Equalization, Diversity, and Channel Coding

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Chapter 7

• Equalization, Diversity, and Channel Coding

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• 7.1 Introduction
• Mobile radio channel (in Ch 45) 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
•  
•  
• 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.

Baseband Signal
Channel coding
Modulation
Carrier
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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.
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• 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
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• (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)
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• Algorithms
• ZeroForcing (ZF)
• Least Mean Squares (LMS)
• Recursive least square (RLS)
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• 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
• For mobile units
• For base station
• to assure the decorrelation (narrow angle of
  incident fields)
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• 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 gt coherence
  bandwidth (wont experience the same fade)
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• Time Diversity
• Xmit signal repeatedly gt 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)
• 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