Statistical Signal Processing in Engineering

17Equalization in Communication Engineering

Deconvolution (Section 5.2.3 and Section 10.1) is the linear filter that compensates for a waveform distortion of convolution. In communication systems, equalization refers to the compensation of the convolutive mixing due to the signals’ propagation (in this context it is called the communication channel), either in wireless or wired digital communications. Obviously, deconvolution is the same as equalization, even if it is somewhat more general as being independent of the specific communication system setup. In MIMO systems (Section 5.3) there are multiple simultaneous signals that are propagating from dislocated sources and cross‐interfering; the equalization should separate them (source separation) and possibly compensate for the temporal/spatial‐channel convolution. The focus of this chapter is to tailor the basic estimation methods developed so far to the communication systems where single or multiple channels are modeled as time‐varying, possibly random with some degree of correlation. Signals are drawn from a finite alphabet of messages and are thus non‐Gaussian by nature [57] . To limit the contribution herein to equalization methods, the estimation of the communication channel (or channel identification, see Section 5.2.3) is not considered as being estimation in a linear model with a known excitation. In common communication systems, channel estimation is part of the alternate communication of a training signal interleaved ...