Series solutions for π/4-DQPSK BER with MRC

Simple series expressions for bit error rate (BER) of π/4 shifted differential quaternary phase-shift keying (π/4-DQPSK) over some common fading environments (Rayleigh, Rician and Nakagami-m) are derived. Both single- and multi-channel reception scenarios are considered. In case of multi-antenna reception, it is assumed that the fading is independent and identically distributed (IID), and the receiver follows optimum maximal ratio combining (MRC). The derived expressions, computed through probability density function (PDF)-based approach, give an exact match with moment-generating function (MGF)-based solutions but get rid of numerical integrations involved in MGF approach. Further, the analytical results presented in this article consist of finite or rapidly converging infinite series and thus a trade-off between precision and complexity can be easily realised by choosing a specific number of terms. Bounds on the error resulting from truncation of the infinite series are also derived. Moreover, it was shown that the series solutions, when reasonably truncated, still provide better approximations than the previous attempts.