Power control for multiple spectrum-sharing networks under random geometric topologies

This paper develops a power control strategy for multiple spectrum-sharing networks of single antenna nodes in a spectrum underlay scenario. A distinguishing feature of the proposed strategy is that it requires only knowledge of the spatial distribution of the nodes, rather than instantaneous channel state information. The strategy seeks to maximize a weighted sum of the throughput of each network while guaranteeing specified successful transmission probabilities. In its native form, this joint power allocation problem is difficult to solve. However, we show that the problem can be transformed into a convex optimization formulation that can be efficiently solved using general purpose tools. Furthermore, we analyze the optimality conditions and obtain a quasi-closed form solution reminiscent of waterfilling. Numerical results demonstrate that spectrum sharing employing the proposed optimal power yields a substantial throughput gain over allocating the spectrum to a single network.