Power allocation in underlay cognitive radio systems with feasibility detection

We consider a cognitive radio system with N secondary user (SU) pairs and a pair of primary users (PU). The SU power allocation problem is formulated as a capacity maximisation problem under PU and SU quality of service and SU peak power constraints. The problem is formulated as a geometric program, solved for both low- and high- signal-to-interference-and-noise ratio (SINR) regimes. We present a novel method of detecting and removing infeasible SU quality of service constraints from the SU power allocation problem that results in considerably improved SU performance. Capacity cumulative distribution functions for Rayleigh fading channels are produced.