The slowest descent method and its application to sequenceestimation

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     

Complementary sequences for ISI channel estimation

A merit factor based on the sequence autocorrelation function, whose minimization leads to the reduction in the Cramer-Rao lower bound (CRLB) for the variance of “two-sided” intersymbol interference (ISI) channel estimation is introduced. Pairs of binary pilot symbol sequences (a preamble and a postamble) for channel estimation are jointly designed to minimize this merit factor. Given that the number of channel taps is L and the length of a pilot symbol sequence is (N+L-1), where N⩾L, we distinguish between the case when N is even and the case when it is odd. For even N, we show that complementary sequences not only minimize the merit factor, but also the CRLB. For a subset of odd N we construct almost-complementary periodic sequence pairs that minimize the merit factor. The optimal pilot symbol block signaling requires alternating between two (in most cases) different binary sequences that form the merit-minimizing pair