Averaging Q(parXpar) for a complex circularly Gaussian random vector X : a novel approach

In this correspondence, we average , where is the Euclidean norm of an complex circularly Gaussian vector . This is done by finding the characteristic function of the decision variable and subsequently applying the Gil-Pelaez theorem to obtain a one-dimensional real integral. The integral is then converted to a contour integral which is evaluated using a variant of the Cauchy's integral formula to obtain an expression for , where is the expectation operator.