## 6 Conclusions  
In this work, we studied the impact of the channel correlations on the performance of AnF cooperative systems. We first briefly reviewed existing works on channel correlations. We then focused on analyzing the effect of the correlation between two channels of each relay on the performance of a multiple AnF relays system with the BRS scheme. Based on the lower and upper bound of the end-to-end received SNR at the destination, we derived the corresponding upper and lower bounds on the system outage probability. In addition, and importantly, we proved that the system can achieve a full DO equal to the number of relays. Moreover, we showed an interesting result that can be stated as \"when the considered channel correlation coefficient increases, the system outage probability decreases\". Figure 8: A comparison among the effects of several channel correlation forms on the system performance with \(K=4\). The scope of future research in this subject is quite broad. Hence, we now would like to discuss only a few interesting and challenging problems which are worth further consideration. Up to now, the equally correlated model, in which correlation coefficients are the same, has been largely investigated [17; 18; 19; 20; 21]. Even though the equally correlated model could be considered as a worst/best-case benchmark and its related results help us to gain fundamental knowledge of the effect of the channel correlations on the performance of cooperative systems, it may fail to precisely predict the actual performance of cooperative systems in reality. To understand the true impact of the channel correlations, non-identical correlated models should be taken into account. Such a study in combination with existing results will create a more complete description of the effect of the channel correlations on the performance of relaying systems. On the other hand, most existing works are focused on studying the performance/behaviour of cooperative systems under a single channel correlation form only, but have ignored the joint consideration of different forms of channel correlation. Although [15; 29] investigate the joint effect of the correlations between source-destination and source-relay channels, between source-destination and relay-destination channels, and between source-relay and relay-destination channels on the performance of DnF systems, only a single relay configuration is considered. In addition, the presented symbol error probability given in [15; 29] cannot be straightforwardly extended to multi-AnF-relay scenarios. Moreover, jointly consider inter-path correlation and correlation between a channel and its outdated estimate is also an interesting problem. Therefore, theoretical analyses and simulations are required to reveal novel insights on the joint effect of multiple channel correlation forms considering multiple AnF relays. With recent advances in antenna design and signal processing, the full-duplex (FD) relaying mode has gained more and more attractiveness from the research community. The advantages of the FD relaying mode lies in the fact that it can address the inefficient use of resources, i.e., dedicated bandwidth or time-slot, of the half-duplex counterpart. Due to its advantages, applications based on FD relay systems will be widely spread in the near future. Hence, investigating the impact of the channel correlations on the performance of FD cooperative systems is necessary and important. In addition, taking the self-interference link between a relay's input and output in FD cooperative systems into account will make the related problems much more challenging. Finally, we note that although the broadcast nature of wireless medium greatly facilitates cooperative communication, it makes wireless data transmission vulnerable to eavesdropping attack.