On power allocation for relay networks with nonorthogonal amplify-and-forward protocols

We consider a power allocation problem for three-node cooperative diversity systems using a relay node. Specifically, we focus on an amplify-and-forward (AF) protocol due to the simple operation at the relay node which makes the mathematical analysis tractable. This protocol consists of two phases. The source transmits the signal to both relay and destination in the first phase. In the second phase, the relay amplifies the received signal, and transmits to the destination. Depending on the source participation in the second phase, the protocol can be categorized into nonorthogonal AF (NAF) or orthogonal AF (OAF). In this paper, we consider the power allocation problem of the NAF protocol in a more general scenario than in previous literatures. We then show that there are only two modes of transmission which can be used if the optimal power allocation process is carried out. They correspond to the direct transmission and OAF with optimal power allocation. That is, the solution for optimal power allocation in the systems with NAF as a relay protocol excludes the nonorthogonal transmission. Instead, the selection between the direct transmission and OAF is optimal, i.e., using NAF protocol all the time is not optimal.