Accurate evaluation for MDPSK with noncoherent diversity

The error probability analysis of M-ary differential phase-shift keying signals with noncoherent diversity combining over general fading channels is not available in the literature except for some simple cases. The difficulty lies in the philosophy which attempts to explicitly determine the phase distribution expressions of the received signal, and this often leads to a mathematically intractable issue. In this paper, we take a novel approach by formulating the phase distribution in terms of joint moment generating functions of the real and imaginary parts of the decision variable at the receiver output. We further derive fast convergent techniques for two-dimensional (2-D) inverse Laplace transform enabling us to accurately evaluate the phase distribution. The error probability formulas thus obtained involve a twofold integral, which can be efficiently evaluated by using our algorithms developed on the basis of the 2-D trapezoidal summation and Gauss-Chebyshev quadrature. The new technique is very general, taking into account the effects of arbitrary diversity order, symbol alphabet size M, and arbitrary diversity branches correlation. Numerical results are also presented for illustration.