BER EXPRESSIONS FOR DIFFERENTIALLY DETECTED PI 4 DQPSK MODULATION/

Closed form bit-error rate (BER) expressions for differentially detect ed pi/4-shifted differentially encoded quadrature phase-shift keying ( QPSK) modulation (pi/4 DQPSK) are derived for both additive white Gaus sian noise (AWGN) and Rayleigh-fading channels, The;derivations are ca rried put in an exact and most general manner in that in-phase (I) and quadrature (Q) channel bit-error probabilities P-epsilon I and P-epsi lon Q are separately obtained in terms of the same-quadrature and cros s-quadrature noise correlation functions, including a measure of noise nonstationarity, We then specialize the general expressions for uncor related noise and equal noise powers in successive symbol periods to o btain a useful bit-error probability expression for the AWGN channel i n the form P-epsilon approximate to Q(root 1.1716.E-b/N-0) where Q(.) is the Gaussian distribution Q-function and E-b/N-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 exten ded to the case of L-fold diversity combining.