Browsing by Author "Del Galdo, Giovanni"

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An adaptively focusing measurement design for compressed sensing based doa estimation
(IEEE, 2015) Ibrahim, Mohamed; Roemer, Florian; Del Galdo, Giovanni
In this paper we propose an adaptive design strategy for the measurement matrix for applying Compressed Sensing (CS) to Direction Of Arrival (DOA) estimation with antenna arrays. Instead of choosing the coefficients of the compression matrix randomly, we propose a systematic design methodology for constructing a measurement matrix that focuses the array towards a specific area of interest and thereby achieves a superior DOA estimation performance. The focusing is performed in a sequential manner, i.e., we start with a uniform measurement design from which regions of interest can be extracted that the subsequent measurements then focus on. By continuously updating these target regions, gradual movement of the sources can also be tracked over time. Numerical results demonstrate that the focused measurements possess a superior SNR leading to significantly enhanced DOA estimates.
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.
Design and analysis of compressive antenna arrays for direction of arrival estimation
(Elsevier, 2017) Ibrahim, Mohamed; Ramireddy, Venkatesh; Lavrenko, Anastasia; König, Jonas; Römer, Florian; Landmann, Markus; Grossmann, Marcus; Del Galdo, Giovanni; S. Thomä, Reiner
In this paper we investigate the design of compressive antenna arrays for direction of arrival (DOA) estimation that aim to provide a larger aperture with a reduced hardware complexity by a linear combination of the antenna outputs to a lower number of receiver channels. We present a basic receiver architecture of such a compressive array and introduce a generic system model that includes different options for the hardware implementation. We then discuss the design of the analog combining network that performs the receiver channel reduction, and propose two design approaches. The first approach is based on the spatial correlation function which is a low-complexity scheme that in certain cases admits a closed-form solution. The second approach is based on minimizing the Cramer-Rao Bound (CRB) with the ´ constraint to limit the probability of false detection of paths to a pre-specified level. Our numerical simulations demonstrate the superiority of the proposed optimized compressive arrays compared to the sparse arrays of the same complexity and to compressive arrays with randomly chosen combining kernels.
DoA estimation with reflectarray according to single pixel camera principle
(IEEE, 2015) Skoblikov, Sergii; Ibrahim, Mohamed; Römer, Florian; S. Thomä, Reiner; Del Galdo, Giovanni
This paper suggests using a tunable reflectarray as a hardware source of Sensing Functions (SFs) for Direction of Arrival (DoA) estimation based on Compressed Sensing (CS). Reflectarray is much more scalable than a conventional antenna array. This higher scalability can be exploited to build a measurement hardware with large aperture and high number of degrees of freedom. We introduce the simplified reflectarray propagation model, based on which we propose a number of possible measurement architectures, for each of them we show how the Sensing Matrix (SM) will be defined. Finally, a typical non-sparse beampattern is obtained using numeric simulation.
Measurement matrix design for compressed sensing based time delay estimation
(IEEE, 2016) Roemer, Florian; Ibrahim, Mohamed; Franke, Norbert; Hadaschik, Niels; Eidloth, Andreas; Sackenreuter, Benjamin; Del Galdo, Giovanni
In this paper we study the problem of estimating the unknown delay(s) in a system where we receive a linear combination of several delayed copies of a known transmitted waveform. This problem arises in many applications such as timing-based localization or wireless synchronization. Since accurate delay estimation requires wideband signals, traditional systems need high-speed AD converters which poses a significant burden on the hardware implementation. Compressive sensing (CS) based system architectures that take measurements at rates significantly below the Nyquist rate and yet achieve accurate delay estimation have been proposed with the goal to alleviate the hardware complexity. In this paper, we particularly discuss the design of the measurement kernels based on a frequency-domain representation and show numerically that an optimized choice can outperform randomly chosen functionals in terms of the delay estimation accuracy.
On the design of the measurement matrix for compressed sensing based DOA estimation
(IEEE, 2015) Ibrahim, Mohamed; Roemer, Florian; Del Galdo, Giovanni
In this paper we investigate the design of the measurement matrix for applying Compressed Sensing (CS) to the problem of Direction Of Arrival (DOA) estimation with antenna arrays. So far, it has been suggested to choose the coefficients randomly since this choice satisfies the restricted isometry property (RIP) with a high probability. We demonstrate that this choice may be sub-optimal since it can result in an effective array with significant sidelobes and blind spots. The sidelobes are especially problematic when we use correlation-based greedy algorithms for the sparse recovery stage as they can lead to detecting spurious peaks. To address the problem, we introduce a design methodology for constructing a measurement matrix that mitigates these unwanted effects to achieve a better DOA estimation performance. Numerical results demonstrate the usefulness of our design.
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.
Temporal wireless synchronization with compressed opportunistic signals
(IEEE, 2016) Ibrahim, Mohamed; Roemer, Florian; Hadaschik, Niels; Tröger, Hans-Martin; Sackenreuter, Benjamin; Franke, Norbert; Robert, Joerg; Del Galdo, Giovanni
In this paper we introduce a wireless temporal synchronization scheme based on wideband signals of opportunity (SOO) such as DVB-T or LTE signals. Since these signals may not be decodable we show that it is necessary that one (reference) node broadcasts an excerpt of the SOO to all other nodes to provide a reference. However, the transmission of this reference signals requires a high bandwidth. Therefore, we propose to replace this transmission with a lower-bandwidth “compressed” version of this reference signal, using ideas from the field of compressed sensing (CS). We show that the high time resolution of the original wideband SOO can be maintained so that accurate temporal synchronization is possible. On the other hand, the compression leads to higher sidelobes in the correlation function which reduces the effective SNR. Therefore, the compression rate allows to control the trade-off between the required bandwidth and the SNR.