Setting CFAR threshold coefficient for non-coherent accumulation result of a square-law detector's outputs

The output of a square-law detector with zero-mean Gaussian noise as input obeys the exponential distribution. The output after non-coherent accumulation changes to a noise that satisfies the chi-square distribution. The problem is discussed in this paper selecting the CFAR threshold coefficient for the non-coherent accumulating result of a square-law detector's output. Two methods of setting the threshold coefficient are proposed separately, the first based on the chi-square distribution, and the second based on the approximate Gaussian distribution. It is indicated in the simulations that the statistical false alarm rate based on the threshold derived from the approximate Gaussian distribution varies with the non-coherent accumulation time and the given false alarm rate, whereas that from the chi-square distribution is completely dependent on the setting value, having no concern with the non-coherent accumulation time.