A Power Allocation Strategy for Multiple Poisson Spectrum-Sharing Networks

This paper develops a power allocation strategy for multiple networks of Poisson-distributed single-antenna nodes that share the available spectrum in a spectrum underlay scenario. This strategy aims to maximize the overall throughput obtained by sharing the spectrum while limiting the degradation of the successful transmission probability of each network. In its original form, this joint power allocation problem is difficult to solve. However, we demonstrate that the problem can be transformed into a convex optimization formulation, which can be efficiently solved. Furthermore, we obtain a quasi-closed-form solution that has a water-filling interpretation by analyzing the optimality conditions. Numerical results indicate that, when a spectrum-sharing scheme employs the proposed optimal strategy of power allocation, the throughput substantially improves over that obtained by exclusively allocating the spectrum to the primary network. Moreover, when the number of spectrum-sharing networks increases, the enhancement is significant, being up to the limit imposed by the maximum allowable degradation in the performance of each network.