Distribution of the envelope of a sum of random sine waves and Gaussian noise

The cumulative distribution of the envelope of the sum of a sinusoidal signal, a number M of randomly phased interfering sine waves, and, possibly, Gaussian noise is expressed as the sum of Marcum's Q-function and an asymptotic series of Laguerre polynomials, much like the ordinary Edgeworth series for the distribution of the sum of a number of independent random variables. A test of the method with M=20 showed that its computation requires about 2% of the time needed for numerical inversion of the characteristic function of the distribution.