Multicluster Design and Control of Large-Scale Affine Formations

Conventional affine formation control (AFC) empowers a network of agents with flexible but collective motions - a potential which has not yet been exploited for large-scale swarms. One of the key bottlenecks lies in the design of an interaction graph, characterized by the Laplacian-like stress matrix. Efficient and scalable design solutions often yield suboptimal solutions on various performance metrics, e.g., convergence speed and communication cost, to name a few. The current state-of-the-art algorithms for finding optimal solutions are computationally expensive and therefore not scalable. In this work, we propose a more efficient optimal design for any generic configuration, with the potential to further reduce complexity for a large class of nongeneric rotationally symmetric configurations. Furthermore, we introduce a multicluster control framework that offers an additional scalability improvement, enabling not only collective affine motions as in conventional AFC but also partially independent motions naturally desired for large-scale swarms. The overall design is compatible with a swarm size of several hundred agents with fast formation convergence, as compared to up to only a few dozen agents by existing methods. Experimentally, we benchmark the performance of our algorithm compared with several state-of-the-art solutions and demonstrate the capabilities of our proposed control strategies.

Joint Simplicial Complex Learning via Binary Linear Programming

Learning the topology of higher-order networks from data is a fundamental challenge in many signal processing and machine learning applications. Simplicial complexes provide a principled framework for modeling multi-way interactions, yet learning their structure is challenging due to the strong coupling across different simplicial levels imposed by the inclusion property. In this work, we propose a joint framework for simplicial complex learning that enforces the inclusion property through a linear constraint, enabling the formulation of the problem as a binary linear program. The objective function consists of a combination of smoothness measures across all considered simplicial levels, allowing for the incorporation of arbitrary smoothness criteria. This formulation enables the simultaneous estimation of edges and higher-order simplices within a single optimization problem. Experiments on simulated and real-world data demonstrate that the proposed joint approach outperforms hierarchical and greedy baselines, while more faithfully enforcing higher-order structural priors.

Robust Covariance-Based DoA Estimation under Weather-Induced Distortion

We investigate robust direction-of-arrival (DoA) estimation for sensor arrays operating in adverse weather conditions, where weather-induced distortions degrade estimation accuracy. Building on a physics-based $S$-matrix model established in prior work, we adopt a statistical characterization of random phase and amplitude distortions caused by multiple scattering in rain. Based on this model, we develop a measurement framework for uniform linear arrays (ULAs) that explicitly incorporates such distortions. To mitigate their impact, we exploit the Hermitian Toeplitz (HT) structure of the covariance matrix to reduce the number of parameters to be estimated. We then apply a generalized least squares (GLS) approach for calibration. Simulation results show that the proposed method effectively suppresses rain-induced distortions, improves DoA estimation accuracy, and enhances radar sensing performance in challenging weather conditions.

Graph Topology Identification Based on Covariance Matching

Graph topology identification (GTI) is a central challenge in networked systems, where the underlying structure is often hidden, yet nodal data are available. Conventional solutions to address these challenges rely on probabilistic models or complex optimization formulations, commonly suffering from non-convexity or requiring restrictive assumptions on acyclicity or positivity. In this paper, we propose a novel covariance matching (CovMatch) framework that directly aligns the empirical covariance of the observed data with the theoretical covariance implied by an underlying graph. We show that as long as the data-generating process permits an explicit covariance expression, CovMatch offers a unified route to topology inference. We showcase our methodology on linear structural equation models (SEMs), showing that CovMatch naturally handles both undirected and general sparse directed graphs - whether acyclic or positively weighted - without explicit knowledge of these structural constraints. Through appropriate reparameterizations, CovMatch simplifies the graph learning problem to either a conic mixed integer program for undirected graphs or an orthogonal matrix optimization for directed graphs. Numerical results confirm that, even for relatively large graphs, our approach efficiently recovers the true topology and outperforms standard baselines in accuracy. These findings highlight CovMatch as a powerful alternative to log-determinant or Bayesian methods for GTI, paving the way for broader research on learning complex network topologies with minimal assumptions.

BUILD with Precision: Bottom-Up Inference of Linear DAGs

Learning the structure of directed acyclic graphs (DAGs) from observational data is a central problem in causal discovery, statistical signal processing, and machine learning. Under a linear Gaussian structural equation model (SEM) with equal noise variances, the problem is identifiable and we show that the ensemble precision matrix of the observations exhibits a distinctive structure that facilitates DAG recovery. Exploiting this property, we propose BUILD (Bottom-Up Inference of Linear DAGs), a deterministic stepwise algorithm that identifies leaf nodes and their parents, then prunes the leaves by removing incident edges to proceed to the next step, exactly reconstructing the DAG from the true precision matrix. In practice, precision matrices must be estimated from finite data, and ill-conditioning may lead to error accumulation across BUILD steps. As a mitigation strategy, we periodically re-estimate the precision matrix (with less variables as leaves are pruned), trading off runtime for enhanced robustness. Reproducible results on challenging synthetic benchmarks demonstrate that BUILD compares favorably to state-of-the-art DAG learning algorithms, while offering an explicit handle on complexity.

Jointly optimal array geometries and waveforms in active sensing: New insights into array design via the Cramér-Rao bound

This paper investigates jointly optimal array geometry and waveform designs for active sensing. Specifically, we focus on minimizing the Cram\'er-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.

Topological Signal Processing and Learning: Recent Advances and Future Challenges

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.

Tracking Network Dynamics using Probabilistic State-Space Models

This paper introduces a probabilistic approach for tracking the dynamics of unweighted and directed graphs using state-space models (SSMs). Unlike conventional topology inference methods that assume static graphs and generate point-wise estimates, our method accounts for dynamic changes in the network structure over time. We model the network at each timestep as the state of the SSM, and use observations to update beliefs that quantify the probability of the network being in a particular state. Then, by considering the dynamics of transition and observation models through the update and prediction steps, respectively, the proposed method can incorporate the information of real-time graph signals into the beliefs. These beliefs provide a probability distribution of the network at each timestep, being able to provide both an estimate for the network and the uncertainty it entails. Our approach is evaluated through experiments with synthetic and real-world networks. The results demonstrate that our method effectively estimates network states and accounts for the uncertainty in the data, outperforming traditional techniques such as recursive least squares.

Line Spectral Estimation with Unlimited Sensing

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 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 be 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.

Optimal Pilot Design for OTFS in Linear Time-Varying Channels

This paper investigates the positioning of the pilot symbols, as well as the power distribution between the pilot and the communication symbols in the OTFS modulation scheme. We analyze the pilot placements that minimize the mean squared error (MSE) in estimating the channel taps. In addition, we optimize the average channel capacity by adjusting the power balance. 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.