Performance analysis of Mixed MUD-RF/Multi-aperture FSO Relay Communication System with Co-channel Interference

This paper discusses the performance of an improved dual-hop mixed radio frequency (RF) / free space optical (FSO) relay communication system in the present of multiple co-channel interferences (CCIs) at the relay node. Multi-user diversity(MUD) technology has been adopted to improve the RF link performance. In order to improve the performance of the FSO link, multi-aperture receiver scheme has been implemented. The multi-user RF link experiences Nakagami-m fading, while the FSO link is subjected to Exponentiated Weibull distributed atmospheric turbulence. Moreover, the CCIs at the relay node are assumed to undergo Nakagami-m fading. For this proposed system, the exact closed-form expression for the outage probability (OP) has been derived. To quickly understand the effects of different parameters on the system performance, the asymptotic expression for the case of high signal-to-noise (SNR) has been further presented. Results show that the diversity order of this proposed system is min (αβM/2,m 1 K), where M represents the number of receiver apertures; K denotes the number of users; α, β and m 1 are the channel parameters. Additionally, the effects of various parameters on system performance have been investigated. Finally, the numerical results have been validated by Monte-Carlo simulations.


2.Proposed system model and channel model
The mixed multi-user diversity RF/multi-aperture FSO relaying communication system model is shown in Fig. 1. As presented in Fig. 1, there are K users adopting opportunistic scheduling to access the relay node R through RF links. The relay node R has the channel state information of each user and the user with the best channel condition is selected to communicate, thereby obtaining diversity gain. At the same time, the received signal at the node R contains multiple CCIs. Then the received signal at the node R is amplified and forwarded through the FSO link to the destination node D equipped with a multi-aperture receiver.  (1) where xk represents the transmitted signal of the k-th best user; hS,k denotes the k-th best S-R channel coefficient; , S k P is the transmit power of the user with the best channel condition; hI,I denotes the i-th interference signal channel fading coefficient and i P is its power; R n denotes zero mean additive white Gaussian noise (AWGN) with a variance of 2 rf  .
Then the signal -S R y is amplified with a variable gain and forwarded from the node R to the node D. The selection combining (SC) diversity receiving scheme is adopted at the node D. Therefore, the received signal at the node D is expressed as: In addition, the RF link is equipped with MUD technology so that the user with the best channel quality is always selected for communication. Therefore, According to the definition of statistics and assuming that each user channel is independent and identically distributed, the CDF of S,k  is as follows: where ri  is the polynomial expansion coefficient and its recursive formula is The total instantaneous interference-to-noise ratio (INR) of the L co-channel interference signals is Assuming that I,i h is independent and identically Nakagami-m distribution. The PDF of the instantaneous SNR I  is given as [12]: is the second type of confluent hypergeometric function defined in [12,Eq.(9.211.4)].

2.2.FSO link
Assuming that the FSO link obeys Exponentiated Weibull distributed model, the CDF of m  can be written as follows [2]: where 0   and 0   are the shape parameters of , 0   is a scale parameter, m  represents average SNR of FSO link.
Considering M FSO apertures with the SC diversity scheme are deployed at the node D to select the link with highest SNR. The equivalent instantaneous SNR of the FSO links can be written as can be derived as follows :

Cumulative distribution function
From Eq.(5), the CDF of the end-to-end SNR can be expressed as follows : Substituting Eq. (10) and (12)

3.2.Exact Outage probability
The exact OP is an important metric to evaluate the system performance, which generally defined as the probability that the instantaneous SNR falls below a threshold SNR th  . The expression is given as follows: Therefore, when m    and k    , by substituting Eq.(17) and (18) into Eq.(15), the asymptotic OP of the system can be derived as: where the negative term in Eq.(15) is ignored because it is negligible for high SNRs. Therefore, with Eq.(19), we can express the asymptotic OP as: where  and  are constant terms and the diversity order is

4.Analytical results
In this section, the effects of various parameters on the system performance have been investigated, such as numbers of users, numbers of interference, averaged INR, numbers of apertures, atmospheric turbulence and fading parameters of RF link. Simultaneously, the analytical results of OP and BER have been verified by Monte-Carlo simulations. Without loss of generality, it is assumed that RF and FSO hops have the same averaged SNR ( m k    ) and channel parameters for the links are fixed and identical. The threshold SNR is set to 10dB th   . Three RF link fading conditions are considered: m=1, m=2 and m=3. It is also assumed that there are two states of the FSO channel: weak and strong turbulence. Table 1 summarizes the main system parameters and Table 2 lists the atmospheric turbulence parameters. In the Monte-Carlo simulation results, the number of channel realizations is set to N=10 7 .  Fig. 2, the outage probability of the system without interference versus averaged SNR under different numbers of users(K) and numbers of apertures(M) is presented. The refractive index structure parameter Cn 2 is set to 2.7×10 -18 for weak turbulence regime and the fading parameter of the RF channel is set to m1=2. It is observed from Fig. 2 that the Monte-Carlo simulation results provide a close agreement to the analytical results for the considered system model. From this figure, it can be found that the values of K and M can affect the system performance and generally increasing the values of K and M improves the system performance. Specially, the OP performance is basically the same for K=1,M=2 and K=1,M=3 on high SNR and at the time the performance depends on the RF link since the system diversity order is Fig. 3, the outage probability of the considered system versus averaged SNR under different numbers of interferences(L) is presented. The averaged INR is set to 5dB and the channel fading parameter of the interference signal is set to m2=1. As expected, as the number of interferences increases, the overall performance of the system degrades, which can be alleviated by increasing the user signal transmission power and its averaged SNR. The relationship between the OP and averaged SNR is shown in Fig. 4 under the influence of different values of K, L and averaged INR, where we consider the weak turbulence condition and set M=2,m1=2,m2=1. From this figure, it is observed that as the number and strength of the interference signal increases, the OP performance degrades. On the other hand, the increase in the number of users can effectively improve OP performance because of multi-user diversity over RF link access. Fig. 5

5.Conclusion
In this work, the performance of the dual-hop mixed multi-user diversity RF/multi-aperture receiver FSO relaying communication system based on variable gain AF protocol in the presence of multiple CCIs at the relay node has been studied. It is assumed that the RF link experiences Nakagami-m fading and the FSO link is subjected to Exponentiated Weibull distributed atmospheric turbulence. For this proposed system, the exact and asymptotic expressions of the OP have been offered. Furthermore, the