On the sum of generalized Gaussian random signals

This paper is concerned with the distribution of the sum of independent generalized Gaussian (GG) signals. We first analyse the properties of the sum of GG signals in detail. Comparing these properties with those of GGD, we get the conclusion that the distribution of the sum of GG signals with shape parameter α ≠ 2 cannot be GGD. In particular, the PDF of the sum of two iid Laplacian signals, and the proof of a special case are given to support the conclusion above. Furthermore, the simulation results also show that if GGD is applied to the model, the distribution of the sum based on high order statistics (HOS) coincides well with each other except for the vicinity of mean.