Moment-Based Approach for Statistical and Simulative Analysis of Turbulent Atmospheric Channels in FSO Communication

Abstract

The free space optical (FSO) or wireless optical communication networks involve atmosphere as the channel, which at times can be turbulent in nature, thus degrading the system performance. These turbulent channels can be analyzed by introducing various channel models and modulation techniques. Various researchers have analyzed the performance by presenting different approaches for each type of channel model. In this paper, we present a unified approach for the performance analysis of the Log-normal, Nakagami-n (Rician), and Rayleigh statistical models by deriving the exact closed-form expressions for average bit error probability and the outage probability of each model. It is achieved by using the alternative form of Q-function and Gauss-Hermite Quadrature approximation to the moment-generating function of the output signal-to-noise ratio (SNR). Furthermore, definite expressions for each type of modulation technique are also derived to describe the channel fading in an FSO communication system. The system of interest includes the M-ary phase shift keying and M-ary quadrature amplitude modulation techniques. Moreover, the average output SNR, the average received irradiance, and the amount of fading (fading strength) are also expressed in simple closed forms for above-mentioned turbulent channels. In addition to this, the performance of the FSO system in the presence of atmospheric turbulence and pointing errors is also investigated. The statistical model is examined for zero and nonzero boresight point errors modeled by Rayleigh and Rician distributions in a Log-normal fading channel. The composite Log-normal PDFs along with asymptotic error rate and outage probability are also presented for such system. The effect of Tikhonov distributed phase noise arise due to BPSK modulation on BER performance is evaluated on three turbulent channels by deriving its closed-form expression using a moment-based approach. The mathematical analysis is verified by comparing the numerical results with Monte-Carlo simulated values and graphs.