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.