Array Gain for Pinching-Antenna Systems (PASS)

Pinching antennas is a novel flexible-antenna technology, which can be realized by employing small dielectric particles on a waveguide. The aim of this letter is to characterize the array gain achieved by pinching-antenna systems (PASS). A closed-form upper bound on the array gain is derived by fixing the inter-antenna spacing. Asymptotic analyses of this bound are conducted by considering an infinitely large number of antennas, demonstrating the existence of an optimal number of antennas that maximizes the array gain. The relationship between the array gain and inter-antenna spacing is further explored by incorporating the effect of mutual coupling. It is proven that there also exists an optimal inter-antenna spacing that maximizes the array gain. Numerical results demonstrate that by optimizing the number of antennas and inter-antenna spacing, PASS can achieve a significantly larger array gain than conventional fixed-location antenna systems.

Secure Beamforming for Continuous Aperture Array (CAPA) Systems

Continuous aperture array (CAPA) is considered a promising technology for 6G networks, offering the potential to fully exploit spatial DoFs and achieve the theoretical limits of channel capacity. This paper investigates the performance gain of a CAPA-based downlink secure transmission system, where multiple legitimate user terminals (LUTs) coexist with multiple eavesdroppers (Eves). The system's secrecy performance is evaluated using a weighted secrecy sum-rate (WSSR) under a power constraint. We then propose two solutions for the secure current pattern design. The first solution is a block coordinate descent (BCD) optimization method based on fractional programming, which introduces a continuous-function inversion theory corresponding to matrix inversion in the discrete domain. This approach derives a closed-form expression for the optimal source current pattern. Based on this, it can be found that the optimal current pattern is essentially a linear combination of the channel spatial responses, thus eliminating the need for complex integration operations during the algorithm's optimization process. The second solution is a heuristic algorithm based on Zero-Forcing (ZF), which constructs a zero-leakage current pattern using the channel correlation matrix. It further employs a water-filling approach to design an optimal power allocation scheme that maximizes the WSSR. In high SNR regions, this solution gradually approaches the first solution, ensuring zero leakage while offering lower computational complexity. Simulation results demonstrate that: 1) CAPA-based systems achieve better WSSR compared to discrete multiple-input multiple-output systems. 2) The proposed methods, whether optimization-based or heuristic, provide significant performance improvements over existing state-of-the-art Fourier-based discretization methods, while considerably reducing computational complexity.

Cramér-Rao Bound Optimization for Near-Field Sensing with Continuous-Aperture Arrays

A Cram\'er-Rao bound (CRB) optimization framework for near-field sensing (NISE) with continuous-aperture arrays (CAPAs) is proposed. In contrast to conventional spatially discrete arrays (SPDAs), CAPAs emit electromagnetic (EM) probing signals through continuous source currents for target sensing, thereby exploiting the full spatial degrees of freedom (DoFs). The maximum likelihood estimation (MLE) method for estimating target locations in the near-field region is developed. To evaluate the NISE performance with CAPAs, the CRB for estimating target locations is derived based on continuous transmit and receive array responses of CAPAs. Subsequently, a CRB minimization problem is formulated to optimize the continuous source current of CAPAs. This results in a non-convex, integral-based functional optimization problem. To address this challenge, the optimal structure of the source current is derived and proven to be spanned by a series of basis functions determined by the system geometry. To solve the CRB minimization problem, a low-complexity subspace manifold gradient descent (SMGD) method is proposed, leveraging the derived optimal structure of the source current. Our simulation results validate the effectiveness of the proposed SMGD method and further demonstrate that i)~the proposed SMGD method can effectively solve the CRB minimization problem with reduced computational complexity, and ii)~CAPA achieves a tenfold improvement in sensing performance compared to its SPDA counterpart, due to full exploitation of spatial DoFs.

CAPA: Continuous-Aperture Arrays for Revolutionizing 6G Wireless Communications

In this paper, a novel continuous-aperture array (CAPA)-based wireless communication architecture is proposed, which relies on an electrically large aperture with a continuous current distribution. First, an existing prototype of CAPA is reviewed, followed by the potential benefits and key motivations for employing CAPAs in wireless communications. Then, three practical hardware implementation approaches for CAPAs are introduced based on electronic, optical, and acoustic materials. Furthermore, several beamforming approaches are proposed to optimize the continuous current distributions of CAPAs, which are fundamentally different from those used for conventional spatially discrete arrays (SPDAs). Numerical results are provided to demonstrate their key features in low complexity and near-optimality. Based on these proposed approaches, the performance gains of CAPAs over SPDAs are revealed in terms of channel capacity as well as diversity-multiplexing gains. Finally, several open research problems in CAPA are highlighted.

Optimal Beamforming for Multi-User Continuous Aperture Array (CAPA) Systems

The optimal beamforming design for multi-user continuous aperture array (CAPA) systems is proposed. In contrast to conventional spatially discrete array (SPDA), the beamformer for CAPA is a continuous function rather than a discrete vector or matrix, rendering beamforming optimization a non-convex integral-based functional programming. To address this challenging issue, we first derive the closed-form optimal structure of the CAPA beamformer for maximizing generic system utility functions, by using the Lagrangian duality and the calculus of variations. The derived optimal structure is a linear combination of the continuous channel responses for CAPA, with the linear weights determined by the channel correlations. As a further advance, a monotonic optimization method is proposed for obtaining globally optimal CAPA beamforming based on the derived optimal structure. More particularly, a closed-form fixed-point iteration is proposed to obtain the globally optimal solution to the power minimization problem for CAPA beamforming. Furthermore, based on the optimal structure, the low-complexity maximum ratio transmission (MRT), zero-forcing (ZF), and minimum mean-squared error (MMSE) designs for CAPA beamforming are derived. It is theoretically proved that: 1) the MRT and ZF designs are asymptotically optimal in low and high signal-to-noise ratio (SNR) regimes, respectively, and 2) the MMSE design is optimal for signal-to-leakage-plus-noise ratio (SLNR) maximization. Our numerical results validate the effectiveness of the proposed designs and reveal that: i) CAPA achieves significant communication performance gain over SPDA, and ii) the MMSE design achieves nearly optimal performance in most cases, while the MRT and ZF designs achieve nearly optimal performance in specific cases.

Performance of Linear Receive Beamforming for Continuous Aperture Arrays (CAPAs)

The performance of linear receive beamforming in continuous aperture array (CAPA)-based uplink communications is analyzed. Continuous linear beamforming techniques are proposed for CAPA receivers under the criteria of maximum-ratio combining (MRC), zero-forcing (ZF), and minimum mean-square error (MMSE). i) For MRC beamforming, a closed-form expression for the beamformer is derived to maximize per-user signal power, and the achieved uplink rate and mean-square error (MSE) in detecting received data symbols are analyzed. ii) For ZF beamforming, a closed-form beamformer is derived using channel correlation to eliminate interference, with a function space interpretation demonstrating its optimality in maximizing signal power while ensuring zero inter-user interference. iii) For MMSE beamforming, it is proven to be the optimal linear receive approach for CAPAs in terms of maximizing per-user rate and minimizing MSE. A closed-form expression for the MMSE beamformer is then derived, along with the achievable sum-rate and sum-MSE. The proposed linear beamforming techniques are then compared with those for conventional spatially discrete arrays (SPDAs). Analytical and numerical results indicate that: i) for both CAPAs and SPDAs, the considered linear beamformers can be represented as weighted sums of each user's spatial response, with weights determined by channel correlation; ii) CAPAs achieve higher sum-rates and lower sum-MSEs than SPDAs under ZF and MMSE beamforming; and iii) SPDAs may outperform CAPAs with MRC beamforming in interference-dominated scenarios.

Beamforming Optimization for Continuous Aperture Array (CAPA)-based Communications

The beamforming optimization in continuous aperture array (CAPA)-based multi-user communications is studied. In contrast to conventional spatially discrete antenna arrays, CAPAs can exploit the full spatial degrees of freedoms (DoFs) by emitting information-bearing electromagnetic (EM) wave through continuous source current distributed across the aperture. Nevertheless, such operation renders the beamforming optimization problem as a non-convex integral-based functional programming problem, which is challenging for conventional discrete optimization methods. A couple of low-complexity approaches are proposed to solve the functional programming problem. 1) Calculus of variations (CoV)-based approach: Closed-form structure of the optimal continuous source patterns are derived based on CoV, inspiring a low-complexity integral-free iterative algorithm for solving the functional programming problem. 2) Correlation-based zero-forcing (Corr-ZF) approach: Closed-form ZF source current patterns that completely eliminate the interuser interference are derived based on the channel correlations. By using these patterns, the original functional programming problem is transformed to a simple power allocation problem, which can be solved using the classical water-filling approach with reduced complexity. Our numerical results validate the effectiveness of the proposed designs and reveal that: i) compared to the state-of-the-art Fourier-based discretization approach, the proposed CoV-based approach not only improves communication performance but also reduces computational complexity by up to hundreds of times for large CAPA apertures and high frequencies, and ii) the proposed Corr-ZF approach achieves asymptotically optimal performance compared to the CoV-based approach.

Diversity and Multiplexing for Continuous Aperture Array (CAPA)-Based Communications

The performance of multiplexing and diversity achieved by continuous aperture arrays (CAPAs) over fading channels is analyzed. Angular-domain fading models are derived for CAPA-based multiple-input single-output (MISO), single-input multiple-output (SIMO), and multiple-input multiple-output (MIMO) channels using the Fourier relationship between the spatial response and its angular-domain counterpart. Building on these models, angular-domain transmission frameworks are proposed to facilitate CAPA-based communications, under which the performance of multiplexing and diversity is analyzed. 1) For SIMO and MISO channels, closed-form expressions are derived for the average data rate (ADR) and outage probability (OP). Additionally, asymptotic analyses are performed in the high signal-to-noise ratio (SNR) regime to unveil the maximal multiplexing gain and maximal diversity gain. The diversity-multiplexing trade-off (DMT) is also characterized, along with the array gain within the DMT framework. 2) For MIMO channels, high-SNR approximations are derived for the ADR and OP, based on which the DMT and associated array gain are revealed. The performance of CAPAs is further compared with that of conventional spatially discrete arrays (SPDAs) to highlight the superiority of CAPAs. The analytical and numerical results demonstrate that: i) compared to SPDAs, CAPAs achieve a lower OP and higher ADR, resulting in better spectral efficiency; ii) CAPAs achieve the same DMT as SPDAs with half-wavelength antenna spacing while attaining a larger array gain; and iii) CAPAs achieve a better DMT than SPDAs with antenna spacing greater than half a wavelength.

Near-Field Sensing: A Low-Complexity Wavenumber-Domain Method

A novel low-complexity wavenumber-domain method is proposed for near-field sensing (NISE). Specifically, the power-concentrated region of the wavenumber-domain channels is related to the target position in a non-linear manner. Based on this observation, a bi-directional convolutional neural network (BiCNN)-based approach is proposed to capture such a relationship, thereby facilitating low-complexity target localization. This method enables direct and gridless target localization using only a limited bandwidth and a single antenna array. Simulation results demonstrate that: 1) during the offline training phase, the proposed BiCNN method can learn to localize the target with fewer trainable parameters compared to the naive neural network architectures; and 2) during the online implementation phase, the BiCNN method can spend 100x less time while maintaining comparable performance to the conventional two-dimensional multiple signal classification (MUSIC) algorithms.

A Primer on Near-Field Communications for Next-Generation Multiple Access

Multiple-antenna technologies are advancing toward the development of extremely large aperture arrays and the utilization of extremely high frequencies, driving the progress of next-generation multiple access (NGMA). This evolution is accompanied by the emergence of near-field communications (NFC), characterized by spherical-wave propagation, which introduces additional range dimensions to the channel and enhances system throughput. In this context, a tutorial-based primer on NFC is presented, emphasizing its applications in multiuser communications and multiple access (MA). The following areas are investigated: \romannumeral1) the commonly used near-field channel models are reviewed along with their simplifications under various near-field conditions. \romannumeral2) Building upon these models, the information-theoretic capacity limits of NFC-MA are analyzed, including the derivation of sum-rate capacity and capacity region, and their upper limits for both downlink and uplink scenarios. \romannumeral3) A detailed investigation of near-field multiuser beamforming design is presented, offering low-complexity and effective NFC-MA design methodologies in both the spatial and wavenumber (angular) domains. Throughout these investigations, near-field MA is compared with its far-field counterpart to highlight its superiority and flexibility in terms of interference management, thereby laying the groundwork for achieving NGMA.