Decision Feedback Based Transceiver Optimization for MIMO Intersymbol Interference Channels

This paper deals with optimizing a transceiver, which consists of a linear time invariant (LTI) matrix filter at the transmitter and a decision feedback (DF) receiver, for single-carrier data transmission over multi-input multi-output (MIMO) intersymbol interference (ISI) channels. Considering a spatial multiplexing approach for transmission of multiple scalar substreams, we adopt some cost function f _o({MSE_i}) to measure the overall system performance, where MSE_i´s are the mean-squared errors (MSE) of the substreams. It is proven that for any cost function f _o the optimum transmitter is of the same specific structure and the original complicated variational optimization problem can be drastically simplified to a problem with scalar variables. The solution can be further simplified if the cost function is specialized to the cases where the composite function f _o diam exp is either Schur-convex or Schur-concave.