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Greedy approaches in general, and orthogonal matching pursuit in particular,are the most commonly used sparse recovery techniques in a wide range ofapplications. The complexity of these approaches is highly dependent on thesize of the dictionary chosen to represent the sparse signal. When thedictionary has to be large to enable high accuracy reconstructions, greedystrategies might however incur in prohibitive complexity. In this paper, wepropose first the formulation of a new type of sparse recovery problems wherethe sparse signal is represented by a set of independent and smallerdictionaries instead of a large single one. Then, we derive a low complexitymultdimensional orthogonal matching pursuit (MOMP) strategy for sparse recoverywith a multdimensional dictionary. The projection step is performed iterativelyon every dimension of the dictionary while fixing all other dimensions toachieve high accuracy estimation at a reasonable complexity. Finally, weformulate the problem of high resolution time domain channel estimation atmillimeter wave (mmWave) frequencies as a multidimensional sparse recoveryproblem that can be solved with MOMP. The channel estimates are latertransformed into high accuracy user position estimates exploiting a newlocalization algorithm that leverages the particular geometry of indoorchannels. Simulation results show the effectiveness of MOMP for high accuracylocalization at millimeter wave frequencies when operating in realistic 3Dscenarios, with practical MIMO architectures feasible at mmWave, and withoutresorting to perfect synchronization assumptions that simplify the problem.

Multidimensional orthogonal matching pursuit: theory and application to high accuracy joint localization and communication at mmWave