2023/08/30 by Meghna Kalra, Kiryung Lee, Kalra, Meghna +1
Engineering · #FOS: Electrical engineering #Radar Systems and Signal Processing #Signal Processing (eess.SP) #Sparse and Compressive Sensing Techniques #Ultrasonics and Acoustic Wave Propagation #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2308.16265
openalex publication_date 2023/08/30 · openalex created_date 2023/09/03 · openalex updated_date 2026/07/28
We consider the problem of resolving overlapping pulses from noisy multi-snapshot measurements, which has been a problem central to various applications including medical imaging and array signal processing. ESPRIT algorithm has been used to estimate the pulse locations. However, existing theoretical analysis is restricted to ideal assumptions on signal and measurement models. We present a novel perturbation analysis that overcomes the previous theoretical limitation, which is derived without a stringent assumption on the signal model. Our unifying analysis applies to various sub-array designs of the ESPRIT algorithm. We demonstrate the usefulness of the perturbation analysis by specifying the result in two practical scenarios. In the first scenario, we quantify how the number of snapshots for stable recovery scales when the number of Fourier measurements per snapshot is sufficiently large. In the second scenario, we propose compressive blind array calibration by ESPRIT with random sub-arrays and provide the corresponding non-asymptotic error bound. Furthermore, we demonstrate that the empirical performance of ESPRIT corroborates the theoretical analysis through extensive numerical results.