Browsing by Author "Alieiev, Roman"

Now showing 1 - 3 of 3

An analytical study of sparse recovery algorithms in presence of an off-grid source
(International Workshop on Compressed Sensing Applied to Radar (Co-SeRa), 2013) Römer, Florian; Alieiev, Roman; Ibrahim, Mohamed; Del Galdo, Giovanni; S. Thomä, R.
Direction of arrival (DOA) estimation has been an active field of research for many decades. If the field is modeled as a superposition of a few planar wavefronts, the DOA estimation problem can be expressed as a sparse recovery problem and the Compressed Sensing (CS) framework can be applied. Many powerful CS-based DOA estimation algorithms have been proposed in recent years. However, they all face one common problem. Although, the model is sparse in a continuous angular domain, to apply the CS framework we need to construct a finite dictionary by sampling this domain with a predefined sampling grid. Therefore, the target locations are almost surely not located exactly on a subset of these grid points. Early solutions to this problem include adaptively refining the grid around the candidate targets found with an initial, mismatched grid [1]. Recent papers try to model the mismatch error explicitly and fit it to the observed data either statistically [2] or by interpolating between grid points [3]. In this paper we take an analytical approach to investigate the effect of recovering the spectrum of a source not contained in the dictionary. Unlike earlier works on the sensitivity of compressed sensing to basis mismatch [4] that have provided a quantitative analysis of the approximation error, we focus on the shape of the resulting spectrum, considering one target source for simplicity. We show that the recovered spectrum is not sparse but it can be well approximated by the closest two dictionary atoms on the grid and their coefficients can be exploited to estimate the grid offset.
ON THE ESTIMATION OF GRID OFFSETS IN CS-BASED DIRECTION-OF-ARRIVAL ESTIMATION
(IEEE, 2014) Ibrahim, Mohamed; Römer, Florian; Alieiev, Roman; Del Galdo, Giovanni; S. Thomä, Reiner
Compressed Sensing (CS) has been recently applied to direction of arrival (DOA) estimation, leveraging the fact that a superposition of planar wavefronts corresponds to a sparse angular power spectrum. However, to apply the CS framework we need to construct a finite dictionary by sampling the angular domain with a predefined sampling grid. Therefore, the target locations are almost surely not located exactly on a subset of these grid points. This leads to a model mismatch which deteriorates the performance of the estimators. In this paper we take an analytical approach to investigate the effect of such grid offsets on the recovered spectra. We show that each off-grid source can be well approximated by the closest two neighboring points on the grid. We propose a simple and efficient scheme to estimate the grid offset for a single source or multiple well-separated sources. We also discuss a numerical procedure for the joint estimation of the grid offsets of closer sources. Simulation results demonstrate the effectiveness of the proposed methods.
Polarimetric compressive sensing based DOA estimation
(VDE, 2014) Roemer, Florian; Ibrahim, Mohamed; Alieiev, Roman; Landmann, Markus; S. Thomae, Reiner; Del Galdo, Giovanni
In this paper, we discuss direction of arrival (DOA) estimation based on the full polarimetric array manifold using a Compressive Sensing (CS)-based formulation. We first show that the existing non-polarimetric CS-based description of the DOA estimation problem can be extended to the polarimetric setting, giving rise to an amplitude vector that possesses a structured sparsity. We explain how DOAs can be estimated from this vector for incoming waves of arbitrary polarization. We then discuss the “gridding” problem, i.e., the effect of DOAs that are not on the sampling grid which was chosen for the discretization of the array manifold. We propose an estimator of these grid offsets which extends earlier work to the polarimetric setting. Numerical results demonstrate that the proposed scheme can achieve a DOA estimation accuracy close to the Cramér-Rao Bound for arbitrarily polarized waves.