Fast, blind, and joint maximum likelihood estimation of MPSK signal parameters

We present a fast algorithm for the joint maximum likelihood (JML) estimate of information-symbols, phase, amplitude, and noise-variance, given baud-sampled M-ary phase shift keyed signals (MPSK) observed in complex additive white Gaussian noise. The algorithm is fast in that it has a complexity that grows as O(N log₂ N), where N is the number of observed symbols. Further, the algorithm only requires one optional division and one square root, and no other transcendental functions. Finally, the algorithm is parallelizable with N processors in O(log₂ N) time using standard parallelizable processing primitives. The performances for phase, amplitude, and SNR estimation are compared to the Cramer Rao Lower Bound (CRLB) for a data-aided estimator.