Equalization in Communication Engineering
Umberto Spagnolini · 2017
Deconvolution is the linear filter that compensates for a waveform distortion of convolution. 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, 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. This chapter aims 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. It also considers the decision feedback equalization (DFE), and reviews analytical tools to establish the equivalence between DFE equalization and its multiple-input-multiple-output (MIMO) counterpart. The key algebraic tool for MIMO-DFE is the Cholesky factorization. For zero-mean random variables (rvs), Cholesky factorization of the correlation matrix is the counterpart of min/max phase decomposition of the autocorrelation sequence.