On the capacity of the Gaussian mixture channel under average and peak power constraints

In many communications systems, the Gaussian mixture model is extensively used to characterize non-Gaussian man-made and natural interference. We study the capacity of the Gaussian mixture noise channel and its capacity-achieving input. In particular, we consider the symmetric and asymmetric Gaussian mixture noise cases. It is shown that, under average and peak power constraints, the capacity-achieving input is discrete with finitely many mass points. Furthermore, some properties of the capacity-achieving distribution are proved and demonstrated by simulations.