Optimal Control of Constrained Cognitive Radio Networks with Dynamic Population Size

In this paper, we consider the problem of optimal control for throughput utility maximization in cognitive radio networks with dynamic user arrivals and departures. The cognitive radio network considered in this paper consists of a number of heterogeneous sub-networks. These sub-networks may be power-constrained and are required to operate in such a way that the average total interference received on primary channels are kept below given thresholds. We develop a control policy that performs joint admission control and resource scheduling. Through Lyapunov optimization techniques, we show that the proposed policy achieves a utility performance within O(¿) of optimality for any positive ¿. We further show that this arbitrarily closeness to optimality comes at the price of having a delay that is O(1/¿) in admitting users. We also propose constant factor approximations of the policy for distributed implementation.