Maxime Ferreira Da Costa

Trong Duy Tran, Maxime Ferreira Da Costa, Linh Trung Nguyen · cmu

Fake path injection is an emerging paradigm for inducing privacy over wireless networks. In this paper, fake paths are injected by the transmitters into a single-input multiple-output (SIMO) communication channel to obscure their physical location from an eavesdropper. The case where the receiver (Bob) and the eavesdropper (Eve) use a linear uniform array to locate the transmitter's (Alice) position is considered. A novel statistical privacy metric is defined as the ratio between the smallest (resp. largest) eigenvalues of Eve's (resp. Bob's) Cramér-Rao lower bound (CRB) on the SIMO channel parameters to assess the privacy enhancements. Leveraging the spectral properties of generalized Vandermonde matrices, bounds on the privacy margin of the proposed scheme are derived. Specifically, it is shown that the privacy margin increases quadratically in the inverse of the angular separation between the true and the fake paths under Eve's perspective. Numerical simulations validate the theoretical findings on CRBs and showcase the approach's benefit in terms of bit error rates achievable by Bob and Eve.

Trong Duy Tran, Maxime Ferreira Da Costa, Salah Eddine Elayoubi et al.

In this paper, we consider resource allocation for a collaborative integrated sensing and communication (ISAC) scenario, in which distributed smart devices can be scheduled to perform sensing and transmit their sensing features to a fusion center. The fusion center aims to perform classification tasks on the environment based on received features. A scalable networksensing framework is proposed to balance the performance of the sensing service with that of the classical enhanced Mobile Broadband (eMBB) service. We adopt a tractable theoretical metric, the discriminant gain, as a proxy for the classification goal. We formulate cross-layer optimization problems to maximize discriminant gain under constraints on energy consumption and eMBB communication quality for the independent and joint scheduling policies. The joint scheduling policy has considerably higher complexity than the independent scheduling policy, in exchange for better collaborative sensing performance. A simplified gain model is proposed to reduce the complexity and practicality of the joint scheduling policy. Both policies are obtained via successive convex approximation and parametric convex optimization. Extensive experiments are conducted to verify the goal-oriented framework and the two policies. It is demonstrated that the two policies outperform the baseline policies with both synthetic and realistic radar simulation datasets. The joint scheduling policy can exploit device correlations and thus performs better than the independent scheduling policy under strong correlations and strict communication constraints.

Santos Michelena, Maxime Ferreira Da Costa, José Picheral

Modeling signals as linear combinations of atoms from a dictionary is ubiquitous in modern signal processing. In the finite-dimensional setting, whenever atoms depend nonlinearly upon unknown parameters, the signal model is said to be separable. In this work, we study least-squares reconstruction of separable signals and establish a unified theoretical framework for their analysis. We introduce the unmixing metric, a distance that captures the distinct roles and sensitivities of linear and nonlinear parameters, and establish local convergence and stability guarantees under its topology. We then analyze variable projection from a geometric perspective, showing that it corresponds to restricting the optimization to the manifold of optimal linear parameters. This viewpoint provides a principled explanation for the improved algorithmic behavior of variable projection observed in practice, and produces sharp theoretical guarantees. The generic theory for separable problems is specialized to the case of point spread function (PSF) unmixing. We introduce a parametric notion of coherence and show that support separation directly controls both the size of the convergence region and the stability of recovery. Numerical experiments corroborate the theoretical predictions and demonstrate the practical relevance of the proposed framework.

Lei Lyu, Maxime Ferreira Da Costa, Urbashi Mitra

In this paper, an atomic hybrid sparse/diffuse (aHSD) channel model in the frequency domain is proposed. Based on a structural analysis of the resolvable paths and diffuse scattering statistics, the Hybrid Atomic-Least-Squares (HALS) algorithm is designed to estimate sparse/diffuse components with a combined atomic and $\ell_2$ regularization. A theoretical analysis of the Lagrange dual problem is conducted, and the conditions required for primal and dual solutions are provided, supporting an off-the-grid delay-time estimator. The Cramér--Rao Bound (CRB) analysis in this paper focuses on the estimation of the channel parameters, resulting in a bound on the aggregate channel. Lower and upper bounds for the CRB on parameters are derived as functions of the minimum separations between frequency parameters. Numerical results via simulations on synthetic and real data validate the efficacy of the HALS estimation strategy and show the improved predictive ability of the CRB analysis for the performance of HALS versus previously considered bounds.