Locally optimum detection for spectrum sensing in cognitive radio

Spectrum sensing is a key feature in cognitive radio networks. We propose a locally optimum (LO) detector, which is known to be optimum at low SNR. This is desirable in cognitive radio since the primary user´s signal may exhibit a very low power at the cognitive user´s transmitter. We focus here on linear modulation in the presence of an unknown phase shift and additive white Gaussian noise. In the case of BPSK modulation, the sufficient statistic of the LO detector is shown to be the sum of the absolute second-order moment (i.e., energy) and second-order moment (pseudo-energy) estimates. For higher size constellation, it is proven that the energy detector is locally optimum. The paper also addresses the issue of noise power uncertainty, to which the energy detector is very sensitive. Although the proposed LO detector is shown to be less sensitive than the energy detector, its performance does deteriorate at high noise power mismatch values. To overcome this problem, we also propose a detector whose probability of false alarm is independent of the noise power. Simulation results show that the proposed detectors in the case of BPSK significantly outperform the energy detector. Further, the complexity of the proposed detectors is only slightly higher than that of the energy detector.