We study hybrid free-space optical (FSO) and radio-frequency (RF) communications, whereby information is conveyed simultaneously using both optical and RF carriers. We consider the case where both carriers experience scintillation, which is a slow fading process compared to typical data rates. A parallel block-fading channel model is proposed, that incorporates differences in signalling rates, power scaling and scintillation models between the two carriers. Under this framework, we study the outage probability in the large signal-to-noise ratio (SNR) regime. First we consider the case when only the receiver has perfect channel state information (CSIR case) and obtain the SNR exponent for general scintillation distributions. Then we consider the case when perfect CSI is known at both the receiver and transmitter, and derive the optimal power allocation strategy that minimises the outage probability subject to peak and average power constraints. The optimal solution involves non-convex optimisation, which is intractable in practical systems. We therefore propose a suboptimal algorithm that achieves the same diversity as the optimal one and provides significant power savings (on the order of tens of dBs) over uniform allocation.
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