Semi-blind methods for communications

Publisher Summary This chapter presents a number of strategies for semiblind equalization of digital communication channels. Traditional equalization techniques are based on a sequence of symbols known by the receiver, the so-called pilot or training sequence, incorporated into the transmitted signal frame. The supervised equalizer is simply obtained by optimal Wiener filtering of the received signal using the pilot sequence as desired output. The constant modulus (CM) criterion—a particular member of the more general family of Godard methods—is the most widespread blind equalization principle, due to its simplicity and flexibility. The CM criterion is easy to implement in an iterative fashion and can also deal with non-CM modulations at the expense of an increased estimation error due to constellation mismatch. Algebraic methods provide an equalization solution in a finite number of operations, and can always be employed as judicious initializations to iterative equalizers. An algebraic CM solution can be obtained, where the CM criterion is formulated as a nonlinear least squares (LS) problem. Through an appropriate transformation of the equalizer parameter space, the nonlinear system becomes a linear LS problem subject to certain constraints on the solution structure.