On the error rates of differentially detected narrowband pi /4-DQPSK in Rayleigh fading and Gaussian noise

Closed-form formulas for the probability density function (PDF) and cumulative distribution function (CDF) of the differential phase of a phase-modulated carrier in Rayleigh-fading and correlated noise is derived and applied to evaluate the bit-error-rate (BER) of pi /4-DQPSK and conventional DQPSK (differential quaternary phase-shift keyed) systems. Under very narrow IF band-limitation and at high SNR, the pi /4-DQPSK outperforms the conventional DQPSK because the former has less spectral splatter during phase transitions between symbol. The performances of these two systems approach one another as the bandwidth parameter BT increases.<
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