1. Chapter 15
Fading Channels

2. Digital Communication Systems

3. 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

4. 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

5. 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

6. 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

7. Fading Channel Manifestation

8. 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

9. Link-budget Considerations for A Fading Channel

10. Large-scale and Small-scale Fading

11. 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 Okumura’s 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

12. 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

13. Path-Loss Measurements in German Cities

14. 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

15. Multi-path Reflected Signal On A Desired Signal

16. 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,

17. Response of A Multi-path Channel As A Function of Position

18. Small-scale Fading: Mechanisms, Degradations And Effects

19. 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

20. 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 symbol’s 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

21. Signal Time-Spreading
Signal time-spreading viewed in the frequency Domain
Obtain the Fourier transform of
Correlation between the channel’s 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 channel’s frequency response (ex while the correlation of at least 0.5)

22. Relationships Among The Channel Correlation Functions

23. Frequency Response And Transmitted Signal

24. Time-History Examples For Channel Conditions
Frequency-nonselective fading
Frequency-selective fading;
(Inter-chip interference induced)
Frequency-selective fading;
(Inter-chip interference induced)

25. Flat-Fading And Frequency-Selective Fading

26. Time Variance Of The Channel
Time variance viewed in the time Domain
Space-time correlation function
Correlation between the channel’s response to a sinusoidal sent at time t1 and the channel’s response to a sinusoidal sent at time t2
Coherent time
A measure of the expected time duration over which the channel’s 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

27. 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

28. 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 velocity=120km/hr, and the carrier frequency=900MHz, then the fading rate is approximately 100Hz and the coherence time is approximately 5 ms

29. A Typical Rayleigh Fading Envelope at 900 MHz

30. Spectral Broadening In Keying A Digital Signal

31. Combination of Specular And Multi-Path Components

32. Error Performance for pi/4 DQPSK

33. Performance Over Fading Channel
Demodulated signal over a discrete multi-path channel
Assume the channel exhibits flat fading

34. Performance Over A Slow Rayleigh Fading Channel

35. Error Performance: Good, Bad, Awful

36. Mitigate The Degradation Effects of Fading

37. 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

38. 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

39. 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

40. 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

41. 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

42. 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

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

44. 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

45. 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

46. 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

47. Error Performance For Various Interleaver Spans

48. Benefits of Interleaving Improve With Velocity

49. Required Eb/N0 Versus Speed

50. 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

51. 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

52. Applications
Viterbi equalizer as applied to GSM

53. Applications
Viterbi equalizer as applied to GSM

54. Applications
RAKE receiver as applied to DS spread-spectrum systems