Sampling and Reconstruction of Multiple-Input Multiple-Output Channels

Abstract

Based on the recent development of sampling and reconstruction results for slowly time-varying single-input single-output channel operators, we derive sampling results in the multiple-input multiple-output setting where all subchannels satisfy an underspread condition, that is, their spreading functions are supported on individual sets of small measure. At the center of our work is the extension of the single-input single-output dual tiling condition to this setting; it characterizes which periodic weighted delta trains can be used to identify a given class of multiple-input multiple-output channel operators satisfying a spreading support constraint. Building on the dual tiling condition, we compute reconstruction formulas for the operator's symbol in closed form and discuss the problem of identifying multiple-input multiple-output operators where only restrictions in size, but not on location and geometry, of the subchannel spreading supports are known.