Zero-mean proper complex Gaussian random processes through nonlinear channels

The statistical characterisation of the output of a memory less nonlinear device having, as an input, a zero mean proper complex Gaussian random process is studied. The closed form expression obtained for the high-order moments involved allowed for neat mathematical expressions for the autocorrelation function and the power spectral density of the signal at the nonlinearity output. Parts of the autocorrelation function and of the power spectral density that correspond to the desired signal and to the intermodulation products of different orders are easily identified.