arXiv subjects

Marius Pesavento

Publications and source records attributed to Marius Pesavento.

At least 19 recordsLinked to original sources

arXiv2026

Ambiguity Analysis and Design of Sparse Arrays via Generalized Vandermonde Rank Conditions

Sparse linear arrays obtained by thinning a uniform linear array (ULA) achieve large effective apertures with a reduced number of physical sensors and have become a key enabling technology across radar, sonar, communications, and integrated sensing and communications. The price of thinning, however, is the emergence of ambiguities in the array manifold: distinct sets of directions of arrival that produce identical sensor measurements, precluding unique identification of multiple sources. Conventional sparse-array design criteria, based on beampattern shaping or estimation-performance optimization, do not fully capture how multiple steering vectors interact jointly to produce such ambiguities. This paper develops a scalable algebraic framework for the multi-source identifiability analysis of thinned ULAs. By relating the rank deficiency of the generalized Vandermonde matrix associated with the sparse steering matrix to that of a thinned Toeplitz matrix, and further to a rank condition on an augmented full-ULA steering matrix with prescribed generators, we obtain a systematic characterization of the ambiguity sets in large sparse arrays together with constructive design guidelines for ambiguity-free geometries. Algebraic and numerical examples demonstrate that the proposed framework characterizes ambiguity sets at scales well beyond the practical reach of previous sparse-array design and synthesis methods

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arXiv2026

Hybrid Downlink Beamforming with Outage Constraints under Imperfect CSI using Model-Driven Deep Learning

We consider energy-efficient multi-user hybrid downlink beamforming (BF) and power allocation under imperfect channel state information (CSI) and probabilistic outage constraints. In this domain, classical optimization methods resort to computationally costly conic optimization problems. Meanwhile, generic deep network (DN) architectures lack interpretability and require large training data sets to generalize well. In this paper, we therefore propose a lightweight model-aided deep learning architecture based on a greedy selection algorithm for analog beam codewords. The architecture relies on an instance-adaptive augmentation of the signal model to estimate the impact of the CSI error. To learn the DN parameters, we derive a novel and efficient implicit representation of the nested constrained BF problem and prove sufficient conditions for the existence of the corresponding gradient. In the loss function, we utilize an annealing-based approximation of the outage compared to conventional quantile-based loss terms. This approximation adaptively anneals towards the exact probabilistic constraint depending on the current level of quality of service (QoS) violation. Simulations validate that the proposed DN can achieve the nominal outage level under CSI error due to channel estimation and channel compression, while allocating less power than benchmarks. Thereby, a single trained model generalizes to different numbers of users, QoS requirements and levels of CSI quality. We further show that the adaptive annealing-based loss function can accelerate the training and yield a better power-outage trade-off.

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arXiv2024

Sequential Maximum-Likelihood Estimation of Wideband Polynomial-Phase Signals on Sensor Array

This paper presents a novel sequential estimator for the direction-of-arrival and polynomial coefficients of wideband polynomial-phase signals impinging on a sensor array. Addressing the computational challenges of Maximum-likelihood estimation for this problem, we propose a method leveraging random sampling consensus (RANSAC) applied to the time-frequency spatial signatures of sources. Our approach supports multiple sources and higher-order polynomials by employing coherent array processing and sequential approximations of the Maximum-likelihood cost function. We also propose a low-complexity variant that estimates source directions via angular domain random sampling. Numerical evaluations demonstrate that the proposed methods achieve Cram\'er-Rao bounds in challenging multi-source scenarios, including closely spaced time-frequency spatial signatures, highlighting their suitability for advanced radar signal processing applications.

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arXiv2024

Adaptive Anomaly Detection in Network Flows with Low-Rank Tensor Decompositions and Deep Unrolling

Anomaly detection (AD) is increasingly recognized as a key component for ensuring the resilience of future communication systems. While deep learning has shown state-of-the-art AD performance, its application in critical systems is hindered by concerns regarding training data efficiency, domain adaptation and interpretability. This work considers AD in network flows using incomplete measurements, leveraging a robust tensor decomposition approach and deep unrolling techniques to address these challenges. We first propose a novel block-successive convex approximation algorithm based on a regularized model-fitting objective where the normal flows are modeled as low-rank tensors and anomalies as sparse. An augmentation of the objective is introduced to decrease the computational cost. We apply deep unrolling to derive a novel deep network architecture based on our proposed algorithm, treating the regularization parameters as learnable weights. Inspired by Bayesian approaches, we extend the model architecture to perform online adaptation to per-flow and per-time-step statistics, improving AD performance while maintaining a low parameter count and preserving the problem's permutation equivariances. To optimize the deep network weights for detection performance, we employ a homotopy optimization approach based on an efficient approximation of the area under the receiver operating characteristic curve. Extensive experiments on synthetic and real-world data demonstrate that our proposed deep network architecture exhibits a high training data efficiency, outperforms reference methods, and adapts seamlessly to varying network topologies.

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arXiv2024

Decentralized Singular Value Decomposition for Large-scale Distributed Sensor Networks

This article studies the problem of decentralized Singular Value Decomposition (d-SVD), which is fundamental in various signal processing applications. Two scenarios are considered depending on the availability of the data matrix under consideration. In the first scenario, the matrix of interest is row-wisely available in each local node in the network. In the second scenario, the matrix of interest implicitly forms an outer product from two different series of measurements. By combining the lightweight local rational function approximation approach with parallel averaging consensus algorithms, two d-SVD algorithms are proposed to cope with the two aforementioned scenarios. We evaluate the proposed algorithms using two application examples: decentralized sensor localization via low-rank matrix completion and decentralized passive radar detection. Moreover, a novel and non-trivial truncation technique, which employs a representative vector that is orthonormal to the principal signal subspace, is proposed to further reduce the communication cost associated with the d-SVD algorithms. Simulation results show that the proposed d-SVD algorithms converge to the centralized solution with reduced communication cost compared to those facilitated with the state-of-the-art decentralized power method.

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arXiv2024

Gridless Parameter Estimation in Partly Calibrated Rectangular Arrays

Spatial frequency estimation from a mixture of noisy sinusoids finds applications in various fields. While subspace-based methods offer cost-effective super-resolution parameter estimation, they demand precise array calibration, posing challenges for large antennas. In contrast, sparsity-based approaches outperform subspace methods, especially in scenarios with limited snapshots or correlated sources. This study focuses on direction-of-arrival (DOA) estimation using a partly calibrated rectangular array with fully calibrated subarrays. A gridless sparse formulation leveraging shift invariances in the array is developed, yielding two competitive algorithms under the alternating direction method of multipliers (ADMM) and successive convex approximation frameworks, respectively. Numerical simulations show the superior error performance of our proposed method, particularly in highly correlated scenarios, compared to the conventional subspace-based methods. It is demonstrated that the proposed formulation can also be adopted in the fully calibrated case to improve the robustness of the subspace-based methods to the source correlation. Furthermore, we provide a generalization of the proposed method to a more challenging case where a part of the sensors is unobservable due to failures.

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arXiv2024

A tensor model for the calibration of air-coupled ultrasonic sensor arrays in 3D imaging

Arrays of ultrasonic sensors are capable of 3D imaging in air and an affordable supplement to other sensing modalities, such as radar, lidar, and camera, i.e. in heterogeneous sensing systems. However, manufacturing tolerances of air-coupled ultrasonic sensors may lead to amplitude and phase deviations. Together with artifacts from imperfect knowledge of the array geometry, there are numerous factors that can impair the imaging performance of an array. We propose a reference-based calibration method to overcome possible limitations. First, we introduce a novel tensor signal model to capture the characteristics of piezoelectric ultrasonic transducers (PUTs) and the underlying multidimensional nature of a multiple-input multiple-output (MIMO) sensor array. Second, we formulate and solve an optimization problem based on this model to obtain the calibrated parameters of the array. Third, we assess both our model and the commonly used analytic model using real data from a 3D imaging experiment. The experiment reveals that our array response model we learned with calibration data yields an imaging performance similar to that of the analytic array model, which requires perfect array geometry information.

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arXiv2023

Maximum A Posteriori Direction-of-Arrival Estimation via Mixed-Integer Semidefinite Programming

We propose a joint sparse maximum a posteriori (MAP) estimator for DOA estimation from multiple snapshots, reformulated as a mixed-integer semidefinite program (MISDP). This enables efficient computation of globally optimal solutions using off-the-shelf MISDP solvers based on the branch-and-bound method. Unlike other nonconvex approaches for joint sparse recovery, such as the greedy methods and sparse Bayesian learning techniques, it provides a solution with an optimality assessment even with early termination. Additionally, we present a more scalable approximate solution approach for the MISDP problem based on randomized rounding. Numerical simulations demonstrate the improved threshold behavior, resolution, and robustness of our proposed method against popular DOA estimation methods. In particular, the proposed method applied with the randomized rounding algorithm exhibits a superior estimation performance at a significantly reduced running time, compared to the deterministic maximum likelihood (DML) estimator.

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arXiv2023

Coordinated Sum-Rate Maximization in Multicell MU-MIMO with Deep Unrolling

Coordinated weighted sum-rate maximization in multicell MIMO networks with intra- and intercell interference and local channel state at the base stations is recognized as an important yet difficult problem. A classical, locally optimal solution is obtained by the weighted minimum mean squared error (WMMSE) algorithm which facilitates a distributed implementation in multicell networks. However, it often suffers from slow convergence and therefore large communication overhead. To obtain more practical solutions, the unrolling/unfolding of traditional iterative algorithms gained significant attention. In this work, we demonstrate a complete unfolding of the WMMSE algorithm for transceiver design in multicell MU-MIMO interference channels with local channel state information. The resulting architecture termed GCN-WMMSE applies ideas from graph signal processing and is agnostic to different wireless network topologies, while exhibiting a low number of trainable parameters and high efficiency w.r.t. training data. It significantly reduces the number of required iterations while achieving performance similar to the WMMSE algorithm, alleviating the overhead in a distributed deployment. Additionally, we review previous architectures based on unrolling the WMMSE algorithm and compare them to GCN-WMMSE in their specific applicable domains.

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arXiv2023

Extended Successive Convex Approximation for Phase Retrieval with Dictionary Learning

Phase retrieval aims at reconstructing unknown signals from magnitude measurements of linear mixtures. In this paper, we consider the phase retrieval with dictionary learning problem, which includes an additional prior information that the measured signal admits a sparse representation over an unknown dictionary. The task is to jointly estimate the dictionary and the sparse representation from magnitude-only measurements. To this end, we study two complementary formulations and develop efficient parallel algorithms by extending the successive convex approximation framework using a smooth majorization. The first algorithm is termed compact-SCAphase and is preferable in the case of less diverse mixture models. It employs a compact formulation that avoids the use of auxiliary variables. The proposed algorithm is highly scalable and has reduced parameter tuning cost. The second algorithm, referred to as SCAphase, uses auxiliary variables and is favorable in the case of highly diverse mixture models. It also renders simple incorporation of additional side constraints. The performance of both methods is evaluated when applied to blind sparse channel estimation from subband magnitude measurements in a multi-antenna random access network. Simulation results demonstrate the efficiency of the proposed techniques compared to state-of-the-art methods.

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arXiv2022

Three more Decades in Array Signal Processing Research: An Optimization and Structure Exploitation Perspective

The signal processing community currently witnesses the emergence of sensor array processing and Direction-of-Arrival (DoA) estimation in various modern applications, such as automotive radar, mobile user and millimeter wave indoor localization, drone surveillance, as well as in new paradigms, such as joint sensing and communication in future wireless systems. This trend is further enhanced by technology leaps and availability of powerful and affordable multi-antenna hardware platforms. The history of advances in super resolution DoA estimation techniques is long, starting from the early parametric multi-source methods such as the computationally expensive maximum likelihood (ML) techniques to the early subspace-based techniques such as Pisarenko and MUSIC. Inspired by the seminal review paper Two Decades of Array Signal Processing Research: The Parametric Approach by Krim and Viberg published in the IEEE Signal Processing Magazine, we are looking back at another three decades in Array Signal Processing Research under the classical narrowband array processing model based on second order statistics. We revisit major trends in the field and retell the story of array signal processing from a modern optimization and structure exploitation perspective. In our overview, through prominent examples, we illustrate how different DoA estimation methods can be cast as optimization problems with side constraints originating from prior knowledge regarding the structure of the measurement system. Due to space limitations, our review of the DoA estimation research in the past three decades is by no means complete. For didactic reasons, we mainly focus on developments in the field that easily relate the traditional multi-source estimation criteria and choose simple illustrative examples.

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arXiv2022

Decentralized Eigendecomposition for Online Learning over Graphs with Applications

In this paper, the problem of decentralized eigenvalue decomposition of a general symmetric matrix that is important, e.g., in Principal Component Analysis, is studied, and a decentralized online learning algorithm is proposed. Instead of collecting all information in a fusion center, the proposed algorithm involves only local interactions among adjacent agents. It benefits from the representation of the matrix as a sum of rank-one components which makes the algorithm attractive for online eigenvalue and eigenvector tracking applications. We examine the performance of the proposed algorithm in two types of important application examples: First, we consider the online eigendecomposition of a sample covariance matrix over the network, with application in decentralized Direction-of-Arrival (DoA) estimation and DoA tracking applications. Then, we investigate the online computation of the spectra of the graph Laplacian that is important in, e.g., Graph Fourier Analysis and graph dependent filter design. We apply our proposed algorithm to track the spectra of the graph Laplacian in static and dynamic networks. Simulation results reveal that the proposed algorithm outperforms existing decentralized algorithms both in terms of estimation accuracy as well as communication cost.

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arXiv2021

Ambiguities in Direction-of-Arrival Estimation with Linear Arrays

In this paper, we present a novel approach to compute ambiguities in thinned uniform linear arrays, i.e., sparse non-uniform linear arrays, via a mixed-integer program. Ambiguities arise when there exists a set of distinct directions-of-arrival, for which the corresponding steering matrix is rank-deficient and are associated with nonunique parameter estimation. Our approach uses Young tableaux for which a submatrix of the steering matrix has a vanishing determinant, which can be expressed through vanishing sums of unit roots. Each of these vanishing sums then corresponds to an ambiguous set of directions-of-arrival. We derive a method to enumerate such ambiguous sets using a mixed-integer program and present results on several examples.

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arXiv2021

Recovery under Side Constraints

This paper addresses sparse signal reconstruction under various types of structural side constraints with applications in multi-antenna systems. Side constraints may result from prior information on the measurement system and the sparse signal structure. They may involve the structure of the sensing matrix, the structure of the non-zero support values, the temporal structure of the sparse representationvector, and the nonlinear measurement structure. First, we demonstrate how a priori information in form of structural side constraints influence recovery guarantees (null space properties) using L1-minimization. Furthermore, for constant modulus signals, signals with row-, block- and rank-sparsity, as well as non-circular signals, we illustrate how structural prior information can be used to devise efficient algorithms with improved recovery performance and reduced computational complexity. Finally, we address the measurement system design for linear and nonlinear measurements of sparse signals. Moreover, we discuss the linear mixing matrix design based on coherence minimization. Then we extend our focus to nonlinear measurement systems where we design parallel optimization algorithms to efficiently compute stationary points in the sparse phase retrieval problem with and without dictionary learning.

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arXiv2021

Probability of Resolution of MUSIC and g-MUSIC: An Asymptotic Approach

In this article, the outlier production mechanism of the conventional Multiple Signal Classification (MUSIC) and the g-MUSIC Direction-of-Arrival (DoA) estimation technique is investigated using tools from Random Matrix Theory (RMT). A general Central Limit Theorem (CLT) is derived that allows to analyze the asymptotic stochastic behavior of eigenvector-based cost functions in the asymptotic regime where the number of snapshots and the number of antennas increase without bound at the same rate. Furthermore, this CLT is used to provide an accurate prediction of the resolution capabilities of the MUSIC and the g-MUSIC DoA estimation method. The finite dimensional distribution of the MUSIC and the g-MUSIC cost function is shown to be asymptotically jointly Gaussian distributed in the asymptotic regime.

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arXiv2019

Inexact Block Coordinate Descent Algorithms for Nonsmooth Nonconvex Optimization

In this paper, we propose an inexact block coordinate descent algorithm for large-scale nonsmooth nonconvex optimization problems. At each iteration, a particular block variable is selected and updated by inexactly solving the original optimization problem with respect to that block variable. More precisely, a local approximation of the original optimization problem is solved. The proposed algorithm has several attractive features, namely, i) high flexibility, as the approximation function only needs to be strictly convex and it does not have to be a global upper bound of the original function; ii) fast convergence, as the approximation function can be designed to exploit the problem structure at hand and the stepsize is calculated by the line search; iii) low complexity, as the approximation subproblems are much easier to solve and the line search scheme is carried out over a properly constructed differentiable function; iv) guaranteed convergence of a subsequence to a stationary point, even when the objective function does not have a Lipschitz continuous gradient. Interestingly, when the approximation subproblem is solved by a descent algorithm, convergence of a subsequence to a stationary point is still guaranteed even if the approximation subproblem is solved inexactly by terminating the descent algorithm after a finite number of iterations. These features make the proposed algorithm suitable for large-scale problems where the dimension exceeds the memory and/or the processing capability of the existing hardware. These features are also illustrated by several applications in signal processing and machine learning, for instance, network anomaly detection and phase retrieval.

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arXiv2019

Coordinated Hybrid Precoding for Interference Exploitation in Heterogeneous Networks

We consider a downlink multiuser massive MIMO system comprising multiple heterogeneous base stations with hybrid precoding architectures. To enhance the energy efficiency of the network, we propose a novel coordinated hybrid precoding technique, where the coordination between the base stations is aimed at exploiting interference as opposed to mitigating it as per conventional approaches. We formulate an optimization problem to compute the coordinated hybrid precoders that minimize the total transmit power while fulfilling the required quality of service at each user. Furthermore, we devise a low-complexity suboptimal precoding scheme to compute approximate solutions of the precoding problem. The simulation results reveal that the proposed coordinated hybrid precoding yields superior performance when compared to the conventional hybrid precoding schemes.

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arXiv2019

Interference Exploitation-based Hybrid Precoding with Robustness Against Phase Errors

Hybrid analog-digital precoding significantly reduces the hardware costs in massive MIMO transceivers when compared to fully-digital precoding at the expense of increased transmit power. In order to mitigate the above shortfall, we use the concept of constructive interference-based precoding, which has been shown to offer significant transmit power savings when compared with the conventional interference suppression-based precoding in fully-digital multiuser MIMO systems. Moreover, in order to circumvent the potential quality-of-service degradation at the users due to the hardware impairments in the transmitters, we judiciously incorporate robustness against such vulnerabilities in the precoder design. Since the undertaken constructive interference-based robust hybrid precoding problem is nonconvex with infinite constraints and thus difficult to solve optimally, we decompose the problem into two subtasks, namely, analog precoding and digital precoding. In this paper, we propose an algorithm to compute the optimal constructive interference-based robust digital precoders. Furthermore, we devise a scheme to facilitate the implementation of the proposed algorithm in a low-complexity and distributed manner. We also discuss block-level analog precoding techniques. Simulation results demonstrate the superiority of the proposed algorithm and its implementation scheme over the state-of-the-art methods.

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