BER expressions for differentially detected /spl pi//4 DQPSK modulation

Closed form bit-error rate (BER) expressions for differentially detected /spl pi//4-shifted differentially encoded quadrature phase-shift keying (QPSK) modulation (/spl pi//4 DQPSK) are derived for both additive white Gaussian noise (AWGN) and Rayleigh-fading channels. The derivations are carried out in an exact and most general manner in that in-phase (I) and quadrature (Q) channel bit-error probabilities P/sub cl/ and P/sub cQ/ are separately obtained in terms of the same-quadrature and cross-quadrature noise Correlation functions, including a measure of noise nonstationarity. We then specialize the general expressions for uncorrelated noise and equal noise powers in successive symbol periods to obtain a useful bit-error probability expression for the AWGN channel in the form P/sub e//spl ap/Q(/spl radic/(1.1716/spl middot/E/sub b//N/sub 0/)) where Q(/spl middot/) is the Gaussian distribution Q-function and E/sub b//N/sub 0/ is the bit energy-to-noise density ratio. Exact BER expressions for the Rayleigh-fading channel that involve the noise parameters are also given and are extended to the case of L-fold diversity combining.