# Unified Performance Analysis of MIMO Mixed RF/FSO Relaying System
## 1 Introduction  
Dual-hop relay technology has gained enormous attention in the last decades because it not only broadens the coverage but also increases the capacity of the wireless communication networks [1]. This technology splits the source to destination channel into two shorter links, which usually has an asymmetric fading distribution (called mixed fading channel) [2]. In this case, it reduces the possibility of the entire communication system falling into deep fading, making the system more robust. Unlike the traditional radio frequency (RF) relaying system, a mixed RF/free space optical (FSO) system combines the advantage of the FSO technique, such as low cost, free license, large bandwidth, high data rate, good security, etc [3]. However, FSO techniques are sensitive to the atmospheric absorption and turbulence. In order to mitigate the impairment caused by atmospheric turbulence, the multiple input multiple output (MIMO) technique can be applied to the FSO link [4]. The MIMO technique has been widely used in RF wireless communication, which is available to increase data rates and mitigate the disadvantages of fading [5]. To the best of our knowledge, the majority of published literature focused on the mixed RF/FSO communication systems with a single optical antenna [6]. Even though Reference [7] investigated a mixed single input multiple output (SIMO) RF/MIMO FSO relay-assisted system, it still does not take into account that the RF link adopts the MIMO technique. In order to take full advantage of the MIMO technique, the performance of the full MIMO mixed RF/FSO communication systems still need further investigation and discussion. Reference [2] firstly analyzed and presented the performance of a dual-hop asymmetric RF/FSO relay system. Based on this framework, there are plenty of researches onmixed RF/FSO relay systems in different circumstances. Reference [8] employed transmit diversity at the source and selection combining at the destination. The relay is equipped with a single RF receive antenna and one aperture. The authors used the cumulative distribution function (CDF)-based method to derive the outage probability, symbol error rate, and average capacity performance. However, compared to the MIMO relay system, when the same diversity gain is achieved, this system requires more antennas. Reference [9] investigated a decode-and-forward (DF) based asymmetric dual-hop mixed RF/FSO communication link. It was assumed that the source was moving and the source to relay link experienced time-selective Rayleigh fading. However, although the source to relay link applied the MIMO technique, the relay to destination link was still single input single output (SISO). Therefore, it was more susceptible to turbulence effects than the MIMO system. The end-to-end diversity order was still limited by the FSO link, which wastes the diversity gain provided by the MIMO RF link. Reference [7] analyzed multi-diversity combining and selection, which enhanced the performance of the relay assisted mixed SIMO RF/ MIMO FSO system. It only derived the outage probability (OP) of the proposed system. However, the bit error rate and average channel capacity of the system has not been given. This reference also did not consider the impact of the pointing error on the entire system, which has a great impact on the optical communication system. Motivated by the practical application scenarios of the mixed RF/FSO systems. In this paper, we investigate the asymmetric dual-hop MIMO mixed RF/FSO DF relaying system. The model studied in this paper avoids the limitations of the model in the previous literature and provides better performance for the relay channel. This model has the characteristics of excellent error performance, high energy efficiency, and strong robustness, attracting attention as an effective solution for the large capacity data transmission demands of \"last mile\" communication. This paper will also provide a direct theoretical basis for future large-capacity and high-speed communication systems.