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.