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Spectrum sensing is a key feature in cognitive radio networks. The authors 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. They 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.
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