Worst-Case Capacity of Gaussian Vector Channels
S. Vishwanath, S. Boyd, and A. Goldsmith
Proceedings of the 2003 Canadian Workshop on Information Theory, Waterloo, ON, Canada
We study the (Shannon) capacity of Gaussian multiple input multiple output (MIMO) systems when the exact distribution of the interference and/or noise is unknown, but the family the distribution belongs to is known (assumed Gaussian). This capacity can be written as a min-max optimizaiton problem over convex sets with matrix variables. We employ Lagrange duality from convex optimization theory to convert the min-max optimization into a single convex optimization, which is easily solved. Our technique is illustrated for several example problems involving multi-user channels and multiple antenna channels.