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25/01/2003 Property of R. Struzak 1
Communication Channel
25/01/2003 Property of R. Struzak 2
Outline
• Information Transmission
• Attenuation: dB
• Equivalent Noise Temperature
• Communication Limits
• Broadband Channel
• BER
25/01/2003 Property of R. Struzak 3
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)
25/01/2003 Property of R. Struzak 4
Frequency Response Measurement
Signal Generator
Transmission Channel
Receiver/Spectrum Analyzer
Synchronized
25/01/2003 Property of R. Struzak 5
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
25/01/2003 Property of R. Struzak 6
Time Response Measurement
Impulse Generator
Transmission Channel
Oscilloscope
Synchronized
25/01/2003 Property of R. Struzak 7
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
25/01/2003 Property of R. Struzak 8
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)
25/01/2003 Property of R. Struzak 9
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
25/01/2003 Property of R. Struzak 10
2-Tone Test
f1 f22f1-f2 2f2-f1
IIP3 = 1/2 + P
P
Sign
al p
ower
(dB
m)
Frequency
f1 ~ f2
25/01/2003 Property of R. Struzak 11
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
25/01/2003 Property of R. Struzak 12
Main Natural PhenomenaAffecting Communication
• Attenuation
• Noise/ interference – Additive (thermal noise)
– Multiplicative (fading)
25/01/2003 Property of R. Struzak 13
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
25/01/2003 Property of R. Struzak 14
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
25/01/2003 Property of R. Struzak 15
Radio Transmission Loss Components
D 0 1 -s c
ITU-R Rec.
25/01/2003 Property of R. Struzak 16
Sum of Two Signals (Deterministic, Linear System)
Resultant signal
25/01/2003 Property of R. Struzak 17
Uncertainty due to Noise
Small uncertainty,Signals can easily be differentiated
Large uncertainty,Signals cannot easily be differentiated
25/01/2003 Property of R. Struzak 18
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
25/01/2003 Property of R. Struzak 19
Equivalent Noise Temperature
Noise-lessReceiver
ActualReceiver
S+N
Identical OutputSignal-to-Noise
Ratio
InternalNoise
S+N
kTeB
25/01/2003 Property of R. Struzak 20
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)
25/01/2003 Property of R. Struzak 21
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
25/01/2003 Property of R. Struzak 22
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
25/01/2003 Property of R. Struzak 23
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
25/01/2003 Property of R. Struzak 25
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
25/01/2003 Property of R. Struzak 26
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.
25/01/2003 Property of R. Struzak 27
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.
25/01/2003 Property of R. Struzak 28
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
25/01/2003 Property of R. Struzak 29
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]
25/01/2003 Property of R. Struzak 30
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
25/01/2003 Property of R. Struzak 31
BER vs Input Signal
Input signal level
BER Errors due to thermal noise,Quantization, Sampling jitter
Errors due to self-induced spurious interference (overload)
25/01/2003 Property of R. Struzak 32
– 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
25/01/2003 Property of R. Struzak 33
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.
25/01/2003 Property of R. Struzak 34
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
25/01/2003 Property of R. Struzak 35
References
• Many good books, e.g.– Pierce JR, An Introduction to Information
Theory, Dover Publ. – Dunlop J, Smith DG, Telecommunications
Engineering, Chapmann & Hall