The locally most powerful test for multiantenna spectrum sensing with uncalibrated receivers

Spectrum sensing is a key component of the cognitive radio (CR) paradigm. Among CR detectors, multiantenna detectors are gaining popularity since they improve the detection performance and are robust to noise uncertainties. Traditional approaches to multiantenna spectrum sensing are based on the generalized likelihood ratio test (GLRT) or other heuristic detectors, which are not optimal in the Neyman-Pearson sense. In this work, we derive the locally most powerful invariant test (LMPIT), which is the optimal detector, among those preserving the problem invariances, in the low SNR regime. In particular, we apply Wijsman's theorem, which provides us an alternative way to derive the ratio of the distributions of the maximal invariant statistic. Finally, numerical simulations illustrate the performance of the proposed detector.