Threshold Setting for Multiple Primary User Spectrum Sensing via Spherical Detector

It is known that the spherical detector (SD) is very efficient for the multiple primary user spectrum sensing in cognitive radios. However, numerical results showed that the decision threshold obtained by the existing approximation methods has high accuracy in large sample scenarios, but it is not the case in small sample situations. In this letter, we develop SD for the practical applications with small observations. Here, two methods to calculate the decision threshold of the SD are proposed. In the first approach, the accurate expression, in the form of Meijer's G-function, for the probability of false-alarm is derived. Based on this, the accurate threshold can be obtained via the numerical solving when a target false-alarm probability is given. In the second method, an approximation method is presented to lead to a simple expression for the decision threshold, which enables us to directly compute the threshold with low computation complexity and high accuracy. Simulation results verify the effectiveness of the two proposed methods.