Exact distributions for bit error rate and channel capacity in free-space optical communication

Bit error rate (BER) and channel capacity are two important metrics to assess the performance of free-space optical communication (FSOC) systems. Due to the fading of the optical signal owing to the atmospheric effects, these two quantities behave as random variables. Most of the studies in this direction have focused on the calculation of only the average of these quantities. However, since the complete information about a random variable is encoded in its distribution, it is more informative to examine the latter itself. In this work, the authors derive exact probability density function (PDF) expressions for the BER and the channel capacity for an arbitrary irradiance model. In particular, they investigate these exact results for log-normal, gamma-gamma, and K distributions. For the BER analysis, they focus on the binary phase shift keying and quadrature phase shift keying modulation schemes. The authors' analytical reults are found to be in conformity with Monte Carlo simulations. The exact PDFs of the BER and the channel capacity reveal that there are several instances when the average is unable to capture the actual behaviour of these quantities, and therefore one must be careful in drawing conclusions based on the first moment only.