Energy efficient opportunistic cooperative transmission with different ratio combinings: from a new perspective

Abstract

In cooperative communication, different ratio combining approaches can be utilized at the receiver based on the channel state information (CSI) available to the destination. In this paper, we focus on optimal energy allocation under amplify-and-forward (AF) cooperative communications when various ratio combining methods are utilized. More specifically, we consider a suite of important and fundamental problems, including signal-to-noise ratio (SNR) maximization under a weighted total energy constraint, weighted total energy minimization under an SNR constraint, weighted total energy minimization under an outage probability constraint and outage probability minimization under instantaneous weighted total energy constraint, and analyze the relationship among these problems. We first consider maximal ratio combining (MRC) and derive exact analytical solutions. To reveal the key factors in the resource allocation problem, we further transform the exact results with multiple parameters into more intuitive results with only two quantities. The resulting solutions provide a new perspective to understand optimal energy-efficient opportunistic cooperative transmissions. We then consider fixed ratio combining (FRC) and show that an explicit analytical solution does not exist to the original problem. To this end, based on the convexity proofs for the objective functions, we utilize numerical convex optimizations to obtain the unique solution. Both numerical and simulation studies are conducted to validate our theoretical analysis.