Spectrum Search Over Multiple Homogeneous Channels

We consider spectrum detection in multiple homogeneous two-state channels. At each time, a secondary user (SU) can simultaneously detect multiple channels with imperfect spectrum detectors. The objective of the SU is to obtain the idle channels as quickly as possible under a false detection constraint. This detection problem is formulated as a restless multiarmed bandit (RMAB) problem that is proven to be PSPACE-hard. A feasible approach, namely myopic policy, is to detect the best channels until idle channels are caught. In this paper, we establish the structure of the myopic policy, prove that the myopic policy is optimal in the case of detecting N - 1 of N channels under certain mild assumptions, and further show that the myopic policy is not optimal generally by constructing a counterexample.