New error bounds for coded free-space optical communication systems

In this paper, error performance bounds are derived for coded FSO communication systems operating over atmospheric turbulence channels, which are modeled as K distribution conditions. Existing upper bounds presented in the open technical literature demonstrate some discrepancy in the low signal-to-noise ratio (SNR). This limitation has its origin in the fact that the K probability density function (PDF) contains a modified Bessel function of the second kind, which precludes simple closed-form expressions for the error performance bounds. Recently, it is shown by the author that the probability density function (PDF) of the K distribution can be approximated accurately by a finite sum of weighted negative exponential PDFs. Based on this interesting result, in this paper, a new approximate closed-form expression is derived for the pairwise error probability (PEP). Compared with the previous published results, which are in the form of an infinite series or an upper bound that are accurate only for a certain range of signal-to-noise ratio (SNR), the presented PEP is in closed-for, and is more accurate both for small and high SNR values. The derived PEP is then applied to derive an upper bound to the bit-error probability for convolutional codes for FSO communication through the K channels. Numerical results are further demonstrated to confirm the analytical results and also to show the good accuracy of the derived expressions.