Optimal Solution for a Joint Power Allocation and Relay Assignment Problem

The ultimate efficiency of a wireless network is achieved when various resources are allocated in a joint optimization process. This paper proposes the optimal solution for a joint power allocation and relay assignment (JPARA) problem subject to the sum-power constraint at the source node. This formulation is applicable to different system models. Specifically, we assume a network consisting of one source node, one destination node, and N relays, where the source node uses orthogonal frequency-division multiplexing (OFDM) to transmit its information to the destination. Each relay should be assigned to one of the subcarriers, and the source node should distribute its power among the subcarriers. We propose an algorithm to find the JPARA solution based on the max-min criterion. The optimality of the proposed algorithm is analytically proved, and its complexity is calculated to be O(N4). We show that our proposed algorithm offers significant improvement in the performance of the worst end-to-end link compared with the separate optimization case. To further improve the performance, a new approach is proposed, in which each subcarrier is assigned a predetermined initial power, and the remaining power is distributed through the proposed JPARA algorithm.

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