Error probabilities for coherent BPSK and QPSK in a slowly flat fading Rayleigh channel with random phase noise

In this paper, the effects of random phase error on the performance of coherent binary phase-shift-keying (BPSK) and quadrature phase-shift-keying (QPSK) signals transmitted over a non-frequency-selective slowly fading Rayleigh channel are investigated. The approximate expressions for the bit error probability (BEP) of coherent BPSK and QPSK signals transmitted over a non-frequency-selective slowly fading Rayleigh channel with a small phase error are presented under high signal-to-noise ration (SNR) conditions. It is assumed that the reference signal generator is unable to track the random channel phase shift perfectly and the phase error, q, is uniformly distributed in a small range (-φ, φ). Furthermore, it is assumed that the uniform phase error model used in this paper does not take into account the effect of the channel SNR and the channel estimator used. We are interested only in determining the maximum value of f under which the degradation in BEP due to an imperfect phase estimator can be compensated by increasing the SNR a certain amount. It is shown that when the random phase error is less than p/3 for BPSK and p/6 for QPSK, the performance degradation is within 3 dB. Simulation results are also presented and compared with the approximate results.