On multiple-input multiple-output Gaussian channels with arbitrary inputs subject to jamming

Abstract

This paper considers communication over channels subject to jamming. By capitalizing on the relationship between the mutual information and the minimum mean-squared error (MMSE), we investigate the interference covariance that minimizes the mutual information of a deterministic multiple-input multiple-output (MIMO) channel subject to Gaussian noise and Gaussian interference with arbitrary (not necessarily Gaussian) input distributions. We show that the worst interference covariance satisfies a fixed-point equation involving key system quantities, including the MMSE matrix. We also specialize the form of the worst interference covariance to the asymptotic regimes of low and high snr. We demonstrate that in the low-snr regime the worst interference covariance injects an appropriate amount of power directly into the channel eigenmodes. In contrast, in the high-snr regime the worst interference covariance minimizes the minimum distance between a modified version of the constellation vectors. Numerical results illustrate that optimization of the interference covariance has the potential to substantially decrease the reliable information transmission rate between a transmitterreceiver pair. The results are also applicable to scenarios where a jammer aims to impair the secrecy rate of wiretap channels.