Closed-form distribution for soft differential detection in fast Rice fading with diversity

A closed-form expression is given for the probability density function of the output of a soft differential demodulator in a fast Rice fading channel with L diversity paths. This expression can be used to evaluate the performance of coded differential BPSK with soft detection for mobile communication applications. As a by-product, the error probability for hard detection in the same channel conditions is also found. Some analytical results are shown and confirmed by simulation.