The slowest descent method and its application to sequence estimation

A new approach to sequence estimation is proposed and its performance is an alyzed for a number of channels of practical interest The proposed approach , termed the slowest descent method, comprises as a special case the zero-f orcing equalizer for intersymbol interference channels and the decorrelator for the multiuser detection problem. The latter two methods quantize the u nconstrained sequence that maximizes the likelihood function. The proposed method can be viewed as a generalization of these two methods in two ways. First, the unconstrained maximization is extended to nonquadratic log-likel ihood functions; second, the decorrelator estimate can be "refined" by comp aring its likelihood to a set of discrete-valued sequences along mutually o rthogonal lines of the least decrease in the likelihood function. The gradi ent descent method for iterative computation of the line of least likelihoo d decrease (i.e., slowest likelihood descent) and its relationship to the e xpectation-maximization (EM) algorithm for unconstrained likelihood maximiz ation is discussed. The slowest descent method is shown to provide a perfor mance comparable to maximum-likelihood for a number of channels. These prob lems can be described by either quadratic or nonquadratic log-likelihood fu nctions.