Relay Placement for Amplify-and-Forward Relay Channels with Correlated Shadowing

In this letter, we investigate the optimal relay placement problem for the amplify-and-forward relay channels. Considering the joint effects of path loss, correlated shadowing, and flat Rayleigh fading, we first derive the approximate outage probability in the high signal-to-noise ratio (SNR) regime. Then, the optimal relay placement problem is formulated to minimize the derived approximate outage probability. It is shown by the analytical results that the correlation coefficients and the standard deviations of shadowing have significant impacts on the optimal relay placement. Somewhat surprisingly, we show that the optimal relay position may not be on the line connecting the source and the destination for certain scenarios.