In this letter, we analyze the error rate performance of M-ary coherent free-space optical (FSO) communications under strong atmospheric turbulence. Specifically, we derive the exact error rates for M-ary phase shift keying (MPSK) and M-ary quadrature amplitude modulation (MQAM) based on moment-generating function (MGF) with negative exponential distributed turbulence, where maximum ratio combining (MRC) receiver is adopted to mitigate the turbulence effects. Additionally, by evaluating the asymptotic error rate in high signal-to-noise ratio (SNR) regime, it is possible to effectively investigate and predict the error rate performance for various system configurations. The accuracy and the effectiveness of our theoretical analyses are verified via numerical results.

In this letter, we investigate tight analytical and asymptotic upper bounds for bit error rate (BER) of constitutional codes over exponentially correlated Nakagami-m fading channels. Specifically, we derive the BER expression depending on an exact closed-form formula for pairwise error event probabilities (PEEP). Moreover, the corresponding asymptotic analysis in high signal-to-noise ratio (SNR) regime is also explored, which is verified via numerical results. This allows us to have explicit insights on the achievable coding gain and diversity order.

In this letter, efficient closed-form formulas for the exact and asymptotic average bit error probability (ABEP) of space shift keying (SSK) systems are derived over Rayleigh fading channels with imperfect channel state information (CSI). Specifically, for a generic 2×NR multiple-input multiple-output (MIMO) system with the maximum likelihood (ML) detection, the impact of imperfect CSI is taken into consideration in terms of two types of channel estimation errors with the fixed variance and the variance as a function of the number of pilot symbols and signal-to-noise ratio (SNR). Then, the explicit evaluations of the bit error floor (BEF) and asymptotic SNR loss are carried out based on the derived asymptotic ABEP formula, which accounts for the impact of imperfect CSI on the SSK system. The numerical results are presented to validate the exactness of our theoretical analysis.

In this letter, we derive a novel and accurate closed-form bit error rate (BER) approximation of the optical wireless communications (OWC) systems for the sub-carrier intensity modulation (SIM) employing binary phase-shift keying (BPSK) with multiple transmit and single receive apertures over strong atmospheric turbulence channels, which makes it possible to effectively investigate and predict the BER performance for various system configurations. Furthermore, we also derive a concise asymptotic BER formula to quantitatively evaluate the asymptotically achievable error performance (i.e., asymptotic diversity and combining gains) in the high signal-to-noise (SNR) regimes. Some numerical results are provided to corroborate the accuracy and effectiveness of our theoretical expressions.