Optimal Precoding for Digital Subscriber Lines

The authors determine the linear precoding policy that maximizes the mutual information for general Multiple-Input Multiple-Output (MIMO) Gaussian channels with arbitrary input distributions, by capitalizing on the relationship between mutual information and Minimum Mean Squared Error (MMSE). The optimal linear precoder can be computed by means of a fixed-point equation as a function of the channel and the input constellation. They show that diagonalizing the channel matrix does not maximize the information transmission rate for non-Gaussian inputs. A full precoding matrix may significantly increase the information transmission rate, even for parallel non-interacting channels. They illustrate the application of their results to typical Gigabit DSL systems.