Off-the-grid Recovery of Time and Frequency Shifts with Multiple Measurement Vectors

Abstract

We address the problem of estimating time and frequency shifts of a known waveform in the presence of multiple measurement vectors (MMVs). This problem naturally arises in radar imaging and wireless communications. Specifically, a signal ensemble is observed, where each signal of the ensemble is formed by a superposition of a small number of scaled, time-delayed, and frequency shifted versions of a known waveform sharing the same continuous-valued time and frequency components. The goal is to recover the continuous-valued time-frequency pairs from a small number of observations. In this work, we propose a semidefinite programming which exactly recovers $s$ pairs of time-frequency shifts from $L$ regularly spaced samples per measurement vector under a minimum separation condition between the time-frequency shifts. Moreover, we prove that the number $s$ of time-frequency shifts scales linearly with the number $L$ of samples up to a log-factor. Extensive numerical results are also provided to validate the effectiveness of the proposed method over the single measurement vectors (SMVs) problem. In particular, we find that our approach leads to a relaxed minimum separation condition and reduced number of required samples.

arXiv commentSuggestions of Professor Reinhard Heckel have been applied

References in corpus (12)

• The Convex Geometry of Linear Inverse Problems
• Atomic Norm Minimization for Modal Analysis from Random and Compressed Samples
• Super-Resolution MIMO Radar
• Two-Dimensional Super-Resolution via Convex Relaxation
• Exploiting Prior Information in Block Sparse Signals
• On the Error in Phase Transition Computations for Compressed Sensing
• Sample Complexity of Total Variation Minimization
• Living near the edge: A lower-bound on the phase transition of total variation minimization
• Vandermonde Decomposition of Multilevel Toeplitz Matrices with Application to Multidimensional Super-Resolution
• Distribution-aware Block-sparse Recovery via Convex Optimization
• Demixing Sines and Spikes Using Multiple Measurement Vectors
• Improved Recovery of Analysis Sparse Vectors in Presence of Prior Information

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• Timely and Painless Breakups: Off-the-grid Blind Message Recovery and Users' Demixing