Linear-time block noncoherent detection of PSK

We propose a new algorithm for noncoherent sequence detection of M-ary phase-shift-keying (M-PSK) symbols transmitted over a block fading channel. The algorithm is of complexity O(T), where T is the sequence length, and is therefore computationally superior to existing maximum-likelihood (ML) detectors of complexity O(T logT). Our detector is based on a new approximation we propose to the noncoherent ML function. We show that by using this close approximation, the detection problem reduces to a nearest lattice point problem for the lattice A_n*, from which we derive our O(T) approach. Simulation results are provided that show the difference in bit error rate is negligibly small for a wide range of signal-to-noise ratios.