Filter design for MIMO sampling and reconstruction

We address the problem of FIR equalizer filter design for multiple-input multiple-output (MIMO) linear time-invariant channels with uniform sampling at the channel outputs. This scheme encompasses Papoulis’ generalized sampling and several nonuniform sampling schemes as special cases. The input signals are modeled as either continuous-time or discrete-time multi-band input signals, with different band structures. We derive conditions on the channel and the sampling rate that allow perfect inversion of the channel. Additionally, we derive a stronger set of conditions under which the equalizer filters can be chosen to be continuous functions of the frequency variable. We also provide conditions for the existence of FIR perfect reconstruction filters, and when such do not exist, we address the optimal approximation of the ideal filters using FIR filters and a min-max end-to-end distortion criterion. The design problem is then reduced to a standard semi-infinite linear program. An example design of FIR equalizer filters is given.