SNR wall for generalized energy detection under noise uncertainty in cognitive radio

Energy detection (ED) is a popular spectrum sensing technique in cognitive radio to detect the primary user. But the detection performance of ED deteriorates in the presence of noise uncertainty and exhibits associated SNR wall phenomenon. In this paper, the generalized energy detector (GED) is investigated, where the squaring operation of amplitude of received samples in conventional energy detector (CED) is replaced by an arbitrary positive operation p. Our aim is to study the effect of noise uncertainty on the detection performance of GED. We consider different distributions of noise uncertainty. Initially, uniform distribution of noise uncertainty is considered and an expression of the SNR wall for the same is derived. It is shown that the SNR wall for uniformly distributed noise uncertainty is independent of p. The study of the detection performance of GED is further extended for log-normally distributed noise uncertainty, where the SNR wall is calculated numerically.