On the Performance of Hadamard Ratio Detector-based Spectrum Sensing for Cognitive Radios

—We consider the problem of multiantenna spectrum
sensing (SS) in cognitive radios (CRs) when the receivers are assumed to be uncalibrated across the antennas. The performance
of the Hadamard Ratio Detector (HRD) is analyzed in such a scenario. Specifically, we first derive the exact distribution of the HRD
statistic under the null hypothesis, which leads to an elaborate but
closed-form expression for the false-alarm probability. Then, we
derive a simpler and tight closed-form approximation for both the
false-alarm and detection probabilities by using a moment-based
approximation of the HRD statistical distribution under both hypotheses. Finally, the accuracy of the obtained results is verified by
simulations.