On the performance of cognitive access with periodic spectrum sensing

The problem of cognitive access of parallel channels occupied by primary users is considered. The transmissions of primary users are modeled as independent continuous-time Markov processes. A secondary cognitive user employs a slotted transmission format and a periodic sensing strategy such that it decides if and where to transmit according to its sensing outcomes. The objective of the cognitive user is to maximize its throughput while satisfying collision constrains imposed by the primary users. Three access policies are analyzed. The optimal access policy is obtained based on a formulation of constrained Markov decision processes. A simple suboptimal memoryless policy is obtained by the use of instantaneous sensing outcome. As an upper bound of the optimal policy, a memoryless policy assuming the access of full channel states is also considered. For a symmetric system, we show that the simple memoryless policy is asymptotically optimal when the collision constraint is tight by proving that the performances of all three policies converge to the same value.