MIMO Encoder and Decoder Design for Signal Estimation

In English We study the joint design of optimal linear MIMO encoders and decoders for filtering and transmission of a vector- valued signal over parallel Gaussian channels subject to a real- time constraint. The objective is to minimize the sum of the estimation error variances at the receiving end. The design problem is nonconvex, but it is shown that a global optimum can be found by solving a related two-stage problem. The first stage consists of a mixed norm minimization problem, where the 2-norm corresponds to the error variance in a corresponding Wiener-Kolmogorov filtering problem and the 1-norm is induced by the channel noise. The second stage consists of a matrix spectral factorization.