Extremely large aperture arrays (ELAAs) introduce additional distance-domain degrees of freedom (DoF) in the electromagnetic near field, enabling a base station (BS) to spatially multiplex users sharing the same angular direction. Although these DoF have been characterized for continuous-aperture (CAP) channel models, it remains unclear how to sample such models to realize the maximum distance-domain DoF in practical, discrete arrays. We model the BS as a two-dimensional (2D) transmit (Tx) aperture of arbitrary shape and multiple collinear users as a linear receive (Rx) array, and we develop joint Tx/Rx sampling strategies that maximize the effective distance-domain DoF—the usable spatial resource in the distance dimension. Our method starts by analyzing the band-limited structure of the kernel of the channel correlation matrix, leading to a two-step sampling scheme. First, we sample the Tx aperture to maximize the kernel bandwidth, yielding a deterministic pattern governed by each element’s squared distance from the array center. Second, we sample the Rx (user) locations under a spacing condition derived via Toeplitz matrix analysis so that the effective distance-domain DoF fully matches the kernel bandwidth. We further obtain a closed-form threshold for the optimal spacing between adjacent collinear users, showing that the optimum depends only on the extreme edges of the Tx aperture, not on its detailed shape. Finally, we analyze and simulate the effects of the proposed sampling on spatial-multiplexing gains and distance-aware channel estimation performance.

Extremely large apertures in the near-field region unlock additional spatial resources in the distance domain, which enables the spatial multiplexing of multiple users even when they share the same angular direction—a capability unattainable in the far-field regime. A fundamental question remains unanswered: "What is the spatial degree of freedom of spatial multiplexing in the distance domain?"To address this, we investigate the spatial degree of freedom (DoF) in the distance domain of a large continuous aperture by considering the line-of-sight (LoS) channel between the aperture and a linear array, whose elements lie in the same direction but are located at different distances relative to the aperture. For simplicity of analysis, we consider the case where the linear array is in the broadside of the aperture. By reformulating the channel as an integral operator with a Hermitian convolution kernel, we derive a closed-form expression for the spatial DoF via the Fourier transform. Analytical and simulation results reveal that the spatial DoF in the distance domain of the aperture is predominantly determined by the aperture’s extreme boundaries rather than its detailed shape.

This paper proposes a novel design of multi-symbol unitary constellation for non-coherent single-input multiple-output (SIMO) communications over block Rayleigh fading channels. To facilitate the design and the detection of large unitary constellations at reduced complexity, the proposed constellations are constructed as the Cartesian product of independent amplitude and phase-shift-keying (PSK) vectors, and hence, can be iteratively detected. The amplitude vector is detected by exhaustive search, whose complexity is sufficiently low in short packet transmission scenarios. To detect the PSK vector, we use the posterior probability as a reliability criterion in the sorted decision-feedback differential detection (sort-DFDD), which results in near-optimal error performance for PSK symbols with equal modulation orders. This detector is called posteriori-based-reliability-sort-DFDD (PR-sort-DFDD) and has polynomial complexity. We also propose an improved detector called improved-PR-sort-DFDD to detect a more generalized PSK structure, i.e., PSK symbols with unequal modulation orders. This detector also approaches the optimal error performance with polynomial complexity. Simulation results show the merits of our proposed multi-symbol unitary constellation when compared to competing low-complexity unitary constellations.

In this paper, we propose a novel multi-symbol unitary constellation structure for non-coherent single-input multiple-output (SIMO) communications over block Rayleigh fading channels. To facilitate the design of large unitary constellations at reduced complexity, the proposed constellations are constructed as the Cartesian product of independent amplitude and phase-shift-keying (PSK) vectors. We exploit this structure to formulate an optimization problem to maximize the minimum distance, which has low complexity compared to optimal unitary constellations. Simulation results show that our proposed multi-symbol unitary constellation has higher minimum distance and better error performance than other low-complexity unitary constellations when using maximum likelihood (ML) detector.

In this paper, an energy-efficient precoding scheme is designed for multi-user visible light communication (VLC) systems in the context of physical layer security, where users' messages are kept mutually confidential. The design problem is shown to be non-convex fractional programming, therefore Dinkelbach algorithm and convex-concave procedure (CCCP) based on the first-order Taylor approximation are utilized to tackle the problem. Numerical results are performed to show the convergence behaviors and the performance of the proposed solution for different parameter settings.