In cognitive radio, spectrum sensing is a fundamental task and is used to detect primary user. Energy detection is a popular spectrum sensing technique. But detection performance of energy detector (ED) deteriorates in low signal-to-noise ratio (SNR) conditions and under noise uncertainty. In this paper, we study generalized energy detector (GED), obtained by replacing squaring operation of amplitude of the received signal in conventional energy detector (CED) with an arbitrary positive power operation p under noise uncertainty. For the worst case of noise uncertainty we analytically show that SNR wall is not dependent on the value of p. We further investigate the detection performance of GED for different values of p under uniformly distributed noise uncertainty and show that CED is the best ED under noise uncertainty. We also show that at noise uncertainty greater than 0.5 dB, the performance gap between different EDs almost vanishes and the detection performances of all EDs almost become the same for all values of p.
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