IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 62, NO. 8, OCTOBER 2013
Abstract—In this paper, we consider a cognitive radio system with N secondary user (SU) pairs sharing a spectrum with a pair of primary users (PUs). The SU power allocation problem is formulated as a capacity maximization problem under PU and SU quality of service (QoS) and SU peak power constraints. We show that our problem formulation is a geometric program and can be solved with convex optimization techniques. We examine the effect of PU transmissions in our formulations. Solutions for both low- and high-signal-to-interference-and-noise ratio (SINR) scenarios are provided.We show that including PU capacity in the optimization problem in some circumstances leads to increased PU performance while not significantly degrading SU capacity. In a practical wireless communication system, accurate channel state information (CSI) is not often available; hence, we formulate power allocation problems with both perfect and imperfect CSI and analyze the performance loss incurred due to imperfect CSI. Furthermore, we present a novel method of detecting and removing infeasible SU QoS constraints from the SU power allocation problem that results in considerably improved SU performance. Cumulative distribution functions of capacity for various Rayleigh fading channels are presented.