Approximate bit error probability analysis of 2PSK and 4PSK with partially coherent, symbol-by-symbol detection in carrier phase noise

The effect of carrier phase noise on the BEP of 2PSK and 4PSK with partially coherent, symbol-by-symbol detection is analysed using an approximate approach. Partially coherent detection is achieved using a decision-aided, maximum likelihood carrier phase estimator. The carrier phase noise is modelled as a Brownian motion. Assuming a small phase noise variance, it is shown that the Brownian phase noise, together with the additive, white, Gaussian channel noise, leads to a Gaussian phase error in the recovered reference and a random signal component for data detection. These results enable the BEP to be numerically evaluated, and the numerical results agree well with the results of computer simulations. Both the effects of carrier phase fluctuations on the matched filter output and the decorrelation of the carrier phase from one symbol interval to the next are taken into account