Resolution-Aliasing Trade-off in Near-Field Localisation

Extremely Large-scale MIMO (XL-MIMO) systems operating in Near-Field (NF) introduce new degrees of freedom for accurate source localisation, but make dense arrays impractical. Sparse or distributed arrays can reduce hardware complexity while maintaining high resolution, yet sub-Nyquist spatial sampling introduces aliasing artefacts in the localisation ambiguity function. This paper presents a unified framework to jointly characterise resolution and aliasing in NF localisation and study the trade-off between the two. Leveraging the concept of local chirp spatial frequency, we derive analytical expressions linking array geometry and sampling density to the spatial bandwidth of the received field. We introduce two geometric tools--Critical Antenna Elements (CAEs) and the Non-Contributive Zone (NCZ)--to intuitively identify how individual antennas contribute to resolution and/or aliasing. Our analysis reveals that resolution and aliasing are not always strictly coupled, e.g., increasing the array aperture can improve resolution without necessarily aggravating aliasing. These results provide practical guidelines for designing NF arrays that optimally balance resolution and aliasing, supporting efficient XL-MIMO deployment.

Aliasing in Near-Field Array Ambiguity Functions: a Spatial Frequency-Domain Framework

Next-generation communication and localization systems increasingly rely on extremely large-scale arrays (XL-arrays), which promise unprecedented spatial resolution and new functionalities. These gains arise from their inherent operation in the near field (NF) regime, where the spherical nature of the wavefront can no longer be ignored; consequently, characterizing the ambiguity function -- which amounts to the matched beam pattern -- is considerably more challenging. Implementing very wide apertures with half-wavelength element spacing is costly and complex. This motivates thinning the array (removing elements), which introduces intricate aliasing structures, i.e., grating lobes. Whereas prior work has addressed this challenge using approximations tailored to specific array geometries, this paper develops a general framework that reveals the fundamental origins and geometric behavior of grating lobes in near-field ambiguity functions. Using a local spatial-frequency analysis of steering signals, we derive a systematic methodology to model NF grating lobes as aliasing artifacts, quantifying their structure on the AF, and providing design guidelines for XL-arrays that operate within aliasing-safe regions. We further connect our framework to established far-field principles. Finally, we demonstrate the practical value of the approach by deriving closed-form expressions for aliasing-free regions in canonical uniform linear arrays and uniform circular arrays.

Point Target Near-Field Bistatic Imaging: Chirp-Based Aliasing Analysis

This paper presents a chirp-based framework for characterising aliasing in a bistatic Near-Field (NF) imaging system equipped with multidimensional antenna arrays. Extending monostatic formulations, we derive closed-form expressions for the maximum spatial frequency, enabling the analytical derivations of the conditions for aliasing-free image reconstruction. The framework also provides a geometric interpretation of aliasing based on the antenna array geometry, target position, and antenna element spacing. Numerical results corroborate theoretical findings and show that the aliasing-free region enlarges with smaller antenna spacing, greater target range, lower array dimensionality, and smaller arrays. These results enable more effective design of bistatic NF imaging systems.

Chirp-Based Aliasing Analysis of Arrays in the Spherical Wavefront Regime

In antenna arrays, wave propagation modeling based on Euclidean principles is typically represented by steering vectors or signals. This paper provides a new, chirp-based, interpretation of steering vectors in the Spherical Wavefront Regime (SWR), establishing a relationship between the spatial spectrum of the received (resp. transmitted) signal and the geometry of the array and the source (resp. target). Leveraging the well-known sampling theorem, we analyze aliasing effects arising from spatial sampling with a finite number of antennas and understand how these effects degrade the Ambiguity Function (AF). Our framework provides geometric insight into these degradations, offering a deeper understanding of the non-space-invariant aliasing mechanisms in the SWR. The proposed approach is formulated for general antenna arrays and then instantiated to Circular Array and to Uniform Linear Array structures operating in Near Field conditions.

Grid Hopping: Accelerating Direct Estimation Algorithms for Multistatic FMCW Radar

This paper presents a novel signal processing technique, coined grid hopping, as well as an active multistatic Frequency-Modulated Continuous Wave (FMCW) radar system designed to evaluate its performance. The design of grid hopping is motivated by two existing estimation algorithms. The first one is the indirect algorithm estimating ranges and speeds separately for each received signal, before combining them to obtain location and velocity estimates. The second one is the direct method jointly processing the received signals to directly estimate target location and velocity. While the direct method is known to provide better performance, it is seldom used because of its high computation time. Our grid hopping approach, which relies on interpolation strategies, offers a reduced computation time while its performance stays on par with the direct method. We validate the efficiency of this technique on actual FMCW radar measurements and compare it with other methods.

Safe peeling for l0-regularized least-squares with supplementary material

We introduce a new methodology dubbed ``safe peeling'' to accelerate the resolution of L0-regularized least-squares problems via a Branch-and-Bound (BnB) algorithm. Our procedure enables to tighten the convex relaxation considered at each node of the BnB decision tree and therefore potentially allows for more aggressive pruning. Numerical simulations show that our proposed methodology leads to significant gains in terms of number of nodes explored and overall solving time.s show that our proposed methodology leads to significant gains in terms of number of nodes explored and overall solving time.