Accurate Performance Analysis of Hadamard Ratio Test for Robust Spectrum Sensing

Abstract—Hadamard ratio test is a well-known approach to robust signal detection in multivariate analysis. Recently, it has been exploited for robust spectrum sensing in cognitive radio, but its detection performance is not yet completely analyzed. This work is devoted to accurate detection performance analysis of the Hadamard ratio method for robust spectrum sensing. By computing the first and second exact negative moments for the signal-presence hypothesis along with employing the Beta distri-bution approximation, we derive accurate analytic formulae for detection probability. This enables us to theoretically evaluate the detection behavior of the Hadamard ratio test. Numerical results are presented to validate our theoretical findings. Index Terms—Cognitive radio, spectrum sensing, general-ized likelihood ratio test, Beta distribution, multiple antennas, robustness. I