Communication Channel

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Communication Channel
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Outline

• Information Transmission
• Attenuation dB
• Equivalent Noise Temperature
• Communication Limits
• Broadband Channel
• BER

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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)

Input signal, frequency domain (amplitude
spectrum)
Output signal, frequency domain (amplitude
spectrum)
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Frequency Response Measurement
Signal Generator
Transmission Channel
Receiver/ Spectrum Analyzer
Synchronized
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Time Response

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

Channel impulse response
Output signal (time domain)
An example of (analogy to) impulse response a
bell rings when hit by clapper
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Time Response Measurement
Impulse Generator
Transmission Channel
Oscilloscope
Synchronized
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T-Domain F-Domain
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Nonlinearity BDR
P1dB-out
1dB
MDS Minimum Detectable Signal (Output Noise
Floor)
P1dB-in
Input power (dBm)
MDS
BDR (Blocking Dynamic Range)
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Nonlinarity SFDR
Extrapolated Third-Order Distortion
Extrapolated Linear Output
OIP2
Output power (dBm)
Extrapolated Second-Order Distortion
OIP3
IIP3 Third-Order Intercept Point IIP2
Second-Order Intercept Point MDS Minimum
Detectable Signal (Output Noise Floor) SFDR
(2/3)(IIP3 MDS) Spurious-Free Dynamic Range
Noise floor
Input power (dBm)
MDS
IIP3
IIP2
SFDR
OIP2 Output Referred Second-Order Intercept
Point
OIP3 Output Referred Third-Order Intercept Point
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2-Tone Test
P
?
Signal power (dBm)
f1
f2
2f1-f2
2f2-f1
Frequency
IIP3 1/2? P
f1 f2
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Communication Channel
Signal transmitted
Signal received
Input signal
Output signal
Information destination
Information source
Transmitter
Propagation Channel
Receiver
Signal transformationsdue to natural
phenomenaexternal noise/signals added
Transmitter signal processing
Receiver signal processing
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Main Natural PhenomenaAffecting Communication

• Attenuation
• Noise/ interference
• Additive (thermal noise)
• Multiplicative (fading)

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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).

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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.
• dB?V 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

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Radio Transmission Loss Components
ITU-R Rec.
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Sum of Two Signals (Deterministic, Linear System)
Resultant signal
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Uncertainty due to Noise
Small uncertainty, Signals can easily be
differentiated
Large uncertainty, Signals cannot easily be
differentiated
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Thermal Noise

• N kTB
• N available noise power from resistor W
• k Boltzmanns constant (1.37 x 10-23 J/o)
• T temperature oK
• B frequency bandwidth Hz

1J1Ws
Thermal Noise fundamental limiting factor
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Equivalent Noise Temperature
Actual Receiver
SN
Internal Noise
Identical Output Signal-to-Noise Ratio
SN
Noise-less Receiver
kTeB
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Communication Channel (2)
Original message m(t)
Transmitter s(t) U(m, f)

• m(t) message (information, data)
• s(t) signal carrying the message
• f f(a,b,c,, t) (carrier function)
• a,b,c, modulation parameters
• U, V, W operators
• ? noise, interference, perturbations
• x(t) perturbed signal at the receiver input
• y(t) reproduced message
• Task make y m (within an acceptable error)

Transport medium x(t) V(s, ?)
Receiver y(t) W(x)
Reproduced (received) message y WV?,U(m,f)
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Shannons 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
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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

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Transmission Time Speed
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Information Transmission
The Shannons channel can transmit the same
amount of information using various combinations
of Time, Bandwidth, and Signal/ Noise
SNR
T
SNR
2T
T
2B
B
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Data Rate per Hz vs. SNR
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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.

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Wideband Channel
C B log21 S/(NoB)
Noise density, W/Hz (const)
Received signal power, W
Bandwidth, Hz
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(1S/N0B) 1.44 loge(1S/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,
S?0.693kTR.
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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

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
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Data Rate vs. Bandwidth(Wideband Channel)
C B log 1 S / kT
Thermal noise asymptote C 1.44 S / kT
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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
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BER vs Input Signal
BER
Errors due to thermal noise, Quantization,
Sampling jitter
Errors due to self-induced spurious
interference (overload)
Input signal level
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Countermeasures Against Errors

• 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

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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.

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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

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References

• Many good books, e.g.
• Pierce JR, An Introduction to Information Theory,
  Dover Publ.
• Dunlop J, Smith DG, Telecommunications
  Engineering, Chapmann Hall