In the paper, we consider the line spectral estimation problem in an unlimited sensing framework (USF), where a modulo analog-to-digital converter (ADC) is employed to fold the input signal back into a bounded interval before quantization. Such an operation is mathematically equivalent to taking the modulo of the input signal with respect to the interval. To overcome the noise sensitivity of higher-order difference-based methods, we explore the properties of the first-order difference of modulo samples, and develop two line spectral estimation algorithms based on the first-order difference, which are robust against noise. Specifically, we show that, with a high probability, the first-order difference of the original samples is equivalent to that of the modulo samples. By utilizing this property, line spectral estimation is solved via a robust sparse signal recovery approach. The second algorithms is built on our finding that, with a sufficiently high sampling rate, the first-order difference of the original samples can be decomposed as a sum of the first-order difference of the modulo samples and a sequence whose elements are confined to three possible values. This decomposition enables us to formulate the line spectral estimation problem as a mixed integer linear program that can be efficiently solved. Simulation results show that both proposed methods are robust against noise and achieve a significant performance improvement over the higher-order difference-based method. methods.

This paper characterizes the performance limits of optimal array designs using orthogonal and coherent waveforms for both linear and planar arrays. For orthogonal waveforms, we show that the single-target Cramér–Rao Bound (CRB) depends on the sum of the so-called spatial variances of the transmit (Tx) and receive (Rx) arrays, or equivalently, the spatial variance of the sum co-array weighted by the multiplicities of the virtual sensors. This reveals that CRB-optimal geometries are inherently redundant, highlighting a fundamental trade-off between mean squared error (MSE) and identifiability in parameter estimation. Moreover, we derive optimal Tx-Rx sensor allocations given a total sensor budget and show that unequal allocation (favoring the Rx) is optimal even for nonredundant arrays, questioning conventional designs. We extend our results to planar arrays, providing a new general condition that the spatial covariances of the Tx and Rx arrays should satisfy for the optimal waveforms to direct power in the target direction. Additionally, we establish a connection between Diophantine equations and array geometries with equal CRB, along with a constructive method for designing such arrays. Our work provides new guidelines for and insights into optimal array and waveform design with relevance in emerging active sensing multiple-input multiple-output systems.

This paper investigates the positioning of the pilot symbols, as well as the power distribution between the pilot and the communication symbols for the orthogonal time frequency space (OTFS) modulation scheme. We analyze the pilot placements that minimize the mean squared error (MSE) in estimating the channel taps. This allows us to identify two new pilot allocations for OTFS that save approximately 50% of the pilot overhead compared to existing allocations. In addition, we optimize the average channel capacity by adjusting the power distribution. We show that this leads to a significant increase in average capacity. The results provide valuable guidance for designing the OTFS parameters to achieve maximum capacity. Numerical simulations are performed to validate the findings.

Developing methods to process irregularly structured data is crucial in applications like gene-regulatory, brain, power, and socioeconomic networks. Graphs have been the go-to algebraic tool for modeling the structure via nodes and edges capturing their interactions, leading to the establishment of the fields of graph signal processing (GSP) and graph machine learning (GML). Key graph-aware methods include Fourier transform, filtering, sampling, as well as topology identification and spatiotemporal processing. Although versatile, graphs can model only pairwise dependencies in the data. To this end, topological structures such as simplicial and cell complexes have emerged as algebraic representations for more intricate structure modeling in data-driven systems, fueling the rapid development of novel topological-based processing and learning methods. This paper first presents the core principles of topological signal processing through the Hodge theory, a framework instrumental in propelling the field forward thanks to principled connections with GSP-GML. It then outlines advances in topological signal representation, filtering, and sampling, as well as inferring topological structures from data, processing spatiotemporal topological signals, and connections with topological machine learning. The impact of topological signal processing and learning is finally highlighted in applications dealing with flow data over networks, geometric processing, statistical ranking, biology, and semantic communication.

In this letter, we propose an analytical solution for recovering a low-rank positive semi-definite (PSD) matrix from its rank-one measurements. We show that by utilizing a set of structured measurement vectors, we can analytically determine the null space of this low-rank PSD matrix. Based on the result, the PSD matrix can be efficiently recovered. Our analysis shows that the proposed method only requires (N - K)(2K + 1)+ K ² measurements to guarantee exact recovery of the PSD matrix, where N and K respectively denote the dimension and the rank of the PSD matrix. Numerical results show that the proposed method achieves a considerable improvement over existing state-of-the-art methods in terms of both sample complexity and computational efficiency. Specifically, the proposed method helps improve the computational efficiency by an order of magnitude as compared with existing methods.

Phase-modulated continuous-wave (PMCW) radars offer better multiple antenna support and flexible waveform design. These radars, however, suffer from the high computational complexity of correlation processing used to obtain the range of targets, particularly due to the use of long code sequences. To address this, we exploit signal sparsity and propose an adaptive sliding block-based fast Fourier transform (FFT) correlator that selectively processes only the relevant range bins and dynamically aligns processing blocks using a time-shift parameter. This sliding mechanism minimizes boundary effects and reduces the number of blocks required for processing. The framework also incorporates external sensor data for context-aware range-bin selection and includes an analytical formulation for optimal block size selection. Simulations demonstrate that the proposed method preserves the signal-to-noise ratio (SNR) and target peaks while significantly reducing processing time. The effectiveness of the proposed method is demonstrated through numerical simulations.

Sparse array design is used to help reduce computational, hardware, and power requirements compared to uniform arrays while maintaining acceptable performance. Although minimizing the Cramér-Rao bound has been adopted previously for sparse sensing, it did not consider multiple targets and unknown target directions. To handle the unknown target directions when optimizing the Cramér-Rao bound, we propose to use the worst-case Cramér-Rao bound of two uncorrelated equal power sources with arbitrary angles. This new worst-case two-target Cramér-Rao bound metric has some resemblance to the peak sidelobe level metric which is commonly used in unknown multi-target scenarios. We cast the sensor selection problem for 3-D arrays using the worst-case two-target Cramér-Rao bound as a convex semi-definite program and obtain the binary selection by randomized rounding. We illustrate the proposed method through numerical examples, comparing it to solutions obtained by minimizing the single-target Cramér-Rao bound, minimizing the Cramér-Rao bound for known target angles, the concentric rectangular array and the boundary array. We show that our method selects a combination of edge and center elements, which contrasts with solutions obtained by minimizing the single-target Cramér-Rao bound. The proposed selections also exhibit lower peak sidelobe levels without the need for sidelobe level constraints.

This paper proposes a scalable method for identifying interactions in higher-order networks from observations of nodal processes. Finding such dependencies is important in many disciplines, including neuroscience, social influence modeling, and beyond. However, current approaches are either limited to extracting pairwise dependencies or struggle with scalability, as estimating higher-order dependencies becomes computationally prohibitive. To overcome these challenges, we introduce a tensorbased graph Volterra model that leverages low-rank decomposition techniques to estimate higher-order interactions efficiently. Our approach not only reduces computational and storage complexity but also acts as an implicit regularizer, improving network estimation in ill-posed settings. We validate our method through simulations and real data experiments, demonstrating competitive performance and enhanced scalability compared to existing techniques.

Ultrafast imaging, which uses unfocussed transmissions to form images, provides very high frame rates at the cost of low signal-to-noise ratio (SNR). This loss of SNR becomes especially apparent when imaging deeper structures. Ultrafast imaging is mostly used in combination with Doppler processing. Even if we apply tissue-separation filters, they lead to significant energy loss and decrease the SNR. Previous work showed that this loss in SNR and, hence, penetration depth can be partially regained using coded transmissions. However, these codes are mostly either standard or randomly generated and can be improved with a design rooted in an optimization scheme. To address this limitation, we design an optimized code tailored to ultrasound imaging with unfocused transmissions represented by a generalized encoding matrix in a linear signal model. We employ the minimization of the Cramér-Rao lower bound (CRB) over the unknown coding matrix as a way to optimize the code. Due to the high computational cost of the resulting optimization problems, we also introduce a trace-constraint optimization problem based on the Fisher information matrix (FIM). Simulation results show that the optimized code provides higher SNR in deep image regions than previously tested coding schemes such as the Barker code, albeit with a trade-off for decreased resolution. On the other hand, the application of least-squares QR (LSQR) mitigates this resolution degradation. Lastly, the optimized code was tested in simulations using a numerical model of a clinical transducer setting, demonstrating its potential for higher SNR in ultrafast Doppler imaging.

Ultrasonography could allow operator-independent examination and continuous monitoring of the carotid artery (CA) but normally requires complex and expensive transducers, especially for 3-D. By employing computational ultrasound imaging (cUSi), using an aberration mask and model-based reconstruction, a monitoring device could be constructed with a more affordable simple transducer design comprising only a few elements. We aim to apply the cUSi concept to create a CA monitoring system. The system’s possible configurations for the 2-D imaging case were explored using a linear array setup emulating a cUSi device in silico, followed by in vitro testing and in vivo CA imaging. Our study shows enhanced reconstruction performance with the use of an aberrating mask, improved lateral resolution through proper choice of the mask delay variation, and more accurate reconstructions using least-squares with QR (LSQR) decomposition compared to matched filtering (MF). Together, these advancements enable B-mode reconstruction and power Doppler imaging (PDI) of the CA with sufficient quality for monitoring using a configuration of 12 transceivers coupled with a random aberration mask with a maximum delay variation of four wave periods (WPs).

In this paper, we design Graph Neural Networks (GNNs) with attention mechanisms to tackle an important yet challenging nonlinear regression problem: massive network localization. We first review our previous network localization method based on Graph Convolutional Network (GCN), which can exhibit state-of-the-art localization accuracy, even under severe Non-Line-of-Sight (NLOS) conditions, by carefully preselecting a constant threshold for determining adjacency. As an extension, we propose a specially designed Attentional GNN (AGNN) model to resolve the sensitive thresholding issue of the GCN-based method and enhance the underlying model capacity. The AGNN comprises an Adjacency Learning Module (ALM) and Multiple Graph Attention Layers (MGALs), employing distinct attention architectures to systematically address the demerits of the GCN-based method, rendering it more practical for real-world applications. Comprehensive analyses are conducted to explain the superior performance of these methods, including a theoretical analysis of the AGNN's dynamic attention property and computational complexity, along with a systematic discussion of their robust characteristic against NLOS measurements. Extensive experimental results demonstrate the effectiveness of the GCN-based and AGNN-based network localization methods. Notably, integrating attention mechanisms into the AGNN yields substantial improvements in localization accuracy, approaching the fundamental lower bound and showing approximately 37% to 53% reduction in localization error compared to the vanilla GCN-based method across various NLOS noise configurations. Both methods outperform all competing approaches by far in terms of localization accuracy, robustness, and computational time, especially for considerably large network sizes.

This paper investigates jointly optimal array geometry and waveform designs for active sensing. Specifically, we focus on minimizing the Cramér-Rao lower bound (CRB) of the angle of a single target in white Gaussian noise. We first find that several array-waveform pairs can yield the same CRB by virtue of sequences with equal sums of squares, i.e., solutions to certain Diophantine equations. Furthermore, we show that under physical aperture and sensor number constraints, the CRB-minimizing receive array geometry is unique, whereas the transmit array can be chosen flexibly. We leverage this freedom to design a novel sparse array geometry that not only minimizes the single-target CRB given an optimal waveform, but also has a nonredundant and contiguous sum co-array—a desirable property when launching independent waveforms, with relevance also to the multi-target case.