MLSE for an unknown channel .I. Optimality considerations

TLDR: It is shown that a fractionally-spaced whitened matched filter, matched to the known data pulse, provides a set of sufficient statistics when a tapped delay line channel model is assumed, and that the problem is ill-posed when the channel impulse response is generalized to a CT, finite-length model.

Abstract: The problem of performing joint maximum-likelihood (ML) estimation of a digital sequence and unknown dispersive channel impulse response is considered starting from a continuous-time (CT) model. Previous investigations of this problem have not considered the front-end (FE) processing in detail; rather, a discrete-time signal model has been assumed. We show that a fractionally-spaced whitened matched filter, matched to the known data pulse, provides a set of sufficient statistics when a tapped delay line channel model is assumed, and that the problem is ill-posed when the channel impulse response is generalized to a CT, finite-length model. Practical approximations are considered that circumvent this ill-posed condition. Recursive computation of the joint-ML metric is developed. Together, the FE processing and metric recursion provide a receiver structure which may be interpreted as the theoretical foundation for the previously introduced technique of per-survivor processing, and they lead directly to generalizations. Several FE processors representative of those suggested in the literature are developed and related to the practically optimal FE.