This paper proposes a goal-oriented design framework for Integrated Sensing and Communications (ISAC) at the network layer. Devices equipped with dual-functional radar and communication (DFRC) transceivers that jointly perform a sensing task and carry data traffic are considered. The goal of the sensing application is to maximize the classification accuracy, while the network aims to preserve throughput for the enhanced Mobile Broadband (eMBB) service and to respect energy constraints. A cross-layer optimization problem that adapts the lower layer parameters (sensing power and scheduling policy) for maximizing the classification accuracy, while respecting constraints related to the available resources (eMBB throughput, device’s maximal power, and total energy), is formulated. A tractable relaxation of the problem is proposed, yielding an approximately optimal policy that is computable by solving successive convex optimization problems. Our numerical experiments, conducted both on a synthetic Gaussian mixture dataset and on a radar simulation dataset, show the superiority of our goal-oriented scheme policy to classical ISAC schemes.

Sketching consists of reducing the dimensionality of data samples, generally by summarizing their essential features, such as retaining a small number of empirical moments. The reduced representation is called a sketch. In this paper, a Preconditioned Gradient Descent algorithm (PGD) is proposed to estimate the parameter of mixture models (MM) in arbitrary dimensions by minimizing the non-convex quadratic loss between the sketch and the characteristic function of an MM of varying parameters. Preconditioning is introduced to dynamically adapt the descent direction to the local landscape of the objective function, accelerating convergence, with no computational overhead per iteration compared with vanilla GD. An analysis of the linear convergence rate of PGD is conducted, and numerical simulations showcase the method's effectiveness, particularly when the weight of the classes is unbalanced or when a substantial number of data samples is available.

This paper tackles the problem of distributed sensing from a goal-oriented communications perspective. The case of sensors sampling sources in the environment and conveying the collected information to a fusion center over a wireless channel is considered. Herein, the objective of the communications is to achieve a reliable estimation of the sources, while preserving network resources. The fusion center task is formulated as a joint distributed sensing problem, where a scheduling policy has to be designed to optimize the applicative goal. Two distinct goals are considered: a) when the objective is to achieve the best possible estimation of the sources given a communication resource constraint; b) when the objective is to minimize the communication resource to estimate the sources up to a pre-determined precision. For both cases, the optimal scheduling policy is formulated as the solution to a constrained optimization problem. Greedy iterative algorithms are proposed to efficiently solve those problems for the particular case of independent sources. Numerical results illustrate the tradeoff between achievable estimation accuracy and resource consumption, and provide insights on the impact of the network structure on the achievable performance.

Harnessing a block-sparse prior to recover signals through underdetermined linear measurements has been extensively shown to allow exact recovery in conditions where classical compressed sensing would provably fail. We exploit this result to propose a novel private communication framework where the secrecy is achieved by transmitting instances of an unidentifiable compressed sensing problem over a public channel. The legitimate receiver can attempt to overcome this ill-posedness by leveraging secret knowledge of a block structure that was used to encode the transmitter’s message. We study the privacy guarantees of this communication protocol to a single transmission, and to multiple transmissions without refreshing the shared secret. Additionally, we propose an algorithm for an eavesdropper to learn the block structure via the method of moments and highlight the privacy benefits of this framework through numerical experiments.

Herein, an atomic norm based method for accurately estimating the location and orientation of a target from millimeter-wave multi-input-multi-output (MIMO) orthogonal frequency-division multiplexing (OFDM) signals is presented. A novel virtual channel matrix is introduced and an algorithm to ex-tract localization-relevant channel parameters from its atomic norm decomposition is designed. Then, based on the extended invariance principle, a weighted least squares problem is pro-posed to accurately recover the location and orientation using both line-of-sight and non-line-of-sight channel information. Numerical results highlight performance improvements over a prior method and the resultant performance nearly achieves the Cramér-Rao lower bound.

Super-resolution estimation is the problem of recovering a stream of spikes (point sources) from the noisy observation of a few numbers of its first trigonometric moments. The performance of super-resolution is recognized to be intimately related to the separation between the spikes to recover. A novel notion of stability of the Fisher information matrix (FIM) of the super-resolution problem is introduced when the minimal eigenvalue of the FIM is not asymptotically vanishing. The regime where the minimal separation is inversely proportional to the number of acquired moments is considered. It is shown that there is a separation threshold above which the eigenvalues of the FIM can be bounded by a quantity that does not depend on the number of moments. The proof relies on characterizing the connection between the stability of the FIM and a generalization of the Beurling–Selberg box approximation problem.

Atomic norm minimization is a convex optimization framework to recover point sources from a subset of their low-pass observations, or equivalently the underlying frequencies of a spectrally-sparse signal. When the amplitudes of the sources are positive, a positive atomic norm can be formulated, and exact recovery can be ensured without imposing a separation between the sources, as long as the number of observations is greater than the number of sources. However, the classic formulation of the atomic norm requires to solve a semidefinite program involving a linear matrix inequality of a size on the order of the signal dimension, which can be prohibitive. In this letter, we introduce a novel “compressed” semidefinite program, which involves a linear matrix inequality of a reduced dimension on the order of the number of sources. We guarantee the tightness of this program under certain conditions on the operator involved in the dimensionality reduction. Finally, we apply the proposed method to direction finding over sparse arrays based on second-order statistics and achieve significant computational savings.

The stability of spike deconvolution, which aims at recovering point sources from their convolution with a point spread function (PSF), is known to be related to the separation between those sources. When the observations are noisy, it is critical to ensure support stability, where the deconvolution does not lead to spurious, or oppositely, missing estimates of the point sources. In this paper, we study the resolution limit of stably recovering the support of two closely located point sources using the Beurling-LASSO estimator, which is a convex optimization approach based on total variation regularization. We establish a sufficient separation criterion between the sources, depending only on the PSF, above which the Beurling-LASSO estimator is guaranteed to return a stable estimate of the point sources, with the same number of estimated elements as that of the ground truth. Our result highlights the impact of PSF on the resolution limit in the noisy setting, which was not evident in previous studies of the noiseless setting. Towards the end, we show that the same resolution limit applies to resolving two close-located sources in conjunction of other well-separated sources.

It is now well understood that convex programming can be used to estimate the frequency components of a spectrally sparse signal from 2m+1 uniform temporal measurements. It is conjectured that a phase transition on the success of the total-variation regularization occurs when the distance between the spectral components of the signal to estimate crosses 1/m. We prove the necessity part of this conjecture by demonstrating that this regularization can fail whenever the spectral distance of the signal of interest is asymptotically equal to 1/m.

The line spectral estimation problem consists in recovering the frequencies of a complex valued time signal that is assumed to be sparse in the spectral domain from its discrete observations. As opposed to discretization-based methods for inverse problems, line spectral estimation reconstructs signals whose spectral supports lie continuously in the Fourier domain. If recent advances have shown that atomic norm relaxation produces highly robust estimates in this context, the computational cost of this approach remains, however, the major flaw for its application to practical systems. In this work, we aim to bridge the complexity issue by studying the atomic norm minimization problem from low dimensional projection of the signal samples. We derive conditions on the sub-sampling matrix under which the partial atomic norm can be expressed by a low-dimensional semidefinite program. Moreover, we illustrate the tightness of this relaxation by showing that it is possible to recover the original signal in poly-logarithmic time for two specific sub-sampling patterns.

Super-resolution theory aims to estimate the discrete components lying in a continuous space that constitute a sparse signal with optimal precision. This work investigates the potential of recent super-resolution techniques for spectral estimation in multi-rate sampling systems. It shows that, under the existence of a common supporting grid, and under a minimal separation constraint, the frequencies of a spectrally sparse signal can be exactly jointly recovered from the output of a semidefinite program (SDP). The algorithmic complexity of this approach is discussed, and an equivalent SDP of minimal dimension is derived by extending the Gram parametrization properties of sparse trigonometric polynomials.