An Accelerated Mixed Weighted-Unweighted MMSE Approach for MU-MIMO Beamforming

Precoding design based on weighted sum-rate (WSR) maximization is a fundamental problem in downlink multi-user multiple-input multiple-output (MU-MIMO) systems. While the weighted minimum mean-square error (WMMSE) algorithm is a standard solution, its high computational complexity--cubic in the number of base station antennas due to matrix inversions--hinders its application in latency-sensitive scenarios. To address this limitation, we propose a highly parallel algorithm based on a block coordinate descent framework. Our key innovation lies in updating the precoding matrix via block coordinate gradient descent, which avoids matrix inversions and relies solely on matrix multiplications, making it exceptionally amenable to GPU acceleration. We prove that the proposed algorithm converges to a stationary point of the WSR maximization problem. Furthermore, we introduce a two-stage warm-start strategy grounded in the sum mean-square error (MSE) minimization problem to accelerate convergence. We refer to our method as the Accelerated Mixed weighted-unweighted sum-MSE minimization (A-MMMSE) algorithm. Simulation results demonstrate that A-MMMSE matches the WSR performance of both conventional WMMSE and its enhanced variant, reduced-WMMSE, while achieving a substantial reduction in computational time across diverse system configurations.

Steady-State Spread Bounds for Graph Diffusion via Laplacian Regularisation

We study how far a diffusion process on a graph can drift from a designed starting pattern when that pattern is produced using Laplacian regularisation. Under standard stability conditions for undirected, entrywise nonnegative graphs, we give a closed-form, instance-specific upper bound on the steady-state spread, measured as the relative change between the final and initial profiles. The bound separates two effects: (i) an irreducible term determined by the graph's maximum node degree, and (ii) a design-controlled term that shrinks as the regularisation strength increases (following an inverse square-root law). This leads to a simple design rule: given any target limit on spread, one can choose a sufficient regularisation strength in closed form. Although one motivating application is array beamforming, where the initial pattern is the squared magnitude of the beamformer weights, the result applies to any scenario that first enforces Laplacian smoothness and then evolves by linear diffusion on a graph. Overall, the guarantee is non-asymptotic, easy to compute, and certifies how much steady-state deviation can occur.

SmartUT: Receive Beamforming for Spectral Coexistence of NGSO Satellite Systems

In this paper, we investigate downlink co-frequency interference (CFI) mitigation in non-geostationary satellites orbits (NGSOs) co-existing systems. Traditional mitigation techniques, such as Zero-forcing (ZF), produce a null towards the direction of arrivals (DOAs) of the interfering signals, but they suffer from high computational complexity due to matrix inversions and required knowledge of the channel state information (CSI). Furthermore, adaptive beamformers, such as sample matrix inversion (SMI)-based minimum variance, provide poor performance when the available snapshots are limited. We propose a Mamba-based beamformer (MambaBF) that leverages an unsupervised deep learning (DL) approach and can be deployed on the user terminal (UT) antenna array, for assisting downlink beamforming and CFI mitigation using only a limited number of available array snapshots as input, and without CSI knowledge. Simulation results demonstrate that MambaBF consistently outperforms conventional beamforming techniques in mitigating interference and maximizing the signal-to-interference-plus-noise ratio (SINR), particularly under challenging conditions characterized by low SINR, limited snapshots, and imperfect CSI.

Beyond Diagonal RIS for ISAC Network: Statistical Analysis and Network Parameter Estimation

This paper investigates the use of beyond diagonal reconfigurable intelligent surface (BD-RIS) with $N$ elements to advance integrated sensing and communication (ISAC). We address a key gap in the statistical characterizations of the radar signal-to-noise ratio (SNR) and the communication signal-to-interference-plus-noise ratio (SINR) by deriving tractable closed-form cumulative distribution functions (CDFs) for these metrics. Our approach maximizes the radar SNR by jointly configuring radar beamforming and BD-RIS phase shifts. Subsequently, zero-forcing is adopted to mitigate user interference, enhancing the communication SINR. To meet ISAC outage requirements, we propose an analytically-driven successive non-inversion sampling (SNIS) algorithm for estimating network parameters satisfying network outage constraints. Numerical results illustrate the accuracy of the derived CDFs and demonstrate the effectiveness of the proposed SNIS algorithm.

UltraRay: Full-Path Ray Tracing for Enhancing Realism in Ultrasound Simulation

Traditional ultrasound simulators solve the wave equation to model pressure distribution fields, achieving high accuracy but requiring significant computational time and resources. To address this, ray tracing approaches have been introduced, modeling wave propagation as rays interacting with boundaries and scatterers. However, existing models simplify ray propagation, generating echoes at interaction points without considering return paths to the sensor. This can result in unrealistic artifacts and necessitates careful scene tuning for plausible results. We propose a novel ultrasound simulation pipeline that utilizes a ray tracing algorithm to generate echo data, tracing each ray from the transducer through the scene and back to the sensor. To replicate advanced ultrasound imaging, we introduce a ray emission scheme optimized for plane wave imaging, incorporating delay and steering capabilities. Furthermore, we integrate a standard signal processing pipeline to simulate end-to-end ultrasound image formation. We showcase the efficacy of the proposed pipeline by modeling synthetic scenes featuring highly reflective objects, such as bones. In doing so, our proposed approach, UltraRay, not only enhances the overall visual quality but also improves the realism of the simulated images by accurately capturing secondary reflections and reducing unnatural artifacts. By building on top of a differentiable framework, the proposed pipeline lays the groundwork for a fast and differentiable ultrasound simulation tool necessary for gradient-based optimization, enabling advanced ultrasound beamforming strategies, neural network integration, and accurate inverse scene reconstruction.

Holographic Joint Communications and Sensing With Cramer-Rao Bounds

Joint Communication and Sensing (JCAS) technology facilitates the seamless integration of communication and sensing functionalities within a unified framework, enhancing spectral efficiency, reducing hardware complexity, and enabling simultaneous data transmission and environmental perception. This paper explores the potential of holographic JCAS systems by leveraging reconfigurable holographic surfaces (RHS) to achieve high-resolution hybrid holographic beamforming while simultaneously sensing the environment. As the holographic transceivers are governed by arbitrary antenna spacing, we first derive exact Cram\'er-Rao Bounds (CRBs) for azimuth and elevation angles to rigorously characterize the three-dimensional (3D) sensing accuracy. To optimize the system performance, we propose a novel weighted multi-objective problem formulation that aims to simultaneously maximize the communication rate and minimize the CRBs. However, this formulation is highly non-convex due to the inverse dependence of the CRB on the optimization variables, making the solution extremely challenging. To address this, we propose a novel algorithmic framework based on the Majorization-Maximization (MM) principle, employing alternating optimization to efficiently solve the problem. The proposed method relies on the closed-form surrogate functions that majorize the original objective derived herein, enabling tractable optimization. Simulation results are presented to validate the effectiveness of the proposed framework under diverse system configurations, demonstrating its potential for next-generation holographic JCAS systems.

On Ambisonic Source Separation with Spatially Informed Non-negative Tensor Factorization

This article presents a Non-negative Tensor Factorization based method for sound source separation from Ambisonic microphone signals. The proposed method enables the use of prior knowledge about the Directions-of-Arrival (DOAs) of the sources, incorporated through a constraint on the Spatial Covariance Matrix (SCM) within a Maximum a Posteriori (MAP) framework. Specifically, this article presents a detailed derivation of four algorithms that are based on two types of cost functions, namely the squared Euclidean distance and the Itakura-Saito divergence, which are then combined with two prior probability distributions on the SCM, that is the Wishart and the Inverse Wishart. The experimental evaluation of the baseline Maximum Likelihood (ML) and the proposed MAP methods is primarily based on first-order Ambisonic recordings, using four different source signal datasets, three with musical pieces and one containing speech utterances. We consider under-determined, determined, as well as over-determined scenarios by separating two, four and six sound sources, respectively. Furthermore, we evaluate the proposed algorithms for different spherical harmonic orders and at different reverberation time levels, as well as in non-ideal prior knowledge conditions, for increasingly more corrupted DOAs. Overall, in comparison with beamforming and a state-of-the-art separation technique, as well as the baseline ML methods, the proposed MAP approach offers superior separation performance in a variety of scenarios, as shown by the analysis of the experimental evaluation results, in terms of the standard objective separation measures, such as the SDR, ISR, SIR and SAR.

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.

Coherence Based Sound Speed Aberration Correction -- with clinical validation in obstetric ultrasound

The purpose of this work is to demonstrate a robust and clinically validated method for correcting sound speed aberrations in medical ultrasound. We propose a correction method that calculates focusing delays directly from the observed two-way distributed average sound speed. The method beamforms multiple coherence images and selects the sound speed that maximizes the coherence for each image pixel. The main contribution of this work is the direct estimation of aberration, without the ill-posed inversion of a local sound speed map, and the proposed processing of coherence images which adapts to in vivo situations where low coherent regions and off-axis scattering represents a challenge. The method is validated in vitro and in silico showing high correlation with ground truth speed of sound maps. Further, the method is clinically validated by being applied to channel data recorded from 172 obstetric Bmode images, and 12 case examples are presented and discussed in detail. The data is recorded with a GE HealthCare Voluson Expert 22 system with an eM6c matrix array probe. The images are evaluated by three expert clinicians, and the results show that the corrected images are preferred or gave equivalent quality to no correction (1540m/s) for 72.5% of the 172 images. In addition, a sharpness metric from digital photography is used to quantify image quality improvement. The increase in sharpness and the change in average sound speed are shown to be linearly correlated with a Pearson Correlation Coefficient of 0.67.

Enhancing Spectrum Efficiency in 6G Satellite Networks: A GAIL-Powered Policy Learning via Asynchronous Federated Inverse Reinforcement Learning

In this paper, a novel generative adversarial imitation learning (GAIL)-powered policy learning approach is proposed for optimizing beamforming, spectrum allocation, and remote user equipment (RUE) association in NTNs. Traditional reinforcement learning (RL) methods for wireless network optimization often rely on manually designed reward functions, which can require extensive parameter tuning. To overcome these limitations, we employ inverse RL (IRL), specifically leveraging the GAIL framework, to automatically learn reward functions without manual design. We augment this framework with an asynchronous federated learning approach, enabling decentralized multi-satellite systems to collaboratively derive optimal policies. The proposed method aims to maximize spectrum efficiency (SE) while meeting minimum information rate requirements for RUEs. To address the non-convex, NP-hard nature of this problem, we combine the many-to-one matching theory with a multi-agent asynchronous federated IRL (MA-AFIRL) framework. This allows agents to learn through asynchronous environmental interactions, improving training efficiency and scalability. The expert policy is generated using the Whale optimization algorithm (WOA), providing data to train the automatic reward function within GAIL. Simulation results show that the proposed MA-AFIRL method outperforms traditional RL approaches, achieving a $14.6\%$ improvement in convergence and reward value. The novel GAIL-driven policy learning establishes a novel benchmark for 6G NTN optimization.