We consider multiple-antenna signal detection of primary user transmissionsignals by a secondary user receiver in cognitive radio networks. The optimaldetector is analyzed for the scenario where the number of primary user signalsis no less than the number of receive antennas at the secondary user. We firstderive exact expressions for the moments of the generalized likelihood ratiotest (GLRT) statistic, yielding approximations for the false alarm anddetection probabilities. We then show that the normalized GLRT statisticconverges in distribution to a Gaussian random variable when the number ofantennas and observations grow large at the same rate. Further, using resultsfrom large random matrix theory, we derive expressions to compute the detectionprobability without explicit knowledge of the channel, and then particularizethese expressions for two scenarios of practical interest: 1) a single primaryuser sending spatially multiplexed signals, and 2) multiple spatiallydistributed primary users. Our analytical results are finally used to obtainsimple design rules for the signal detection threshold.
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