On the Performance of Free-Space Optical Systems over Generalized Atmospheric Turbulence Channels with Pointing Errors

Abstract

Generalized fading has been an imminent part and parcel of wireless communications. It not only characterizes the wireless channel appropriately but also allows its utilization for further performance analysis of various types of wireless communication systems. Under the umbrella of generalized fading channels, a unified performance analysis of a free-space optical (FSO) link over the Malaga (M) atmospheric turbulence channel that accounts for pointing errors and both types of detection techniques (i.e. indirect modulation/direct detection (IM/DD) as well as heterodyne detection) is presented. Specifically, unified exact closed-form expressions for the probability density function (PDF), the cumulative distribution function (CDF), the moment generating function (MGF), and the moments of the end-to-end signal-to-noise ratio (SNR) of a single link FSO transmission system are presented, all in terms of the Meijer's G function except for the moments that is in terms of simple elementary functions. Then capitalizing on these unified results, unified exact closed-form expressions for various performance metrics of FSO link transmission systems are offered, such as, the outage probability (OP), the higher-order amount of fading (AF), the average error rate for binary and M-ary modulation schemes, and the ergodic capacity (except for IM/DD technique, where closed-form lower bound results are presented), all in terms of Meijer's G functions except for the higher-order AF that is in terms of simple elementary functions. Additionally, the asymptotic results are derived for all the expressions derived earlier in terms of the Meijer's G function in the high SNR regime in terms of simple elementary functions via an asymptotic expansion of the Meijer's G function. Furthermore, new asymptotic expressions for the ergodic capacity in the low as well as high SNR regimes are derived in terms of simple elementary functions via utilizing moments. All the presented results are verified via computer-based Monte-Carlo simulations.

Besides addressing the pointing errors with zero boresight effects as has been addressed above, a unified capacity analysis of a FSO link that accounts for nonzero boresight pointing errors and both types of detection techniques (i.e. heterodyne detection as well as IM/DD) is also addressed. Specifically, an exact closed-form expression for the moments of the end-to-end SNR of a single link FSO transmission system is presented in terms of well-known elementary functions. Capitalizing on these new moments expressions, approximate and simple closed-form results for the ergodic capacity at high and low SNR regimes are derived for lognormal (LN), Rician-LN (RLN), and M atmospheric turbulences. All the presented results are verified via computer-based Monte-Carlo simulations.

Based on the fact that FSO links are cost-effective, license-free, and can provide even higher bandwidths compared to the traditional radio-frequency (RF) links, the performance analysis of a dual-hop relay system composed of asymmetric RF and FSO links is presented. This is complemented by the performance analysis of a dual-branch transmission system composed of a direct RF link and a dual-hop relay composed of asymmetric RF and FSO links. The performance of the later scenario is evaluated under the assumption of the selection combining (SC) diversity and the maximal ratio combining (MRC) schemes. RF links are modeled by Rayleigh fading distribution whereas the FSO link is modeled by a unified GG fading distribution. More specifically, in this work, new exact closed-form expressions for the PDF, the CDF, the MGF, and the moments of the end-to-end SNR are derived. Capitalizing on these results, new exact closed-form expressions for the OP, the higher-order AF, the average error rate for binary and M-ary modulation schemes, and the ergodic capacity are offered.

Cognitive radio networks (CRN) have also proved to improve the performance of wireless communication systems and hence based on this, the hybrid system analyzed above is extended with CRN technology wherein the outage and error performance analysis of a dual-hop transmission system composed of asymmetric RF channel cascaded with a FSO link is presented. For the RF link, an underlay cognitive network is considered where the secondary users share the spectrum with licensed primary users. Indoor femtocells act as a practical example for such networks. Specifically, it is assumed that the RF link applies power control to maintain the interference at the primary network below a predetermined threshold. While the RF channel is modeled by the Rayleigh fading distribution, the FSO link is modeled by a unified Gamma-Gamma turbulence distribution. The FSO link accounts for pointing errors and both types of detection techniques (i.e. heterodyne detection as well as IM/DD). With this model, a new exact closed-form expression is derived for the OP and the error rate of the end-to-end SNR of these systems in terms of the Meijer's G function and the Fox's H functions under amplify-and-forward relay schemes. All new analytical results are verified via computer-based Monte-Carlo simulations and are illustrated by some selected numerical results.