On the maximal-ratio combining of FSO and RF links over generalized distributions and its applications in hybrid FSO/RF systems

Abstract

Recently, generalized fading distributions have gained substantial research interest due to their applicability and adaptability in practical scenarios. In this paper, we derive the exact closed-form expressions for the probability density function (PDF) and cumulative distribution function (CDF) of the maximal-ratio combining (MRC) of the free space optics (FSO) and radio frequency (RF) links over the most generalized Malaga and α-η-κ-μ fading models. Further, with the help of derived MRC channel statistics (i.e. PDF and CDF), closed-form expressions for outage probability and average symbol error rate (SER) for the hybrid FSO/RF system based on MRC and adaptive combining schemes are derived. In an adaptive combining scheme, the MRC of FSO and RF links is employed at the receiver, if the operating FSO link quality is unacceptable for transmission. Further, the derived expressions are unified for both intensity modulation/direct detection (IM/DD) and heterodyne detection (HD) techniques. We have considered the effects of atmospheric path loss, atmospheric turbulence-induced fading and non-zero boresight pointing errors in case of the FSO link. We have also determined the optimum switching threshold and beam waist values for the adaptive combining scheme to achieve optimal performance. Moreover, computationally less complex asymptotic expressions are calculated and the diversity gains of MRC and adaptive combining schemes are determined. Finally, the performances of single-link FSO, hard-switching-based hybrid FSO/RF, MRC, and adaptive-combining-based hybrid FSO/RF systems are compared and the inferences are reported under various turbulence conditions, link distances, weather conditions, and severity of the pointing errors.