Quickest Detection in Multiple On-Off Processes

We consider the quickest detection of idle periods in multiple on-off processes. At each time, only one process can be observed, and the observations are random realizations drawn from two different distributions depending on the current state (on or off) of the chosen process. The objective is to catch an idle period in any of the on-off processes as quickly as possible subject to a reliability constraint. We show that this problem presents a fresh twist to the classic problem of quickest change detection that considers only one stochastic process. A Bayesian formulation of the problem is developed for both infinite and finite number of processes based on the theory of partially observable Markov decision process (POMDP). While a general POMDP is PSPACE-hard, we show that the optimal decision rule has a simple threshold structure for the infinite case. For the finite case, basic properties of the optimal decision rule are established, based on which a low-complexity threshold policy is proposed which converges to the optimal decision rule for the infinite case as the number of processes increases. This problem finds applications in spectrum sensing in cognitive radio networks where a secondary user searches for idle channels in the spectrum. Index Terms Quickest change detection, Bayesian formulation, on-off process, spectrum sensing, cognitive radio, Partially Observable Markov Decision Process (POMDP). This work was supported by the Army Research Office under Grant W911NF-08-1-0467 and by the National Science Foundation under Grant CCF-0830685. Part of this work was presented at MILCOM in November, 2008, at ICASSP in April, 2009, and at Allerton Conference in September, 2009. Qing Zhao and Jia Ye are with the Department of Electrical and Computer Engineering, University of California, Davis, CA 95616. Emails: {qzhao,jiaye}@ucdavis.edu. ∗ Corresponding author. Phone: 1-530-752-7390. Fax: 1-530-752-8428. TO APPEAR IN IEEE TRANSACTIONS ON SIGNAL PROCESSING. 2