Distribution of quadratic form in Gaussian mixture variables and an application in relay networks

In this paper series expansion is developed for the probability distribution function (PDF) and the cumulative distribution function (CDF) of an indefinite Hermitian quadratic form in complex random variables with Gaussian mixture distribution. The moment generating function is inverted by contour integration using the residue theorem. The series expansion result is computationally efficient. Bit error rate (BER) calculation, involving quadratic form in Gaussian mixture variables, in wireless relay network employing BPSK transmission is presented as an application.