Approximation of the central chi-squared distribution for on-line computation of the threshold for energy detector

Despite the simplicity of the energy detector, its use in cognitive radio systems is limited by the need of a priori information about the noise level. In the absence of such information, it is necessary to estimate the variance of the noise in one way or another and recalculate the threshold of detection on false alarm. If the noise is additive white Gaussian (AWGN) with zero mean, then the threshold is compared to a test statistic that has a central chi-squared distribution. However, calculation of a threshold of detection in the operational (on-line) mode is difficult. In this paper, various approximations of the central chi-squared distribution are investigated. These approximations will allow simplifying the operational calculation of the detection threshold.