(l1,l2)-RIP and Projected Back-Projection Reconstruction for Phase-Only Measurements

This letter analyzes the performances of a simple reconstruction method, namely the Projected Back-Projection (PBP), for estimating the direction of a sparse signal from its phase-only (or amplitude-less) complex Gaussian random measurements, i.e., an extension of one-bit compressive sensing to the complex field. To study the performances of this algorithm, we show that complex Gaussian random matrices respect, with high probability, a variant of the Restricted Isometry Property (RIP) relating to the l1 -norm of the sparse signal measurements to their l2 -norm. This property allows us to upper-bound the reconstruction error of PBP in the presence of phase noise. Monte Carlo simulations are performed to highlight the performance of our approach in this phase-only acquisition model when compared to error achieved by PBP in classical compressive sensing.Comment: 4 pages, 2 figure

One Bit to Rule Them All : Binarizing the Reconstruction in 1-bit Compressive Sensing

This work focuses on the reconstruction of sparse signals from their 1-bit measurements. The context is the one of 1-bit compressive sensing where the measurements amount to quantizing (dithered) random projections. Our main contribution shows that, in addition to the measurement process, we can additionally reconstruct the signal with a binarization of the sensing matrix. This binary representation of both the measurements and sensing matrix can dramatically simplify the hardware architecture on embedded systems, enabling cheaper and more power efficient alternatives. Within this framework, given a sensing matrix respecting the restricted isometry property (RIP), we prove that for any sparse signal the quantized projected back-projection (QPBP) algorithm achieves a reconstruction error decaying like O(m-1/2)when the number of measurements m increases. Simulations highlight the practicality of the developed scheme for different sensing scenarios, including random partial Fourier sensing.Comment: ITWIST 202

An Ultra-wideband Battery-less Positioning System for Space Applications

An ultra-wide bandwidth (UWB) remote-powered positioning system for potential use in tracking floating objects inside space stations is presented. It makes use of battery-less tags that are powered-up and addressed through wireless power transfer in the UHF band and embed an energy efficient pulse generator in the 3-5 GHz UWB band. The system has been mounted on the ESA Mars Rover prototype to demonstrate its functionality and performance. Experimental results show the feasibility of centimeter-level localization accuracy at distances larger than 10 meters, with the capability of determining the position of multiple tags using a 2W-ERP power source in the UHF RFID frequency band.Comment: Published in: 2019 IEEE International Conference on RFID Technology and Applications (RFID-TA

One bit at a time : the use of quantized compressive sensing in radar signal processing

This thesis studies the harsh quantization of radar signals. More specifically, what can be achieved in terms of localization of targets using FMCW radars from 1-bit dithered measurements and processing. The first part of this thesis leverages the framework of Quantized Compressive Sensing to achieve high quality localizations using coarse 1-bit measurements from an FMCW radar. The gain provided by the added dither is highlighted through simulations and actual radar measurements and are compared with the developed reconstruction bounds. Range and angle estimations are achieved using the PBP and QIHT algorithms. The second part highlights some difficulties inherent to adding a random dither to radar signals and in response, studies an alternative way of dithering the measurements by altering instead their phases. This method, compared to the additive case, is shown to be a viable alternative in the search for an implementation of 1-bit quantization of radar signal that has theoretical guarantees and is cost-effective to implement. This new way of dithering radar signals is compared using Monte-Carlo simulations against its additive counter-part and using actual radar data. This alternative way of dithering is linked to the Phase-Only acquisition, that only measures the phase of complex signals, and its reconstruction performances are studied through the lens of the guarantees provided to PBP using the (l1,l2 )-Restricted Isometry Property. This property is proved for complex Gaussian random matrices. The thesis does not finish by the study of yet another way of acquiring a quantized version of a signal but by studying the quantization of the processing itself. Indeed, using low resolution processing could enable more power-efficient implementations. To that end, we study the reconstruction guarantees of the Projected Back Projection algorithm in the setting where the back-projection used is a 1-bit quantized version with additive dithering of the one used in high resolution processing. We show a uniform bound on the l2-reconstruction that behaves as O(m^-2 ). This study is then extended to the case of back-projection operators that have a factorized representation. These factorized representations, among which the FFT is the most well-known, can often be computed efficiently thanks to their sparse and factorized structures. This thesis shows that in cases where either the power or the amount of data that one can use for the estimation is limited, lowering the individual resolution of the measurements and possibly of the processing, can allow for better results than sub-sampling those high-resolution measurements to fit within the limitations. This was shown throughout the thesis using both theory and simulations often accompanied by real radar measurements.(FSA - Sciences de l'ingénieur) -- UCL, 202

Proceedings of the first edition of the International Symposium on Computational Sensing (ISCS23)

The International Symposium on Computational Sensing (ISCS) brings together researchers from optical microscopy, electron microscopy, RADAR, astronomical imaging, biomedical imaging, remote sensing, and signal processing. With a particular focus on applications and demonstrators, the purpose of this symposium is to be a forum where researchers in computational sensing working in seemingly unrelated applications can learn, discover, and exchange on their new findings and challenges. This 3-day symposium in the heart of Europe features 6 keynotes speakers and is open to extended abstracts for scientific presentations and show-and-tell demonstrations.Comment: This is the proceedings of the first edition of ISCS which took place in June 2023 in Luxembourg city. More info at ISCS2023.co

Keep the phase! Signal recovery in phase-only compressive sensing

We demonstrate that a sparse signal can be estimated from the phase of complex random measurements, in a "phase-only compressive sensing" (PO-CS) scenario. With high probability and up to a global unknown amplitude, we can perfectly recover such a signal if the sensing matrix is a complex Gaussian random matrix and the number of measurements is large compared to the signal sparsity. Our approach consists in recasting the (non-linear) PO-CS scheme as a linear compressive sensing model. We built it from a signal normalization constraint and a phase-consistency constraint. Practically, we achieve stable and robust signal direction estimation from the basis pursuit denoising program. Numerically, robust signal direction estimation is reached at about twice the number of measurements needed for signal recovery in compressive sensing

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Localization of Rotating Targets Using a Monochromatic Continuous-Wave Radar

A simple and efficient localization method for rotating objects is introduced. The estimation of the position is performed using only a continuous-wave radar with multiple receiving antennas. The method relies on the establishment of a linear relation between the interelement phase shifts and frequency, which is exploitable in the near-to-intermediate field. The method is introduced, and its independence with respect to the shape of the target demonstrated. Monte Carlo simulations are performed to study the variance of the proposed estimator. An experimental validation is carried out with a rotating cylinder and shows good agreement with simulations

Unlimited Sampling Radar: Life Below the Quantization Noise

peer reviewedIn this paper, the trade-off between the quantization noise and the dynamic range of ADCs used to acquire radar signals is revisited using the Unlimited Sensing Framework (USF) in a practical setting. Trade-offs between saturation and resolution arise in many applications, like radar, where sensors acquire signals which exhibit a high degree of variability in amplitude. To solve this issue, we propose the use of the co-design approach of the USF which acquires folded version of the signal of interest and leverages its structure to reconstruct it after its acquisition. We demonstrate that this method outperforms other standard acquisition methods for Doppler radars. We show this theoretically by providing mathematical insights on why the perfect reconstruction of Doppler signals from their folded measurements is possible. Our findings are corroborated via numerical simulations. Taking our theory all the way to practice, we develop a prototype USF-enabled Doppler Radar and show the clear benefits of our method. In each experiment, we show that using the USF increases sensitivity compared to a classic acquisition approach.U-AGR-7061 - C20/IS/1499710/SENCOM (01/09/2021 - 31/08/2024) - OTTERSTEN Björ