A Variational Approach for Assessing the Capacity of a Memoryless Nonlinear MIMO Channel

A transmission over a memoryless discrete-time noisy multiple-input-multiple-output (MIMO) channel is considered here in this letter, where the signal is distorted according to a nonlinear function at the receiver side, and the input signal is constrained to have a fixed even moment. A variational approach is proposed to analyze the capacity of such a memoryless nonlinear MIMO channel whose output is perturbed by additive white Gaussian noise (AWGN). The optimal input distribution that achieves the channel capacity is derived through a methodology based on multidimensional Hermite polynomials.