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Chapter 15 Fading Channels.

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Presentation on theme: "Chapter 15 Fading Channels."— Presentation transcript:

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


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