Chapter 7
Equalization, Diversity, and Channel Coding
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7.1 Introduction
• Mobile radio channel (in Ch 4+5) is particularly dynamic
due to
* Multipath fading
* Doppler spread
• As a result, they have a strong negative impact on BER of
any modulation technique (in Ch 6)
• To improve received signal quality in hostile mobile radio
environment, Equalization, Diversity + Channel Coding
can be used independently or in tandem.
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Equalization
• Compensates for intersymbol interference (ISI) created by
multipath within time depressive channels.
• Equalizers must be adaptive since the channel is generally
unknown and time varying.
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Diversity
• Usually implemented by using two or more receiving
antennas.
• Is employed to reduce the depth and duration of the fades
experienced by a receiver.
• Spatial diversity
• Time diversity (RAKE receiver)
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Channel coding
• Improve link performance by adding redundant data bits in the
transmitted message
Baseband
Signal
Channel
coding
Modulation
Carrier
• Used by the receiver to detect or correct some (or all) of errors
introduced by the channel in a particular sequence of message bits
• Block codes, convolutional codes.
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7.2 fundamentals of equalization
• since the mobile fading channel is random and time
varying, equalizers must take the time varying
characteristics of the mobile channel, and thus are called
adaptive equalizers.
• General operating modes of an adaptive equalizer:
* Training
* Tracking
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(7.2)
(7.3)
(7.4)
(7.5)
• Eq 7.5: an equalizer is actually an inverse filter of the
channel.
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7.3 A Generic Adaptive Equalizer
• Figure 7.2 (P. 359)
• A time-varying filter which must be constantly be returned.
• Uses ek to minize a cost function and updates the equalizer
weights in a manner that iteratively reduces the cost
function.
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•
Based on classical equalization theory, the most common
cost function is the mean square error (MSE) between the
desired signal and the output of the equalizer
(7.14)
(7.15)
(7.16)
(7.17)
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7.4 Equalizers in a communications Receiver
7.5 Survey of Equalization Techniques
• Classification of equalizers
See Fig 7.3 (P 365)
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7.6 Linear Equalization
7.7 Nonlinear Equalization
7.8 Algorithms for Adaptive Equalization
• various factors on the performance of an algorithm (P 372)
• Algorithms:
* ZeroForcing (ZF)
* Least Mean Squares (LMS)
* Recursive least square (RLS)
• Comparison (P. 379)
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7.10 Diversity Techniques
• Diversity exploits the random nature of radio propagation
by finding independent (or at least highly uncorrelated)
signal paths for communication.
• By having more than one path to select from, both the
instantaneous and average SNRs at the receiver may be
improved by as much as 20-30 dB.
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• For examples:
* Microscopic diversity can be used to mitigate small-scale fading
effects. (deep fading)
* Macroscopic diversity for reducing the large-scale fading
(selecting different base stations), can also be used for uplink.
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• Selection Diversity Improvement
(7.57)
(7.58)
(7.59)
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• To implement selection diversity
* Antenna switch
* Maximal ratio combining
• Maximal ratio combining improvement
(7.63)
(7.64)
(7.65)
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(7.66)
(7.67)
(7.68)
(7.69)
(7.70)
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* The control algorithms for setting the gains and phases for
maximal ratio combining are similar to those required in equalizer
and RAKE receiver. (Fig. 7.14 P. 387)
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• Practical Considerations for space diversity
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2
* For mobile units  
* For base station  x 10
to assure the decorrelation (narrow angle of incident fields)
• Reception Methods of Space Diversity
*
*
*
*
Selection diversity
Feedback diversity (or scanning diversity)
Maximal Ratio Combining
Equal Gain Diversity
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• Polarization Diversity
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• Frequency Diversity
• Signal xmitted on more than one fc >= coherence
bandwidth (won’t experience the same fade)
•
• Time Diversity
• Xmit signal repeatedly >= coherence time
• RAKE Receiver for CDMA (multipath channel)(P. 391)
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• Interleaving also used
for time diversity (P. 394 Fig 7-17)
Interleavers
Channel Coding
* Block interleaver (Fig 7.17)
* Convolutional interleaver
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• Channel Coding
* Mainly for error control
* Block Codes
- Forward error correction (FEC) codes
- Hamming Codes
- Hadamard Codes
- Golay Codes
- Cyclic Codes
- BCH cyclic
- Reed-Solomon Codes
* Convolutional code (Fig 7-19 P. 408)
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• Trellis Coded Modulation (P. 412)
* Combines both coding and modulation
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