Closed Form Expressions for Detection Threshold and Sample Size for Spectrum Sensing Considering Instantaneously Non-Identically Distributed Samples

Abstract

This letter proposes a spectrum sensing method based on the likelihood ratio test (LRT) considering instantaneously non-identically distributed samples and assuming that the distribution of a test statistic varies in every acquired sample. Since, in reality, it is impossible to perform the ideal LRT that fully reflects such a change of a sample statistic, we propose a practical sensing method that optimally approximates the ideal log-likelihood ratio (LLR) with respect to its statistical mean. In both the ideal LRT and the proposed practical LRT, we finally derive closed form expressions for the detection threshold value and the sample size that are essential design parameters to guarantee predefined false alarm and missed detection constraints.