Giannakis, “Sequential and cooperative sensing for multi-channel cognitive radios

Abstract—Effective spectrum sensing is a critical prerequisite for multi-channel cognitive radio (CR) networks, where multiple spectrum bands are sensed to identify transmission opportunities, while preventing interference to the primary users. The present paper develops sequential spectrum sensing algorithms which ex-plicitly take into account the sensing time overhead, and optimize a performance metric capturing the effective average data rate of CR transmitters. A constrained dynamic programming problem is formulated to obtain the policy that chooses the best time to stop taking measurements and the best set of channels to access for data transmission, while adhering to hard “collision ” constraints im-posed to protect primary links. Given the associated Lagrange mul-tipliers, the optimal access policy is obtained in closed form, and the subsequent problem reduces to an optimal stopping problem. A basis expansion-based sub-optimal strategy is employed to miti-gate the prohibitive computational complexity of the optimal stop-ping policy. A novel on-line implementation based on the recursive least-squares (RLS) algorithm along with a stochastic dual update procedure is then developed to obviate the lengthy training phase of the batch scheme. Cooperative sequential sensing generalizations are also provided with either raw or quantized measurements col-lected at a central processing unit. The numerical results presented verify the efficacy of the proposed algorithms. Index Terms—Cognitive radio, optimal stopping, sequential de-tection, spectrum sensing. I