Abstract
Closed-form expressions for the detection probability, the false alarm probability and the energy detector constant threshold are derived using approximations of the central chi-square and non-central chi-square distributions. The approximations used show closer proximity to the original functions when compared to the expressions used in the literature. The novel expressions allow gains up to 6% and 16% in terms of measured false alarm and miss-detection probability, respectively, if compared to the Central Limit Theorem approach. The throughput of cognitive network is also enhanced when these novel expressions are implemented, providing gains up to 9%. New equations are also presented that minimize the total error rate to obtain the detection threshold and the optimal number of samples. The analytical results match the results of the simulation for a wide range of SNR values.
Highlights
Introduction and backgroundThe growing demand for wireless communications has impacted the dynamics of spectrum management and the challenge of accommodating more users into a finite number of frequency bands is being investigated since the publication of [1]
A gain up to 7% is presented when the constant thresholdCDR−AA is employed in comparison withCDR−central limit theorem (CLT), for γ = −7 dB. These results show that in an unfavorable situation where the measured signal-tonoise ratio (SNR) is different from the project SNR γ, there is a moderate gain in terms of throughput for the cognitive radio network when we use the new approaches presented in this work
4 Conclusions Exploring the approximations of the accumulated density functions of the central chisquare and non-central chi-square distributions, we arrive at new approximations of false alarm probability, detection probability and constant threshold for the energy detector
Summary
2.1 Methods/experimental The research content of this article is divided into two parts, the first being a theoretical analysis of approximations of probability distributions, in the second part through the expressions computational simulations were performed with the MATLAB®2018 software from the company Mathworks®
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