Moments of the sum of circularly symmetric random variables (Corresp.)

Let(X_1,Y_1), ⋯ ,(X_N, Y_N)beNindependent pairs of circularly symmetric random variables, A simple expression is derived for the even moments of the (Euclidean) norm of the vector sum(X_1, Y_1)+⋯ + (X_N, Y_N)in terms of the moments of(X_i ^2 + Y_i ^2)1/2, i = 1,⋯,N. As an application of our results we find an expression for the moments of the "envelope" of a sum of randomly phased cosinusoids.