Optimal Sequential Channel Sensing for Cognitive Radios for IID and Non-Identical Channels

In this paper, we consider an unlicensed or Secondary User (SU) that performs sequential spectrum sensing of channels in the band of the licensed or the Primary user (PU). The sensing not only decides the availability of the channel but also measures its strength. Using these two attributes for a channel (as state) the SU decides either to stop sensing, use a channel and obtain a reward or to continue sensing at a cost in the hope of achieving a channel with better attributes. We aim to find a stopping rule such that an expected reward over a finite duration of time for the SU is maximized. We model our problem in the elegant framework of an optimal stopping problem (OSP). We consider two scenarios, (i) where the channel states are independent and identically distributed (iid) over the channels and (ii) where channel states are independent but not identically distributed over the channels. It is shown that the optimal solution for the first scenario is a simple threshold based policy. Moreover, for the second scenario we extend the results of the first scenario and propose an optimal sensing order and sensing rule based on multiple thresholds, which is also easy to implement.