Quantifying the accuracy of high SNR BER approximation of MPSK and MDPSK in fading channels

We study the relation between the exact bit-error rate (BER) and the approximate BER, which is obtained by dividing the symbol-error rate by the number of bits per symbol, for M-ary phase-shift keying (MPSK) and M-ary differential PSK (MDPSK) in fading channels. The asymptotic BER estimation error of the approximate BER is quantified analytically through our asymptotic analysis. Our results show that the accuracy of the approximate BER of both MPSK and MDPSK depends on the fading severity. We also show analytically that the approximate BER is excellent for both MPSK and MDPSK in large signal-to-noise ratio regimes for an additive white Gaussian noise channel.