Optimal Power Operation of Energy Detector for Random Signals in Gaussian Noise

A simplified expression for the probability of detection and based on that a numerically solved expression for optimal power operation of improved energy detector for random signals in Gaussian noise is proposed. The expression for the optimal power operation of energy detector which maximizes the probability of detection is a function of the system settings viz. probability of false alarm, average signal to noise ratio and sample size. The expression is obtained by numerical curve fitting tool in regression analysis of MATLAB and it has 97.895% of accuracy rate on an average when it is compared with the numerical results. The expression reduces the effort to find the optimum value of power operation based on the system settings to improve the detection performance of current wireless systems, which uses the energy detector. One of such wireless system is cognitive radio, where detecting the presence of primary user signal is crucial for reliable operation.