techniques that will enable you to plan, design and predict the performance of a
microwave link.
Intuitive ExpectationsIntuitive Expectations
• If the antenna is bigger, the receive power will increase.
• If the link is longer the receive power will decrease.
• We will need a higher power to transmit a higher data rate.
• The higher the power received, the lower the percentage
outage.
• The longer the feeder, the lower the receive power.
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 13/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 13
Next StepsNext Steps
• All the parameters affect each other in an interactive way.
• The next sections will deal with particular parameters
whilst keeping one eye on the final goal
• In the next section we shall concentrate on the antenna
and methods of predicting the receive signal power.
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 14/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 14
1.5 Module 1: Self-Assessment Exercise
Designing by guessing.
As intuitive engineers we should have some idea regarding what a
microwave link should look be like and what its values should be.
Try and picture a microwave link in your mind and imagine what the
relevant parameters might be. It will be interesting to refer to these
“guesstimates” as we gain knowledge regarding the design of microwave
links.
Name of DesignerFrequency of Operation
Rate of transmission (bits per
second)
Mast Height
Antenna Diameter
Path Length
Transmit Power
Receive Power
Feeder length (metres)Feeder loss (dB)
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 15/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 15
2 Antennas and The Link Budget
2.1 The Microwave Antenna
The microwave antennas used for point to point links fall into the category of “aperture”
antennas, the parabolic dish antenna being the most common example. A propagating
electromagnetic wave has a power density P d (in watts per square metre) associated with
it. The aperture (known for these purposes as the “effective aperture” Ae) of the antenna
is measured in square metres and the antenna serves to convert the power density into an
actual power Pr (the suffix “r” standing for “received”) in accordance with the formula
ed r =
The Microwave AntennaThe Microwave Antenna
• Parabolic antennas are a form of
“aperture” antenna.
• The antenna faces an incoming
electromagnetic wave that has a
power density P d .
• The antenna converts this to a
received power P r .
Antennas and The Link Budget
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 16/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 16
The effective aperture of a microwave antenna is typically 60% of its measured aperture.
For example, a parabolic dish of 1 metre has an effective aperture of approximately
46.0 π × square metres.
The Microwave AntennaThe Microwave Antenna
• The “aperture” can be thought of as
a hole through which energy passes.
• This energy is delivered to the
antenna output..
Antennas and The Link Budget
ed r A P P =
E
H
Pd
Pr
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 17/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 17
The Microwave AntennaThe Microwave Antenna
• The “effective aperture” is linked to
the physical aperture.
• For an antenna presenting a circular
cross section of diameter D when
viewed from the front
Antennas and The Link Budget
46.0
2 D Ae
π ×≈
D
2.2 Significant Parameters
Although Ae is a vital parameter of a microwave antenna, it is not quoted very often.
Much more popular are the parameters of “gain” and “beamwidth”. It is important to
appreciate that an antenna performs both as a transmitter and as a receiver. Indeed, the
laws of physics dictate that the gain and beamwidth of an antenna as a receiver and as a
transmitter are exactly the same.
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 18/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 18
2.2.1 Beamwidth
A major purpose of a microwave antenna is to form the microwave energy into a narrow
beam rather than spread it widely. The narrower the beam, the higher the power densitythat will be achieved. The beamwidth is measured in degrees between the two points
either side of the principal axis (the principal axis is the name given to the line from the
antenna on which the power density is a maximum) at which the power density is half is
maximum value. This is often known as the “3 dB beamwidth”.
2.2.2 Gain
The Isotropic AntennaThe Isotropic Antenna
• A hypothetical antenna that
distributes its transmitted power
equally in all directions.
• As the surface area of a sphere
radius r is the power density
produced at a distance r is given by
Antennas and The Link Budget
24 r π
24 r
P P t
d π
=
r
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 19/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 19
Antenna GainAntenna Gain
• A practical microwave antenna will
produce a higher power density byconcentrating the energy into a
narrow beam.
• For an antenna of gain Gt , the power
density produced is, by definition
Antennas and The Link Budget
r
24 r
G P P t t
d π
=
The connection between beamwidth and power density means that beamwidth and gain
are inter-linked. The narrower the beamwidth, the higher the gain.
The gain of an antenna is measured as the increase in power density achieved as a
multiple of the density that would be produced by a theoretic “isotropic” antenna that
distributes the power equally in all directions. Given that the surface area of a sphere of
radius r is equal to 4πr 2, it is possible to say that the power density Pd is related to the
power transmitted Pt by the equation24 r
P P t
d π
= . The power density at the same
distance produced by an antenna with gain Gt is 24 r
G P t t
π . Notice that this gain,
Gt, refers to the principal direction of the antenna and will be very sensitive to errors in
the pointing direction.
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 20/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 20
2.3 Calculating the Received Power
If the power density is known, and the effective aperture of the receive antenna equals
Ae, then we can calculate the power received, Pr, using the equation
et t
r Ar
G P P
24π =
This is a simplified form of “link budget” that will allow us to predict the received power
level given the other parameters.
Example
The transmitting antenna on a point-to-point microwave link has a gain of 500. The
receiving antenna has an effective aperture of 2 m2. If the transmit power is 0.5 W and
the link is 20 km long it is possible to determine the power received, Pr, from the
equation
W
Ar
G P P e
t t r
8
2
2
1095.9)2000(4
25005.0
4
−×=××
=
=
π
π
Note that we have quoted a “gain” for the transmit antenna and an “effective aperture”
for the receive antenna. Identical antennas are normally used for transmit and receive
purposes and catalogues will normally quote only the gain. It is important to be able to
convert gain to effective aperture. For the purpose of achieving this we will rely on the
fact that the gain of the antenna as a transmitter is exactly the same as when used as a
receiver. The gain as a receiver, relative to an isotropic antenna is its effective aperture
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 21/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 21
as a multiple of the effective aperture of an isotropic antenna. If it has ten times the
effective aperture, it will capture ten times the power. It can be shown that the effective
aperture of an isotropic antenna at wavelength λ isπ
λ 4
2. Thus the gain, G, of the
antenna is given by
2
4
λ
π e AG = and hence
π
λ
4
2
G Ae =
Expressing the above equation in decibels gives
=210
4log10
λ
π e AG dBi (the “i” standing for “isotropic”)
Our formula for receive power now becomes
2
2
22
4
444Pr
=
==
r GG P
G
r
G P A
r
G P
r t t
r t t
e
t t
π
λ
π
λ
π π
Expressing this in terms of decibels gives
)(log20)(log20)4(log20)dBi()dBi()dBm()dBm( 101010 λ π +−−++= r GG P P r t t r
Now (Pt-Pr = Path loss). So
r t GGr −−−+= )(log20)(log20)4(log20LossPath 101010 λ π dB
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 22/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 22
Changing the units of distance from metres to kilometres and using the formula
f 3.0=λ where f is the frequency in Gigahertz gives.
[ ] r t r t GG f kmd P P −−+−+=− log20)3.0log(20)(1000log20)4log(20 π
r t
r t r t
GG f d
GG f d P P
−−++=
−−++++=−
1010
1010
log20log204.92
log20log2046.106098.21
The expression 92.4 + 20log(d) + 20log(f) equals the path loss when the gain of the
antennas is unity (0 dBi). This is known as the Free Space Loss (FSL).
r t GG f d −−++= 1010 log20log204.92FSL dB
where d is the path length in kilometres and f is the frequency in GHz.
Calculating the received power Calculating the received power
• This equation allows us to calculate
the received power given the other
parameters.
Antennas and The Link Budget
24 r
G P P t t
d π
= ed r A P P =
et t
r Ar
G P P
24π =
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 23/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 23
Calculating the received power Calculating the received power
• Example.
Antennas and The Link Budget
watts1095.9)20000(4
25005.0P
watts5.0
m20000
m2
500
8
2r
2
−×=××
=
=
=
=
=
π
t
e
t
P
r
A
G
Pt
Gt
Pr
Aer
Antenna CharacteristicsAntenna Characteristics
• Radiation pattern, gain, and antenna properties in general
have the same same characteristics whether the antennais being used as a transmitter or receiver.
• Considering the antenna as a receiver. The gain equals
its effective aperture as a multiple of the effective aperture
of an isotropic antenna.
• Aperture of isotropic antenna
Antennas and The Link Budget
dBi4
log10
4
4
210
2
2
=
=
=
λ
π
π
λ
λ
π
e
e
e
AG
G A
AGπ
λ
4
2
=
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 24/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 24
Calculating Received Power Calculating Received Power
• Substituting Effective Aperture in terms of Gain.
Antennas and The Link Budget
2
2
22
4
444Pr
=
==
r GG P
Gr G P A
r G P
r t t
r t t e
t t
π
λ
π λ
π π
)(log20)(log20)4(log20 101010 λ π +−−++= r GG P P r t t r
Calculating Received Power Calculating Received Power
• Changing units from metres to kilometres and from
wavelength in metres to frequency in Gigahertz:
Antennas and The Link Budget
)(log20)(log20)4(log20 101010 λ π +−−++= r GG P P r t t r
)(log20)(log204.92 1010 d f GG P P r t t r −−−++=
)/3.0(log20)1000(log20)4(log20 101010 f d GG P P r t t r +−−++= π
FSLGG P P r t t r −++=
[ ] [ ])km(log20)GHz(log204.92 1010 d f FSL ++=
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 25/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 25
2.4 Linking Gain to Beamwidth
Let us assume that an aperture antenna has a narrow, conical beam of beamwidth θ
radians.
At a distance r, the diameter of the circle illuminated is r θ and the area is4
22θ π r
Remembering that the area illuminated by an isotropic antenna is 4πr 2, the gain is given
by
( )
degrees 230
radians 4
16
4
422
2
G
G
r
r G
≈
≈
=≈
θ
θ θ π
π
Remember, G is a ratio (not in dB).
θ
r
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 26/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 26
Linking Gain andLinking Gain and BeamwidthBeamwidth
• A practical microwave antenna will
produce a gain by concentrating the
energy into a narrow beam.
• For an antenna of gain Gt , the area
illuminated will be reduced compared
with that illuminated by an isotropic
antenna by a factor equal to its gain.
Antennas and The Link Budget
r
θ r θdegrees230
4
16
4
4
2
222
t
t
t
t
G
G
G
G
r r
≈
≈
≈
≈
θ
θ
θ
π θ π
2.5 Linking Gain and Antenna Diameter
Remembering that
4 and 4
2
2 D A AG ee π
λ π ≈= where D is the antenna diameter in metres.
Hence
f D
Df DG
1010
22
log20log204.20Gain(dB)
0.3
)GHz(
++=
=
=
π
λ
π
The above formula ignores inefficiencies and imperfections. A more realistic formula for
the gain is
)(log20)(log205.17Gain(dB) 1010 GHz f m D ++=
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 27/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 27
Linking Gain and Antenna Diameter Linking Gain and Antenna Diameter
• The above equation ignores inefficiencies in the
antenna system. A more realistic equation is
Antennas and The Link Budget
22
2
2
3.0
4
4
=
≈
≈=
Df DG
D A AG ee
π
λ
π
π
λ
π
f DG 1010 log20log204.20 ++≈
f DG 1010 log20log205.17 ++≈
2.6 Linking Diameter and Beamwidth
( )
22(degrees)Beamwidth(GHz)frequency(m)Diameter
22
3.0230
230
0.3
2
≈××
≈
×≈
≈
=
θ
π θ
θ
π
Df
Df
G
Df G
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 28/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 28
Linking Antenna Diameter andLinking Antenna Diameter and BeamwidthBeamwidth
• From the previous slides:
Antennas and The Link Budget
22
3.0230
230
3.0
2
≈
×≈∴
≈
≈
θ
π θ
θ
π
Df
Df
G
Df G
• Diameter (metres) x frequency (GHz) x Beamwidth (degrees) 22
2.7 EIRP
The term “Equivalent Isotropic Radiated Power” (EIRP) is applied to a transmitting
antenna. It is the power that would have to be transmitted by an isotropic antenna to
produce the same power density. Mathematically it is very simple to express:
(ratio)(watts))EIRP(watts
(dBi)(dBm)EIRP(dBm)
t t
t t
G P
G P
×=
+=
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 29/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 29
EIRPEIRP
• A commonly used term - “Equivalent Isotropic Radiated Power”.
Antennas and The Link Budget
)ratio()watts()watts(
)dBi()dBm()dBm(
t t
t t
G P EIRP
G P EIRP
×=
+=
2.8 Feeders, Combiners and Splitters
A microwave station includes what is often referred to as “plumbing”; usually lengths of
waveguide and connectors. The “plumbing” exists to connect the transmitter and
receiver to the antenna. For most systems its main component will be a length of feeder
known as “waveguide”. Waveguide is the most common transmission line over the 3 –
30 GHz range. Coaxial cable becomes very lossy at frequencies above 3 GHz.
Waveguide can look similar to a large coaxial cable, the most significant difference being
that it has no inner conductor: effectively it traps the energy in the form of a radio wave
and causes this energy to propagate along the waveguide. The size of the is very much
frequency dependent with the width being approximately 0.7λ (where λ is the
wavelength). You can find rectangular, circular or elliptical guide for various purposes.
One crucial parameter that affects the loss of the guide is the conductivity of the inner
coating. Copper is most commonly used due to its high conductivity. However,
occasionally, at the highest frequencies (where losses are greatest), silver-plated
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 30/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 30
waveguide is used (silver has the highest conductivity of any metal). Manufacturers
tables should be referred to in order to select a feeder for the frequency range used and to
predict the loss incurred.
Feeders and CombinersFeeders and Combiners
Antennas and The Link Budget
• Co-axial cable is not suitable at frequencies above about 3 GHz.
• A hollow metal tube known as “waveguide” is used over the
frequency range 3 - 30 GHz.
• The size of the waveguide depends on the frequency being used
and typically has a width of 0.7λ.
• Usually made of copper or brass with a copper plating inner
coating. Occasionally silver plated.
• Losses typically 0.1 dB per metre. The higher the frequency, the
higher the loss.
2.8.1 Splitters and Combiners
The same antenna is used for transmitting and receiving. A sophisticated form of
combiner known as a “diplexing filter” is used to ensure that the high power transmitter
does not interfere with the very sensitive receiver. If a combined transmitter and receiver
is purchased “off the shelf” this filter will be an integral part of its construction.
Occasionally, the same transceiver will receive from two antennas whilst transmitting
from only one antenna. This arrangement requires a sophisticated “diversity
splitter/combiner” enable its implementation.
Such splitters and combiners inevitably have an “insertion loss” associated with them.
These losses must be considered when calculating the received signal strength.
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 31/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 31
Feeders and CombinersFeeders and Combiners
Antennas and The Link Budget
• A diplexer is a sophisticated device that makes it possible totransmit and receive from the same antenna.
• The received signal is sometimes the combination of two
antennas.
• Combiners and splitters have an insertion loss that must be
considered when predicting the received signal level.
• All miscellaneous losses must be considered.
2.9 The Link Budget
Producing a link budget is a disciplined way of calculating the received signal power in a
way that minimises the risk of omitting essential parameters. All parameters are quoted
in dB so that calculations entail only addition and subtraction. As an example consider
an 11 GHz system using two, 35 dBi, antennas. The path length is 20 km. Feeder losses
amount to 1.5 dB at the transmitter and receiver ends. Combiner losses total 2 dB. The
transmit power is 500 mW (27 dBm). The link budge shows that the received power is
expected to be -–47.2 dBm.
TRANSMIT
Transmit Power 27 dBm
Antenna Gain 35 dBi
Feeder Loss 1.5 dB
EIRP 60.5 dBm
PATH LOSS
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 32/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 32
Path Length 20 km
Frequency 11 GHz
Free Space Loss 139.2 dB
RECEIVE
Antenna Gain 35 dBi
Feeder Losses 1.5 dB
Net Gain 33.5 dB
MISC
Combiner Losses 2 dB
RECEIVE
POWER
-47.2 dBm
It is a straightforward matter to convert the link budget to a spreadsheet thus making it
easy to assess the impact of changing different parameters.
The Link BudgetThe Link Budget
Antennas and The Link Budget
• The Link Budget is usually of the form of a table that ensures no
sources of losses or gains are forgotten.
• Expressing all powers, losses and gains in dB, dBi, dBm etc.
Allows us to simply add or subtract the relevant amounts.
• The simplified link budget equation is given below. Each element
would be arrived at by considering its constituent parts.
Received Power = EIRP - FSL + Rx antenna gain - Misc Losses
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 33/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 33
The Link BudgetThe Link Budget
Antennas and The Link Budget
• Being able to determine the received power level is a
significant achievement.
• However, the question “Is this power level sufficient?”
must be answered.
• To be able to answer this question requires an
understanding of system noise.
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 34/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 34
2.10 Module 2: Self-Assessment Exercises
1. An antenna operates at a frequency of 15 GHz. If it has a diameter of 1.8
metres, estimate its gain.
2. Two such antennas are to be used over a link of length 12 km. Determinethe path loss.
3. Repeat the calculation of question 2 for antennas of the same size butoperating at a frequency of 30 GHz.
4. Estimate the beamwidth of a 1.8 metre antenna at 7 GHz, 15 GHz and 30GHz.
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 35/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 35
5. A transceiver outputs a power of 27 dBm via a feeder of 3 dB loss to an
antenna of diameter 0.9 metres. If the frequency of operation is 12 GHz,estimate the EIRP from the antenna.
6. For the situation described in question 5, estimate the power that would
be gathered by an identical antenna at a distance of 4 km.
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 36/192
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 37/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 37
3 Noise Considerations
3.1 Introduction
Noise ConsiderationsNoise Considerations
• Thermal Noise forms the fundamental limitation of any
telecommunications system.
• The level of thermal noise is directly proportional to
bandwidth and absolute temperature.
• k is Boltzmann’s constant and equals 1.38x10-23
joules/kelvin.
Noise Considerations
kTBPower Noise = watts
The fundamental limitation of any telecommunications system is thermal noise. The
random motion of electrons develops an alternating voltage such that a certain amount of
power will be delivered into a load resistor (which will in turn, generate its own thermal
noise). The level of thermal noise generated by a resistor, for example, is proportional to
the system bandwidth ( B), measured in hertz and also the absolute temperature (T ),
measured in kelvins (0°C = 273 K). The governing equation that describes the power
that will be delivered into a matched load is
wattsPower kTB=
k is known as Boltzmann’s constant and has a value 1.38 x 10-23
joules per kelvin.
An antenna will gather thermal noise along with a wanted signal. The amount of thermal
noise gathered depends on where the antenna is looking. A high quality satellite station
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 38/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 38
antenna “looking” at deep space can have a thermal noise temperature as low as 40
kelvins. A typical television satellite receiver will typically have a noise temperature of
160 K. However, we will be dealing with terrestrial systems whereby the antenna will be
looking at the earth’s atmosphere which is generally assumed to be at the “standard”
temperature of 290 K (usually referred to as T 0). In this circumstance the thermal noise
level will be watts/Hz1000.42901038.1 2123 −− ×=××× B .
Noise ConsiderationsNoise Considerations
• An antenna can be thought of as a noise gathering device.
• The figure for “absolute temperature” depends on where
the antenna is looking.
• For terrestrial systems, “normal” values such as 290 K are
suitable.
• For high quality satellite systems, values of T as low as 40
K are achievable.
• Cheaper systems (e.g. Sky TV) have values of 160 K.
Noise Considerations
3.2 Noise Figure and Noise Temperature.
The Signal to Noise ratio at the output of any electronic device, such as an amplifier or
even a length of feeder, will be worse that that at the input. This is because all devices
will contribute some noise to add to the existing thermal noise. In order to be able to
quantify the noise performance of a device it is assumed that the device includes a noise
generator at its input. The output power of this noise generator is assumed to be BkT e
where eT is known as the “effective noise temperature” of the device. The lower the
value of T e the better the performance of the system.
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 39/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 39
Receiver Noise Figure and NoiseReceiver Noise Figure and NoiseTemperatureTemperature
• No radio receiver is perfect, they all add noise to the
system.
• The SNR at the output of any amplifier is worse than at the
input.
• This is accounted for mathematically by imagining a noise
generator at the input of the amplifier.
• This noise generator has a power output of kT e B where T eis the noise temperature of the amplifier.
Noise Considerations
Knowing T e makes it possible to calculate the noise power at the output of the amplifier.
The total effective noise power at the input equals ( ) BT T k BkT kTB ee +=+ which
means that, if the device is an amplifier of gain G, the noise power at the output of the
amplifier will be ( ) BGT T k e+ . Values of T e will vary from a few tens of kelvins to
several thousand. As a result, the parameter is not particularly intuitive and the term
“noise figure” is often preferred.
Noise figure gives a direct impression of the amount by which a device makes the signal
to noise ratio worse. For example, if a device has a noise temperature of 290 kelvins and
the thermal noise power at the input was k (290) B then the noise power at the output
would be double what it would be if the device was perfect. The noise figure of this
device is 2 (or 3 dB) as the SNR at the output is 3 dB worse than that at the input. It is
possible to convert from noise temperature to noise figure by equating the noise power at
the output in terms of both effective noise temperature and noise figure.
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 40/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 40
( )
( )
0
0
00
00
1
1
T
T F
F T T
F T T T
BFGkT BGT T k
e
e
e
e
+=
−=
=+
=+
However, the term Noise Figure has a serious drawback. The equations described above
involving Noise Figure are only valid if the noise power at the input of the device is
thermal noise equating to a temperature of 290 kelvins. Use of Noise Figure under any
other circumstances is a mistake. Abuse of the term Noise Figure is widespread. Be
careful.
Effective Noise Temperature, on the other hand can be used regardless of the level ofnoise at the input of a device.
Receiver Noise Figure and NoiseReceiver Noise Figure and NoiseTemperatureTemperature
Noise Considerations
kTB
kTeB
G K(T+Te)BG
k(T o+T e )BG =kToBGF
• F is known as the noise figure of the amplifier.
• If the value of T at the input equals the “standard” temperature, To, of
290 K, then noise at the output equals
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 41/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 41
Receiver Noise Figure and NoiseReceiver Noise Figure and NoiseTemperatureTemperature
Noise Considerations
kToB
kTeB
G k(To+Te)BG= kToBGF
o
e
oeo
T
T F
F T T T
+=
=+
1
( )1−= F T T oe
Receiver Noise Figure and NoiseReceiver Noise Figure and NoiseTemperatureTemperature
• Using F is “convenient”. It can be expressed in dB, rather than as a ratio.
• In dB form is represents the “amount by which the SNR
gets worse”.
• However, the equation is only valid if the noise at the input
equals kT o B.
• Abuse of Noise Figure is widespread. Be careful.
Noise Considerations
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 42/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 42
3.3 Assessing the Receiver Threshold Level.
The SNR directly affects the error ratio (BER). Thus receiver noise performance directly
affects the BER achieved. For example, suppose an SNR of 14 dB is required to achieve
a BER of 1 x 10-6 with a system that has an 8 MHz bandwidth. We can determine the
minimum required signal power (the “threshold” level) in order to achieve this if the
receiver noise figure is known. If the noise figure is, say, 4 dB (a typical value;
equivalent to a ratio of 2.5) we can say that the noise temperature is 290(2.5-1) = 438 K.
Thus the equivalent noise power referred to the input is
( ) ( ) dBm)-101(watts1004.81084382901038.1 14623 =×=×+×=+ −− BT T k e
As the required SNR is 14 dB, it is simple to calculated the required signal power to be –
87 dBm. This establishes the minimum signal level required. Consulting manufacturers
literature will usually reveal information regarding the required signal level for a given
BER.
Assessing the minimum signal levelAssessing the minimum signal level• The error ratio experienced on a system depends on the SNR.
• We need to establish a required SNR in order to determine the minimum
required receive power (known as the receiver “threshold”).
• For example, a minimum SNR of 14 dB is required in order to deliver a
BER of better than 1x10-6. The system bandwidth is 8 MHz and the
receiver noise figure is 4 dB.
• 4 dB is a ratio of 2.5. Noise temperature is therefore 290(2.5-1) = 438 K.
• k(T+Te)B = 1.38x10-23(290+438)8x106 = 8.04x10-14 watts (=-101 dBm)
• SNR required of 14 dB is a ratio of 25. 25 x 8.04 x10-14 =2.0x10-12 watts
or -87 dBm. This establishes the minimum signal level.
• Note: receiver manufacturers will often quote their own threshold level.
Noise Considerations
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 43/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 43
3.4 Threshold levels and the Link Budget
So far link budgets have been introduced as a method of predicting the received signal
power. Now that we have a method of determining a minimum value for this signal
power allows us to establish minimum values for the various items of equipment that we
use. For example we could determine the minimum antenna sizes required given the
system parameters listed below.
Transmit Power -6 dBm
Receiver Threshold -87 dBm
Feeder/misc losses 5 dB
Transmit Frequency 6 GHz
Path Length 40 km
The required calculation is summarised below.
FSL 92.4 + 20log(6) +20 log (40)=140 dB
Misc Losses 5 dB
Tx Power -6 dBm
Rx Threshold -87 dBm
Allowable losses 81 dB
FSL + Misc Losses 145 dB
Required Antenna Gains 64 dBi
Each Antenna Gain must be 32 dBi
Diameter ( )metres88.010 20
6.155.1732
=−−
The calculation shows that 90 centimetre diameter antennas should be suitable.
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 44/192
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 45/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 45
3.5 Cascaded Systems.
Suppose we have a system that comprises of two amplifiers in tandem, with the output of
one forming the input to the other. The amplifiers have gains and effective noise
temperatures 2211 ,,, ee T GT G respectively. Suppose the noise power at the input to the
first amplifier equals kTB then the noise at the output of this first amplifier will be
( ) 11 BGT T k e+ . This is fed into the second amplifier with the result that the noise power
at the output will be ( )[ ]{ } 2211 BGT GT T k ee ++ . This can be equated to ( ) 21G BGT T k e+
where Te is the overall noise temperature of the system. Equating these quantities results
in the overall noise temperature being linked to the individual parameters by
1
21 G
T
T T eee += . This can be extended to more than two amplifiers resulting in the
general equation
.................21
3
1
21
GG
T
G
T T T ee
ee ++=
Examining the above equation shows that the first amplifier in a system (often referred to
as a “low noise amplifier”) is most crucial in determining the overall noise temperature as
the noise temperature of any subsequent devices is divided by the gain of the first
amplifier.
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 46/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 46
Noise Figure and Noise Temperature of Noise Figure and Noise Temperature of “cascaded systems”“cascaded systems”
Noise Considerations
G1 ,Te1 G2 ,Te2
k(T+Te1 )BG1 k{[(T+Te1 ) G1 ]+ Te2 } B G2
k(T)B
k{[(T+Te1 ) G1 ]+ Te2 } B G2 =k(T+Te)B G1 G2
1
21
G
TeTeT +=
.............21
3
1
21
GG
Te
G
TeTeT ++=
The same reasoning can be applied to determining the noise temperature of an attenuator.
Remember that feeders in a microwave communications system will act as attenuators.
The signal will be attenuated at the output but, in a matched system, the noise power at
the output will be the same as at the input. Using the same equations as before, the noise
power at the output is ( ) BGT T k e+ . Equating this to the noise power at the input gives
( )
( )
( )
−=
−=
=+
=+
11
1
GT
G
GT T
T GT T
kTB BGT T K
e
e
e
Remember that, for an attenuator, G will be less than one.
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 47/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 47
Noise Figure and Noise Temperature of Noise Figure and Noise Temperature of attenuatorsattenuators (and feeders)(and feeders)
• For a matched attenuator receiving thermal noise at its
input, the noise at the output equals the noise at the input.
Noise Considerations
Ik(T)B k(T+Te)BG
( )
( )
( )11
)1(
−=
−=
+=
+=
GT
G
GT T
GT T T
BGT T k kTB
e
e
e
• Note that, for an attenuator, G will
be less than 1.
As an example consider the situation where an antenna is connected to a receiver via a
feeder of loss 2.5 dB. If the temperature of the feeder is 290 K and the Noise Figure of
the receiver is 4 dB it is possible to determine the noise figure of the combination.
Receiver Noise Figure 4 dB (ratio of 2.5)
Receiver Noise Temperature 1.5 x 290 = 435 K
Attenuation 2.5 dB G = 1/1.778 = 0.562
Noise Temperature of Attenuator 290(1.778-1)=226 K
Overall Noise Temperature 226+(435÷0.562) = 1000 K
Overall Noise Figure 1+(1000÷290) = 4.45 (or 6.5 dB)
Thus the presence of the attenuating feeder has worsened the noise figure from 4 dB to
6.5 dB.
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 48/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 48
The situation described above can be improved by installing a low noise, “mast head
amplifier” in between the antenna and the feeder. If this has a gain of 15 dB and a Noise
Figure of 3 dB we can determine the new Noise Figure in the usual manner.
Noise Temperature of MHA 290 K
Gain of MHA 31.6
Overall Noise Temperature 290+(1000÷31.6) = 321.6 K
Overall Noise Figure 1+(321.6÷290) = 2.11 (or 3.24 dB)
Notice that this new Noise Figure is lower than that of the receiver alone. It is the Noise
Figure of the MHA, rather than that of the receiver, that forms the lower limit of the
resultant Noise Figure.
Cascaded System ExampleCascaded System Example
• An antenna is connected to a receiver via a feeder of loss
2.5 dB. If the temperature of the feeder is 290 K and the
Noise Figure of the receiver is 4 dB, determine the noisefigure of the overall combination.
Noise Considerations
• Noise Figure 4 dB. Ratio of 2.5.
• Noise temperature = 1.5x290=435 K.
• G for attenuator is 0.562. Noise temperature of
attenuator is 290(0.778)=226 K
• Overall noise temperature is 226+435/0.562=1000 K
• Overall noise figure = 1+1000/290=4.45 (6.48 dB)
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 49/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 49
Cascaded System Example - Low NoiseCascaded System Example - Low NoiseAmplifier Amplifier
• To improve the previously described situation, a Low Noise
amplifier is connected between the antenna and the feeder.This has a gain of 15 dB and a Noise Figure of 3 dB.
Determine the new noise figure.
Noise Considerations
• Noise Figure 3 dB. Ratio of 2. Noise temperature = 290 K
• G for amplifier is 31.6.
• Overall noise temperature is 290+1000/31.6=321.6 K
• Overall noise figure = 1+321.6/290=2.11 (3.24 dB)
3.5.1 Down Converters
It has been shown that the loss of a feeder severely affects the noise performance of a
system. As frequencies rise, so does the loss of waveguide feeder. At frequencies above
about 20 GHz a length of waveguide feeder longer than a few metres is not practical from
a loss viewpoint. To this end a mast head amplifier is used that not only provides low
noise gain but also converts the signal to a much lower frequency thus allowing it to be
fed to the receiver with a much lower loss using a much less expensive feeder.
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 50/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 50
Cascaded Systems - The Down-converter Cascaded Systems - The Down-converter
• Waveguide itself becomes very lossy (~1 dB/m) as
frequencies of 40 GHz are approached.• This would lead to very poor noise performance.
• This problem is overcome by a low noise amplifier that not
only amplifies with a low noise figure but also modulates
the incoming signal with a sub-carrier that reduces the
frequency to a lower value (~1 GHz).
• Low loss coaxial cable is then used to carry the signal to
the receiver.
Noise Considerations
3.6 Shannon and Nyquist
We have previously made an assumption that we needed a SNR of 14 dB in order to
achieve a satisfactory BER. SNR and bandwidth are linked to the maximum capacity by
Shannon’s Theorem which states that.
( )SNR 1logBandwidthCapacityMaximum 2 +×=
A further limitation is imposed by Nyquist’s Theorem that states that the maximum
symbol rate possible equals twice the bandwidth. As an example if a channel of
bandwidth 7 MHz is available with a SNR of 12 dB (a ratio of 15.8), the maximum
theoretical capacity is ( )8.151log107 26 +× = 28 Mbps. Nyquists theorem imposes a
symbol rate limit of 14 Megasymbols per second. It must be borne in mind, however,
that these figures are theoretical maxima. It is very rare to see 50% of these figures
achieved in practice.
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 51/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 51
SNR RequirementsSNR Requirements
• The required Signal to Noise ratio is chiefly influenced by the
modulation scheme and the maximum permitted error ratio.• Shannon’s and Nyquist’s Theorems provide fundamental
limits.
Noise Considerations
• Shannon’s Theorem States that:
Maximum Capacity = Bandwidth x log2(1 + SNR)
• Nyquist’s Theorem States that:
Maximum Symbol Rate = 2 x Bandwidth
SNR Requirements: ExampleSNR Requirements: Example
• Bandwidth 7 MHz, SNR 12 dB.• Maximum Capacity = 7x106 log2(1+15.8) = 28 Mbps
• Maximum Symbol Rate = 14 Megasymbols per second
• Remember: these are theoretical maxima. It is very rare to
exceed 50% of the calculated value in practice.
Noise Considerations
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 52/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 52
It should also be noticed that Nyquist’s Theorem imposes a limit on the symbol rate
rather than the bit rate that can be sent over a given bandwidth. The link between symbol
rate and bit rate depends on the modulation scheme which determines how many bits can
be sent in each symbol. If we have a binary modulation scheme such as BPSK or
GMSK, we can send only one bit per symbol (or modulation “state”). If we use QPSK,
the fact that there are four states means that each symbol can carry 2 bits of information.
Similarly, 8PSK will carry 3 bits per symbol and 16QAM will carry 4 bits per symbol.
There is a general trend that the higher the number of bits per symbol, the higher the
required SNR. On the other hand, the higher the number of bits per symbol, the narrower
the bandwidth required for a given capacity.
Symbol Rate and Bit RateSymbol Rate and Bit Rate
• Binary modulation systems such as BPSK and FSK send only
one bit per symbol.
• More sophisticated modulation schemes such as 8PSK and
16QAM have 3 and 4 bits per symbol respectively.
Noise Considerations
BPSK 8PSK 16QAM
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 53/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 53
The table below compares the different systems.
Modulation Scheme C/I for BER 1x10-6
Bandwidth for 8 Mbps
BPSK 10 dB 12 MHz
4PSK 14 dB 6 MHz
8PSK 19 dB 3 MHz
16PSK 24.5 dB 2 MHz
SNR requirements of different systemsSNR requirements of different systems
Noise Considerations
ModulationScheme
C/I for BER1 x 10-3
C/I for BER1 x 10-6
BPSK 7 dB 10 dB
4PSK 10 dB 14 dB
8PSK 15 dB 19 dB
16PSK 21.5 dB 24.5 dB
• The variety of C/I requirements for different modulation
schemes leads to the parameter “Energy per bit” (Eb) being
used as having global relevance.
It is clear that it is not possible to think of a single value for a “good” SNR; it depends onthe modulation scheme being used. As a result, the term “energy per bit”, Eb, is
commonly used as it has global relevance.
In the table above, it uses an 8 Mbit/s system as a reference. The basic building block of
microwave transmission systems in the “pleisiosynchronous digital hierarchy” (PDH) is
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 54/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 54
the 2 Mbit/s system that can carry thirty 64 kbit/s voice-equivalent channels. In link
specifications it is common to see terms such as “2 x 2” used meaning that the link is
carrying two, 2 Mbit/s systems. Further multiplexing yields 8 Mbit/s, 34 Mbit/s and 140
Mbit/s links. The synchronous digital hierarchy uses higher rates of 155 Mbit/s and also
622 Mbit/s.
Bandwidth requirements of differentBandwidth requirements of differentsystemssystems
Noise Considerations
ModulationScheme
Bandwidthrequirement for 8 Mbps system
BPSK 12 MHz
4PSK 6 MHz
8PSK 3 MHz
16PSK 2 MHz
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 55/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 55
Signal in Noise ExampleSignal in Noise Example
• An 8 Mbps QPSK receiver has a bandwidth of 6 MHz and
requires a SNR of requires a signal to noise ratio of 14 dB.Determine its threshold receive level if it has a noise factor
of 4 dB.
Noise Considerations
• Assuming input noise is at the level k (290) B, the effective
noise power at the input is (4 dB is a ratio of 2.5)
1.38x10-23 x 290 x 6 x 106 x 2.5 = 6 x 10-14 watts
= -102 dBm
• To deliver a signal to noise ratio of 14 dB we need a
minimum level (the “threshold”) of -88 dBm.
Data Rates CarriedData Rates Carried
• The basic “building block” of digital microwave systems is a
2 Mbit/s link that will carry, if required, 30 individual 64 kbit/s
channels. The 64 kbit/s channel is the traditional “digitisedspeech (PCM)” channel.
• Systems are often quoted as “2x2” (i.e. 4 Mbit/s) etc..
• Further multiplexing leads to the “Pleisiosynchronous Digital
Hierarchy” where four 2 Mbit/s link form an 8 Mbit/s link, four
8 Mbit/s form a 34 Mbit/s link and four 34 Mbit/s systems
form a 140 Mbit/s link.
• The synchronous digital hierarchy (SDH) specifies higher
rates of 155.52 Mbit/s and 622 Mbit/s.
Noise Considerations
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 56/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 56
3.7 Module 3: Self-Assessment Exercises
Note Boltzmann’s constant k = 1.38 x 10-23 J/K
1. An antenna has a noise temperature of 280 kelvins. Determine the noise power gathered if the noise bandwidth of the receiver is 14 MHz.
2. An amplifier has a noise bandwidth of 2 MHz and a noise temperature of350 kelvins. If the noise power at the input equals k(480)B watts and thesignal power at the input is 0.172 picowatts, determine the signal to noise
ratio at the output of the amplifier.
3. A microwave system has a bandwidth of 4 MHz. The receiver noise
figure is 3 dB. Determine the noise temperature of the receiver and the
minimum required signal power in order to deliver a SNR of 13 dB. Stateany assumptions made.
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 57/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 57
4. A 10 GHz microwave link of length 30 km has 1.2 m diameter antennas.
The minimum required receive power has been determined to be –84dBm. Miscellaneous losses total 6 dB. Determine a suitable transmit
power.
5. A microwave link has a receiver with a noise bandwidth of 3 MHz. Thenoise temperature of the antenna is 290 kelvins. The receiver consists of
a mast head amplifier with a gain of 15 dB and a Noise Figure of 1.2 dB,
a feeder of 4.5 dB loss and a demodulator with a Noise Figure of 3.5 dB.
Determine the SNR with and without the mast head amplifier if the power gathered by the antenna is –97 dBm.
6. A Microwave link provides a 2 MHz channel with a SNR of 12 dB. Use
Shannon’s theorem to determine the maximum possible capacity of the
channel. Note:
( )
2log
loglog
1logBandwidthCapacity
10
102
2
x x
SNR
=
+×=
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 58/192
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 59/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 59
4 Fading
4.1 Introduction
Early experimenters in microwave radio were surprised to note that, even when it was
possible to view the far end of a link with binoculars, the signal received was by no
means constant. This fact launched vast and ongoing investigations into atmospheric
effects on the propagation of electromagnetic waves of the order of a few centimetres in
wavelength. In the “early days”, when frequencies used were generally less than 10
GHz, rain effects were minimal and the main area of concern was that of “multipath
fading”. The result of such fading is that it is not possible to guarantee the signal level in
the same way that it is on cable systems. A considerable margin must be built into the
designed receive power level in order to compensate for this fading.
FadingFading
• Unfortunately, the strength of the received signal
will vary with time, often quite dramatically.
• The two main contributors to “fading” are:
multipath propagation and;
hydrometeors (e.g. rain)
• It is important to be able to predict the likely
extent of fading and build in a “margin” to allow
for this in our link design.
Fading
4.2 Multipath Fading
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 60/192
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 61/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 61
4.2.1 Predicting the likelihood of a fade.
In order to compensate for multipath fading it is necessary to build in a margin so that,
even when the signal is fading, the signal level is sufficient to deliver an acceptable BER.It is therefore necessary to be able to estimate the likelihood of a fade of a particular
depth. The ITU publish recommended prediction methods, the relevant recommendation
being ITU-R P.530. These are updated every two years, the latest (530-10) having been
released in 2001. The complicated nature of the physical process involved in multipath
fading is reflected in the equations and formulas that are put forward. These are
generally based on experimental evidence gathered over many years on many different
links. The main formula governing multipath fading is that for predicting the percentage
of the time that a fade will exceed a depth of A dB. This is given as
( ) 10001.0033.02.10.3 101 Ah f
pw L Kd p −−−
×+= ε
In the above equation, K is known as the “radio climactic factor” and will be examined
further later. D is the path length in km, f is the frequency in GHz and ε p is the path
inclination in milliradians. h L is the altitude of the lower of the two antennas, above sea
level.
MultipathMultipath FadingFading
• Multipath fading exhibits Rayleigh characteristics.
• The deeper the fade the lower the probability
• Percentage time that a fade of depth A dB is exceeded is
proportional to 10-A/10.
• ITU-R report 530-9 gives the formula for percentage as
Fading
( ) 10001.0033.02.10.3 101 Ah f pw
L Kd p −−−
×+= ε
d is the path length in km
f is the frequency in GHz
K is the “radio climactic factor”
ε p is path inclination in milliradians
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 62/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 62
MultipathMultipath FadingFading
• Formulas come into the following categories:
Deterministic Heuristic
Empirical
• The multipath formula is empirical. It is based on
experimental evidence and the formula is created to fit the
results.
Fading
4.2.1.1 Radio Climatic Factor
ITU-R P.530-10 gives a formula for the climatic factor, K as shown below.
10029.02.410
dN K
−−= where dN 1 is the maximum gradient in refractive index that is
likely to be experienced. This depends on geographic location and typically varies
between –100 and –700. This leads to variations in K between about 1x10-4
and 7x10-4
.
In the United Kingdom, a value of –200 is appropriate leading to a value for K of
approximately 2.4x10-4
.
As an example, consider a 20 km path at a frequency of 7 GHz. The path is assumed to
be horizontal with antennas at an elevation of 100 metres above sea level.
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 63/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 63
( )
10
101.07033.00.34
10001.0033.02.10.3
106.2
1020104.2
101
A
A
Ah f pw
L Kd p
−
−−×−
−−−
×=
×××=
×+= ε
This equation allows us to draw up a table showing the likelihood of a fade of a particular
depth being exceeded.
Depth of Fade (dB) Percentage of time
exceeded
10 0.260
15 0.08220 0.026
25 0.008
Of particular interest is the fade depth that will be exceeded for 0.01% of the time. This
is found to be 24 dB.
MultipathMultipath FadingFading
• ITU-R P.530 gives a formula for K
• dN 1 can be found from ITU-R P.453-8
• values for dN 1 vary between -700 and -100.
• Values for K vary between about 1.23x10-4 and
6.76x10-3
Fading
10029.02.410
dN K
−−=
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 64/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 64
MultipathMultipath FadingFading
dN 1 ~ -200 in the United Kingdom.
Fading
( ) 42000029.02.4 104.210 −−−− ×== K
MultipathMultipath FadingFading
εp is the slope of the path in milliradians
d is in kilometres.
hr,e is the height of the two antennas (a.s.l.) in
metres.
For a flat path εp equals zero.
Fading
d hh er
p−=ε
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 65/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 65
MultipathMultipath FadingFading
For a flat path, with antennas at an elevation of 100
metres, 20 km in length with an operating
frequency of 7 GHz the probability formula
becomes:
Fading
( ) 10001.0033.02.10.3 101 Ah f
pw L Kd p
−−−×+= ε
10
101.07033.00.34
1060.2
1020104.2
A
Aw p
−
−−×−
×=
×××=
MultipathMultipath FadingFading
The formula can be used to produce a table of depth of fade
against the percentage that the fade is exceeded.
Fading
Depth of fade in dB Percentage of timeexceeded
10 0.260
15 0.082
20 0.0260
25 0.0082
It can be seen that, if 99.99% availability is required, a “fade
margin” of 24 dB would have to be designed in.
4.3 Rain Fading.
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 66/192
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 67/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 67
Rain FadingRain Fading
• Rain and other “hydrometeors” will absorb power from the
propagating electromagnetic wave and cause an additional,
variable, insertion loss. Again, a “margin” will have to be
designed in to ensure that the required availability is
maintained.
• Not surprisingly, this component is very climate dependent.
The “rainfall rate exceeded for 0.01% of the time”
(measured in mm/hr) is a key parameter. Such information
can be found in ITU-R P.837. The parameter is designated
R0.01.
Fading
4.4 Accommodating Rain and Multipath Fading
Using the ITU Recommendations, it is possible to establish a margin for multipath fading
and a margin for rain fading. The link planner should not simply add these two together
to give a total required margin as rain fading and multipath fading are highly likely to
occur simultaneously. Rather, the emphasis should be to use the margin available to
predict the “outage time” (as a percentage) for both rain and multipath and add these two
percentages together to give an estimate of the total outage. This outage prediction can
then be assessed as acceptable or not and adjustments made accordingly.
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 68/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 68
Rain FadingRain Fading
• R0.01 is approximately 25 mm/hr for the UK.
• Next, ITU-R P.838 must be used to convert this to aattenuation rate in dB/km, γR .
• Rain attenuation is polarisation and frequency dependent
• For a flat, vertically polarised path at 7 GHz, k=0.00265,
α=1.312. Hence γR = 0.18 dB/km.
Fading
α γ kR R =
Rain FadingRain Fading• The longer the path, and the higher the level of rainfall, the less likely
it is that it will be raining along the entire length of the path.
• This is accounted for by introducing a parameter known as the
“effective path length” that is equal to
• Thus a 20 km path would have an effective length, for rainfall
attenuation purposes of 10.9 km.
• 0.01% attenuation rate would be (0.18x10.9) = 2 dB.
• Insignificant compared with multipath margin (at these frequencies).
Fading
2435
1
01.0015.00
0
==
+
− Red
d d
d
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 69/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 69
Rain FadingRain Fading
• For different percentages, p, the value for 0.01% can be
modified according to the formula.
Fading
)log043.0546.0(
01.0
1012.0 p p
p A
A +−=
Accommodating both Rain andAccommodating both Rain andMultipathMultipath FadingFading
• Note that it would be regarded as highly unusual to add the
rain and multipath margins together.
• A more common approach would be to decide on the
maximum unavailability then build in the larger of the two
calculated margins.
• The “cause of outage” requiring the lower margin would
then increase the unavailability by a very small amount.
• Rain and multipath fading would not be expected to occur
simultaneously.
Fading
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 70/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 70
4.5 Selective Fading in Digital Systems.
Problems, in the form of high Bit Error Rates, can occur in digital systems even if the
wideband receive power is high. This is usually due to multipath propagation with delayslonger than just one or two nanoseconds resulting in the distortion of the signal. Such
multipath propagation may not induce a deep fade in the wideband power but, rather,
produce a notch in the received spectrum at a particular frequency. Such fading is
referred to as “selective fading” with the type of fading studied up to this point being
known as “non-selective”.
Selective Fading in Digital SystemsSelective Fading in Digital Systems
• The multipath fading that we have discussed so far caused
an outage by reducing the signal strength below the
threshold.
• High error rates (hence a further “outage”) can occur indigital systems with the signal distorted by multipath without
the wideband power necessarily reducing significantly.
• A method of predicting the unavailability due to this
phenomenon is required.
• Again ITU-R P.530 offers guidance.
Fading
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 71/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 71
Selective Fading in Digital SystemsSelective Fading in Digital Systems
• The resilience of receivers to such distortion is measured by
means of introducing a two-ray system whereby the delay
and relative strength of the second signal can be adjusted.
• Attenuation is adjusted for a number of values of τ so that
the pre-decided minimum value of BER is reached.
• The result is a set of “signature curves”.
Fading
Tx Rx
I
Note: relative amplitude
of the two paths is given
the parameter b.
Selective Fading in Digital SystemsSelective Fading in Digital Systems
• Measurements produce the above “signature curves”.
• For a fixed BER the relative strength of second path
depends on the delay and the notch position.
Fading
0.1
0.2
0.3
0.4 τ=32 ns
τ=16 ns
τ=8 ns
1-b
0.0 2 4-2-4 Notch offset (MHz)
Contours for BER of 10-6
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 72/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 72
Selective Fading in Digital SystemsSelective Fading in Digital Systems
• From a set of curves the parameters, signature width,
signature depth and reference delay can be obtained.
These can be quoted by the manufacturer.
Fading
0.1
0.2
0.3
0.4 τ=32 ns
τ=16 ns
τ=8 ns
1-b
0.0 2 4-2-4 Notch offset (MHz)
Contours for BER of 10-6
Minimum phase and Non-minimum phaseMinimum phase and Non-minimum phase
• A slightly different set of curves is produced if the stronger
signal is delayed. This is known as the “non-minimum
phase” configuration.
• The same parameters must be measured for the minimum
and non-minimum phase configurations.
Fading
Tx Rx
I
Note: relative amplitude
of the two paths is given
the parameter b.
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 73/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 73
Manufacturers publish data that makes it possible to predict the effect of selective fading
on a link. These take the form of parameters from “signature curves” that describe the
level of multipath required to induce a particular error rate for a given delay. Three vital
parameters are provided: the signature width, W in GHz (usually related to the system
bandwidth); the delay,τ r , required to cause the bit error rate when the average depth of
notch caused by the multipath was B dB. In fact, these parameters are established for two
slightly different configurations known as the “minimum phase” and “non-minimum
phase” configurations. This leads to the suffixes M and NM being introduced to
differentiate between the two configurations. Once these parameters are obtained, it is
necessary to relate them to the link in hand by means establishing relevant link
parameters. Two such parameters are identified: the mean time delay τ m and; the
“multipath activity factor” η . The mean delay is related to the path length by the
following equation (p.530-10)
ns 50
7.0
3.1
= d
mτ and the multipath activity factor is given by
( ) 75.002.0
1 P
e−−=η where
( )100
101 001.0033.02.10.3
0
Lh f p Kd
P
−−×+
= ε
Once the necessary parameters have been calculated, the outage probability P s, can be
determined from
×+×= −−
NM r
m B NM
M r
m B M s
NM M W W P .
220
.
220
101015.2τ
τ
τ
τ η
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 74/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 74
Considering a 20 km, 7 GHz link at 100 metres altitude as before (hence we can take K to
be equal to 2.4 x 10-4
) we find that
( )
( )013.01
026.0100
101
ns0.250
7.0
75.002.0
001.0033.02.10.3
0
3.1
=−=
=×+
=
= =
−
−−
P
h f p
m
e
Kd P
d
L
η
ε
τ
If examination of the manufacturer’s data reveals that
ns;4GHz;008.0dB;5 r ===== τ NM M NM M W W B B then the probability of
outage can be calculated to be
6
2205
2205
105.2
4
2.010008.0
4
2.010008.0013150.2
−
−−
×=
×+××= s P
Determining the outage probability due toDetermining the outage probability due toselective fadingselective fading
• Step 1: estimate the mean time delay on the path
Fading
• Step 2: estimate the “multipath activity factor”,η for the path.
ns50
7.03.1
=
d mτ
( )
( )100
101
1
001.0033.02.10.3
0
75.02.0 0
Lh f p
P
Kd P
e
−−
−
×+=
−=
ε
η
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 75/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 75
Determining the outage probability due toDetermining the outage probability due toselective fadingselective fading
• Step 3: Obtain values for signature width (W ), signature
depth ( B dB) and reference delay τ from the manufacturers
data.
Fading
• Step 4: Calculate the outage probability P s.
×+×= −−
NM r
m B NM
M r
m B M s
NM M W W P ,
220
,
220 101015.2
τ
τ
τ
τ η
Determining the outage probability due toDetermining the outage probability due toselective fading - exampleselective fading - example
• Considering a 20 km, 7 GHz link at 100 m altitude as before.(Hence we can take K to be 2.4 x 10-4) Steps 1 and 2:
Fading
• Step 3: From manufacturers details W M =W NM =0.008 GHz (it
seems we have an 8 MHz system here); B M = B NM =5 dB; τ r =4 ns.
( ) 013.01
0260.01001020104.2
75.0026.02.0
100001.07033.00.340
=−=
=÷×××=
−
×−×−
e
P
η
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 76/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 76
Determining the outage probability due toDetermining the outage probability due toselective fading - exampleselective fading - example
Fading
• Step 4: Calculate the probability of outage.
6
2205
2205
105.2
4
2.010008.0
4
2.010008.0013.015.2
−
−−
×=
××+×××=S P
• Note that this probability is dependent on path length,
frequency and bandwidth, but NOT on received signal level.
4.6 Atmospheric Absorption
Resonances with oxygen and water molecules present in the atmosphere lead to energy
being absorbed by the atmosphere in a frequency-dependent way. This absorption loss
adds to the free space loss and, as a result, is not a “fade” as the loss is constant.
However, it does require a margin to be built into the link design. Generally speaking,
atmospheric absorption is negligible below 10 GHz, rising to approximately 0.1 dB/km at
20 GHz. There is a resonant peak of about 0.2 dB/km at about 24 GHz apart from which
the level is approximately 0.1 dB/km up to 40 GHz.
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 77/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 77
Atmospheric AbsorptionAtmospheric Absorption
Fading
• Resonances with oxygen and water molecules lead to
energy being absorbed in a frequency dependent way by theatmosphere. This adds to the path loss.
• Atmospheric absorption is not, strictly speaking, an example
of fading as it is a constant loss. Nevertheless it is
necessary to design a margin into the link in order to
compensate for such absorption.
• Atmospheric absorption is negligible below 10 GHz, rising to
approximately 0.1 dB/km at 20 GHz. It is approximately 0.1
dB/km between 20 GHz and 40 GHz apart from a resonant
peak of 0.2 dB/km at approximately 24 GHz.
Atmospheric AbsorptionAtmospheric Absorption
Fading
• Graph showing losses due to
water vapour and oxygen
absorption. Total atmospheric
absorption is obtained by
summing the two losses. L O S S
d B / K m
20
10
1
0.1
0.01
FREQUENCY GHz.
1 10 100
Additional Loss Due To Atmospheric Content.
W a t e
r v a p
o u r
O x y g e n
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 78/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 78
Estimating Link PerformanceEstimating Link Performance
Fading
• Now we appreciate the fading mechanisms and their effects,
we can look again at our 7 GHz, 20 km system. Suppose weuse a 100 milliwatt (20 dBm) transmitter. The threshold is
assumed to be -87 dBm with miscellaneous losses amounting
to 5 dB. 60 cm antennas are used.
• Step 1: Estimate antenna gains to be
17.5+20log(0.6)+20log(7) = 30 dBi
• Step 2: Free space loss = 92.4+20 log(20)+20 log(7)=135 dB
• Step 3: calculate unfaded receive level to be
20-5-135+30+30=-60 dBm
4.7 Estimating Link Performance
Now that we have established methods of predicting the outages from multipath fading,
rain fading and selective fading, it is possible to estimate the link performance
considering all these factors. As an example, we shall consider our 20 km, 7 GHz
system. We shall assume that the transmit power is 20 dBm and the threshold level is –
87 dBm. Further, we shall assume that 60 cm antennas are used.
Firstly, we need to predict the unfaded signal level. The antenna gains can be estimated
by using the formula dBi30)log(20)log(205.17 =++= f DG the free space loss is
dB.135)7log(20)20log(204.92 =++ If miscellaneous losses amount to 5 dB, the total
loss is 80 dB, resulting in an unfaded receive level of –60 dBm, thus providing a fade
margin of 27 dB. We have previously derived a formula for multipath fading for a 7
GHz, 20 km link that links fade depth with a percentage of time.
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 79/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 79
101060.2 AW p −×=
For a fade of 27 dB, the percentage is found to be 5.19x10-3
%. The rain fadingcalculations are such that the percentage fading will be less that 0.001%, the smallest
figure for which the figures in the recommendation are valid. The probability of an
outage occurring due to selective fading has been calculated to be 2.5x10-6 or 0.00025%.
Adding the two figures together suggests a total outage of 0.0052 + 0.00025 = 0.0055%.
Estimating Link Performance -Estimating Link Performance - multipathmultipath
fadingfading
Fading
• As the frequency is below 10 GHz, atmospheric absorption
can be ignored.
• The unfaded receive level can be seen to be 27 dB above the
threshold. This gives us a “fade margin” of 27 dB.
• We have previously derived a formula
for a link of this length and frequency
• For A = 27 dB, pW is found to be 5.19x10-3%
101060.2 A
W p −
×=
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 80/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 80
Estimating Link Performance - rain fadingEstimating Link Performance - rain fading
Fading
• We have previously shown that the rain fading margin for a 20
km, 7 GHz path for 0.01% of the time is 2 dB.• Although the likelihood is that rain fading can be ignored, we
can determine the percentage outage given a fade of 27 dB
from the formula
• For a value of Ap of 27 dB,
• Examining this equation it is found that the outage will be far
less than 0.001%, which is the valid range of the equation. We
can therefore ignore outages due to rain fading.
( ) p p p
A
A10log043.0546.0
01.0
12.0 +−=
( )5.11210log043.0546.0 =+− p
p
Estimating Link Performance - selectiveEstimating Link Performance - selectivefadingfading
Fading
• We have previously shown that the selective fading outage
probability for a 20 km, 7 GHz, 8 MHz bandwidth path is
0.0025%. This is not affected by the received power level.
• Summing the outages, we would predict a total outage of
0.0052 +0.00025 = 0.0055%.
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 81/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 81
4.8 Conclusion.
Methods of predicting the percentage outage due to multipath fading (both non-selectiveand selective) and rain fading have been examined and examples of implementation
shown. The link examined has produced estimates of outage that would, in practice, be
satisfactory. It is however, easy to visualise a link (longer in length, higher in frequency)
for which the initial prediction would suggest an unsatisfactory performance. In such
cases, diversity techniques can be used to improve the performance. The next section
introduces such methods and methods for predicting their effectiveness.
What’s next?What’s next?
Fading
• We have obtained encouraging estimates of outage. The link,
if implemented, would provide a high quality service.
• However, we must be able to accommodate situations where
the initial prediction is for an unsatisfactory performance.
• Diversity techniques can be used to improve the performance.
• The next session reviews and analyses diversity improvement
methods.
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 82/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 82
4.9 Module 4: Self-Assessment Exercises.
1. A 24 km microwave link is located in Sweden and operates at a
frequency of 18 GHz. One antenna is 1100 m above sea level and the
other is at 800 m above sea level. Estimate the percentage time for whicha fade exceeding 25 dB would occur.
2. A 21 km microwave link, located in Italy, operates at a frequency of 28GHz. Horizontal polarisation is used. Determine the rain-produced
attentuation for a 0.01% time period.
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 83/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 83
3. A horizontal 18 km, 14 GHz link, at an elevation of 200 m above sea
level, operating in the United Kingdom uses equipment for which the
relevant details are:
ns32
dB10
MHz34
r =
==
=
τ
NM M B B
W
for a BER of 10-6. Determine the probability of the BER exceeding this
value.
4. Estimate the atmospheric absorption on an 11.5 GHz link of path length
20 km.
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 84/192
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 85/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 85
5 Diversity Techniques
5.1 Introduction
The 20 kilometre, 7 GHz path that we have examined in the previous section would have
an outage prediction of less than 0.01% and would generally be regarded as giving very
good performance. If, however, the path length, bandwidth or operating frequency was
increased, the outage prediction may well exceed 0.01% and remedial action must be
taken. Sometimes it is possible to remedy such a situation by increasing the transmit
power or by adopting larger antennas. However, it must be borne in mind that selective
fading is not affected by signal strength and that sometimes the options described will not
be economic. In such circumstances, the adoption of diversity techniques would form the
best solution.
Diversity TechniquesDiversity Techniques
• Our 20 km, 7 GHz, 8 MHz bandwidth link just
meets the 0.01% unavailability requirement.
• It is sensible to assume that, if we made the path
longer, or increased the bandwidth, or increased
the operating frequency, we would struggle to
meet the requirements.
• Sometimes it is possible to improve the situation
by increasing the transmit power, or antenna size.
• Occasionally, these steps alone are not sufficient.
Diversity Techniques
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 86/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 86
5.2 The Theory Behind Diversity Systems
When a diversity protection system is implemented, effectively a separate link is
established to carry the same traffic. The output is either the better of the two signals or,
ideally, a combination of the two signals to provide an optimum output. Fading is a rare
event. In a diversity system, a simultaneous fade on both links should be even rarer. If
for example, each link had a fading probability of 1% (or 0.01), the probability of a
simultaneous fade on the two links would be 0.01 x 0.01 = 0.0001 or 0.01%.
This calculation would be correct if the two links were not correlated. However, because
the two links operate over the same route, the fact that there is a fade on one link means
that the probability of a fade occurring on the second link at that time would be greaterthan normal as it has been established that the conditions required for fading on the link
do exist. Thus the “diversity improvement” as it is known would not be as great as
indicated in the calculation given above. Nevertheless, a diversity improvement is
achievable. The ITU-R recommendation P.530-10 gives guidance on how this
improvement may be calculated.
Diversity TechniquesDiversity Techniques
• Diversity basically relies on establishing more than
one link and selecting the best performing link at any
one time or, ideally, combining the outputs from the
two links to provide the optimum output.
• Suppose we had estimated the unavailability to be 1%
on a particular link.
• If we established a separate, but virtually identical, linkthat would also have a 1% unavailability.
• The probability of both links being simultaneously
unavailable could be calculated to be 1%x1%=0.01%.
Diversity Techniques
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 87/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 87
Diversity TechniquesDiversity Techniques
• Performing the calculation described would be valid
only if the two links established were independent of
each other (zero correlation between fading
characteristics).
• However, as they are very similar links between the
same two points, one would intuitively expect there to
be correlation between the two links.
Diversity Techniques
5.3 Types of Diversity
All diversity systems involve establishing an alternative route for the traffic to take. The
major forms of diversity system are:
• Space Diversity: this consists of two antennas receiving at each end. These antennas
are usually positioned one above the other for maximum improvement. In this way
the signal can pass from one end to the other via either of the receiving antenna.
• Frequency Diversity: two transceivers operating at different frequencies carry the
same information over the same antenna. The improvement is afforded by the fact
that fading is a frequency-dependent phenomenon and will not occur with great
severity on two frequencies at the same time.
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 88/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 88
• Polarisation Diversity: the same information is transmitted at both horizontal and
vertical polarisations simultaneously with the hope being that a particular fade is not
as severe on both polarisations.
• Angle Diversity: by placing two feedhorns near the focus of the antenna it is possible
to have the energy split between two slightly different radiation patters, one with its
principal direction slightly offset from the other. It is hoped that, if the signal to one
feedhorn suffers a severe fade, then the signal to the second feedhorn will not be as
deep.
Diversity Techniques - most commonDiversity Techniques - most commontypes of diversity systemstypes of diversity systems
• Space diversity:- two receive antennas (usually one
above the other) at each end.
• Frequency diversity:- effectively two transceivers at
separate frequencies passing the same information
over the same antenna.• Polarisation diversity:- transmitting the same
information via two orthogonal feeders.
• Angle diversity:- usually achieved by having two
separate feedhorns near the focus of the antenna,
each providing a different radiation pattern.
Diversity Techniques
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 89/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 89
5.4 Improvement Factor
The improvement factor I is the radio of the probability of a fade without diversity
protection to that probability with protection. For Space Diversity systems, ITU-RP.530-10 provides the equation
( ( ) 1004.10
48.012.087.0 1004.0exp1 V A pd f S I −−−×−−=
where S is the separation in metres, V is the difference in gain between the transmitting
and receiving antennas (usually zero) and p0 is the multipath occurrence factor, expressed
as a percentage. As an example, consider a 20 km, 7 GHz link for which the power
transmitted has been reduced to give a fade margin of 15 dB. It has previously been
calculated that for a fade of 25 dB, the probability was 0.008%. Thus for a fade of 15 dB,
the probability would be 0.08%. This makes p0 equal to 0.08 ( )
53.210 5.1 =× . If space
diversity is used with a separation of 5 metres then the improvement factor is given by
95.5
105.2207504.0exp1 5.104.148.012.087.0
=
××××−−= −− I
Thus, the outage probability would be reduced by a factor of 5.95 from 0.08% to 0.013%.
The ITU recommendation also gives details of the range of validity of the equations
published. In this case, the frequency range is 2 – 11 GHz, path lengths of 43 – 240
kilometres and antenna separations of 3 to 23 metres. Caution should be exercised when
using the equations outside this range. However, the following general rules should
remain true:
• The bigger the separation, the bigger the improvement.
• The longer the path length the bigger the improvement
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 90/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 90
• The improvement factor is not very frequency-dependent, exhibiting a slight decrease
with increasing frequency.
Diversity Techniques - estimatingDiversity Techniques - estimatingimprovementimprovement
• The ITU provide a recommended method of estimating the
improvement provided by a diversity technique.
• Essentially, this involves estimating the degree of correlation
between the fading of the two links.
• The term “Improvement Factor” ( I ) is used where
• p(A) is the probability of a fade without diversity; pd (A) is the
probability with diversity.
Diversity Techniques
)()(
A p A p
I d
=
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 91/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 91
Diversity Techniques - space diversityDiversity Techniques - space diversity
• ITU-R P.530 gives the following equation for the improvement
factor.
• S is the vertical separation in metres. V is the difference in gain
between the Tx and Rx antennas (usually zero).
Diversity Techniques
( )[ ] ( )( )
(%)factoroccurencemultipath
1004.0exp1
0
1004.10
48.012.087.0
=
×−−= −−−
p
where
pd f S I V A
Diversity Techniques - space diversityDiversity Techniques - space diversity• In our original link, we predicted a multipath (non-selective)
outage of 0.008% for a margin of 25 dB. To make the situation
more realistic for diversity purposes, let’s assume that the
transmit power was reduced so as to make the fade margin 15
dB. That would give an outage probability of 0.08%.
• Therefore the relevant parameters are: A=15; f =7; d =20; p0=2.5.
If the antennas are separated by 5 metres the improvement factor
is
• Thus the outage probability with diversity would be expected to
be 0.013%.
Diversity Techniques
( )[ ] ( )( )
95.5
105.2207504.0exp1 101504.148.012.087.0
=
×−−= −− I
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 92/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 92
Diversity Techniques - space diversityDiversity Techniques - space diversity
• The equation was produced by examining data produced on links
covering the frequency range 2 - 11 GHz; path lengths 43 - 240
km and antenna separations of 3 to 23 metres.
• Care must be taken when operating outside these parameters.
However, the equation doesn’t immediately “collapse” and the
general rules hold:
The bigger the separation the bigger the improvement
The longer the path length the bigger the improvement
Improvement factor is not very frequency-dependent exhibiting a
slight decrease with increasing frequency.
Diversity Techniques
Diversity Techniques - space diversityDiversity Techniques - space diversity
• The equation was produced by examining data produced on links
covering the frequency range 2 - 11 GHz; path lengths 43 - 240
km and antenna separations of 3 to 23 metres.
• Care must be taken when operating outside these parameters.
However, the equation doesn’t immediately “collapse” and the
general rules hold:
The bigger the separation the bigger the improvement
The longer the path length the bigger the improvement
Improvement factor is not very frequency-dependent exhibiting a
slight decrease with increasing frequency.
Diversity Techniques
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 93/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 93
5.5 Improvement for Other Types of Fading
The improvement factor described above is the improvement factor for non-selective
multipath fading. ITU-R P.530-10 describes equivalent procedures for estimating the
improvement factor for selective fading and also for estimating the improvement factor
when other diversity techniques are involved. It should be noted that diversity techniques
do not provide a significant improvement in rain fading performance as the rain fade will
affect all elements simultaneously. For this reason rain fading forms the final limitation
on path length at the higher microwave frequencies.
Diversity Techniques - space diversityDiversity Techniques - space diversity
• The equations considered so far have dealt with the
“non-selective” fading aspects of the unprotected
system.
• A separate procedure must be followed to determine
the new outage probability for the selective fading.
• These two must then be summed in order to obtain
the new outage estimate.
Diversity Techniques
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 94/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 94
Diversity Techniques - other methodsDiversity Techniques - other methods
• ITU-R P.530 describes equivalent procedures for
estimating the improvement factor for Frequency,
Angle and Polarisation diversity techniques.
Diversity Techniques
5.6 Combining Diversity Techniques
The link planner is not restricted to choosing just one diversity method. It is perfectly
legitimate to use two or more methods to increase the improvement afforded. It is
common to combine, for example, frequency and space diversity. Again, ITU-R P.530-
10 gives details regarding the improvement that is likely to be obtained.
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 95/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 95
Diversity Techniques - combiningDiversity Techniques - combiningmethodsmethods
• Greater improvement can be obtained by
implementing more than one technique; e.g. frequency
and space diversity.
Diversity Techniques
TxRx f 1
f 2
f 1
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 96/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 96
5.7 Module 5: Self-Assessment Exercises
1. A 28 km microwave link, located in Sweden operates at a frequency of
21 GHz. Identical antennas are used at both ends and the path is horizontal
with antennas at an elevation of 1200 metres above sea level. Without anydiversity it is found to have a fade margin of 16 dB. Determine the
probability of outage. Estimate the improvement factor provided if space
diversity is employed with an antenna separation of 4 metres.
2. Using the procedures of ITU-R P.530-10, page 28, evaluate the improvement possible
by utilising frequency diversity with a separation of 200 MHz instead of space diversity.
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 97/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 97
6 Interference Issues
6.1 Introduction
In carrying out link budgets we have always had to be aware that there is a minimum
level that the received signal must not drop below. The ultimate limiting factor is thermal
noise. However, in practice, interference will add to the effect of thermal noise raising
the minimum required receive signal power and thus rendering the receiver less sensitive.
Interference IssuesInterference Issues
• Interference is a problem because it “de-sensitises”
the receiver.
• It does this by effectively raising the noise floor.
• Remembering our 8 MHz bandwidth system, we
calculated a threshold of -87 dBm by deducing that
the noise floor was -101 dBm and that the SNR
requirement was 14 dB.
• If interference adds to this noise floor, then thethreshold will be raised and fade margins reduced.
Interference Issues
6.2 Quantifying the effect of interference.
The effect of interference can be calculated by adding the interfering power to the noise
floor to arrive at the increased “effective noise floor”. The threshold of the receiver
increased by the same amount that the noise floor is raised by. Unfortunately, quoting
power levels in dBm does not make it easy to add such powers together. It is necessary
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 98/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 98
to convert from dBm to milliwatts before adding. An example of this process is
illustrated below.
Interference Issues - adding powersInterference Issues - adding powers
• In order to add powers it is necessary to convert
from dBm to milliwatts.
• X dBm = 10X/10 milliwatts
• X dBm + Y dBm = 10log10(10X/10 + 10Y/10) dBm
• E.g. if an interfering signal of -98 dBm is added to
the noise floor of -101 dBm, the resultant power
level is 10log10(10-9.8 + 10-10.1) = -96.2 dBm
• The noise floor has effectively increased by 4.8 dB,
making the new threshold -82.2 dBm.
Interference Issues
6.3 The Theory Behind Diversity Systems
When a diversity protection system is implemented, effectively a separate link is
established to carry the same traffic. The output is either the better of the two signals or,
ideally, a combination of the two signals to provide an optimum output. Fading is a rare
event. In a diversity system, a simultaneous fade on both links should be even rarer. If
for example, each link had a fading probability of 1% (or 0.01), the probability of a
simultaneous fade on the two links would be 0.01 x 0.01 = 0.0001 or 0.01%.
6.4 Co-channel and Adjacent Channel Interference
It is obvious that a nearby transmitter operating at the same frequency will pose an
interference threat. However, this is not the only circumstance in which interference will
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 99/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 99
occur. No filter is perfect and power from other frequencies can cause problems.
Interference from one system to another at the same frequency is known as “co-channel”
interference. Interference at other frequencies is known as “adjacent channel”
interference. Just how “adjacent” a channel can be and cause interference depends on the
quality of the filters used in both transmitter and receiver. Basically, the greater the
separation between frequencies used by the interferer and the “victim”, the better.
Interference Issues : co-channel andInterference Issues : co-channel andadjacent channel interference.adjacent channel interference.
• The spectrum is divided into “slots” often referred to as
“channels”. The width of each slot determines the bandwidthof the system.
Interference Issues
7.000 7.008 7.016 7.024 7.0326.992 7.0487.040
Used ChannelAdjacent Channels
• Interference within the bandwidth of the channel being used
is known as “co-channel”. The slots either side are known as
“adjacent channels.
• Possible channel allocations
for a 7GHz system.
MHz
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 100/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 100
Interference Issues : co-channel andInterference Issues : co-channel andadjacent channel interference.adjacent channel interference.
• Co-channel interference is the most serious.
• Adjacent channel interference is reduced by the
selectivity of the filter at the receiver. Typically, it
will be attenuated by 20 dB.
• Interference at frequencies outside this region will
be attenuated further and is less likely to pose a
threat to the system.
Interference Issues
6.5 Interference Scenarios
The best defence that microwave systems have against interference is the fact that the
antennas only “look” at a very narrow beam. Any interference entering from outside this
beam will be severely attenuated. Indeed, the fact that, when transmitting, the narrow
beam results in very high power densities means that microwave systems are more likely
to cause interference than be victims. Some frequency bands are shared between satellite
and terrestrial systems. Satellite receivers operate on very low receive power levels. As
such they are very susceptible to interference. Care must be taken to ensure that any
terrestrial systems that are less than a specified distance away from a satellite earth
station are coordinated in such a way so as to avoid interference. This will include
ensuring that the main beam of the terrestrial system is not directed at the earth station.
Satellite system operators are generally given the opportunity to object to proposals to
implement terrestrial systems.
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 101/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 101
Interference Issues : possible scenariosInterference Issues : possible scenarios
• Off beam gain of a parabolic antenna is typically 45
dB down on main beam (Effective gain of -10 dBi).
This makes high interference levels unlikely.
• Terrestrial microwave links are more likely to cause
interference to satellite systems than be victims
themselves. This has licencing implications.
Interference Issues
Interference on terrestrial systems is most likely to occur when repeaters are used on a
long distance system. If the same frequency is used for two consecutive hops then the
final receiver can receive signals from both transmitting antennas. There will be a
somewhat unpredictable time delay between the two signals arriving, leading to
demodulation problems. This problem can be alleviated by either:
• Using different frequencies on consecutive hops
• Using orthogonal polarisations on consecutive hops
• Ensuring that consecutive hops are not co-linear but, rather, follow a “zigzag” pattern.
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 102/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 102
Interference Issues : possible scenariosInterference Issues : possible scenarios
• Multi-hop paths present a possible interference
problem because of “overshoot”.
Interference Issues
• The effect can be reduced by using orthogonal
polarisations on consecutive hops and/or by
changing the direction between consecutive hops
by more than the antenna beamwidth.
Interference Issues : reductionInterference Issues : reductiontechniquetechnique
• Offsetting the direction of the hops.
Interference Issues
Interfering antennas no
longer “look at” each other.
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 103/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 103
One situation in which an interference assessment should be made occurs when one site
acts as a “hub” for a number of links. The assessment should allow the likely degree of
receiver de-sensitisation to be quantified. This would include consideration of the power
being received on each of the links together with allowances for frequency differences,
polarisation differences and the radiation patterns of the antennas involved.
Interference Issues : possible scenariosInterference Issues : possible scenarios
• Microwave transmission systems often have a
“hub”.
• This hub receives signals from many different links.
Interference Issues
6.6 Reduction Techniques
It is possible to purchase microwave antennas that are referred to as “high performance”.
These will have the same gain in the principal direction as a standard antenna of the same
diameter. However, they will have a superior “off beam” performance and, in particular,
will have a higher “front to back” ratio. This is achieved by ensuring that “spill over”
from the feeder is reduced and, also, by using thicker metal for the reflector.
Additionally, it is important to appreciate that a frequency band for point to point
microwave communication will, in reality, consist of two bands. This is so that duplex
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 104/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 104
operation can be implemented. The two bands may be referred to as “go” and “return” or
simply as the “higher” and “lower” frequencies. When you have a site at the hub of a
network receiving signals from many links. The interference situation can be alleviated
by ensuring that the hub does not receive on the same frequency on all of the links. This
is achieved by judicious allocation of the higher and lower duplex frequencies on the
different links.
Interference Issues : reductionInterference Issues : reductiontechniquestechniques
• High performance antennas can be purchased.
These are less susceptible to “off-beam”interference.
• Frequency planning of the duplex links can also
help alleviate problems
Interference Issues
6.7 Anomalous Propagation
Under “normal” conditions the curvature of the earth will provide a shield from
interference when there is no line of sight from the interferer to the victim. However,
from time to time, atmospheric conditions will exist such that the electromagnetic wave
becomes trapped within a layer a few hundred metres in height. In this way, the level
received on a transhorizon path can very nearly equal that expected if there was clear line
of sight. The phenomenon by which energy is trapped within an atmospheric layer is
referred to as “ducting”.
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 105/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 105
Interference Issues : anomalousInterference Issues : anomalouspropagationpropagation
• Terrestrial microwave systems are very much “line
of sight” systems. The signal tends not to
propagate over the horizon.
• However, on rare occasions, interference occurs
from distant systems under conditions known as
“ducting”.
• Ducting falls into a category of propagation
conditions referred to as “anomalous” (“highlyunusual”; “noticeably different”).
Interference Issues
Interference Issues : ductingInterference Issues : ducting
Interference Issues
Normal conditions: no interference threat
Anomalous conditions: interference threat
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 106/192
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 107/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 107
Interference Issues :Interference Issues : IntermodulationIntermodulationproductsproducts
Interference Issues
• No amplifier is perfectly linear. For an input vi, the
output is generally:
• The “even numbered” terms are out of band
(harmonics), the “odd numbered” terms are “in band”
and therefore more serious.
.....432
0 ++++= iiii dvcvbvavv
Interference Issues :Interference Issues : IntermodulationIntermodulationproductsproducts
Interference Issues
• If a number of signals at different frequency are
combined within an amplifier, the third, fifth andseventh order terms produce an interesting effect.
Original Signals
Intermodulation Products
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 108/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 108
Interference Issues :Interference Issues : IntermodulationIntermodulationproductsproducts
Interference Issues
• If a broadband receiver is receiving multiple carriers, twodominant signals can severely interfere with a third carrier.
• If two signals at the input to an amplifier are at f 1 and f 2, the
most damaging intermodulation products will be at 2 f 2 - f 1 and
2 f 1 - f 2.
• A weak signal at these frequencies will be interfered with.
• Lesser effects occur at 3 f 2 -2 f 1 and 3 f 1 -2 f 2.
IntermodulationIntermodulation products (example)products (example)
Interference Issues
• A broadband receiver receives two signals. One at 10.02 GHz
and another at 10.035 GHz. Determine the frequencies of thefour most dominant intermodulation products.
• 2 f 2 - f 1 = 10.050 GHz
• 2 f 1 - f 2 = 10.005 GHz
• 3 f 2 - 2 f 1 = 10.065 GHz
• 3 f 1 - 2 f 2 = 9.990 GHz
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 109/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 109
6.9 Module 6: Self-Assessment Exercises
1. A particular receiver has a receive power threshold of –87 dBm in orderto deliver a SNR of 14 dB. The antenna also receives two interference
signals: one at a level of –98 dBm and another at a level of –104 dBm.
Determine the degraded threshold of the receiver in the presence of theseinterfering signals
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 110/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 110
2. A mast is at the “hub” of a 12 GHz microwave network. Three links
converge on this hub. One is of 2 km length, one 5 km length and one 16
km in length. All the antennas are 1.2 metres in diameter and the transmitfrom all transmitters is 500 mW. The 16 km link is susceptible to
interference from the two shorter links. In the direction of the 2 km link, the
gain of the receiving antenna is 0 dBi, and in the direction of the 5 km linkthe gain is –5 dBi. Estimate the interference power gathered by the antenna
and compare it with that received from its wanted signal.
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 111/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 111
3. A receiver at the hub of a microwave network operates on a frequency of
12.260 GHz. Interfering signals are received at frequencies of 12.060 GHz,
12.200 GHz, 12.400 GHz and 12.540 GHz. Which of these interferingsignals requires most attention from the viewpoint of intermodulation
products causing interferenc
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 112/192
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 113/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 113
7 Repeatered Systems
7.1 Introduction
Examining the effects of fading, in particular rain fading at higher microwave
frequencies, it is clear that; the longer the link, the harder it will be to meet a performance
objective. Additionally, as links become longer, it will become necessary to build higher
and higher masts in order to maintain visibility. For the above reasons, it is often
necessary to design your link so that it has more than one “hop”. It is necessary to place
a repeater at the point where each hop is terminated. Shorter links will also require
repeaters to be used if the path from one end to the other is obstructed.
RepeateredRepeatered SystemsSystems
• Severe difficulties occur attempting to establish
single hops greater than about 50 km due to both
fading and visibility problems.
• Longer paths require repeaters.
• Shorter paths with visibility problems will also
require repeaters.
Repeatered Systems
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 114/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 114
RepeateredRepeatered SystemsSystems
• Longer paths require repeaters.
• Shorter paths with visibility problems will also
require repeaters.
Repeatered Systems
7.2 Active and Passive Repeaters
Repeaters are said to be either “active” or “passive”. An active repeater has an amplifier
that attempts to restore the signal to its original quality before re-transmitting. On digital
systems, a far better performance is achieved by demodulating the signal at each repeater
station and re-transmitting a restored baseband signal. The advantage that digital systems
have on repeatered systems comes from the ability to reproduce a noise-free signal at
each repeater. In that way the total error rate is approximately equal to the sum of the
error rates on the individual hops. It is impossible to recreate a noise free signal on an
analogue system. All the calculations regarding the link between signal to noise ratio and
error rate have assumed that the original signal is noise free. In an analogue system, the
noise will accumulate as the signal progresses from hop to hop. As a consequence of
this, analogue radio systems are vastly inferior to digital systems when multi-hop links
are used.
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 115/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 115
ActiveActive RepeateredRepeatered SystemsSystems
• Active repeaters have a transceiver at each
repeater station, demodulating and re-transmitting
the message.
• On digital systems the BER on the entire system is
approximately the sum of the individual BER’s.
• On analogue systems, the noise will accumulate,
causing serious problems.
Repeatered Systems
ActiveActive RepeateredRepeatered Systems (Analogue)Systems (Analogue)
• The Signal to Noise ratio on a point to point link is
calculated assuming that the signal is “clean” when
it leaves the transmitter.
• On the second hop the signal will be noisy as it
leaves the transmitter. Noise accumulates from
hop to hop.
• Analogue systems are vastly inferior to digital
systems when multi-hops are considered.
Repeatered Systems
Clean Signal Noisy Signal Noisier Signal
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 116/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 116
ActiveActive RepeateredRepeatered Systems (Analysis)Systems (Analysis)
• Repeatered digital microwave systems can be
analysed by regarding each hop as an individual
single hop system.
• The total unavailability can be approximated to be
the sum of the individual unavailabilites (provided
that the individual unavailabilities are fractions of a
percent).
Repeatered Systems
Clean Signal Noisy Signal Noisier Signal
When analysing a repeatered system in which all the repeaters are active, each hop can be
regarded as if it was a separate link. Sometimes, there may be enough margin in the link
budget to allow the use of a passive repeater. A passive repeater has no power supply but
merely re-directs the signal towards the receiver. There are two alternative methods of
implementing a passive repeater: back to back antennas and; billboard reflectors.
7.2.1 Back-to-back antennas
The construction of a passive back-to-back antenna repeater involves placing the two
antennas at the appropriate height on the mast as would be the case if two individual links
were being implemented. However, there would not be an feeders running up the tower
to the antennas, nor would there be a cabinet containing transceivers and associated
equipement. Rather, the one antenna would be connected directly to the other via a short
section of waveguide.
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 117/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 117
PassivePassive RepeateredRepeatered SystemsSystems
• On short, obstructed links, it is possible to avoid the
expense of a passive repeater and, instead use a
passive repeater.
• The diagram shows a back to back antenna
configuration of a passive repeater.
• Total path loss is the sum of the individual hops.
Repeatered Systems
PassivePassive RepeateredRepeatered Systems (Example)Systems (Example)
• Example: A 14 GHz microwave system is carried
over a 6 km path. The path is obstructed at its mid
point and a passive repeater is installed. The
antennas used have a 1.2 m diameter. Estimate
the path loss and compare with that of a single hop
of the same length.
Repeatered Systems
3 km 3 km f = 14 GHz
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 118/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 118
PassivePassive RepeateredRepeatered Systems (Solution)Systems (Solution)
• Antenna Gain ~ 17.5 +20log(1.2)+20log(14)= 42 dBi
• FSL (3 km) = 92.4+20log(3)+20log(14)=124.9 dB
• Loss per hop = 124.9 - 84 = 40.9 dB
• Total loss = 81.8 dB
• For a single (6 km) hop, FSL = 130.9 dB. Path loss = 130.9 - 84 = 46.9
dB.
• Passive repeaters increase the path loss substantially.
Repeatered Systems
3 km 3 km f = 14 GHz
7.2.2 Reflector repeaters
As illustrated by the slides shown below, reflectors form an attractive alternative to back
to back antennas when the repeater is placed well to the side of the line joining the two
ends of the link. One advantage of reflectors is that it is usually easier to construct a
large reflector than it is to construct large antennas. Additionally mounting reflectors on
the side of existing buildings is more likely to be a possibility. The analyses given show
that you get less path loss if the reflector is placed near one end of the link. When
conducting the calculations, a check should always be made to ensure that the predicted
path loss is greater than the loss for an unrepeatered link. If that is not the case the loss
for an unrepeatered link should be used. Such reflectors are not suitable for placing close
to the line joining the two ends of the link. In such situation, a double reflector may be
used. The design considerations for such systems are outlined below.
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 119/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 119
PassivePassive RepeateredRepeatered Systems (Reflectors)Systems (Reflectors)
• As an alternative to back-to-back antenna systems, “billboard
reflectors” can be used as passive repeaters. These simply reflect
the signal from one antenna to the other.
• Gain of the repeater depends on its size, the frequency of
operation and the angle between the paths.
Repeatered Systems
Reflector Systems (Analysis)Reflector Systems (Analysis)
• For a reflector of surface area A, the gain is given by:
• G = 42.8 + 40 log f(GHz) + 20 log A (m2) + 20 log [cos (θ/2)] dB
• Overall free space path loss is then FSL1 + FSL2 - G where FSL1
and FSL2 are the losses of the individual parts of the path.
Repeatered Systems
θ
FSL1 FSL2
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 120/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 120
Reflector Systems (Example)Reflector Systems (Example)
• Considering a 6 km, 14 GHz path as before with 1.2 m antennas,
determine the size of billboard required to limit the path loss to 81.8
dB.
Repeatered Systems
120 degrees
3 km 3 km
f = 14 GHz
Reflector Systems (Example)Reflector Systems (Example)
• FSL1 = FSL2 = 124.9 dB.
• Path loss = 124.9 + 124.9 - 42 - 42 - G = 81.8 dBi
• G = 84 dB = 42.8 + 40 log 14 + 20 log A (m2) + 20 log [cos (60)]
• 1.4 dB = 20 log A
• A = 1.2 square metres.
Repeatered Systems
120 degrees
3 km 3 km
f = 14 GHz
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 121/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 121
Reflector Systems (Example)Reflector Systems (Example)
• Comparison with non-symmetric split.
• G = 84 dB
• Path loss = 129.3 + 115.3 - 42 - 42 - 84 = 76.6 dBi (compared with 81.8 dBi)
• Conclusion is that placing the reflector near one of the sites is
advantageous.
• Limitation occurs when it is so close to one end that path loss equals that of
a single hop (always check to ensure your prediction for path loss is greater
than that for a single hop).
Repeatered Systems
120 degrees5 km
1.2 m2
1 km
Reflector Systems (Double Reflectors)Reflector Systems (Double Reflectors)
• Where the angle between the paths is greater than about 130 degrees, the
gain of the antenna reduces noticeably (120 degrees is the “-6 dB angle”;
130 degrees is the “-7.5 dB angle).
• Double reflector systems can be used for greater angles.
Repeatered Systems
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 122/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 122
Double Reflectors (Analysis)Double Reflectors (Analysis)
• Provided adequate clearance is provided (the 15λ clearance shown is taken
as sufficient), the gain of the double reflector is approximately equal to the
gain of the smaller of the two.
• If the direction of propagation is changed at the reflector then each reflector
will change the direction of propagation by a different amount.
Repeatered Systems
15λ
Double Reflectors (Analysis)Double Reflectors (Analysis)
• Remember
• G = 42.8 + 40 log f(GHz) + 20 log A (m2) + 20 log [cos (θ/2)] dB
• Compute G for both reflectors and take the smaller of the two.
Repeatered Systems
θ1
θ2 θθ = θ2+180 - θ1
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 123/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 123
Double Reflectors (Optimisation)Double Reflectors (Optimisation)
• G = 42.8 + 40 log f(GHz) + 20 log A
(m2) + 20 log [cos (θ/2)] dB
• θ2 and θ1 should be as small as
possible.
• E.g. if θ has to be 160 degrees. θ2 =
20 degrees and θ1 = 40 degrees will
be a better solution than θ2 = 60
degrees and θ1 = 80 degrees.
• However, the smaller the angle the
harder it is to ensure that the onereflector does not obstruct the other.
Repeatered Systems
θ1
θ2
θ
θ = θ2+180 - θ1
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 124/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 124
7.3 Module 7: Self-Assessment Exercises
1. A 7 GHz, 20 km link is obstructed at its mid-point and requires a repeater
formed from two “back-to-back” parabolic antennas. The transmitter gives
an output power of 20 dBm into the antenna. The minimum required receivesignal level is –50 dBm. Determine the minimum antenna sizes required if:
a) The repeater is an active repeater
b) The repeater is a passive repeater
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 125/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 125
2. As an alternative to the back-to-back parabolic repeater, it is suggested
that a single flat, billboard reflector moved to the side of the path so that the
angle between the two paths is 120 degrees can provide the required signal
level. Determine the required size of the reflector. (Hint: the path length
from each antenna to the reflector will be greater than 10 km).
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 126/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 126
3. The size requirements for the billboard reflector are found to be excessive.
It is known that such reflectors are more effective if they are placed nearer to
one end of the link. Accordingly a suitable site is found 600 metres to the
side of one end of the link. The reflection angle is now 90 degrees and the
two “hops” are 20 km and 0.6 km in length. Re-calculate the size
requirements for the billboard reflector.
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 127/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 127
4.
A town is surrounded by a ridge of hills. In order to provide a 15 km, 14
GHz hop into the town from a neighbouring village, it is necessary to install
a double billboard reflector on the ridge, some 400 m from its terminal. 1.2
metre antennas are used on the two terminals. The reflector is configured
such that reflection angles of 30 degrees and 50 degrees are obtained.
Determine suitable reflector sizes if the maximum path loss is 70 dB.
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 128/192
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 129/192
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 130/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 130
Clearance RequirementsClearance Requirements
• We need to be able to calculate the “earth bulge”.
• Then, the terrain data needs to be extracted from
mapping information.
Clearance Issues
Earth Bulge
Clearance
8.2 Earth Bulge
The amount by which the bulge of the earth tends to obstruct the path between the
transmitter and the receiver can be determined using standard geometrical techniques.
However, the fact that the atmosphere is not uniform causes electromagnetic waves to
follow a curved path. In a standard atmosphere, the wave tends to follow the curvature of
the earth. This is helpful to radio engineers as it reduces the effective earth bulge to
typically 75% of its calculated value. However, the atmosphere is not static and
occasionally it will cause the radio wave to follow a path such that the effect of the
curvature of the earth is exaggerated. In carrying out calculations in such cases it is
necessary to increase the actual curvature of the earth by as much as 50%.
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 131/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 131
Earth BulgeEarth Bulge
Using the law of intersecting cords
If h is required in metres and R, d are
in kilometres:
Clearance Issues
d 2
d 1
h
2R
h - earth bulge
R - earth radius
d 1,2 - distances from hop ends
R
d d h
Rhd d
2
2
21
21
=
=
R
d d h
2
1000 21=
Earth BulgeEarth Bulge
Clearance Issues
R
d d h
2
1000 21=
• Earth bulge is a maximum where d 1=d 2=d/ 2.
• Then the earth bulge = Taking the earth radius tobe 6373 km:
R
d 2125
Path Length (km) Max Earth Bulge (m)
10 2.0
20 7.9
30 17.7
40 31.4
50 49.0
60 70.6
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 132/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 132
Modified Earth RadiusModified Earth Radius
Clearance Issues
• Radio signals will continue slightly beyond the horizon. This isbecause the refractive index of the atmosphere tends to reduce withheight causing the radio wave to bend in the direction of curvature of the earth.
• Thus the effect of the earth bulge does not have as big an effect asfirst calculated.
• The effective earth bulge can be calculated by assuming the earth’sradius is larger than its physical value.
Radio horizonVisible horizon
Modified Earth RadiusModified Earth Radius
Clearance Issues
• The actual Earth’s radius is multiplied by a factor given the value k (often referred to as the k -factor).
• For a “standard atmosphere”, k = 1.33 reducing the effective earth
bulge to 0.75 of its calculated value.
• k varies with atmospheric conditions.
k = 1.0k = 1.33
k = 2.0k = 4.0
k = ∞
k = 0.66
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 133/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 133
Variability ofVariability of k k -Factor -Factor
Clearance Issues
• Just as we need to know the extent of multipath fading for, say, 0.1%of the time, we also need to know the minimum value of the k-factor of the same percentage in order to establish the necessary clearance.
• The value exceeded for 99.9% of the time depends on the climate andon the path length (as very anomalous atmospheric structures willtend not to occur over large distances simultaneously.
10 20 40 80
k
0.3
0.5
0.7
0.9
Value of k exceeded for
99.9% of the worst month.
Path length (km)
8.3 The Fresnel Parameter
TheThe FresnelFresnel Parameter Parameter
Clearance Issues
• The amount of clearance required depends on the path length, theposition of the obstruction along the path and the frequency of operation.
• The Fresnel Parameter links these together to give a universallyapplicable parameter.
d 1
cb
h
21 d d cb +>+
221 λ ++=+ d d cb
• There exists a value of h such that
d 2
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 134/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 134
TheThe FresnelFresnel Parameter Parameter
Clearance Issues
• The locus of points for which this is true form an ellipsoid in threedimensions known as the “First Fresnel Zone” and the values of h atpoints along the path are known as the F 1 values.
• If h<<(d 1+d 2) then F 1 in metres is given approximately by
d 1
cbh
221 λ ++=+ d d cb
• There exists a value of h such that
d 2
( )21
211 3.17
d d f
d d F
+=
• f is in GHz, d 1, d 2 are measured in kilometres.
TheThe FresnelFresnel EllipsoidEllipsoid
Clearance Issues
( )21
211 3.17
d d f
d d F
+=
d 1 d 2
F 1
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 135/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 135
8.4 ITU-R Recommendations
Once the Fresnel zone radius has been established, it is possible to use ITU-R
recommendations in order to determine the amount of clearance that should be afforded
in any particular location.
Clearance RequirementsClearance Requirements
Clearance Issues
• The antennas should be sufficiently high to meet the more
onerous of the following requirements.
For k = 1.33, clearance of 1.0 F 1 should be obtained.
For k = “minimum exceeded for 99.9% of the time”, clearance of
0.3 F 1 should be obtained if the obstacle is rounded or zero if
there is a sharp single isolated obstacle.
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 136/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 136
Clearance Requirements (example)Clearance Requirements (example)
Clearance Issues
• A 30 km, 14 GHz path has an isolated obstacle 12 metresin height at a distance of 13 km from one end.
12 m
30 km
13 km
Clearance Requirements (example)Clearance Requirements (example)
Clearance Issues
• k = 1.33. Earth Bulge at 13 km from one end = 17.7/1.33 = 13.3 m
• Add 12 m obstacle height to give 25.3 m in total.
• F1 at 13 km from one end = 12.5 metres
• Total required clearance 37.8 metres.
• Each antenna should be 37.8 metres in height.
12 m
30 km
13 km
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 137/192
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 138/192
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 139/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 139
Diffraction over “average terrain”Diffraction over “average terrain”
Clearance Issues
• The description “knife-edge” may not apply to a particular
obstacle.
• An approximate formula for average terrain exists based
on the “normalized clearance” expressed as a multiple of
F 1.
• Path loss ~ 10 - 20 h/ F 1 dB.
• Note: valid for values of h larger than F 1 (obstructed paths
only).
Diffraction over “average terrain”Diffraction over “average terrain”(example)(example)
Clearance Issues
• A 30 km, 14 GHz path propagates over “average terrain”
of height equal to the height of the base of the antenna
towers.
• The antennas are 15 m above ground level.
• Determine the diffraction loss when the k-factor is 0.7.
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 140/192
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 141/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 141
Fading due to Ground ReflectionsFading due to Ground Reflections
Clearance Issues
• Multipath caused by ground reflection can cause severe fades.
• Smooth ground causes more severe fading than rough ground.
Diffracted Rays
Reflected Ray
Fading due to Ground ReflectionsFading due to Ground Reflections
• As the path length difference between the reflected and direct
ray alters, “constructive” and “destructive” interference is
experienced. Destructive interference can cause a severe
reduction in signal strength.
Clearance Issues
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 142/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 142
Fading due to Ground ReflectionsFading due to Ground Reflections
Clearance Issues
Direct Ray
Reflected Ray
Resultant
Constructive
Interference
Fading due to Ground ReflectionsFading due to Ground Reflections
Clearance Issues
Direct Ray
Reflected Ray
Resultant
DestructiveInterference
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 143/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 143
Protecting against Reflection FadesProtecting against Reflection Fades
Clearance Issues
• The effect is that an “interference pattern” develops in which
the strength of the received signal varies with height.
“Null” or “Trough”
“Peak”
The effect of surface roughness on the probability of fading is considered in ITU-R
P.530-10. A more accurate equation for the geoclimatic factor, K is given by
42.0003.09.3 110 −−−= adN s K where a s is the “standard deviation of terrain
heights” for the area of interest. Note that K reduces with increasing values of S a. A
minimum value for S a. of 6 metres should be adopted. As an example of the effect of this
refinement of the equation consider the situation where K is calculated for a value for
1dN of -200.
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 144/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 144
Approximate Formula
(independent of 1dN ) K = 2.4 x 10-4
6=a s K = 2.4x10
-4
12=a s K = 1.8 x 10-4
24=a s K = 1.3 x 10-4
42=a s K = 1.0 x 10-4
It can be seen that the approximate formula assumes a “worst case” for fading, agreeing
with the more accurate figure when the value for standard deviation of terrain heights is
at the lowest possible value. However, the value itself may not be particularly relevant
for a particular path as data is provided by making height measurements over a wide area.
The area where reflections take place on a particular path are subject to local variations
that may render the standard calculation methods irrelevant. A preliminary study into the
mechanics of reflection and possible counter measures is given here
8.6.2 The Rayleigh Criterion.
The likelihood of a fade occurring is influenced by the “coherence” of the reflected wave.
To provide a deep fade it must have the characteristics of a single sinusoid. This is only
the case if the surface is extremely smooth. But any definition of “smoothness” is related
to the wavelength. The effect of roughness is also influenced by the grazing angle
between the transmitter, receiver and reflection point. The Rayleigh criterion involves
evaluating the expression for the phase difference between two elements of a reflected (or
“scattered” wave). The expression incorporates the grazing angle, θ , the frequency f
(GHz) and the standard deviation of heights, s (metres) at the reflection point and is given
by θ sin42 f . If this expression is less than 0.1 then the reflections can be regarded as
mirror-like (or “specular”). If the expression is greater than 10 then the reflections will
be diffuse and troublesome fading from ground reflections are unlikely. Between these
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 145/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 145
two values a transition occurs and it is difficult to be conclusive about the likely
occurrence of reflection fading.
TheThe RayleighRayleigh CriterionCriterion
• The phase difference ∆θ betweentwo rays reflecting from twodifferent surfaces separated by
distance s is given by
s
Clearance Issues
θ λ
θ π φ sin42
sin4 sf
s≈=∆
θ
ition trans10sin420.1
diffuse 10sin42
specular 1.0sin42
<<
>
<
θ
θ
θ
sf
sf
sf
8.6.3 Protection against reflection fades
Once the possibility of problematic reflection fades, judging by the Rayleigh criterion,
has been identified, it is necessary to be aware of the procedures by which the probability
of fading can be reduced. ITU-R P.530-10 itemises four possible methods by which this
reduction can be achieved:
• Use of vertical polarisation
• Shielding of the reflection point• Moving of reflection point to poorer reflecting surface
• Optimum choice of antenna heights
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 146/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 146
8.6.3.1 Use of vertical polarisation
Vertically polarized waves will reflect less strongly from horizontal surfaces than will
horizontally polarized waves. Vertical polarisation should be the polarisation of choice
for paths where the possibility of ground reflection exists.
8.6.3.2 Shielding of the reflection point
Judicious use of the terrain and/or buildings can result in the reflected wave being
attenuated due to diffraction over an obstacle. Checks should be made to ensure that the
reflected path is obstructed over the complete range of likely values of earth bulge k
factor.
Protecting against Reflection FadesProtecting against Reflection Fades
Clearance Issues
• Shielding of Reflection point
• Checks must be made to ensure that shielding occursthroughout the range of k-factors that will be experienced.
8.6.3.3 Moving of the reflection point.
It may be that a smooth reflecting surface (for example, a body of water) occurs at the
mid-point of a path. If equal antenna heights are adopted, the reflection point will be at
the mid-point. By adjusting antenna heights, the reflection point can be moved.
Lowering an antenna will cause the reflection point to move towards that antenna.
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 147/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 147
Protecting against Reflection FadesProtecting against Reflection Fades
Clearance Issues
• Moving of Reflection point to
poorer reflecting surface
8.6.3.4 Optimisation of antenna heights.
Ground reflection will cause constructive and destructive interference. It is the
destructive interference that causes us most concern. Also, because the path length
differences are small (a few tens of centimeters) resulting in low relative time delays (less
than a nanosecond), reflection fading will be “flat” rather than “selective”. As the height
of the receiving antenna is varied, it will move through “peaks” and “troughs” that are
caused by the reflection. It is possible to place the receiving antenna in a peak thus
taking advantage of the reflection to elevate the signal level.
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 148/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 148
Protecting against Reflection FadesProtecting against Reflection Fades
Clearance Issues
• Optimum choice of antenna heights.
“Null” or “Trough”
“Peak”
However, there is a problem with this strategy: if the reflection point is a body of water
whose level varies or; the k -factor of the earth changes significantly; the pattern of peaks
and troughs will move in a vertical direction. In this circumstance, it will be necessary to
implement a diversity system such as space diversity where the likelihood of both
antennas experiencing nulls simultaneously is very low.
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 149/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 149
Protecting against Reflection FadesProtecting against Reflection Fades
Clearance Issues
• A problem – the interference pattern is not stationary.Changes in earth curvature k-factor and variations in the tidecause the pattern to move with time.
In order to determine the whether the pattern of peaks and troughs will move
significantly, it is necessary to estimate the amount by which the path length difference
between the direct and reflected waves will vary. If this varies by more than a
wavelength then diversity should be used.
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 150/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 150
Protecting against Reflection FadesProtecting against Reflection Fades
• The pattern moves because thepath length difference changes.
2/d
Clearance Issues
2/d
h
• If the reflection point is at themidpoint, then (by Pythagoras):
( ) ( )2/2/2 22d hd d −+=∆
8.6.3.4.1 Ground reflection example
Consider a situation where a 20 km microwave path uses antennas that are 25 m above
sea level. At the mid-point of the path exists a tidal inlet. The height of the water surface
in the inlet varies from 6 metres below sea level to 4 metres above sea level. Assuming a
k-factor of 1.33, determine the maximum frequency that can be employed to limit the
variation in path length difference to 1 wavelength.
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 151/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 151
Protecting against Reflection FadesProtecting against Reflection Fades
• Example:
• Antenna heights: 25 m a.s.l.
• Ground heights vary from 6 m below s.l. to 4 m a.s.l.
2/d
Clearance Issues
2/d
h
33.1km;20 == k d
Solution:
Earth bulge at midpoint = kRd /125 2 = 5.9 metres.
At 6 metres below sea level the path length difference (by Pythagoras)
063.0100001.2510000222
=
−+×= metres
At 4 metres above sea level the path length difference
023.0100001.15100002 22 =
−+×=
The difference between these two values equals 0.040 metres. This equals a wavelength
at frequency of98 105.7040.0103 ×=÷× Hz. This corresponds to a frequency of
7.5 GHz which should be regarded as the maximum frequency at which a non-diversity
system could be implemented.
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 152/192
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 153/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 153
Using Field MeasurementsUsing Field Measurements
Clearance Issues
• If the reflection coefficient of the ground is low, or thereflecting surface is very rough, the difference between the
peak and the trough will be very small.• One advantage of reflection fades is that the reflecting surface
is always there (unlike atmospheric ducts).
• It is therefore possible to measure the variation of signalstrength with height and assess the seriousness of theproblem.
• The difference between the peak and the null indicates thelikely depth of reflection fading that will be experienced.
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 154/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 154
8.7 Module 8: Self-Assessment Exercises.
1. Determine the earth bulge for a K-factor of 0.8 on a link of length 25 km.
2. Determine the radius of the first Fresnel zone at the midpoint of a 50 km
path at frequencies of 3 GHz, 10 GHz and 30 GHz.
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 155/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 155
3. A 30 km path has a sharp, knife-edge obstacle, 10 m in height, 8 km from
one end. The minimum k factor experienced (exceeded 99.9% of the
time) is 0.7. Determine suitable antenna heights.
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 156/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 156
4. Determine the diffraction loss at a k factor of 0.5 if the antenna heights
determined by the result of question 3 are adopted.
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 157/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 157
9 Performance Objectives
9.1 Introduction:
It has been demonstrated that 100% reliability is an unrealistic expectation from a
microwave radio system. Nevertheless, microwave links must form a viable alternative
to fixed line networks if they are to be considered for general use. This includes being
able to satisfy expectations regarding performance. In assessing reliability, the ITU-R
makes a distinction between “unavailability” and “outages” as described in the slide
below.
DefinitionsDefinitions
• Unavailability: System “not working” for 10
consecutive seconds.
“Not working” defined as BER worse that 1 x 10-3.
• Outages: Exist for less than 10 seconds and the
system is still regarded as “available” (even though
the user cannot access it).
Outages are subject to “performance objectives”.
Unavailability and Performance Objectives
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 158/192
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 159/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 159
Propagation ProblemsPropagation Problems
• Multipath problems: unlikely as multipath outages
tend to be short-lived (much less than 10 seconds).
• Diffraction loss: obeying clearance rules should
avoid this.
• Ducting: generally restricted to well-known
geographical regions. Can be combatted with
space diversity.
• Rain: the most likely cause of “propagation related”
unavailability at high (10 GHz+) microwave
frequencies.
Unavailability and Performance Objectives
9.3 Equipment-related Unavailability
The prevalence of unavailability due to equipment problems depends on the reliability of
the equipment (quantified by the Mean Time Between Failures: MTBF) and the average
length of time that the system is down for each failure (quantified as the Mean Time To
Repair: MTTR).
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 160/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 160
Equipment ProblemsEquipment Problems
• Definitions
MTBF: Mean Time Between Failures (usually several
thousand hours)
MTTR: Mean Time To Restore.
• Availability
• Unavailabity
Unavailability and Performance Objectives
%100×+
= MTTR MTBF
MTBF A
AU −=100
Equipment ProblemsEquipment Problems
• Example:
For a single transceiver and associated equipment MTBF = 50,000 hours
MTTR = 6 hours
Link MTBF = (Terminal MTBF) x 0.5 = 25,000 hours
• If we have a 12 hop link the total unavailability =
12x0.024=0.29% (approximately 25 hours per year).
Unavailability and Performance Objectives
%024.0
%976.99%100625000
25000
=
=×+
=
U
A
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 161/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 161
9.3.1 Hot Standby
The effective mean time to repair can be reduced to nearly zero by implementing a “hot
standby” facility for the equipment. It is possible for two receivers to be permanently
connected to the system so that either one can be utilised. This provides a seamless
continuity of service should one receiver fail.
Equipment Problems: Hot StandbyEquipment Problems: Hot Standby• A “hot standby” is a duplicate system permanently
powered up and ready to replace the active system
should a fault occur.
• Should a transmitter fail, for example, a replacement
is switched into its place. This can occur in as short
a time as 20 ms.
• With MTBF as long as 50000 hours, unavailability
due to transmitter or receiver failure becomes
negligible.
Unavailability and Performance Objectives
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 162/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 162
Implementing Hot StandbyImplementing Hot Standby
• Transmitter Hot Standby.
Cannot have both connected simultaneously.
An RF switch is required to connect the Hot Standby to the
antenna system in the event of the Main Transmitter failing.
Unavailability and Performance Objectives
Main
Transmitter
Hot
Standby
Implementing Hot StandbyImplementing Hot Standby• Receiver Hot Standby.
It is possible to connect two receivers to the antenna
system simultaneously, via a coupler.
Unavailability and Performance Objectives
Main
Receiverr
HotStandby
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 163/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 163
In the case of the transmitter, it is not possible to connect the main and the standby
transmitter simultaneously (as they would interfere with each other). It is necessary to
have a switch that automatically disconnects the main transmitter and connects the
standby transmitter to the antenna should the main transmitter fail. This does result in a
very brief period when the service is down.
The fact that it is possible to connect the main and standby receivers simultaneously leads
to the question “what fraction of the total receive power should be channeled through to
each receiver?” being asked. If an equal power is sent to each receiver, then an insertion
loss of approximately 4 dB will be incurred. This is seen as a waste of power as the use
of the standby receiver should be an extremely rare occurrence. It is more common to
split the received power so that the level received by the standby receiver is typically 10
dB below that received by the main receiver. This means that the power would be higher
most of the time with a 10 dB reduction in margin occurring when the main receiver fails.
Receiver Hot Standby: Coupler AnalysisReceiver Hot Standby: Coupler Analysis
• A symmetrical coupler will have an insertion loss of
at least 3 dB (usually nearer 4 dB) that must be
accounted for in the link budget.
• Asymmetrical couplers can put more insertion loss
in the standby leg and less in the main leg.
Unavailability and Performance Objectives
From Antenna From AntennaTo Main
To Standby
To Main
To Standby
Symmetrical Coupler Asymmetrical Coupler
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 164/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 164
Receiver Hot Standby: Coupler AnalysisReceiver Hot Standby: Coupler Analysis
• Suppose a coupler produces a 1 dB resistive loss.
• That means that, if we have 10 nW at the input, we will have a
total of 8 nW at the output.
• If this is divided equally, each arm of the coupler will receive 4
nW, equivalent to a loss of 10log10(2.5)=4dB.
• Alternatively, one arm could receive 7.27 nW and the other arm
0.727 nW.
• The losses would then be 1.4 dB and 11.4 dB respectively.
• The choice of having only 1.4 dB loss “permanently” and an
extra 10 dB degradation of fade margin during standby periods
is argued to be superior to having 4 dB loss in both “main” and “
standby” modes.
Unavailability and Performance Objectives
9.4 Unavailability Objectives
Some unavailability is inevitable. However, there are internationally agreed objectives that the link planner
should aim to meet. In forming the objectives, the ITU-T gives due consideration to the importance of the
link being planned and describe three different categories: High Grade; Medium Grade and Local Grade.
Connections between cellular mobile radio sites are classed as Local Grade.
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 165/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 165
Unavailability ObjectivesUnavailability Objectives
• ITU-T G.821 divides a hypothetical long-distance channel into
“High Grade”, “Medium Grade” and “Local Grade” services.
• Objectives for High Grade circuits of length L, where L isbetween 280 km and 2500 km are:
• Local Grade (e.g. GSM interconnect) objectives proposed vary
between 0.01% and 0.2%. This affects repair philosophy.
Unavailability and Performance Objectives
( )%2500
3.0100 L A ×−=
9.5 Performance Standards
When the system is available, it will still suffer outages. Performance Standards specify
the maximum amount of outages that will be tolerated. Again different categories of link
are defined with performance standards specified accordingly. Traditionally, the number
of one-second periods containing one or more errors would be reported. The “errored-
second ratio” (ESR) became a benchmark by which services were compared. However,
with the advent of high capacity services with data rates up to 155 Mbits/s it is apparent
that a single second will contain 155 million bits and a single error would probably not be
a serious issue. It was therefore decided to adopt a block of data as the standard unit of
transmission and define performance standards on this basis. It is then necessary to be
able to translate from a fade margin that has been calculated to a ratio for Severely
Errored Seconds (second periods during which 30% of blocks received contain errors).
An example is shown below whereby this is done when rain fading is considered.
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 166/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 166
Performance StandardsPerformance Standards
• These standards define the required system
performance when it is available.
• Causes of degradation in performance:
Multipath Fading (as previously analysed)
Background Errors (Gaussian noise has no absolute
maximum value and, hence some errors will occur)
Wind (causes misalignment of antennas)
Unavailability and Performance Objectives
Performance Criteria: High CapacityPerformance Criteria: High Capacity
ServicesServices• ES: Errored-second; any 1 second period in which an error occurs.
• Not an appropriate measure when 1 second can contain several
million bits. Instead, a block of data is considered and new terms
are introduced.
• EBR: Errored Block Ratio; refers to blocks containing one or more
errors. Block size is specified for each system rate.
• ESR: Errored Second Ratio; A 1-second period that contains one
or more errored blocks.
• SESR: Severely Errored Second Ratio; A 1-second period that
contains greater than 30% or errored blocks.
• BBE: Background Block Error; An errored block not occurring aspart of an SES.
• In-service measurements of block errors is possible.
Unavailability and Performance Objectives
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 167/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 167
Performance CriteriaPerformance Criteria
• Local Grade (including links between cellular
sites)
SESR should not exceed 0.00015 during the worst
month.
ESR should not exceed 0.012 during the worst
month
Unavailability and Performance Objectives
Linking SNR, BER, ES, ESR and SESRLinking SNR, BER, ES, ESR and SESR
• We have seen that SNR affects the BER. This will in turn affect
the other parameters.
• As an example, consider the procedure to predict the SESR
caused by rain attenuation.
• Step 1: for the system under consideration use ITU-R P.530-9 to
estimate the BER that will result is SES ( BERSES )
• Step 2: calculate the receive level without rain attenuation and
hence calculate the rain attenuation margin.
• Step 3: calculate the annual time percentage that the rain
attenuation will exceed the margin.
• Step 4: translate this to a worst month percentage (see ITU-RP.841)
Unavailability and Performance Objectives
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 168/192
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 169/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 169
10 Solutions to Self-Assessment Questions
10.1 Module 1: Self-Assessment Exercise
Designing by guessing.
As intuitive engineers we should have some idea regarding what a
microwave link should look like and what its values should be.
Try and picture a microwave link in your mind and imagine what the
relevant parameters might be. It will be interesting to refer to these
“guesstimates” as we gain knowledge regarding the design of microwave
links.
Name of Designer Chris Haslett
Frequency of Operation 10 GHz
Rate of transmission (bits per
second)
8 Mbit/s
Mast Height 30 metres
Path Length 20 km
Antenna Diameter 1.2 metres
Transmit Power 1 watt
Receive Power 1 nanowattFeeder length (metres) 30 metres
Feeder loss (dB) 2 dB
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 170/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 170
10.2 Module 2: Self-Assessment Exercise
1. An antenna operates at a frequency of 15 GHz. If it has a diameter of
1.8 metres, estimate its gain.
41000dBi46log20log205.17 ==++≅ D f G
Alternatively
dBi8.46480006.0
2
==
≅λ
π DG
2. Two such antennas are to be used over a link of length 12 km. Determine
the path loss.
dB45.592-137.5Loss
dBi92GainsAntenna
5.13715log2012log204.92
log20log204.92
==
=
=++=
++= f d SL
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 171/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 171
3. Repeat the calculation of question 2 for antennas of the same size but
operating at a frequency of 30 GHz.
dB39.5104-143.5Loss
dBi104GainsAntenna
5.14330log2012log204.92
log20log204.92dBi52log20log205.17
==
=
=++=
++= =++≅ f d FSL D f G
4. Estimate the beamwidth of a 1.8 metre antenna at 7 GHz, 15 GHz and 30
GHz.
)30(4.0);15(8.0);7(7.18.1
22GHz GHz GHz
f Beamwidth °°°=≈
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 172/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 172
5. A transceiver outputs a power of 27 dBm via a feeder of 3 dB loss to an
antenna of diameter 0.9 metres. If the frequency of operation is 12 GHz,
estimate the EIRP from the antenna.
dBm62.23-2738.2EIRP
dBi2.389.0log2012log205.17
=+==++=G
6. For the situation described in question 5, estimate the power that would
be gathered by an identical antenna at a distance of 4 km.
dBm-25.6
20log(12))20log(4)(92.4-38.262.2FSL-GainAntennaRxEIRPPowerRx
=
+++=+=
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 173/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 173
10.3 Module 3: Self-Assessment Exercises
Note Boltzmann’s constant k = 1.38 x 10-23
J/K
1. An antenna has a noise temperature of 280 kelvins. Determine the noise power gathered if the noise bandwidth of the receiver is 14 MHz.
dBm102.7-watts105.4
watts10142801038.1
14
623
=×=
××××=−
−kTB
2. An amplifier has a noise bandwidth of 2 MHz and a noise temperature of
350 kelvins. If the noise power at the input equals k(480)B watts and the
signal power at the input is 0.172 picowatts, determine the signal to noise
ratio at the output of the amplifier.
dB8.8
5.7
102350)(48010.381
101.72
outputatSNR
watts102350)(480outputatPower Noise
watts101.72outputatPowerSignal
623-
13-
6
13-
=
=×+×
×
=
×+=
×=
Gk
G
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 174/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 174
3. A microwave system has a bandwidth of 4 MHz. The receiver noise
figure is 3 dB. Determine the noise temperature of the receiver and the
minimum required signal power in order to deliver a SNR of 13 dB.
State any assumptions made.
dBm-92
watts104.620104)580(
SNR required powernoise powersignalRequired
kelvins290isantennaof retemperatu NoiseAssuming
kelvins290)1(290
0.210
136
3.0
=
×=××=
×=
=−=
==
−k
F T
F
e
4. A 10 GHz microwave link of length 30 km has 1.2 m diameter antennas.
The minimum required receive power has been determined to be –84
dBm. Miscellaneous losses total 6 dB. Determine a suitable transmit
power.
dBm-14(-84)69.7PowerTx
dB69.778.2-6141.9lossPath
dB141.920log(10))2020log(3092.4FSL
dBi39.120log(10)20log(1.2)17.5antennam1.2of Gain
=+=
=+==++=
=++=
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 175/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 175
5. A microwave link has a receiver with a noise bandwidth of 3 MHz. The
noise temperature of the antenna is 290 kelvins. The receiver consists of
a mast head amplifier with a gain of 15 dB and a Noise Figure of 1.2 dB,
a feeder of 4.5 dB loss and a demodulator with a Noise Figure of 3.5 dB.
Determine the SNR with and without the mast head amplifier if the
power gathered by the antenna is –91 dBm.
dB16.5(-107.5)-91-SNR
dBm107.5-watts1078.1)290(
1411010359105273.92
MHAwith
dB10(-101)-91-SNR
dBm101-watts1057.7)290(
153910359527
:MHAwithout
527attenuator dB4.5
K 359dB3.5
K 92.3dB2.1
14
45.05.15.1
14
45.0
==
=×=+
=×÷+÷+=
==
=×=+
=×+=
⇒
⇒
⇒
−
−
BT k
T
BT k
T
e
e
e
e
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 176/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 176
6. A Microwave link provides a 2 MHz channel with a SNR of 12 dB. Use
Shannon’s theorem to determine the maximum possible capacity of the
channel. Note:
( )
2log
loglog
1logBandwidthCapacity
10
102
2
x x
SNR
=
+×=
Mbit/s1.8101.82log
8.16log102Capacity
8.1510
6
10
106
2.1
=×=××=
==SNR
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 177/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 177
10.4 Module 4: Self-Assessment Exercises.
1. A 24 km microwave link is located in Sweden and operates at a
frequency of 18 GHz. One antenna is 1100 m above sea level and the
other is at 800 m above sea level. Estimate the percentage time for whicha fade exceeding 25 dB would occur.
( )
( )
( )
%1009.1
105.121241012.9
101
1012.9
10
400
5.1224
8001100
3
10/25800001.018033.02.10.34
10/001.0033.02.10.3
4
0029.02.4
1
1
−
−×−×−−
−−−
−
−−
×=
×+×=
×+=
×=
=
−=
=−=
Ah f pw
dN
p
L Kd p
K
dN
ε
ε
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 178/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 178
2. A 21 km microwave link, located in Italy, operates at a frequency of 28
GHz. Horizontal polarisation is used. Determine the rain-produced
attentuation for a 0.01% time period.
dB8710.78.1nAttenuatio
km7.10
2.19241
24 length patheff
2.1935
1 length patheff
dB/km1.8)40(187.0
021.1
187.0Italyformm/hr40
01.0015.00
0
021.1
01.0
=×=
=+
=
==
+=
===
==
== ≈
− R
R
H
H
ed
d d
d
kR
k k R
α γ
α α
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 179/192
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 180/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 180
4. Estimate the atmospheric absorption on an 11.5 GHz link of path length
20 km.
From graph, water vapour and oxygen absorption both equal approximately
0.02 dB/km. Adding these two values gives 0.04 dB/km. Therefore a 20 km
path will suffer atmospheric absorption of approximately 0.8 dB.
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 181/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 181
10.5 Module 5: Self-Assessment Exercises
1. A 28 km microwave link, located in Sweden operates at a frequency of
21 GHz. Identical antennas are used at both ends and the path is horizontal
with antennas at an elevation of 1200 metres above sea level. Without anydiversity it is found to have a fade margin of 16 dB. Determine the
probability of outage. Estimate the improvement factor provided if space
diversity is employed with an antenna separation of 4 metres.
From previous solution to Module 4 Question 1, K = 9.12 x 10-4
( )
( ){ }( ){ }
63.2
1023.62821404.0exp1
1004.0exp1
23.6
10
%156.010281012.9
101
101604.148.012.087.0
1004.10
48.012.087.0
10160
10161200001.021033.00.34
10001.0033.02.10.3
=
×−−=
−−=
=
=
=××=
×+=
−−
−−
−×−×−
−−−
A
w
Ah f pw
pd f S I
p p
Kd p Lε
Probability of fade reduced from 0.156% to 0.059%.
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 182/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 182
2. Using the procedures of ITU-R P.530-10, page 28, evaluate the
improvement possible by utilising frequency diversity with a separation of
200 MHz instead of space diversity.
008.0
1021
2.0
2821
80
1080
108
10
=
×=
∆= F
f
f
fd I
This suggests that frequency diversity is not suitable for links such as this.
Note that improvement would be gained if the link was shorter and operated
at a lower frequency and had a higher fade margin.
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 183/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 183
10.6 Module 6: Self-Assessment Exercises
1. A particular receiver has a receive power threshold of –87 dBm in order
to deliver a SNR of 14 dB. The antenna also receives two interference
signals: one at a level of –98 dBm and another at a level of –104 dBm.Determine the degraded threshold of the receiver in the presence of these
interfering signals
dBm-81.61495.56-thresholdDegraded
dBm-95.56
mW1027.77floornoise plussinterferer of Total
mW103.98dBm104-
mW1015.85dBm98-
:sInterferer
mW107.94dBm101-14-87-Floor Noise
11-
11-
11-
11-
=+=
=
×=
×=×=
×===
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 184/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 184
2. A mast is at the “hub” of a 12 GHz microwave network. Three links
converge on this hub. One is of 2 km length, one 5 km length and one 16
km in length. All the antennas are 1.2 metres in diameter and the
transmit from all transmitters is 500 mW. The 16 km link is susceptible
to interference from the two shorter links. In the direction of the 2 km
link, the gain of the receiving antenna is 0 dBi, and in the direction of the
5 km link the gain is –5 dBi. Estimate the interference power gathered
by the antenna and compare it with that received from its wanted signal.
Wanted signal:
dBm29.6-81.4138-27PowerReceive
dBi40.71.2log2012log2017.5GainAntenna
dB13816log2012log204.92
=+=
=++=
=++= FSL
Signal on 2 km link
dBm3.5240.7120-27 powerReceive
dBi40.7gainsantennaTotal
dB120
−=+=
=
= FSL
Signal on 5 km link
dBm65.3-35.7128-27 powerReceive
dBi35.7gainsantennaTotaldB128
=+=
== FSL
Adding interfering powers
-65.3 dBm + - 52.3 dBm = -52.1 dBm.
This is 22.5 dB below the wanted signal power.
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 185/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 185
3. A receiver at the hub of a microwave network operates on a frequency of
12.260 GHz. Interfering signals are received at frequencies of 12.060
GHz, 12.200 GHz, 12.400 GHz and 12.540 GHz. Which of these
interfering signals requires most attention from the viewpoint of
intermodulation products causing interference?
If 12.400 GHz is regarded as f 1 and 12.540 GHz is regarded as f 2 then:
2 f 1 – f 2 = 24.800-12.540=12.260 GHz, the wanted signal frequency.
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 186/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 186
10.7 Module 7: Self-Assessment Exercises
1. A 7 GHz, 20 km link is obstructed at its mid-point and requires a repeater
formed from two “back-to-back” parabolic antennas. The transmitter gives
an output power of 20 dBm into the antenna. The minimum required receivesignal level is –50 dBm. Determine the minimum antenna sizes required if:
a) The repeater is an active repeater
b) The repeater is a passive repeater
The link consists of two, 10 km hops. Total loss allowed is 70 dB. For the
active system this effectively means that each hop can suffer a loss of 70 dB.
metres60.010
log2016.917.530
20log20log717.5Gain
each)dBi(30dBi59.3gainsantennaCombineddB3.1297log2010log204.92
204.4
==
++=
++=
==++=
− D
D
D
FSL
For the passive system, each hop can suffer only 35 dB loss.
metres27.410
log2016.917.547
20log20log717.5Gain
each)dBi(47dBi94.3gainsantennaCombined
206.12
==
++=
++=
=
D
D
D
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 187/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 187
2. As an alternative to the back-to-back parabolic repeater, it is suggested
that a single flat, billboard reflector moved to the side of the path so that the
angle between the two paths is 120 degrees can provide the required signal
level. Determine the required size of the reflector if 1.35 metre diameter
antennas are used at each end of the link. (Hint: the path length from each
antenna to the reflector will be greater than 10 km).
2
205.46
m212
10
log205.46
6log208.338.421.117
)2/120log(cos20log20log4042.8117.1
117.1
74--261.170
dB130.5520log(7)5)20log(11.592.421
74-21dB70
GainsAntenna-21LossPath
km55.11sin(60)
10 nowlengthPath
=
=
=
−++=
+++=
==
=++==
+=
+=
==
A
A
A
A f
G
G
FSL FSL
-G FSL FSL
-G FSL FSL
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 188/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 188
3. The size requirements for the billboard reflector are found to be excessive.
It is known that such reflectors are more effective if they are placed nearer to
one end of the link. Accordingly a suitable site is found 600 metres to the
side of one end of the link. The reflection angle is now 90 degrees and the
two “hops” are 20 km and 0.6 km in length. Re-calculate the size
requirements for the billboard reflector.
2
206.22
m5.13
10
log206.22
3log208.338.422.96
)2/90log(cos20log20log4042.896.2
96.2
74--240.270
dB9.04120log(7)20log(0.6)92.42
dB135.320log(7)20log(20)92.41
74-21dB70
GainsAntenna-21LossPath
=
=
=
−++=
+++=
=
=
=++=
=++=
+=
+=
A
A
A
A f
G
G
FSL
FSL
-G FSL FSL
-G FSL FSL
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 189/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 189
4.
A town is surrounded by a ridge of hills. In order to provide a 15 km, 14
GHz hop into the town from a neighbouring village, it is necessary to install
a double billboard reflector on the ridge, some 400 m from its terminal. 1.2
metre antennas are used on the two terminals. The reflector is configured
such that reflection angles of 30 degrees and 50 degrees are obtained.
Determine suitable reflector sizes if the maximum path loss is 70 dB.
2m24.2
0.7log20
)50log(cos20log20)14log(408.428.91
anglelargerwithreflectorgConsiderin
dB8.91-84-107.4138.470
dBi0.2420log(14)20log(1.2)17.5GainAntenna
dB4.1074.0log2014log204.922
dB4.13815log2014log204.921
=
=
+++=
= +=
=++=
=++=
=++=
A
A
A
GG
FSL
FSL
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 190/192
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 191/192
© AIRCOM International limited 2001 Microwave Link Planning
P-TR-005-M101-ver4 191
3. A 30 km, 7 GHz path has a sharp, knife-edge obstacle, 10 m in height, 8
km from one end. The minimum k factor experienced (exceeded 99.9%
of the time) is 0.7. Determine suitable antenna heights.
For k factors of 1.33 and 0.7 we need to obtain the required clearance,
bearing in mind that the most significant obstacle could be either the knife
edge or earth bulge. Also, we need to note that, at k-factor of 0.7, the
clearance objective is 0 for the knife-edge or 0.3 F1 for the smooth earth
(depending on which is the most significant obstacle).
Considering earth bulge:
91.174
3.17midpointatradiuszoneFresnel
0.7)(k m25.2and1.33)(k m29.13
51
Bulge2
==
====
f
d k
d
Clearance requirement at k = 1.33 = 17.91+13.29 = 31.2 metres
Clearance requirement at k = 0.7 = 25.2+0.3x17.91 = 30.6 metres
Considering obstacle
m84.15
307
2283.171
:endonefrom8kmradiuszoneFresnel
0.7)(k 29.731.33);(k 20.38 :heightobstaclegConsiderin
)7.0(73.19);33.1(38.106373
)22)(8(500
:endonefromkm8atBulge
=
×
×=
==
=====
F
k k k
Clearance requirement at k=1.33: 15.84+20.38 = 36.22 metres
Clearance requirement at k=0.7 = 29.73 metres
Highest value is 36.22 metres and therefore antenna heights of 36.22 metres
should be adopted.
8/17/2019 Tranmission Planning
http://slidepdf.com/reader/full/tranmission-planning 192/192
© AIRCOM International limited 2001 Microwave Link Planning
4. Determine the diffraction loss at a k factor of 0.5 if the antenna heights
determined by the result of question 3 are adopted.
Bulge at k=0.5:
112
metres1.38:nObstructio
m37.6 :10mAdd
m6.275.06373
)22)(8(500
21
+=
=×
d d
hv
λ