10 research outputs found
Low-rank Matrix Sensing With Dithered One-Bit Quantization
We explore the impact of coarse quantization on low-rank matrix sensing in
the extreme scenario of dithered one-bit sampling, where the high-resolution
measurements are compared with random time-varying threshold levels. To recover
the low-rank matrix of interest from the highly-quantized collected data, we
offer an enhanced randomized Kaczmarz algorithm that efficiently solves the
emerging highly-overdetermined feasibility problem. Additionally, we provide
theoretical guarantees in terms of the convergence and sample size
requirements. Our numerical results demonstrate the effectiveness of the
proposed methodology.Comment: arXiv admin note: substantial text overlap with arXiv:2308.0069
HDR Imaging With One-Bit Quantization
Modulo sampling and dithered one-bit quantization frameworks have emerged as
promising solutions to overcome the limitations of traditional
analog-to-digital converters (ADCs) and sensors. Modulo sampling, with its
high-resolution approach utilizing modulo ADCs, offers an unlimited dynamic
range, while dithered one-bit quantization offers cost-efficiency and reduced
power consumption while operating at elevated sampling rates. Our goal is to
explore the synergies between these two techniques, leveraging their unique
advantages, and to apply them to non-bandlimited signals within spline spaces.
One noteworthy application of these signals lies in High Dynamic Range (HDR)
imaging. In this paper, we expand upon the Unlimited One-Bit (UNO) sampling
framework, initially conceived for bandlimited signals, to encompass
non-bandlimited signals found in the context of HDR imaging. We present a novel
algorithm rigorously examined for its ability to recover images from one-bit
modulo samples. Additionally, we introduce a sufficient condition specifically
designed for UNO sampling to perfectly recover non-bandlimited signals within
spline spaces. Our numerical results vividly demonstrate the effectiveness of
UNO sampling in the realm of HDR imaging.Comment: arXiv admin note: text overlap with arXiv:2308.0069
Harnessing the Power of Sample Abundance: Theoretical Guarantees and Algorithms for Accelerated One-Bit Sensing
One-bit quantization with time-varying sampling thresholds (also known as
random dithering) has recently found significant utilization potential in
statistical signal processing applications due to its relatively low power
consumption and low implementation cost. In addition to such advantages, an
attractive feature of one-bit analog-to-digital converters (ADCs) is their
superior sampling rates as compared to their conventional multi-bit
counterparts. This characteristic endows one-bit signal processing frameworks
with what one may refer to as sample abundance. We show that sample abundance
plays a pivotal role in many signal recovery and optimization problems that are
formulated as (possibly non-convex) quadratic programs with linear feasibility
constraints. Of particular interest to our work are low-rank matrix recovery
and compressed sensing applications that take advantage of one-bit
quantization. We demonstrate that the sample abundance paradigm allows for the
transformation of such problems to merely linear feasibility problems by
forming large-scale overdetermined linear systems -- thus removing the need for
handling costly optimization constraints and objectives. To make the proposed
computational cost savings achievable, we offer enhanced randomized Kaczmarz
algorithms to solve these highly overdetermined feasibility problems and
provide theoretical guarantees in terms of their convergence, sample size
requirements, and overall performance. Several numerical results are presented
to illustrate the effectiveness of the proposed methodologies.Comment: arXiv admin note: text overlap with arXiv:2301.0346
Joint Waveform and Passive Beamformer Design in Multi-IRS-Aided Radar
Intelligent reflecting surface (IRS) technology has recently attracted a
significant interest in non-light-of-sight radar remote sensing. Prior works
have largely focused on designing single IRS beamformers for this problem. For
the first time in the literature, this paper considers multi-IRS-aided
multiple-input multiple-output (MIMO) radar and jointly designs the transmit
unimodular waveforms and optimal IRS beamformers. To this end, we derive the
Cramer-Rao lower bound (CRLB) of target direction-of-arrival (DoA) as a
performance metric. Unimodular transmit sequences are the preferred waveforms
from a hardware perspective. We show that, through suitable transformations,
the joint design problem can be reformulated as two unimodular quadratic
programs (UQP). To deal with the NP-hard nature of both UQPs, we propose
unimodular waveform and beamforming design for multi-IRS radar (UBeR) algorithm
that takes advantage of the low-cost power method-like iterations. Numerical
experiments illustrate that the MIMO waveforms and phase shifts obtained from
our UBeR algorithm are effective in improving the CRLB of DoA estimation
Quantized Phase-Shift Design of Active IRS for Integrated Sensing and Communications
Integrated sensing and communications (ISAC) is a spectrum-sharing paradigm
that allows different users to jointly utilize and access the crowded
electromagnetic spectrum. In this context, intelligent reflecting surfaces
(IRSs) have lately emerged as an enabler for non-line-of-sight (NLoS) ISAC.
Prior IRS-aided ISAC studies assume passive surfaces and rely on the
continuous-valued phase shift model. In practice, the phase-shifts are
quantized. Moreover, recent research has shown substantial performance benefits
with active IRS. In this paper, we include these characteristics in our
IRS-aided ISAC model to maximize the receive radar and communications
signal-to-noise ratios (SNR) subjected to a unimodular IRS phase-shift vector
and power budget. The resulting optimization is a highly non-convex unimodular
quartic optimization problem. We tackle this via a bi-quadratic transformation
to split the problem into two quadratic sub-problems that are solved using the
power iteration method. The proposed approach employs the M-ary unimodular
sequence design via relaxed power method-like iteration (MaRLI) to design the
quantized phase-shifts. As expected, numerical experiments demonstrate that our
active IRS-ISAC system design with MaRLI converges to a higher value of SNR
when we increase the number of IRS quantization bits
Submodular Optimization for Placement of Intelligent Reflecting Surfaces in Sensing Systems
Intelligent reflecting surfaces (IRS) and their optimal deployment are the
new technological frontier in sensing applications. Recently, IRS have
demonstrated potential in advancing target estimation and detection. While the
optimal phase-shift of IRS for different tasks has been studied extensively in
the literature, the optimal placement of multiple IRS platforms for sensing
applications is less explored. In this paper, we design the placement of IRS
platforms for sensing by maximizing the mutual information. In particular, we
use this criterion to determine an approximately optimal placement of IRS
platforms to illuminate an area where the target has a hypothetical presence.
After demonstrating the submodularity of the mutual information criteria, we
tackle the design problem by means of a constant-factor approximation algorithm
for submodular optimization. Numerical results are presented to validate the
proposed submodular optimization framework for optimal IRS placement with worst
case performance bounded to
Moving Target Detection via Multi-IRS-Aided OFDM Radar
An intelligent reflecting surface (IRS) consists of passive reflective
elements capable of altering impinging waveforms. The IRS-aided radar systems
have recently been shown to improve detection and estimation performance by
exploiting the target information collected via non-line-of-sight paths.
However, the waveform design problem for an IRS-aided radar has remained
relatively unexplored. In this paper, we consider a multi-IRS-aided orthogonal
frequency-division multiplexing (OFDM) radar and study the theoretically
achievable accuracy of target detection. In addition, we jointly design the
OFDM signal and IRS phase-shifts to optimize the target detection performance
via an alternating optimization approach. To this end, we formulate the IRS
phase-shift design problem as a unimodular bi-quadratic program which is
tackled by a computationally cost-effective approach based on power-method-like
iterations. Numerical experiments illustrate that our proposed joint design of
IRS phase-shifts and the OFDM code improves the detection performance in
comparison with conventional OFDM radar
Matrix Completion via Memoryless Scalar Quantization
We delve into the impact of memoryless scalar quantization on matrix
completion. We broaden our theoretical discussion to encompass the coarse
quantization scenario with a dithering scheme, where the only available
information for low-rank matrix recovery is few-bit low-resolution data. Our
primary motivation for this research is to evaluate the recovery performance of
nuclear norm minimization in handling quantized matrix problems without the use
of any regularization terms such as those stemming from maximum likelihood
estimation. We furnish theoretical guarantees for both scenarios: when access
to dithers is available during the reconstruction process, and when we have
access solely to the statistical properties of the dithers. Additionally, we
conduct a comprehensive analysis of the effects of sign flips and
prequantization noise on the recovery performance, particularly when the impact
of sign flips is quantified using the well-known Hamming distance in the upper
bound of recovery error.Comment: arXiv admin note: substantial text overlap with arXiv:2310.0322