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

• Published in: IEEE communications letters Vol. 18; no. 2; pp. 233 - 236
• Main Authors: CHO, Yeon-Jea, PARK, Dong-Jo
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.02.2014; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Applied sciences; Closed-form solutions; Cognitive radio; energy detection; Exact sciences and technology; Information, signal and communications theory; log-likelihood ratio test; Noise; OFDM; Radiocommunication specific techniques; Radiocommunications; Random variables; Reactive power; Sensors; Signal and communications theory; Signal representation. Spectral analysis; Signal, noise; spectrum sensing; Telecommunications; Telecommunications and information theory; Design criterion; Logarithmic function; Test statistic; Likelihood ratio; Cognitive radio; log-likelihood ratio test; False alarm rate; Spectrum analysis; Likelihood ratio test; spectrum sensing; energy detection; Optimal approximation; Signal analysis; Software radio
• ISSN: 1089-7798; 1558-2558
• DOI: 10.1109/LCOMM.2013.112713.131925

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.