Energy Detection Limits Under Log-Normal Approximated Noise Uncertainty

We revisit, in this letter, the impact of noise uncertainty on the performance of the well known energy detector. Mainly, we reconsider the case of a Log-Normal approximated noise uncertainty suggested in the work of Alexander Sonnenschein and Philip M. Fishman. We show that under a Log-Normal noise uncertainty, closed form expressions of the detector´s performances and limits can be provided. Thus we show that, relying on mild approximations, we can design a detector with a fixed probability of false alarm function of the uncertainty, and present a new expression of the SNR-wall that depends on the desired performances of the detector as well as the introduced uncertainty parameter.