Optimization of Digital Postdetection Filters for PSK Differential Detectors

A digital transversal postdetection filter for use in differential PSK demodulation is proposed, and a method for optimizing the weighting coefficients is presented. This low-pass filter is implemented using a finely spaced (relative to the symbol rate) tapped delay line whose tap weights are determined so as to minimize the overall mean-square error at the detector outputs. It is shown that even though the detector output signal is quadratic, the optimization problem can be formulated in a way similar to the well-known minimum-mean-square equalizer for linear signals. The filter design technique also accommodates nonideal detector structures, such as those employing hard limiters.