Fast multichannel spectrum scanning with multiple simultaneous observations

This paper considers the problem of how to quickly and accurately scan a multichannel spectrum to determine the availability of each channel for a secondary user in a cognitive radio network. The secondary user is able to simultaneously observe more than one channel. We consider a sequential decision setup. After taking each sample, the secondary user should decide either to stop or continue scanning. If the secondary user decides to stop scanning, it then needs to make decisions on the busy/idle status of each channel. If the secondary user decides to continue scanning, it then needs to select a subset of the channels to sense. Two scenarios are investigated. In the first scenario, there is a strict delay constraint on the scanning process. That is, the spectrum scanning needs to be completed within a certain period of time. In the second scenario, there is no strict delay constraint. That is, the spectrum scanning continues until the completion of the detection process. In both scenarios, optimal algorithms for multichannel scanning with multiple simultaneous observations are developed to minimize a cost function that strikes a balance between detection error probabilities and detection delay. Low-complexity approximation schemes are also developed to reduce the complexity of the optimal schemes. Simulation examples are provided to illustrate the effectiveness of the proposed algorithms.