# Unified Performance Analysis of MIMO Mixed RF/FSO Relaying System
## 8 Numerical Simulation and Discussion  
In this section, numerical simulation of the considered asymmetric dual-hop MIMO mixed RF/FSO DF single relaying system's OP, BER, and capacity are presented, respectively. For the MIMO RF link, the system transmitter and receiver's number are \(N_{t}=2\), \(N_{r}\in\{2,3\}\). For the MIMO FSO link, laser wavelength \(\lambda=1550\) nm, transmitter and receiver's number \(M\in\{1,2\}\), \(N\in\{1,2,3,4,6\}\), outer scale \(\alpha=4.3407\), inner scale \(\beta=1.3088\). For the number of series expansion terms considering the pointing error, we assume J = 20 is accurate enough for our simulation channel conditions. Figure 2 illustrates the outage probability of the MIMO mixed RF/FSO system with pointing error in the case of different optical antennas. Where \(w_{s}/R_{a}\ =3\sigma_{s}/R_{a}\ =1.\ \gamma_{th}\) = 10 dB. It can be seen from the figure that even in the presence of pointing errors, the outage probability of the system decreases as the number of optical antennas increases. For example, the outage probability of \((N_{t},N_{r},M,N)=(2,3,2,3)\) scheme yield \(4.854\times 10^{-3}\) when the SNR is 40 dB; while \((N_{t},N_{r},M,N)=(2,3,1,1)\) only yields 0.1957. Figure 3 presents the outage probability of the MIMO mixed RF/FSO system under the different pointing error influence. The simulation parameters are as follows \((N_{t},N_{r},M,N)=(2,3,2,2)\),\(w_{s}/R_{a}\ =8\),\(\gamma_{th}\) = 10 dB. It can be observed that the outage probability is greatly affected by the pointing error. The severity degree of the pointing errors increases as the value of \(\sigma_{s}/R_{a}\) increases, and the outage probability also increases. For example, the outage probability of the system achieves \(5.394\times 10^{-2}\) when the average SNR is 50 dB and \(\sigma_{s}/R_{a}\ =1\), while the system achieves 0.3767 when \(\sigma_{s}/R_{a}\ =4\). Figure 4 is a plot of outage probability of the considered MIMO mixed RF/FSO system without pointing error when \(\gamma_{th}=5\) dB. We assume that the average SNRs of each link are the same. As can be seen, the system's diversity order mainly depends on the minimum diversity order of each link. For example, when \((N_{t},N_{r},M,N)=(2,2,1,1)\), the slope of the OP curve is \(-\beta/2\), which means the diversity order depends on the FSO link. On the other hand, when \((N_{t},N_{r},M,N)=(2,2,4,4)\), the slope of the OP curve is \(-4\), which means the diversity order depends on the RF link. Figure 5 illustrates the bit error rate (BER) performance of the considered MIMO mixed RF/FSO system without pointing error vs. average SNR per hop. As seen, the system performance improves when the number of antennas is increased, since this also increases the performance against fading and reduces the decoding error at the relay. We  
Figure 3: Outage probability of MIMO mixed RF/FSO system with different pointing error. Figure 2: Outage probability of different scheme MIMO mixed RF/FSO systems with pointing error. can also see the same characteristics as the OP performance and the end-to-end diversity gain is determined by the minimum diversity gain of each hop. Therefore, in different scenarios, we can flexibly combine the number of source, relay, and receiver antennas to obtain the same diversity gain; for example, when the complexity of the relay is limited, we can reduce the number of the relay's antennas and increase the number of antennas at the source and receiver to obtain the same diversity gain. Figure 6 presents a comparison of the average ergodic capacity of different schemes of MIMO mixed RF/FSO systems without pointing error. It can be seen that the MIMO system can significantly increase the system's end-to-end channel capacity compared with the SISO system. For instance, the ergodic capacity of the system of  
Figure 4: Outage probability of different scheme MIMO mixed RF/FSO system. Figure 5: BER of MIMO mixed RF/FSO system. \((1,1,1,1)\) is 6.12 bits/s/Hz at the SNR of 45 dB.