On the Product of Complex Gaussians With Applications to Radar

The joint probability density function (pdf) of a complex vector, which is the product of a complex Gaussian scalar and a complex Gaussian vector, added to another complex Gaussian vector, is derived. The pdf, cumulative distribution function, moments, and moment generating function of the squared norm and norm of this vector are then derived. The derived result is then used to characterize the performance of energy detector (square law detector) for radar system.