A closed-form solution to the power minimization problem over two orthogonal frequency bands under QoS and Cognitive Radio interference constraints

This paper considers a Cognitive Radio (CR) channel composed of a secondary user (SU) and a primary user (PU). An analysis of the power minimization over several orthogonal frequency bands at the SU level under the following constraints is provided: a minimum Quality of Service (QoS) constraint, maximum peak and average interference to the PU constraints. The general solution, when it exists, is a water-filling type of solution which can be computed via iterative algorithms. It turns out that, in the case of two orthogonal bands a closed-form analytical solution can be found and a complete analysis of the feasibility of these opposing constraints is presented in details. Several numerical results that sustain and give inside into the analysis are also discussed.