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OutlineIntroduction

Independent Fading PathsReceiver diversity techniques

Transmitter Diversity

Chapter 3: Physicallayer transmission techniques

Section 3.5: Diversity techniques

Mobile Communications Chapter 3: Physicallayer transmissions Section 3.5: Diversity techniques 1
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OutlineIntroduction



1 Introduction

2 Independent Fading PathsSpace diversityFrequency diversityTime diversity

3 Receiver diversity techniquesMaximal Ratio Combining (MRC)EqualGain Combining (EGC)Selection combining (SC)Threshold Combining (TC)

4 Transmitter DiversityChannel Known at TransmitterChannel Unknown at Transmitter

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OutlineIntroduction



Introduction

As observed in Section 3.2, Rayleigh fading induces a very largepower penalty on the performance of modulation over wirelesschannels.

One of the most powerful techniques to mitigate the effects of fadingis to use diversitycombining of independently fading signal paths.

Diversitycombining exploits the fact that independent signal pathshave a low probability of experiencing deep fades simultaneously.

These independent paths are combined in some ways such that thefading of the resultant signal is reduced.

Diversity techniques that mitigate the effect of multipath fading arecalledmicrodiversity.

Diversity to mitigate the effects of shadowing from buildings andobjects is called macrodiversity. Macrodiversity is generallyimplemented by combining signals received by several base stations

or access points.Mobile Communications Chapter 3: Physicallayer transmissions Section 3.5: Diversity techniques 3
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OutlineIntroduction



Space diversityFrequency diversityTime diversity

Space diversity

There are many ways of achieving independent fading paths in awireless system.

One method is to use multiple transmit or receive antennas, alsocalled an antenna array, where the elements of the array areseparated in distance. This type of diversity is referred to as space

diversity.

Note that with receiver space diversity, independent fading paths aregenerated without an increase in transmit signal power or bandwidth.

Coherent combining of the diversity signals leads to an increase inSNR at the receiver over the SNR that would be obtained with justa single receive antenna.

Space diversity also requires that the separation between antennas islarge enough so that the fading amplitudes corresponding to eachantenna are approximately independent.


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OutlineIntroduction




Frequency diversity

Frequency diversity is achieved by transmitting the same narrowbandsignal at different carrier frequencies.

This technique requires additional transmit power to send the signalover multiple frequency bands.

Spread spectrum techniques are sometimes described as providingfrequency diversity since the channel gain varies across thebandwidth of the transmitted signal.

However, this is not equivalent to sending the sameinformationsignal over indepedently fading paths.


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OutlineIntroduction




Time diversity

Time diversity is achieved by transmitting the same signal atdifferent times.

Time diversity does not require increased transmit power, but it doesdecrease the data rate since data is repeated in the diversity timeslots rather than sending new data in these time slots.

Time diversity can also be achieved through coding and interleaving.

Time diversity cannot be used for stationary wireless applications,since fading gains are highly correlated over time.


Outline
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OutlineIntroduction



Maximal Ratio Combining (MRC)EqualGain Combining (EGC)Selection combining (SC)Threshold Combining (TC)

Maximal Ratio Combining (MRC)

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OutlineIntroduction




Maximal Ratio Combining (cont.)

In receiver diversity the independent fading paths associated withmultiple receive antennas are combined to obtain a resultant signalthat is then passed through a standard demodulator.

Under the use of receive antennas over flatfading (singlechanneltap, i.e., = 1) channels, the received signals are

=+ = 1 (1)

where =+= and (0 0).

Weight each branch with : Cophasing. If not cophasing,

then what happens ?Combine signals from these receive antennas, one have

=

=1

=

=1

+

=1

(2)


OutlineM i l R ti C bi i (MRC)
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OutlineIntroduction




Maximal Ratio Combining (cont.)

After combining the signals, the resultant SNR is

SNR=

=1

20

=1

2

(3)

One needs to find=1 to maximize SNR ?.The solution to the simple optimization problem can be obtained bytaking partial derivatives of(3) or using the Swartz inequality. Inparticular, the solution is

=

0

(4)

and the resultant combined SNR is

=

=12

0=

=1 (5)

The increases linearly with the numberofdiversitybranches .Mobile Communications Chapter 3: Physicallayer transmissions Section 3.5: Diversity techniques 9

OutlineMaximal Ratio Combining (MRC)
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IntroductionIndependent Fading Paths

Receiver diversity techniquesTransmitter Diversity


Maximal Ratio Combining: An example of 2 Rxantennas

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estimator*2h 2h

Maximum

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MRC: Probability of error in symbol detection

The detection performance of a diversity system, whether it usesspace diversity or another form of diversity, in terms of probability ofsymbol error for demodulation in AWGN with SNR can bedetermined by

=

0

()() (6)

We can obtain a simple upper bound on the average probability oferror by applying the Chernoff bound() 22 to the function.

Recall that for static channel gains with MRC, we can approximate

the probability of error as

=

2 =(1++)2

(7)


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MRC: Probability of error in symbol detection (cont.)

Integrating over the chisquared distribution for yields

=1

1

1 +2 (8)

In the limit of high SNR and assuming that the s are identicallydistributed with =, one will have

2

(9)

The distribution of the combined SNR () leads to a decrease in due to diversity combining.

The resultant performance advantage is called the diversity gain.


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Diversity order

For some diversity systems, their averaged probability of error can beexpressed in the form

= (10)

where is a constant depending on the specific modulation and

coding, is the averaged received SNR per branch and is calledthe diversity order of the system.

The diversity order indicates how the slope of the average probabilityof error as a function of averaged SNR changes with diversity.

Recall that a general approximation for average error probability in

Rayleigh fading with no diversity is =(2). Thisexpression has a diversity order of one, consistent with a singlereceive antenna.

The maximum diversity order of a system with antennas is ,and when the diversity order equals the system is said to achievefull diversity order

.Mobile Communications Chapter 3: Physicallayer transmissions Section 3.5: Diversity techniques 13

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g ( )EqualGain Combining (EGC)Selection combining (SC)Threshold Combining (TC)

Diversity order: Numerical results of MRC

0 5 10 15 20 25 3010

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104

103

102

101

100

b(dB)

Pb

M = 1

M = 2

M = 4

M = 8

M = 10


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EqualGain Combining (EGC)Selection combining (SC)Threshold Combining (TC)

EqualGain Combining (EGC)

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OutlineIntroduction

Maximal Ratio Combining (MRC)E l G i C bi i (EGC)
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EqualGain Combining (cont.)

MRC requires knowledge of the timevarying SNR on each branch,which can be very difficult to measure.

A simpler technique is equalgain combining, which cophases thesignals on each branch and then combines them with equalweighting, i.e., =

.

The SNR of the combiner output, assuming the same noise PSD 0in each branch, is then given by

= 1

0

=1 2

(11)


OutlineIntroduction

Maximal Ratio Combining (MRC)E l G i C bi i (EGC)


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t oduct oIndependent Fading Paths



Selection combining (SC)

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OutlineIntroduction

Maximal Ratio Combining (MRC)Equal Gain Combining (EGC)
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Selection combining (cont.)

In selection combining (SC), the combiner outputs the signal onthe branch with the highest SNR.

Since only one branch is used at a time, SC often requires just onereceiver that is switched into the active antenna branch.

A dedicated receiver on each antenna branch may be needed forsystems that transmit continuously in order to simultaneously andcontinuously monitor SNR on each branch.

Since only one branch output is used, cophasing of multiplebranches is not required.

As a result, this technique can be used with either coherent ordifferential modulation.


OutlineIntroduction

Maximal Ratio Combining (MRC)Equal Gain Combining (EGC)
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Selection combining (cont.)

Under SC implementation, the pdf of is

() =

1

1 (12)

As a result, the averaged output SNR of the combiner in Rayleigh

fading is

=

=11 (13)

The average SNR gain increases with M, but not linearly.

The biggest gain is obtained by going from no diversity (= 1) to

twobranch diversity (= 2).


OutlineIntroduction

I d d F di P h

Maximal Ratio Combining (MRC)EqualGain Combining (EGC)
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Equal Gain Combining (EGC)Selection combining (SC)Threshold Combining (TC)

SC: averaged probability of error in BPSK detection

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2

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b(dB)

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M = 1

M = 2

M = 4

M = 8

M = 10


OutlineIntroduction

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qua Ga Co b g ( GC)Selection combining (SC)Threshold Combining (TC)

Threshold Combining (TC)

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OutlineIntroduction

Independent Fading Paths

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q g ( )Selection combining (SC)Threshold Combining (TC)

Threshold Combining (cont.)

SC for wireless systems transmitting continuously may require adedicated receiver on each branch to continuously monitor branchSNR.

A simpler type of combining, called threshold combining, avoidsthe need for a dedicated receiver on each branch by scanning each

of the branches in sequential order and outputting the first signalwith SNR above a given threshold .

As in SC, since only one branch output is used at a time, cophasingis not required.

Thus, this technique can be used with either coherent or differential

(noncoherent) modulation.

There are several criteria the combiner can use to decide whichbranch to switch to.

The simplest criterion is to switch randomly to another branch.


OutlineIntroduction

Independent Fading PathsChannel Known at Transmitter


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Channel Unknown at Transmitter

Transmitter Diversity: Introduction

In transmit diversity, there are multiple transmit antennas with thetransmit power divided among these antennas.

Transmit diversity is desirable in cellular systems where more space,power, and processing capability is available on the transmit siderather than the receive side.

Transmit diversity design depends on whether or not the complexchannel gain is known at the transmitter or not.

When this gain is known, the system is very similar to receiverdiversity.

However, without this channel knowledge, transmit diversity gainrequires a combination of space and time diversity via a noveltechnique called the Alamouti scheme.


OutlineIntroduction

Independent Fading PathsChannel Known at TransmitterCh l U k T i
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Channel Known at Transmitter: Transmission model

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OutlineIntroduction

Independent Fading PathsChannel Known at TransmitterCh l U k t T itt
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p gReceiver diversity techniques



Channel known at transmitter: detailed implementations

Consider a transmit diversity system with transmit antennas andone receive antenna.

Assume the path gain associated with the th transmit antennagiven by =

is known at the transmitter via limited feedbacklinks from mobile terminals.

This is referred to as having channel side information (CSI) at thetransmitter or CSIT.

Let denote the transmitted signal with total energy per symbol

This signal is multiplied by a complex gain , 0 1 and

sent through the th transmit antenna.

Due to the average total energy constraint , the weights

must satisfy

=12 = 1


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Independent Fading PathsChannel Known at TransmitterChannel Unknown at Transmitter
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p gReceiver diversity techniques



Channel known at transmitter (cont.)

The weighted signals transmitted over all antennas are added viasignal superposition at the receive antenna, which leads to areceived signal given by

=

=1 + (0 0) (14)One can obtain the weights that achieve the maximum SNR:

=

=12

(15)

and the resultant SNR is

= 0

=1

2 ==1

(16)

where = 2

0 equal to the branch SNR between the th transmitantenna and the receive antenna.

Thus, we see that transmit diversity when the channelgainsareknownatMobile Communications Chapter 3: Physicallayer transmissions Section 3.5: Diversity techniques 26

OutlineIntroductionIndependent Fading Paths

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Channel unknown at transmitter: the Alamouti scheme

We now consider the same model as in the previous subsection butassume that the transmitter no longer knows the channel gains =

, so there is no CSIT.

In this case it is not obvious how to obtain diversity gain. Consider,for example, a naive strategy whereby for a twoantenna system we

divide the transmit energy equally between the two antennas.Thus, the transmit signal on antenna will be =

5 where is

the transmit signal with energy per symbol .

Assume two antennas have complex Gaussian channel gains

=2

=1

with zeromean and unit variant (0= 1).

The received signal is

=

5(1+2)+ (17)



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The Alamouti scheme (cont.)

Note that 1+2 is the sum of two complex Gaussian randomvariables, and is thus a complex Gaussian as well with mean equal tothe sum of means (zero) and variance equal to the sum of variances.

Thus

5(1+2) is a complex Gaussian random variable withzeromeanand unitvariance(1), so the received signal has the

same distribution as if we had just used one antenna with thefull energy per symbol.

In other words, we have obtained no performance advantagefromthe two antennas, since we could not divide our energy intelligentlybetween them or obtain coherent combining through cophasing.

Transmit diversity gain can be obtained even in the absence ofchannel information with an appropriate scheme to exploit theantennas.



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A particularly simple and prevalent scheme for this diversity thatcombines both space and time diversity was developed by Alamouti.

Alamoutis scheme is designed for a digital communication systemwith twoantennatransmit diversity.

The scheme works over two symbol periods where it is assumed

that the channel gain is constant over this time duration.

Over the first symbol periodtwo different symbols 1 and 2 eachwith energy 2are transmitted simultaneously from antennas 1and 2, respectively.

Over the next symbol period, symbol

2 is transmitted fromantenna 1 and symbol 1 is transmitted from antenna 2, each withsymbol energy 2.



Receiver diversity techniques

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Assume complex channel gains =2=1 between the thtransmit antenna and the receive antenna.

The received symbol over the first symbol periodis

1=11+22+1 (18)

and the received symbol over the second symbol period is

2= 12+21+2 (19)

where

2=1 is the AWGN noise sample at the receiver associated

with the th symbol transmission. We assume the noise sample haszeromean and power of0.




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The receiver uses these sequentially received symbols to form thevector y= [1 2 ]

given by

y=

1 22 1

12

+

12

= Hs+n (20)

where H= 1 22 1 , s= [1 2] and n= [1 2].Let us define the new vector z= Hy. The structure ofHimplies that

HH = 12 + 22 I2 (21)is diagonal and thus

z= [1 2]

=12 + 22 I2s+n (22)

where

n= Hn is a complex Gaussian noise vector with mean zero

and covariance matrix nn= 12 + 22 I20.Mobile Communications Chapter 3: Physicallayer transmissions Section 3.5: Diversity techniques 31



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The diagonal nature ofz effectively decouples the two symboltransmissions, so that each component ofz corresponds to one ofthe transmitted symbols:

=

12 + 22

+

= 1 2 (23)

The received SNR thus corresponds to the SNR for given by

=

12 + 2220

(24)

where the factor of 2 comes from the fact that is transmittedusing half the total symbol energy .The received SNR is thus equal to the sum of SNRs on each branch,identical to the case of transmit diversity with MRC assuming thatthe channel gains are known at the transmitter.Thus, the Alamouti scheme achieves a diversity order of 2, themaximum possible for a twoantenna transmit system, despite the

fact that channel knowledge is not available at the transmitter.Mobile Communications Chapter 3: Physicallayer transmissions Section 3.5: Diversity techniques 32



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y qTransmitter Diversity

The Alamouti scheme: An example of 2 Txantennas

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y qTransmitter Diversity

The Alamouti scheme: BER results of BPSK




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Possible problems to be considered in theses

In Alamoutis scheme, wireless channels are assumed to be flat andblockfading.

Doubly selective channels can be considered in Alamoutis schemeby using OFDM and BEMs.

The study results can be employed in LTE downlink transmissions

with mobile terminals.

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section 3 5 diversity

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