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Greedy sparse recovery has become a popular tool in many applications,although its complexity is still prohibitive when large sparsifyingdictionaries or sensing matrices have to be exploited. In this paper, weformulate first a new class of sparse recovery problems that exploitmultidimensional dictionaries and the separability of the measurement matricesthat appear in certain problems. Then we develop a new algorithm, SeparableMultidimensional Orthogonal Matching Pursuit (SMOMP), which can solve thisclass of problems with low complexity. Finally, we apply SMOMP to the problemof joint localization and communication at mmWave, and numerically show itseffectiveness to provide, at a reasonable complexity, high accuracy channel andposition estimations.

Separable multidimensional orthogonal matching pursuit and its application to joint localization and communication at mmWave