Optimum space-time processors with symbol-rate sampling are bandlimited

This correspondence considers the problem of joint transmitter and receiver design for multiple-input multiple-output (MIMO) channels under the mean-square error (MSE) criterion when the system is not necessarily bandlimited. It is proven that the optimum space-time filters are strictly bandlimited to a frequency set. The aggregated bandwidth of this set is at most the number of the substreams times symbol rate. The optimal frequency sets corresponding to different substreams are disjoint, if two maximum channel eigenmodes are not equal for the same Nyquist translate.