# Robust communication

In wireless communication we often have co-channel interference which is additive but not necessarily Gaussian. Motivated by this we considered information transmission over covariance-constrained additive noise channels. We explicitly characterized the worst additive noise channels under such covariance constraints. We showed that the minimax strategy is Gaussian noise with a covariance that can be explicitly characterized. Moreover, we showed that the optimal transmit strategy is a Gaussian signal set corresponding to the waterfilling solution to the minimax noise covariance. We also demonstrated that we can attach an operational significance to the rates under mismatched decoding. The utility of these results were also demonstrated by its application to finding the sum rate point of the non-degraded multiple-antenna broadcast channel capacity by several researchers in 2003.

Narrowband interference (NBI) could occur in transmission media such as twisted pair or coaxial cable. We analyzed the effect of such interference on the data throughput for finite-blocklength transmission over noisy inter-symbol interference channels. It was shown that the worst narrowband interference spreads its power over the “sweet spots” of the signal (i.e. where the signal puts highest power). If the rank of the covariance matrix of the NBI is M<N (where N is the rank of the signal and is M dimension of the space) then the worst interferer is shown to put its power along the M largest eigendirections of the signal.