Opportunistic Spectrum Access by Exploiting Primary User Feedbacks in Underlay Cognitive Radio Systems: An Optimality Analysis

We consider an underlay cognitive radio (CR) communication system in which a cognitive secondary user (SU) can access multiple primary spectrum channels only when its interference to the primary users (PU) is limited. To identify and exploit instantaneous transmission opportunities, the SU probes a subset of primary channels by overhearing the primary feedback signals so as to learn the primary receiver's channel condition and the interference tolerance level, then chooses appropriate power to transmit its data. In such context, the SU cannot probe all the channels for its limited number of receiving antennas, then a crucial optimization problem faced by the SU is to probe which channel(s) in order to maximize the long-term throughput given the past probing history. In this paper, we tackle this optimization problem by casting it into a restless multi-armed bandit (RMAB) problem that is of fundamental importance in decision theory. Given the specific and practical constraints posed by the problem, we analyze the myopic probing policy which consists of probing the best channels based on the past observation. We perform an analytical study on the optimality of the developed myopic probing policy. Specifically, for a family of generic and practically important utility functions, we establish the closed-form conditions to guarantee the optimality of the myopic probing policy, and also illustrate our analytical results via simulations on several typical network scenarios.