On Robust Weighted-Sum Rate Maximization in MIMO Interference Networks

This paper studies the \emph{robust weighted-sum rate} optimization problem in the presence of channel uncertainty over a $K$-user Gaussian Interference Channel (GIFC), where multiple antennas are present at all transmitters and receivers. Motivated by recent results on \emph{interference alignment} that show the optimality of linear precoders and simple receivers in achieving the maximum degrees-of-freedom available in the GIFC, we consider linear transmit precoding and two simple decoding schemes: single-stream decoding and single-user decoding. The resulting precoder design problems are then posed as specific optimization problems. Unfortunately, due to the hardness of these problems, optimal solutions cannot be efficiently obtained. Instead of resorting to ad-hoc algorithms, we show that it is possible to design algorithms using a systematic approach. Towards this end, this paper develops new provably convergent iterative algorithms for precoder design through ingenious sub-problem formulations such that each of these sub-problems can be solved optimally. The sub-problems are solved in closed-form for certain cases and formulated as standard convex problems for the rest. To complement these contributions on achievable schemes, we generalize the genie-MAC outer bounding technique to incorporate channel uncertainty using notions of compound-MAC capacity and then obtain computable outer bounds using an alternating optimization approach. Thus, we introduce one of the first approaches to obtain tighter outer bounds on the capacity region of the GIFC in the presence of channel uncertainty.