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Chapter 15

- Fading Channels

Digital Communication Systems

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

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

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

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

Fading Channel Manifestation

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

Link-budget Considerations for A Fading Channel

Large-scale and Small-scale Fading

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

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

Path-Loss Measurements in German Cities

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

Multi-path Reflected Signal On A Desired Signal

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,

Response of A Multi-path Channel As A Function of

Position

Small-scale Fading Mechanisms, Degradations And

Effects

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

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

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)

Relationships Among The Channel Correlation

Functions

Frequency Response And Transmitted Signal

Time-History Examples For Channel Conditions

Frequency-nonselective fading

Frequency-selective fading (Inter-chip

interference induced)

Frequency-selective fading (Inter-chip

interference induced)

Flat-Fading And Frequency-Selective Fading

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

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

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

A Typical Rayleigh Fading Envelope at 900 MHz

Spectral Broadening In Keying A Digital Signal

Combination of Specular And Multi-Path Components

Error Performance for pi/4 DQPSK

Performance Over Fading Channel

- Demodulated signal over a discrete multi-path

channel - Assume the channel exhibits flat fading

Performance Over A Slow Rayleigh Fading Channel

Error Performance Good, Bad, Awful

Mitigate The Degradation Effects of Fading

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

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

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

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

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

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

Diversity Techniques

- The goal is to utilize additional independent (or

at least uncorrelated) signal paths to improve

the received SNR - Error performance improvement

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

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

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

Error Performance For Various Interleaver Spans

Benefits of Interleaving Improve With Velocity

Required Eb/N0 Versus Speed

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

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

Applications

- Viterbi equalizer as applied to GSM

Applications

- Viterbi equalizer as applied to GSM

Applications

- RAKE receiver as applied to DS spread-spectrum

systems

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