Small Sample Size Performance of the Energy Detector

We examine the small sample size performance of the energy detector for spectrum sensing in AWGN. By making use of the cube-of-Gaussian approximation of chi-squared random variables, we derive a novel, simple, and accurate analytical expression for the minimum number of samples required to achieve a desired probability of detection and false alarm. This way, the number of samples can be calculated by the energy detector with low complexity. We also propose a useful approximation for the performance of cooperative energy detection.