An analysis of energy detector based on improved approximations of the chi-square distributions

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.