Jointly optimal power assignment for multi-source multi-destination relay networks

In this paper, the total transmission power of a multi-source multi-destination relay network is minimized under the constraint that the signal to interference plus noise ratio (SINR) requirement of each source-destination pair is satisfied. The optimization problem involves K power variables, where K is the number of source-destination pairs in the network, and an exhaustive search is prohibitive for large K. In this work, we develop an asymptotically tight approximation of the SINR that allows us to reformulate the original optimization problem to a single-variable optimization problem, which can be easily solved by numerical search of the single variable. Then, the corresponding optimal transmission power at each source and relay can be calculated directly. The proposed optimization scheme is scalable and leads to a power assignment algorithm that exhibits the same optimization complexity for any number (K) of source-destination pairs in the network. Moreover, for the special case of transmission over orthogonal channels, we derive analytically the solution to the optimization problem. Extensive numerical studies illustrate our theoretical developments.