Fading Channels

1
Chapter 15

• Fading Channels

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Digital Communication Systems
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Challenges of Communicating Over Fading Channels

• Sources of noise degrade the system performance
• AWGN (ex. Thermal noise)
• Man-made and natural noise
• Interferences
• Band-limiting filter induces the ISI effect
• Radio channel results in propagation loss
• Signal attenuation versus distance over free
  space. For example,
• Multi-path fading ? cause fluctuations in the
  received amplitude, phase, angle of arrival

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Characterizing Mobile-radio Propagation

• Large-scale fading
• Signal power attenuation due to motion over large
  area
• Is caused by the prominent terrain (ex. hills,
  forest, billboard) between the transmitter and
  the receiver
• Statistics of path loss over the large-scale
  fading
• Mean-path loss (nth-power law)
• Log-normal distributed variation about the mean
• Is evaluated by averaging the received signal
  over 10 to 30 wavelengths

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Characterizing Mobile-radio Propagation

• Small-scale fading
• Time-spreading of the signal
• Time delays of multi-path arrival
• Time-variant behavior of the channel
• Motion between the transmitter and the receiver
  results in propagation path changes
• Statistics of envelop over the small-scale fading
• Rayleigh fading if there are large number of
  reflective paths, and if there is no line-of
  sight signal components
• Rician pdf while a line-of-sight propagation path
  is added to the multiple reflective paths

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Basic Mechanisms for Signal Propagation

• Reflection
• Electromagnetic wave impinges on a smooth surface
  with very large dimensions relative to the RF
  wavelength
• Diffraction
• Propagation path between the transmitter and the
  receiver is obstructed by a dense body, causing
  secondary waves to be formed behind the
  obstructing body
• Scattering
• A radio wave impinges on either a large, rough
  surface or any surface whose dimensions are on
  the order of l or less, causing the energy to be
  spread out

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Fading Channel Manifestation
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Baseband Waveform in A Fading Channel

• A transmitted signal can be represented by
• The complex envelop of s(t) is represented by
• In a fading channel, the modified baseband
  waveform is

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Link-budget Considerations for A Fading Channel
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Large-scale and Small-scale Fading

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Large-scale Fading

• Channel model
• Okumura made some of the path-loss measurements
  for a wide range of antenna heights and coverage
  distance
• Hata transformed Okumuras data into parametric
  formulas
• The mean path-loss is a function of
  distance between a transmitter and receiver
• n-th power of d
• n is equal to 2 in free space, n can be lower
  while a very strong guided wave is present, and n
  can be larger while obstructions are present

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Large-scale Fading

• Path-loss variations
• denotes a zero-mean, Gaussian random
  variable (in decibels) with standard deviation
• The choice of the value for is often
  based on measurements
• It is not unusual for to take on values as
  height as 6 to 10 dB

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Path-Loss Measurements in German Cities
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Small-Scale Fading

• Assumptions
• Antenna remains within a limited trajectory, so
  that the effect of large-scale fading is a
  constant
• Antenna is traveling and there are multiple
  scatter paths with a time-variant propagation
  delay , and a time-variant multiplicative
  factor
• Noise is free
• Derive the bandpass signal within a small-scale
  fading channel

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Multi-path Reflected Signal On A Desired Signal
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Multi-path Reflected Signal Without A Desired
Signal

• As the magnitude of the line-of sight component
  approaches zero,
• the Rician pdf approaches a Rayleigh pdf.
  That is,

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Response of A Multi-path Channel As A Function of
Position
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Small-scale Fading Mechanisms, Degradations And
Effects
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Signal Time-Spreading

• Signal time-spreading viewed in the Time-Delay
  Domain
• Wide-sense stationary uncorrelated scattering
  (WSSUS) model
• The model treats signal arriving at a receive
  antenna with different delays as uncorrelated
• Multi-path-intensity profile describes the
  average received signal power as a function of
  the time delay
• Multi-path-intensity profile usually consists
  multiple discrete multi-path components
• The time between the first and the last received
  component represents the maximum excess delay
• The threshold level relative to the strongest
  component might be chosen 10 dB or 20 dB

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Signal Time-Spreading

• Degradation Categories viewed in the Time-Delay
  Domain
• Frequency selective fading
• The maximum excess delay time is larger than the
  symbol time
• The received multi-path components of a symbol
  extend beyond the symbols duration
• Yield inter-symbol interference (ISI) distortion
  that is the same as the ISI caused by an
  electronic filter
• Mitigate the ISI distortion is possible because
  many of the multi-path components are resolvable
  by the receiver
• Frequency non-selective fading or flat fading
• The maximum excess delay time is smaller than the
  symbol time
• All of the received multi-path components of a
  symbol arrive within a symbol time
• No ISI induces
• Performance degradation due to the un-resolvable
  phasor components can add up destructively to
  reduce SNR
• Signal diversity and using error-correction
  coding is the most efficient way to improve the
  performance

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Signal Time-Spreading

• Signal time-spreading viewed in the frequency
  Domain
• Obtain the Fourier transform of
• Correlation between the channels response to two
  signals as a function of the frequency difference
  between the two signals
• Coherent bandwidth
• A statistical measure of the range of the
  frequencies over which the channel passes all
  spectral components with approximately equal gain
  and linear phase
• Approximately, the coherent bandwidth and
  the excess delay spread are reciprocally
  related
• The relationship between the coherent bandwidth
  and the root-mean-squared (rms) delay spread
  depends on the correlation of the channels
  frequency response (ex. while
  the correlation of at least 0.5)

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Relationships Among The Channel Correlation
Functions
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Frequency Response And Transmitted Signal
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Time-History Examples For Channel Conditions
Frequency-nonselective fading
Frequency-selective fading (Inter-chip
interference induced)
Frequency-selective fading (Inter-chip
interference induced)
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Flat-Fading And Frequency-Selective Fading
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Time Variance Of The Channel

• Time variance viewed in the time Domain
• Space-time correlation function
• Correlation between the channels response to a
  sinusoidal sent at time t1 and the channels
  response to a sinusoidal sent at time t2
• Coherent time
• A measure of the expected time duration over
  which the channels response is essentially
  invariant
• Provide knowledge about the fading rapidity of
  the channel
• Using the dense-scatter channel model, the
  normalized correlation function with an
  unmodulated CW signal is described by

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Degradation Categories Viewed in Time Domain

• Fast fading
• The channel coherence time is less than the time
  duration of a transmission symbol
• Channel will change several times during the time
  span of a symbol
• Mobile moves fast
• Result in an irreducible error rate
• It is difficult to adequately design a match
  filter
• Slow fading
• Symbol period is less than the coherence time
• On can expect the channel state to virtually
  remain unchanged during the symbol time
• Mobile moves slowly
• The primary degradation in a slow-fading, as with
  flat-fading, is the loss in SNR

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Time Variance Viewed In Doppler-shift Domain

• Signal spectrum at the antenna terminal
• The spectrum shape is the result of the
  dense-scatter channel model
• The maximum Doppler-shift is
• is the Fourier transform of
• Yields knowledge about the spectral spreading of
  a transmitted sinusoidal in the Doppler-shift
  domain
• Doppler spread and coherence time
  are reciprocally related
• example the velocity120km/hr, and the carrier
  frequency900MHz, then the fading rate is
  approximately 100Hz and the coherence time is
  approximately 5 ms

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A Typical Rayleigh Fading Envelope at 900 MHz
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Spectral Broadening In Keying A Digital Signal
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Combination of Specular And Multi-Path Components
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Error Performance for pi/4 DQPSK
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Performance Over Fading Channel

• Demodulated signal over a discrete multi-path
  channel
• Assume the channel exhibits flat fading

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Performance Over A Slow Rayleigh Fading Channel

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Error Performance Good, Bad, Awful

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Mitigate The Degradation Effects of Fading
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Mitigation To Combat Frequency Selective Fading

• Equalization can mitigate the effects of
  channel-induced ISI
• Can help modify the system performance from
  awful to bad
• Gather the dispersed symbol energy back into its
  original time interval
• Equalizer is an inverse filter of the channel
• Equalizer filter must also change or adapt to the
  time-varying channel characteristics

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Mitigation To Combat Frequency Selective Fading

• Decision feedback equalizer (DFE)
• Once an information symbol has been detected, the
  ISI that it induces on future symbols can be
  estimated and subtracted before the detection of
  subsequent symbols
• Maximum-likelihood sequence estimation (MLSE)
  equalizer
• Test all the possible data sequence and choose
  the most probable of all the candidates
• Implemented by using Viterbi decoding algorithm
• MLSE is optimal in the sense that it minimizes
  the probability of a sequence error

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Mitigation To Combat Frequency Selective Fading

• Direct-sequence spread spectrum (DS/SS)
  techniques
• Mitigate frequency-selective ISI distortion
• Effectively eliminate the multi-path interference
  by its code correlation receiver
• RAKE receiver coherently combines the multi-path
  energy
• Frequency hopping spread spectrum (FH/SS)
  technique
• Frequency diversity
• OFDM
• Avoid the use of equalizer by lengthening the
  symbol duration
• DAB, DVBT systems
• Pilot signal

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Mitigation To Combat Fast Fading

• Robust modulation techniques
• Non-coherent scheme or differential scheme
• Not require phase tracking
• Increase the symbol rate by adding the signal
  redundancy
• Error-correction coding

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Mitigation To Combat Loss in SNR

• Diversity methods to move the performance bad
  to good
• Diversity is used to provide the receiver with
  uncorrelated renditions of the signal of interest
• Time diversity
• Transmit the signal on L different time slots
  with time separation of at least T0
• Interleaving with coding technique
• Frequency diversity
• Transmit the signal on L different carriers with
  frequency separation of at least f0
• The signal bandwidth W is expanded and the
  frequency diversity order is achieved by W/f0
• There is the potential for the frequency-selective
  fading unless the equalizer is used

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Mitigation to Combat Loss in SNR

• Spread-spectrum systems
• Frequency hopping spread spectrum
• Spatial diversity
• Multiple receive antennas, separated by a
  distance of at least 10 wavelengths
• Coherently combine all the antenna outputs
• Polarization diversity
• Space-time coding technique

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Diversity Techniques

• The goal is to utilize additional independent (or
  at least uncorrelated) signal paths to improve
  the received SNR
• Error performance improvement

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Diversity Combining Techniques

• Selection
• The sampling of M antenna signals and sending the
  largest one to the demodulator
• Relatively easy to implement
• Not optimal
• Feedback
• The M signals are scanned in a fixed sequence
  until one that exceeds a given threshold is found
• The error performance is somewhat inferior to the
  other methods
• Feedback diversity is quite simple to implement
• Maximal ratio combining
• The signal are weighted according to their
  individual SNR
• The individual signals must be co-phase before
  being summed
• Produce an average SNR by

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Modulation Types For Fading Channels

• Amplitude-based signal modulation (e.g. QAM) is
  vulnerable to performance degradation in a fading
  channel
• Frequency or phase-based modulation is the
  preferred choice in a fading channel
• The use of MFSK is more useful than binary signal
• In a slow Rayleigh fading channel, binary DPSK
  performs well

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Interleaver

• The primary benefit of an interleaver is to
  provide time diversity
• The larger the time span, the greater chance that
  of achieving effective diversity
• The interleaver time span is usually larger
  than the conerence time
• In a real-time communication system, too large
  interleaver time ( e.g. ) is
  not feasible since the inherent time delay would
  be excessive
• The interleaver provides no benefit against
  multi-path unless there is motion between the
  transmitter and the receiver
• As the motion increases in velocity, so does the
  benefit of a given interleaver to the error
  performance

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Error Performance For Various Interleaver Spans
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Benefits of Interleaving Improve With Velocity
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Required Eb/N0 Versus Speed
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Key Parameters for Fading Channels

• Fast-fading distortion
• Mitigation
• Choose a modulation/demodulation technique that
  is most robust under fast-fading channel
• For example, avoiding scheme that require PLLs
• Sufficient redundancy that the symbol rate
  exceeds the fading rate and does not exceed the
  coherent bandwidth
• Pilot signal
• Error-correction coding

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Key Parameters for Fading Channels

• Frequency-selective fading distortion
• Mitigation
• Adaptive equalization, spread-spectrum, OFDM
• Viterbi algorithm
• Once the distortion effects have been reduced,
  diversity technique, error-correction coding
  should be introduced to approach AWGN performance
• Fast-fading and frequency-selective fading
  distortion

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Applications

• Viterbi equalizer as applied to GSM

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Applications

• Viterbi equalizer as applied to GSM

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Applications

• RAKE receiver as applied to DS spread-spectrum
  systems