Optimal Power Allocation in a Spectrum Sharing System with Partial CSI

This paper studies an optimal power allocation strategy in spectrum-sharing cognitive radio systems. In reality, it is difficult for the secondary users (SUs) to obtain perfect channel state information (CSI) related to the primary users (PUs) due to the lack of cooperation between the SUs and the PUs. We assume that only instantaneous CSI of the secondary link and statistical CSI of the other links is available to the SUs. This assumption not only reveals the realistic challenges, but also brings mathematical challenges in solving the optimization problem in closed form, since the performance evaluated with statistical CSI involves expectation operations. We reformulate the objective function in closed form and derive the optimal power allocation solution. The feasibility of the solution is discussed. Furthermore, we provide several interesting insights into the achievable performance based on the properties of the solution.