Cognitive Radio with Imperfect Spectrum Sensing: The Optimal Set of Channels to Sense

Opportunistic channel sensing and access problem of a secondary user with multiple potential primary channels is investigated. The secondary user can sense a limited number of channels, and channel sensing is imperfect. If the secondary user can access all channels sensed free, it is proved that the secondary user should sense the channels with the largest rewards, where the reward of a channel is the reward that the secondary user can acquire if it senses the channel and accesses the channel if the channel is sensed free. If the secondary user can access only a limited number of sensed-free channels, in general it may not be optimal to sense the channels with the largest rewards. However and interestingly, for some special cases (for example, when all the channels have the same detection probability), simple rules are given for the optimal selection of channels to sense. For the general case, methods are given to reduce the searching complexity for the optimal set of channels to sense.