Some Complex Statistical Distributions in Multichannel Complex-Valued Signal Detection Theory

The probability density functions(PDF's)and cumulative distribution functions(CDF's) of complex random variables RVA's)are basis for calculating the probabilities of false alarm(PFA's)and probabilities of detection(PD's)in complex-valued signal detection theory.In this paper,some relationship between the complex statistical distributions and the real ones is investigated. The PDF's and CDF's of the complex F and complex Beta distributions,both central and noncentral,and the PDF of the central complex t distribution are derived.