25/01/2003property of r. struzak 1 communication channel

25/01/2003 Property of R. Struzak 1

Communication Channel


Outline

• Information Transmission

• Attenuation: dB

• Equivalent Noise Temperature

• Communication Limits

• Broadband Channel

• BER


Frequency Response

• All communication channels modify/ distort signals transmitted.

• A linear, time-invariant channel is characterized in frequency domain by its transfer function (frequency response or frequency characteristics): H() = Y() / X()

• Valid for fixed (or moving slowly) systems (otherwise other effects have to be taken into account, e.g. Doppler frequency shift)

Output signal, frequency domain (amplitude spectrum)

Input signal, frequency domain (amplitude spectrum)


Frequency Response Measurement

Signal Generator

Transmission Channel

Receiver/Spectrum Analyzer

Synchronized


Time Response

• The time domain and frequency domain are uniquely linked by the Fourier transform

( ) ( )

( ) ( ) ( )

j th t H f e d

y t h t x t d

Channel impulse response

Output signal (time domain)

An example of (analogy to) impulse response: a bell rings when hit by clapper


Time Response Measurement

Impulse Generator

Transmission Channel

Oscilloscope

Synchronized


T-Domain & F-Domain

-0.5

0

0.5

1

-10 -5 0 5 10 15

(sin x) / x

x

2

2

( ) ( ) e

( ) ( ) e

sinA signal in the form of rectangular pulse in time domain is represented in frequency domain by spectrum of type

A signal whose spectrum is limited and f

j ft

j ft

h t H f df

H f h t dt

x

x

sinlat in frequency domain is represented in time domain by pulso of type

x

x


Nonlinearity: BDR2 3

0 1 2 3 ...y a a x a x a x

Noise Floor

Out

put p

ower

(dB

m)

Input power (dBm)

P1dB-inMDS

1dBP1dB-out

BDR (Blocking Dynamic Range)

MDS = MinimumDetectable Signal (Output Noise Floor)


Nonlinarity: SFDR

IIP3 = Third-Order Intercept PointIIP2 = Second-Order Intercept PointMDS = Minimum Detectable Signal (Output Noise Floor)SFDR = [(2/3)(IIP3 – MDS)] = Spurious-Free Dynamic Range

OIP2 = Output Referred Second-Order Intercept PointOIP3 = Output Referred Third-Order Intercept Point

Input power (dBm)

Out

put p

ower

(dB

m)

Noise floor

OIP2

OIP3

MDS SFDR IIP3 IIP2

Extrapolated Linear OutputExtrapolated Third-Order Distortion

Extrapolated Second-Order Distortion


2-Tone Test

f1 f22f1-f2 2f2-f1

IIP3 = 1/2 + P

P

Sign

al p

ower

(dB

m)

Frequency

f1 ~ f2


Transmitter Propagation Channel ReceiverInformation

sourceInformationdestination

Signal transformationsdue to natural phenomena;

external noise/signals added

Signaltransmitted

Signalreceived

Communication Channel

Transmitter signal processing

Receiver signal processing

Input signal Output signal


Main Natural PhenomenaAffecting Communication

• Attenuation

• Noise/ interference – Additive (thermal noise)

– Multiplicative (fading)


Loss & dB

• Abbreviation for decibel(s). One tenth of the common logarithm of the ratio of relative powers, or power ratios, equal to 0.1 B (bel).

1 2

1110

2 2

2 21 1 1 1

10 102 22 2 2 2

1 1 110 10

2 2 2;

10log

/10log 10log

/

20log 20log

watt

dB w t

Z Z

at

dB

PP

P P

H Z E Z

H Z E Z

P H E

P H E


Various dBs• dBi: In the expression of antenna gain, the number of decibels of gain of an

antenna referenced to the zero dB gain of a free-space isotropic radiator. • dBm: dB referenced to one milliwatt. ‘dBm’ is often used in communication

work as a measure of absolute power values. Zero dBm means one milliwatt.

• dBV : dB referenced to 1 microvolt. Used often for receiver sensitivity measurement.

• dBmV: dB referenced to one millivolt across 75 ohms. This is 1.33 × 10-5 milliwatts.

• dBv: dB relative to 1 volt peak-to-peak. ‘dBv’ is often used for television video signal level measurements.

• dBW: dB referenced to one watt. Zero dBW means one watt. • Note: There are also other ‘dBs’ in use!

Source: Telecommunication Glossary 2000


Radio Transmission Loss Components

D 0 1 -s c

ITU-R Rec.


Sum of Two Signals (Deterministic, Linear System)

Resultant signal


Uncertainty due to Noise

Small uncertainty,Signals can easily be differentiated

Large uncertainty,Signals cannot easily be differentiated


Thermal Noise

N = kTBN – available noise power from resistor [W]

k – Boltzmann’s constant (1.37 x 10-23 [J/o])

T – temperature [oK]

B – frequency bandwidth [Hz]

Thermal Noise = fundamental limiting factor

1J=1Ws


Equivalent Noise Temperature

Noise-lessReceiver

ActualReceiver

S+N

Identical OutputSignal-to-Noise

Ratio

InternalNoise

S+N

kTeB


Communication Channel (2)

m(t) = message (information, data)s(t) = signal carrying the messagef = f(a,b,c,…, t) (carrier function)a,b,c, … = modulation parameters U, V, W = operators = noise, interference, perturbationsx(t) = perturbed signal at the receiver

inputy(t) = reproduced message

Task: make y ≈ m (within an acceptable

error)

Reproduced (received) message

y = W{V[,U(m,f)]}

Original messagem(t)

Transmitters(t) = U(m, f)

Transport mediumx(t) = V(s, )

Receivery(t) = W(x)


Shannon’s Law

• The maximum rate of information transmission without errors through a communication channel equals the channel capacity

• The channel capacity of a noisy channel is limited. It depends on the channel bandwidth B and signal-to-noise power ratio SNR: it is proportional to B, and increases with SNR

Notes: (1) Isolated system. (2) AWGN (Additive White Gaussian Noise) only. (3) Noise-like signal using full bandwidth. (4) No signal-noise correlation. (5) Ideal coding, but Shannon says nothing how to implement such a code. Special coding required that may take very log time, but the signal latency is ignored. (6) Claude Shannon, 1948


Communication Limits

• Claude Shannon defined the limits for communication channels

• C: channel capacity (max. data rate), bps

• B: frequency band, Hz

• S/N: received signal-to-noise power ratio

2log (1 )R C S N


Transmission Time & Speed

1

10

100

1000

10000

0.001 0.01 0.1 1 10

Transmission Rate MBytes/s

Tim

e to

Tra

nsm

it 1

0 M

byt

es, s

eco

nd

s

1 minute

1 hour

10 kBytes/s


Data Rate per Hz vs. SNR

0.001

0.01

0.1

1

10

0.001 0.01 0.1 1 10 100 1000

SNR

Bit

s/se

c/H

z


Bit Rate & Boud Rate

• The bit rate defines the rate at which information is passed

• The boud (or signalling) rate (Bd) is a unit of modulation rate and defines the number of symbols per second.

• Each symbol represents n bits, and has M signal states, where M = 2n. This is called M-ary signalling.


Wideband Channel

C = B log2{1 + [S/(NoB)]}

Bandwidth, Hz

Noise density, W/Hz (const)Received signal power, W

Capacity (data rate), bit/s

With signal power S and noise power density N0 constant, enlargement of the bandwidth increases also noise. For B , (S/N0B) 0 and log2(1+S/N0B) = 1.44 loge(1+S/N0B) 1.44S/N0B, or R 1.44S/N0. With thermal noise only, C 1.44S/kT. R does not become greater with any further increase of B. In these conditions, S0.693kTR.


Wideband Channel 2

• With large bandwidth involved, the assumption of flat channel frequency response and/or white noise is likely not to be valid. In such a case, the following equation is frequently used:

2

1

2

( )log 1 ; and are the power spectrum

( )

densities of the signal and noise, respectively.

f

s

Nf

fC

f

Delogne P, Bellanger M, The impact of Signal Processing on an Efficient Use of the Spectrum, Radio Science Bulletin No 289, june 1999, 23-28


Data Rate vs. Bandwidth(Wideband Channel)

0.001

0.01

0.1

1

10

0.001 0.01 0.1 1 10 100

B

CS / kT = 10

S / kT = 1

S / kT = 0.1

Thermal noise asymptote: C = 1.44 S / kT

C = B log [1+ S / kT]


BER vs. S/N• BER or bit error ratio: The number

of erroneous bits divided by the total number of bits transmitted, received, or processed over some stipulated period.

• It is usually expressed as a coefficient and a power of 10; e.g. 2.5 erroneous bits out of 100,000 bits transmitted would be 2.5 × 10-5.

• Acceptable BER: 10-3 for a voice link, 10-9 for a data link

• BER decreases with S/N to a degree that depends on the signal processing applied

BER

S/N


BER vs Input Signal

Input signal level

BER Errors due to thermal noise,Quantization, Sampling jitter

Errors due to self-induced spurious interference (overload)


– Repeating transmission/ Error control– Increase S/N (filtration/ frequency, time,

direction selection)– Noise-resistant Modulation/ Demodulation /

Encoding/ Decoding– Spreading/De-spreading signals

Applied during signal generation, transmission, reception in digital/ analogue technology

Countermeasures Against Errors


Retransmission Schemes

• Stop and Wait– Only one packet at a time can be transmitted. The tranbsmitter

waits for an acknowledgment (ACK), positive or negative, from the receiver. If no ACK is received after a fixed amount of time (timeout) the packet is retransmitted

• Go-Back-N– Extension of Stop and Wait. Transmitter sends up to N packets

without reception of corresponding ACK. On reception of negative ACK or when the timeout expires, the packets are retransmitted.

• Selective Repeat– Extension of Go-Back-N. Only the packet in error is

retransmitted. Requires packet buffering and reordering at the receiver end.


Channel Summary

• Information is carried by signals that are limited in time, frequency, and energy

• Signal travel distance with limited speed – require time to travel at a distance

• During transmission, signal suffer attenuation and is affected by noise, etc.

• The channel capacity is limited


References

• Many good books, e.g.– Pierce JR, An Introduction to Information

Theory, Dover Publ. – Dunlop J, Smith DG, Telecommunications

Engineering, Chapmann & Hall

25/01/2003property of r. struzak 1 communication channel

Documents

property of

signal transmitted signal

communication channel

tdomain fdomain slide

clapper slide

order distortion slide

linear output

frequency characteristics