In this work, the performance and the capacity analysis of a fixed-gain amplify-and-forward (AF)-based dual-hop asymmetric radio frequency-free space optical (RF-FSO) communication system is performed. The RF link experiences Nakagami-m fading and the FSO link experiences Gamma-Gamma turbulence. For this mixed RF-FSO cooperative system, novel and finite power series-based mathematical expressions for the cumulative distribution function, probability density function, and moment generating function of the end-to-end signal-to-noise ratio are derived. Using these channel statistics new finite power series-based analytical expressions are obtained for the outage probability, the average bit error rate (BER) for various binary and M-ary modulation techniques, and the average channel capacity of the considered system. The same analysis is also performed for the scenario when the FSO link undergoes significant pointing errors along with the Gamma-Gamma distributed turbulence. As a special case analytical expressions for the outage probability, BER, and channel capacity are also presented for a dual-hop asymmetric RF-FSO system where the RF link is Rayleigh distributed. Simulation results validate the proposed mathematical analysis. The effects of fading, turbulence, and pointing error are studied on the outage probability, average BER, and the channel capacity.

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Abstract-In this letter, we derive the probability density function (PDF) and cumulative distribution function (CDF) of the minimum of two non-central Chi-square random variables with two degrees of freedom in terms of power series. With the help of the derived PDF and CDF, we obtain the exact ergodic capacity of the following adaptive protocols in a decode-and-forward (DF) cooperative system over dissimilar Rician fading channels: (i) constant power with optimal rate adaptation; (ii) optimal simultaneous power and rate adaptation; (iii) channel inversion with fixed rate. By using the analytical expressions of the capacity, it is observed that the optimal power and rate adaptation provides better capacity than the optimal rate adaptation with constant power from low to moderate signal-to-noise ratio values over dissimilar Rician fading channels. Despite low complexity, the channel inversion based adaptive transmission is shown to suffer from significant loss in capacity as compared to the other adaptive transmission based techniques over DF Rician channels.