Convex relaxation algorithms for energy-infeasibility tradeoff in cognitive radio networks

In cognitive radio networks, uncontrolled access of secondary users degrades the performance of primary users and can even lead to system infeasibility, as the secondary users are allowed to transmit simultaneously on a shared spectrum. We study the feasibility of the total energy consumption minimization problem subjecting to power budget and Signal-to-Interference-plus-Noise Ratio (SINR) constraints. Finding the largest set of secondary users (i.e., the system capacity) that can be supported in the system is hard to solve due to the nonconvexity of the cardinality objective. We formulate this problem as a vector-cardinality optimization problem, and propose a convex relaxation that replaces the objective with a continuous and convex function. Motivated by the sum-of-infeasibilities heuristic, a joint power and admission control algorithm is proposed to compute the maximum number of secondary users that can be supported. Numerical results are presented to show that our algorithm is theoretically sound and practically implementable.