BER of subcarrier MPSK and MDPSK systems in atmospheric turbulence

Bit-error rate (BER) performance of subcarrier $M$-ary phase-shift keying (MPSK) and $M$-ary differential PSK (MDPSK) is analyzed for optical wireless communications over Gamma-Gamma and lognormal turbulence channels. We study the relation between the exact BER and the approximate BER, which is obtained by dividing the symbol-error rate by the number of bits per symbol, for subcarrier MPSK and MDPSK modulations. The asymptotic BER performance gap between the exact and the approximate BERs is quantified analytically through our asymptotic analyses. The accuracy of the approximate BER of both MPSK and MDPSK depends on the channel conditions. Under weak turbulence conditions, the approximate BER expression can be used to predict the system performance with high accuracy, while under strong turbulence conditions the approximate BER becomes inaccurate and can only serve as a loose lower bound of the exact BER. The asymptotic BER performance loss of MDPSK with respect to MPSK is also quantified analytically.