Noncoherent Lattice Decoding of PAM and ASK

In this paper we present a novel maximum-likelihood polynomial-time algorithm for noncoherent detection of PAM over fading channels. The algorithm is based on a geometric interpretation of the noncoherent detection metric. This interpretation leads to a novel low complexity decoder based on an angular criterion, rather than the usual Euclidean distance sense. We prove that the ML estimate of the data must lie in a reduced search space which is of log-linear complexity with the block length. We then provide an algorithm that enumerates the codewords and their corresponding metrics in an efficient, recursive manner. We also consider detection of ASK, by combining the maximum-likelihood algorithm with a simple phase estimator