Double differential MPSK on the fast Rician fading channel

An analysis of adjacent and nonadjacent double differential M -ary PSK (M-ary D²PSK) on the fast Rician fading channel is presented. The probability density function (PDF) of the first-order phase error (FOPE) and the probability density functions of the second-order phase error (SOPE) for both adjacent and nonadjacent D²PSK on a fading channel have been derived. Asymptotic approximations for these PDFs are proposed in the case of channels with weak fading (including the additive white Gaussian noise (AWGN) channel) and high signal-to-noise ratio. For nonadjacent D²PSK with independent FOPEs a simplified PDF of SOPE has been obtained. The derived PDFs allow calculation of error performance of D²PSK, as well as of DPSK, on the Rician channel including the AWGN channel and the Rayleigh channel and verification of some results reported in the literature earlier. It is shown that nonadjacent D²PSK can be optimized by choosing a proper separation between the first-order phase differences