  We consider multi-antenna cooperative spectrum sensing in cognitive radio
networks, when there may be multiple primary users. A detector based on the
spherical test is analyzed in such a scenario. Based on the moments of the
distributions involved, simple and accurate analytical formulae for the key
performance metrics of the detector are derived. The false alarm and the
detection probabilities, as well as the detection threshold and Receiver
Operation Characteristics are available in closed form. Simulations are
provided to verify the accuracy of the derived results, and to compare with
other detectors in realistic sensing scenarios.
