Algorithm Design and Convergence Analysis for Coexistence of Cognitive Radio Networks in Unlicensed Spectrum

This paper focuses on achieving the low-cost coexistence of the networks in an unlicensed spectrum by making them operate on non-overlapping channels. For achieving this goal, we first give a universal convergence analysis framework for the unlicensed spectrum allocation algorithm. Then, a one-timescale iteration-adjustable unlicensed spectrum allocation algorithm is developed, where the step size and timescale parameter can be jointly adjusted based on the system performance requirement and signal overhead concern. After that, we derive the sufficient condition for the one-timescale algorithm. Furthermore, the upper bound of convergence error of the one-timescale spectrum allocation algorithm is obtained. Due to the multi-timescale evolution of the network states in the wireless network, we further propose a two-timescale iteration-adjustable joint frequency selection and frequency allocation algorithm, where the frequency selection iteration timescale is set according to the slow-changing statistical channel state information (CSI), whereas the frequency allocation iteration timescale is set according to the fast-changing local CSI. Then, we derive the convergence condition of two-timescale algorithms and the upper bound of the corresponding convergence error. The experimentalresults show that the small timescale adjustment parameter and large step size can help decrease the convergence error. Moreover, compared with traditional algorithms, the two-timescale policy can achieve throughput similar to traditional algorithms with very low iteration overhead.