Opportunistic Cooperation with Receiver-Based Ratio Combining Strategy

Abstract

In cooperative wireless communication systems, many combining techniques could be employed at the receiver, such as maximal ratio combining (MRC), equal gain combining (EGC), etc. To address the effect of receiver diversity combining on optimum energy allocation, we analyze the problem of minimizing average total transmit energy under a SNR constraint when different ratio combining methods are utilized at destination. For maximal ratio combining (MRC), based on the explicit analytical solution an asymptotic solution for normalized optimum total energy in terms of μ and η was derived in the high-SNR scenario. For fixed ratio combining (FRC), we find that there does not exist an explicit analytical solution to the optimum energy allocation problem. However, the convexity proof for the energy function provides a way of using numerical convex optimization methods to find the unique solution. Our results also show that, while direct transmission ($\mathcal{E}^*\_r = 0$) is optimum for certain channel states when the destination uses MRC, the relay should always transmit, i.e. $\mathcal{E}^*\_r > 0$ for all channel states, when the combining ratio β is a fixed number.