Precise outage analysis of mixed RF/unified-FSO DF relaying with HD and 2 IM-DD channel models

This paper derives and analyzes the outage probability of mixed radio frequency (RF)/unified free space optical (FSO) dual-hop decode-and-forward (DF) relaying scheme, where heterodyne detection (HD) and intensity modulation-direct detection (IM-DD) are considered for FSO detection. In doing that, we correctly utilize, for the first time to the best of our knowledge, a precise channel capacity result for the IM-DD channel. Moreover, this is the first time that not only the (IM-DD input-independent) but also the (IM-DD cost-dependent) AWGN channel is considered in such system analysis. This work assumes that the first hop (RF link) follows Naka-gami-m fading, while the second hop (FSO link) follows Málaga (M) turbulence with pointing error. These fading and turbulence models include other ones (such as Rayleigh fading and Gamma-Gamma turbulence) as special cases, so our analysis can be considered as a generalized one from both RF and FSO fading models point of view. Additionally, the system outage probability is investigated asymptotically in high signal-to-noise ratio (SNR) regime, where a new non-reported diversity order and coding gain analysis are shown. Interestingly, we find that in the FSO hop, based on SNR, the HD or IM-DD cost-dependent results in a same diversity order which is twice the one of IM-DD input-independent. However, based on transmitted power all these FSO detectors result in a same diversity order. Furthermore, we offer simulation results which confirm the derived exact and asymptotic expressions.