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.

Near-Field Sensing Enabled Predictive Beamforming: From Estimation to Tracking

A near-field sensing (NISE) enabled predictive beamforming framework is proposed to facilitate wireless communications with high-mobility channels. Unlike conventional far-field sensing, which only captures the angle and the radial velocity of the user, NISE enables the estimation of the full motion state, including additional distance and transverse velocity information. Two full-motion state sensing approaches are proposed based on the concepts of estimation and tracking, respectively. 1)AGD-AO approach: The full motion state of the user is estimated within a single CPI. In particular, the gradient descent is adopted to estimate the transverse and radial velocities of the user based on the maximum likelihood criteria, while the distance and the angle are calculated by the kinematic model. In this process, moment estimations are leveraged to adaptively tune the step size, thereby leading to a smoother and faster gradient descent. 2) EKF approach: The full motion state of the user is tracked across multiple CPIs. Based on the noisy measurements in multiple CPIs, the EKF iteratively predicts and updates the current motion state to achieve a low tracking error. Based on the obtained full motion state, the beam prediction, and Doppler frequency compensation can be carried out with minimum pilot overhead. Numerical results are provided to validate the effectiveness and efficiency of the proposed approach compared to the conventional far-field predictive beamforming and feedback-based approaches. It is also revealed that: 1)the proposed AGD-AO can achieve stable descending with small gradients, thereby accelerating convergence; 2) compared to far-field predictive beamforming and feedback-based schemes, both of the proposed methods exhibit superior performance; and 3) by incorporating multiple CPIs, the EKF method exhibits greater robustness in low SNR regions.

Hybrid Beamforming Design for Near-Field ISAC with Modular XL-MIMO

A novel modular extremely large-scale multiple-input-multiple-output (XL-MIMO) integrated sensing and communication (ISAC) framework is proposed in this paper. We consider a downlink ISAC scenario and exploit the modular array architecture to enhance the communication spectral efficiency and sensing resolution while reducing the channel modeling complexity by employing the hybrid spherical and planar wavefront model. Considering the hybrid digital-analog structure inherent to modular arrays, we formulate a joint analog-digital beamforming design problem based on the communication spectral efficiency and sensing signal-to-clutter-plus-noise ratio (SCNR). By exploring the structural similarity of the communication and sensing channels, it is proved that the optimal transmit covariance matrix lies in the subspace spanned by the subarray response vectors, yielding a closed-form solution for the optimal analog beamformer. Consequently, the joint design problem is transformed into a low-dimensional rank-constrained digital beamformer optimization. We first propose a manifold optimization method that directly optimizes the digital beamformer on the rank-constrained Stiefel manifold. Additionally, we develop an semidefinite relaxation (SDR)-based approach that relaxes the rank constraint and employ the randomization technique to obtain a near-optimal solution. Simulation results demonstrate the effectiveness of the proposed modular XL-MIMO ISAC framework and algorithms.

Near-Field Localization and Sensing with Large-Aperture Arrays: From Signal Modeling to Processing

The signal processing community is currently witnessing a growing interest in near-field signal processing, driven by the trend towards the use of large aperture arrays with high spatial resolution in the fields of communication, localization, sensing, imaging, etc. From the perspective of localization and sensing, this trend breaks the basic far-field assumptions that have dominated the array signal processing research in the past, presenting new challenges and promising opportunities.