Enhanced Performance of Generalized Energy Based Spectrum Sensing with Adaptive Threshold

Abstract

In this paper, we employ generalized energy detector (GED) (with parameter, p) for spectrum sensing and study its performance under additive white Gaussian noise with Gaussian primary user statistics. Here, we consider the distribution of test statistics of GED to follow Gamma distribution. To evaluate the performance of GED, we setup the test bench under Gamma distribution of test statistics to obtain probability of detection over probability of false alarm and probability of error (P E ) over signal-to-noise ratio (SNR). Later, we optimize the threshold for GED under Gamma distribution for test statistics and obtain a closed form expression for optimal threshold. The optimal threshold is employed to study the performance of GED. The enhanced performance of GED with optimal threshold is observed under Gamma distributed test statistics, and in particular, for GED parameter p = 1 under Gamma distribution. This choice of $p$ consistently provides least P E over SNR under optimized threshold setup. However, without employing optimized threshold, the performance of GED for different values of $p$ is almost similar. In our performance analysis, we choose the number of samples, $N = 10$ which means that the demand for sensing time is less. Further, we study the performance of the GED under the influence of different types of fading channels. Again we observe the performance of GED does not change much for different $p$ values under the influence of fading.