MLSE FOR AN UNKNOWN CHANNEL .1. OPTIMALITY CONSIDERATIONS

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 invest igations of this problem have not considered the front-end (FE) proces sing in detail; rather, a discrete-time signal model has been assumed, We show that a fractionally-spaced whitened matched filter, matched t o the known data pulse, provides a set of sufficient statistics when a tapped delay line channel model is assumed, and that the problem is i ll-posed when the channel impulse response is generalized to a CT, fin ite-length model, Practical approximations are considered that circumv ent this ill-posed condition, Recursive computation of the joint-ML me tric is developed, Together, the FE processing and metric recursion pr ovide a receiver structure which may be interpreted as the theoretical foundation for the previously introduced technique of per-survivor pr ocessing, and they lead directly to generalizations, Several FE proces sors representative of those suggested in the literature are developed and related to the practically optimal FE.