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

An amplify-and-forward relaying network where the source is orthogonal to all the relays but the relays are nonorthogonal (SORNAF) is studied. The problem of relay power optimization in a SORNAF relaying scheme is formulated as a nonconcave 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. The upper bound approaches zero almost exponentially as the number of relays increases, showing that SAF relaying is asymptotically strictly suboptimal. A suboptimal power allocation, which is significantly superior to the SAF algorithm in terms of outage performance, is also proposed for SORNAF relaying.