Adaptive Equalization for Wireless Channels - Adaptive Signal Processing in Wireless Communications - page 261

output, both the CSE and FEQ can adapt based on this cost. If the FEQ uses a relatively
higher step size than the CSE, then the CSE will adapt slowly, and the FEQ will track it
and quickly reach its best value for the current CSE setting. This concatenation of adap-
tive equalizers allows the use of traditional cost functions. The penalty is that the FEQ
step size has an upper bound for stability, and the CSE step size must be much lower,
so adaptation cannot be very swift. This need for step-size-based timescale separation
is present for most coupled adaptive systems adapting over a single cost function, for
example, the adaptive CSE and target response in the MMSE filter [10, 65].

9.6 Summary

This chapter has discussed the design of adaptive equalizers. We began with a historical
perspective and a discussion of the need for an adaptive equalizer. We then discussed
popular methods of creating adaptation rules, making them converge quickly, and reduc-
ing their computational load, all of which are necessary if the equalizer is part of a small
wireless device. As specific examples of creating adaptation rules, we discussed recent
literature on adaptive equalization in two currently popular communication standards,
multicarrier and ultrawideband. We concluded with a discussion of the interaction of an
adaptive equalizer and other adaptive blocks within the receiver.

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