Performance Analysis of Amplify-and-Forward Systems with Single Relay Selection in Correlated Environments  
[PERSON]  
1 Department of Nanobio Materials and Electronics, Gwangju Institute of Science and Technology, Gwangju 61005, Korea; [EMAIL_ADDRESS]  
[PERSON]  
Although SRS and related performance analysis have been extensively investigated, most of the existing works assume that wireless channels are statistically independent. However, in reality, wireless channels are likely to be correlated due to feedback delay, common scatterers, geometry of the channels, or characteristics of the channels [7; 8; 9]. Particularly, in wireless cooperative sensor networks, nodes are commonly low-complexity and densely deployed. Therefore, feedback delay and common scatterers among nodes highly exist. An illustration of a general cooperative system, in which a source \(S\) communicates with a destination \(D\) via \(K\) number of relays, \(\{R_{k}\}_{k=1}^{K}\), in a correlated environment, is given in Figure 1. In the given system, correlations may exist between the source-relay (first-hop) channels, between the relay-destination (second-hop) channels, between the actual and the corresponding estimate channels, between the source-\(R_{k}\) and \(R_{k}\)-destination channels, or between the source-destination and source-relay (relay-destination) channels. A detailed description of channel correlations is given in Table 1.  
Here in this work, we first review existing works on the effects of channel correlations on the performance of AnF systems. We then focus on our main contribution, which is to analyze the effect of the channel correlation between the two channels of each relay (source-\(R_{k}\) and \(R_{k}\)-destination channels) on the performance of a multiple AnF relay system with the BRS scheme. We quantify the system DO which is the foremost important performance measure that characterises the system behaviour in the signal-to-noise ratio (SNR) region. In addition, and importantly, from the system DO, we reveal novel insights on the impact of the considered correlation on the system performance. Particularly, we prove  
\begin{table}
\begin{tabular}{p{142.3 pt} p{142.3 pt}} \hline \hline
**Channel** & **Description** \\ \hline \(\hat{\rho}_{ij}\) & Correlation between the actual channel (\(h_{ij}\)) and the corresponding estimate \(\hat{h}_{ij}\) \\ \hline \(\rho_{k}\) & Correlation between two channels of the relay \(R_{k}\) \\ \hline \(\rho_{SD}^{SR_{k}}\) & Correlation between \(h_{SR_{k}}\) and \(h_{SD}\) channels \\ \hline \(\rho_{SD}^{R,D}\) & Correlation between \(h_{R_{k}D}\) and \(h_{SD}\) channels \\ \hline \(\rho_{SR_{k}}^{SR_{k}}\) & Correlation between the first-hop channels \\ \hline \(\rho_{R_{k}D}^{R,D}\) & Correlation between the second-hop channels \\ \hline \hline \end{tabular}
\end{table}
Table 1: A summary of channel correlation forms.  
Figure 1: A multi-relay system in a general correlated environment.  
that the considered correlation does not affect the system DO. Moreover, we show that the considered correlation has a constructive effect on the system performance.  
The remainder of this paper is organized as follows. Section 2 introduces a general system model. A brief overview of existing works on channel correlations is given in Section 3. In Section 4, we present our investigation for the effect of the channel correlation between two channels of each relay on the system performance. Simulation results are provided in Section 5, followed by our conclusion and discussion on future research directions in Section 6.