## 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.

### Papers

**Download:**worstnoise.pdf**Abstract:**This paper started with a simple question: is the maximum entropy noise the worst noise for additive channels? In the case of scalar channels with a power constraint on the noise, this is true, as is well known. However, we show that in the vector case, with covariance constraints, the answer is yes and no. Yes, if the transmit power is large enough and no otherwise. Along the way we give a solution to the mutual information game with covariance constraints and show that Gaussian solutions form saddle points, but there could also be other saddlepoints. We also demonstrate that the information rates can be achieved using mismatched (Gaussian) decoders.**Download:**nbi.pdf**Abstract:**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). More precisely, the auto-correlation matrix of worst-case narrowband (rank-deficient) interference is shown to have the same eigendirections as the signal. Moreover, if the rank of the covariance matrix of the NBI is M- S. N. Diggavi and T. M. Cover, "Is Maximum Entropy Noise the Worst?," in
*Proc. International Symposium on Information Theory, Ulm*, 1997, p. 278.