Adaptive symbol-by-symbol reception of MPSK on the Gaussian channel with unknown carrier phase characteristics

An adaptive version of the optimum, decision-aided, symbol-by-symbol receiver obtained in our previous works for M-ary phase shift keying over the Gaussian channel with unknown carrier phase characteristics is considered. It uses a first-order adaptive filter for carrier reference tracking, and the filter gain is adapted on-line based on the observed signal samples using a least-mean-square-error criterion. The phase tracking performance of the filter in the steady-state tracking mode is analyzed using a linearized model. The phase tracking error variance is minimized due to the risk function used in designing the filter gain adaptation algorithm. The bit-error probability for quadrature phase shift-keying is obtained, both analytically and via computer simulations.