Adaptive symbol-by-symbol reception of PSK on channels with unknown phase

We propose an adaptive symbol-by-symbol receiver for phase shift-keying (PSK) over the Gaussian channel with unknown carrier phase. The statistical properties of the carrier phase are assumed unknown to the receiver, other than the fact that it is slowly varying so that a piecewise-constant approximation can be made. The coherent reference for detection is obtained using a first-order filter whose gain is adapted on-line, based on the received signal samples. The performance of the receiver is analyzed both via analysis and simulations.