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Capacity limit of cognitive radio with dynamic frequency hopping under imperfect spectrum sensing

In this paper, we investigate the capacity limit of a single secondary user (SU) communication link in a cognitive radio system. An SU transmitter establishes the communication with its receiver by dynamically hopping in a frequency spectrum pool, and by sensing the spectrum to exploit the temporal communication opportunities. We characterize the performance of sensing by false-alarm and miss-detection probabilities. Firstly, focusing on a high channel input power region, we develop an upper bound on the SU capacity by assuming a Gaussian distributed output. A lower bound on the SU capacity is also derived using a Gaussian input. We then show that the lower bound closely approaches the upper bound at a high channel input power level. This means that the Gaussian input is nearly optimal in this case. Furthermore, we characterize the impact of primary user activities and sensing performance on the SU capacity by developing a closed-form tight approximation. Secondly, paying attention to a low channel input power region, we propose a genie-aided upper bound and a lower bound using the Gaussian input. By comparing these two bounds, a closed-form approximation to the capacity is developed and the near optimality of the Gaussian input is demonstrated. Finally, numerical results are provided to complement the theoretical discussion.