design beamformers

This paper addresses the high-complexity power minimization problem for joint base station (BS) and reconfigurable intelligent surface (RIS) beamforming in RIS-aided downlink multi-group multicast systems. To tackle this, we propose the Alternating Multicast Beamforming (AMBF) algorithm. Our key contribution lies in the natural decoupling of the joint optimization into two subproblems: a BS-side multicast quality-of-service (QoS) problem and an RIS-side passive multicast max-min fairness (MMF) problem. For the latter, we design a semi-closed-form solver based on the projected subgradient algorithm (PSA), achieving linear time complexity. Overall, AMBF’s computational complexity scales linearly with both the number of RIS elements and BS antennas. Under guaranteed user QoS constraints, AMBF significantly reduces both transmit power and computational overhead, outperforming state-of-the-art methods in both performance and efficiency.

This work addresses the weighted sum-rate maximization problem under per-cluster power constraints in downlink distributed antenna systems. By exploiting the fact that optimal beamformers lie in the low-dimensional subspace spanned by the channels of their respective antenna clusters, the original high-dimensional constrained optimization problem is reformulated—for the first time—as an unconstrained optimization over a product of ellipsoidal manifolds. The authors systematically develop the Riemannian geometry of this manifold, including its tangent space, metric, projection, and retraction operators, and design a tailored Riemannian conjugate gradient algorithm. The proposed method achieves solution quality comparable to that of WMMSE and conventional manifold-based approaches while significantly improving computational efficiency and scalability, with pronounced advantages as the number of antenna clusters increases.

It remains unclear whether the conventional discrete Fourier transform (DFT) constitutes an optimal sparsifying transform for finite-dimensional antenna arrays in millimeter-wave (mmWave) communications. This work proposes a complex-domain ℓ⁴-norm maximization framework that extends real-valued dictionary learning techniques to the complex field, enabling the learning of sparsifying transforms tailored to mmWave MIMO channels. Two efficient algorithms are developed and evaluated on both real-world and synthetic channel data, consistently yielding transform bases that outperform DFT in enhancing beamspace sparsity. The results empirically demonstrate the suboptimality of DFT and provide new theoretical insights and algorithmic tools for mmWave channel modeling and beamforming design.

Beamforming optimization for multi-user continuous aperture arrays (CAPAs) suffers from non-convex functional programming due to conventional discrete array (SPDA) modeling. Method: We first derive the closed-form structure of the optimal CAPA beamformer; propose a globally optimal algorithm based on monotonic optimization; and design low-complexity maximum-ratio transmission (MRT), zero-forcing (ZF), and minimum mean-square error (MMSE) schemes, rigorously proving their asymptotic optimality in the large-antenna limit. Our approach integrates variational calculus, Lagrangian duality, and inverse function theory for continuous mappings. Results: Experiments demonstrate that CAPAs significantly outperform SPDAs in spectral efficiency and robustness. The MMSE scheme closely approaches the global optimum across most SNR regimes, while MRT and ZF maintain near-optimal performance in low- and high-SNR regimes, respectively.

To address the dual bottlenecks of prohibitive interconnect overhead and soaring computational complexity in Extremely Large-Scale Antenna Array (ELAA) systems, this paper proposes a practically deployable distributed signal processing framework. We first establish a unified taxonomy for ELAA distributed processing, categorizing it into three paradigms: single-base-station ELAA, cooperative distributed antenna systems, and ELAA integrated with emerging technologies. The framework systematically incorporates distributed optimization, graph-model-driven antenna grouping, clustering-based processing, edge-cloud coordination, approximate message passing, and sparse reconstruction algorithms. We rigorously characterize the performance limits and operational conditions of each approach. Finally, we identify three key future research directions: scalability enhancement, low-latency coordination, and hardware-aware optimization. Our work provides a comprehensive, scalable, low-overhead, and robust signal processing design guideline for 6G air interfaces.

This work investigates the joint optimization of array geometry and waveform design in active sensing systems to approach the Cramér-Rao bound (CRB) performance limit for parameter estimation, balancing mean squared error and identifiability. By analyzing the CRB under both orthogonal and coherent waveforms for linear and planar arrays, it reveals that single-target estimation performance is governed by the sum of the spatial variances of the transmit and receive arrays. Building on this insight, the study proposes an asymmetric allocation strategy of transmit and receive sensors, departing from conventional symmetric designs. It further establishes a connection between Diophantine equations and CRB-equivalent array constructions, leveraging weighted virtual array multiplicity and beam steering optimization to derive a general optimality criterion. This yields constructible high-performance array configurations, offering a new paradigm for MIMO active sensing systems.

This study addresses the challenge of spatial interference suppression in near-field beam focusing for sparse arrays, particularly in non-terrestrial distributed scenarios such as coherent satellite formations. By leveraging Lagrangian duality theory, the authors establish a unified analytical framework that reveals a generalized matched-filter relationship between the optimal beamformer and the effective spatial covariance matrix, and for the first time provides an analytical characterization of near-field focused beamforming performance. Key contributions include proving the finite support property of the dual measure, which guarantees convergence of the cutting-plane method; uncovering an asymptotic logarithmic growth of the average signal-to-interference ratio (SIR) with the number of array elements; and developing a Riemannian conjugate gradient algorithm on the unit torus manifold to implement constant-modulus beamforming. Numerical experiments demonstrate that the proposed approach closely approaches the theoretical SIR upper bound, confirming that array geometry—not the optimization algorithm—primarily governs performance.

This work addresses the challenge in large-scale MU-MIMO long-term beamforming where the condition number of the channel covariance matrix deteriorates with the dynamic range of user signal-to-noise ratios, leading to a sharp increase in conjugate gradient (CG) inversion iterations and consequently higher latency and energy consumption. To mitigate this, the paper proposes a hardware-oriented low-rank preconditioning framework that constructs a preconditioner in the beamspace domain using dominant eigenpairs of the covariance matrix. By integrating randomized complex eigendecomposition (RC-EVD) with Cholesky-based QR factorization (QRC), the approach reformulates the core computations into GEMM operations and small-scale triangular solves amenable to systolic array implementation. This novel fusion of beamspace sparsification and low-rank preconditioning significantly accelerates CG convergence. Ray-tracing simulations demonstrate a 2–3× reduction in iteration count while maintaining post-equalization SINR performance comparable to exact matrix inversion.

This work addresses the challenges of sidelobe and grating lobe leakage in sparse arrays for extremely large-scale MIMO systems, which, while cost-effective and aperture-preserving, suffer from interference, whereas rotatable antennas that mitigate such leakage incur high control overhead. To overcome this trade-off, the paper proposes a user-group-oriented sparse rotatable antenna architecture that partitions users into service groups, each served by a dedicated sparse subarray. It jointly optimizes aperture allocation, antenna orientation, and beamforming to maximize the minimum SINR. Leveraging group-level geometric information, the design enables low-complexity configuration and reveals an approximately decoupled beam structure—inter-group leakage suppression and intra-group orthogonalization—that guides antenna placement and allocation. A two-layer structured algorithm, integrating analysis-guided initialization, multi-start search, and closed-form orientation rules, achieves near-ideal performance with substantially reduced hardware cost, significantly outperforming both compact and omnidirectional sparse baselines.

This work addresses the challenges of slow convergence, high computational complexity, and lack of user prioritization in joint signal enhancement and suppression using reconfigurable intelligent surfaces (RIS) in multi-user wireless systems. To overcome these limitations, the authors propose a unified RIS optimization framework that incorporates adaptive gradient scaling for fast, parameter-free convergence, a low-complexity beamforming recovery method that avoids matrix decomposition, and a novel user prioritization mechanism based on RIS subarray allocation, complemented by a modular architecture supporting flexible addition or removal of components. Evaluated across three representative scenarios, the proposed scheme closely approaches theoretical performance bounds, significantly outperforms conventional semidefinite relaxation methods, and demonstrates near-optimality, scalability, and effectiveness in both cooperative and competitive multi-user environments under real-world channel conditions.