Optimal Power Sharing Strategies in NAF Multiple-Relay Networks with CSI

This paper addresses the problem of optimal power allocation among relaying nodes for a non-orthogonal amplifyand- forward (NAF) half-duplex relay network where multiple relays exploit channel state information (CSI) to cooperate with a pair of source and destination to maximize the source-destination mutual information (MI). In particular, assuming that the relays have complete CSI of all source-relay, source-destination, and relay-destination links, we investigate an optimal power sharing scheme via optimal power amplification coefficients at the relays. Given the nature of broadcasting and receiving collisions in NAF, the considered problem is non-convex. To overcome this drawback, we propose a novel method by evaluating the MI in different sub-domains of the vector channels. It is then demonstrated that the globally optimal solution can be obtained. In particular, the optimal solutions are derived in closed-form for the system under the total average power constraint (TAPC) and for the system under both TAPC and individual average power constraint (IAPC) at each relay. Numerical results are provided to quantify the significant gains offered by the proposed power sharing schemes over conventional schemes using either channel distribution information (CDI) or channel inversion (CI).