On Optimal Power Allocation for Source-Orthogonal Relay-Non-orthogonal Amplify-and-Forward Relaying

An Amplify-and-Forward relaying network where the Source is Orthogonal to all the Relays but the relays are Non-orthogonal (SORNAF) is studied. The problem of relay power optimization in a SORNAF relaying scheme is formulated as a non-concave fractional program. Selection Amplify-and-Forward (SAF) relaying is a possible power allocation strategy previously proposed for the SORNAF scheme. A necessary condition for the optimality of the SAF power allocation is derived in terms of instantaneous channel coefficients, based on which, an upper bound on the SAF optimality probability is calculated.