Son Duong

Son T. Duong, Tho Le-Ngoc

Extremely large aperture arrays operating in the near-field regime unlock additional spatial resources, which can be exploited to simultaneously serve multiple users even when they share the same angular direction. This work investigates the distance-domain degrees of freedom (DoF), defined as the DoF when a user varies only its distance to the base station and not the angle. To obtain the distance-domain DoF, we investigate a line-of-sight (LoS) channel between a base station (source) and observation region representing users. The base station is modeled as a large two-dimensional transmit (Tx) array with an arbitrary shape. The observation region is modeled as an arbitrarily long linear receive (Rx) array, where elements are collinearly aligned but located at varying distances from the Tx array. We assume that both the Tx and Rx arrays have continuous apertures with an infinite number of elements and infinitesimal spacing, which establishes an upper bound for the distance-domain DoF in the case of a finite number of elements. First, we analyze an ideal case where the Tx array is a single piece and the Rx array is on the broadside of the Tx array. By reformulating the channel as an integral operator with a Hermitian convolution kernel, we derive a closed-form expression for the distance-domain DoF via the Fourier transform. Our analysis shows that the distance-domain DoF is predominantly determined by the extreme boundaries of both the Tx and Rx arrays rather than their detailed interior structure. We further extend the framework to non-broadside configurations by employing a projection method that converts the problem to an equivalent broadside case. Finally, we extend the analytical framework to modular arrays and show the distance-domain DoF gain over a single-piece array under a fixed total physical length.

Ngoc N. Tran, Son Duong, Hoang Phan et al.

Self-supervised learning aims to extract meaningful features from unlabeled data for further downstream tasks. In this paper, we consider classification as a downstream task in phase 2 and develop rigorous theories to realize the factors that implicitly influence the general loss of this classification task. Our theories signify that sharpness-aware feature extractors benefit the classification task in phase 2 and the existing data shift between the ideal (i.e., the ideal one used in theory development) and practical (i.e., the practical one used in implementation) distributions to generate positive pairs also remarkably affects this classification task. Further harvesting these theoretical findings, we propose to minimize the sharpness of the feature extractor and a new Fourier-based data augmentation technique to relieve the data shift in the distributions generating positive pairs, reaching Sharpness & Shift-Aware Contrastive Learning (SSA-CLR). We conduct extensive experiments to verify our theoretical findings and demonstrate that sharpness & shift-aware contrastive learning can remarkably boost the performance as well as obtaining more robust extracted features compared with the baselines.