The slowest descent method and its application to sequence estimation

A new approach to sequence estimation is proposed and its performance is analyzed for a number of channels of practical interest. The proposed approach, termed the slowest descent method, comprises as a special case the zero-forcing equalizer for intersymbol interference channels and the decorrelator for the multiuser detection problem. The latter two methods quantize the unconstrained 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-likelihood functions; second, the decorrelator estimate can be "refined" by comparing its likelihood to a set of discrete-valued sequences along mutually orthogonal lines of the least decrease in the likelihood function. The gradient descent method for iterative computation of the line of least likelihood decrease (i.e., slowest likelihood descent) and its relationship to the expectation-maximization (EM) algorithm for unconstrained likelihood maximization is discussed. The slowest descent method is shown to provide a performance comparable to maximum-likelihood for a number of channels. These problems can be described by either quadratic or nonquadratic log-likelihood functions.