Machine learning for modelling unstructured grid data in computational physics: a review

Unstructured grid data are essential for modelling complex geometries and dynamics in computational physics. Yet, their inherent irregularity presents significant challenges for conventional machine learning (ML) techniques. This paper provides a comprehensive review of advanced ML methodologies designed to handle unstructured grid data in high-dimensional dynamical systems. Key approaches discussed include graph neural networks, transformer models with spatial attention mechanisms, interpolation-integrated ML methods, and meshless techniques such as physics-informed neural networks. These methodologies have proven effective across diverse fields, including fluid dynamics and environmental simulations. This review is intended as a guidebook for computational scientists seeking to apply ML approaches to unstructured grid data in their domains, as well as for ML researchers looking to address challenges in computational physics. It places special focus on how ML methods can overcome the inherent limitations of traditional numerical techniques and, conversely, how insights from computational physics can inform ML development. To support benchmarking, this review also provides a summary of open-access datasets of unstructured grid data in computational physics. Finally, emerging directions such as generative models with unstructured data, reinforcement learning for mesh generation, and hybrid physics-data-driven paradigms are discussed to inspire future advancements in this evolving field.

Achieving Full-Bandwidth Sensing Performance with Partial Bandwidth Allocation for ISAC

This letter studies an uplink integrated sensing and communication (ISAC) system using discrete Fourier transform spread orthogonal frequency division multiplexing (DFT-s-OFDM) transmission. We try to answer the following fundamental question: With only a fractional bandwidth allocated to the user with sensing task, can the same delay resolution and unambiguous range be achieved as if all bandwidth were allocated to it? We affirmatively answer the question by proposing a novel two-stage delay estimation (TSDE) method that exploits the following facts: without increasing the allocated bandwidth, higher delay resolution can be achieved via distributed subcarrier allocation compared to its collocated counterpart, while there is a trade-off between delay resolution and unambiguous range by varying the decimation factor of subcarriers. Therefore, the key idea of the proposed TSDE method is to first perform coarse delay estimation with collocated subcarriers to achieve a large unambiguous range, and then use distributed subcarriers with optimized decimation factor to enhance delay resolution while avoiding delay ambiguity. Our analysis shows that the proposed TSDE method can achieve the full-bandwidth delay resolution and unambiguous range, by using only at most half of the full bandwidth, provided that the channel delay spread is less than half of the unambiguous range. Numerical results show the superiority of the proposed method over the conventional method with collocated subcarriers.

Wireless Communication with Flexible Reflector: Joint Placement and Rotation Optimization for Coverage Enhancement

Passive metal reflectors for communication enhancement have appealing advantages such as ultra low cost, zero energy expenditure, maintenance-free operation, long life span, and full compatibility with legacy wireless systems. To unleash the full potential of passive reflectors for wireless communications, this paper proposes a new passive reflector architecture, termed flexible reflector (FR), for enabling the flexible adjustment of beamforming direction via the FR placement and rotation optimization. We consider the multi-FR aided area coverage enhancement and aim to maximize the minimum expected receive power over all locations within the target coverage area, by jointly optimizing the placement positions and rotation angles of multiple FRs. To gain useful insights, the special case of movable reflector (MR) with fixed rotation is first studied to maximize the expected receive power at a target location, where the optimal single-MR placement positions for electrically large and small reflectors are derived in closed-form, respectively. It is shown that the reflector should be placed at the specular reflection point for electrically large reflector. While for area coverage enhancement, the optimal placement is obtained for the single-MR case and a sequential placement algorithm is proposed for the multi-MR case. Moreover, for the general case of FR, joint placement and rotation design is considered for the single-/multi-FR aided coverage enhancement, respectively. Numerical results are presented which demonstrate significant performance gains of FRs over various benchmark schemes under different practical setups in terms of receive power enhancement.

Generative CKM Construction using Partially Observed Data with Diffusion Model

Channel knowledge map (CKM) is a promising technique that enables environment-aware wireless networks by utilizing location-specific channel prior information to improve communication and sensing performance. A fundamental problem for CKM construction is how to utilize partially observed channel knowledge data to reconstruct a complete CKM for all possible locations of interest. This problem resembles the long-standing ill-posed inverse problem, which tries to infer from a set of limited observations the cause factors that produced them. By utilizing the recent advances of solving inverse problems with generative artificial intelligence (AI), in this paper, we propose generative CKM construction method using partially observed data by solving inverse problems with diffusion models. Simulation results show that the proposed method significantly improves the performance of CKM construction compared with benchmarking schemes.

FFT-Enhanced Low-Complexity Near-Field Super-Resolution Sensing

In this letter, a fast Fourier transform (FFT)-enhanced low-complexity super-resolution sensing algorithm for near-field source localization with both angle and range estimation is proposed. Most traditional near-field source localization algorithms suffer from excessive computational complexity or incompatibility with existing array architectures. To address such issues, this letter proposes a novel near-field sensing algorithm that combines coarse and fine granularity of spectrum peak search. Specifically, a spectral pattern in the angle domain is first constructed using FFT to identify potential angles where sources are present. Afterwards, a 1D beamforming is performed in the distance domain to obtain potential distance regions. Finally, a refined 2D multiple signal classification (MUSIC) is conducted within each narrowed angle-distance region to estimate the precise location of the sources. Numerical results demonstrate that the proposed algorithm can significantly reduce the computational complexity of 2D spectrum peak searches and achieve target localization with high-resolution.

Generating CKM Using Others' Data: Cross-AP CKM Inference with Deep Learning

Channel knowledge map (CKM) is a promising paradigm shift towards environment-aware communication and sensing by providing location-specific prior channel knowledge before real-time communication. Although CKM is particularly appealing for dense networks such as cell-free networks, it remains a challenge to efficiently generate CKMs in dense networks. For a dense network with CKMs of existing access points (APs), it will be useful to efficiently generate CKMs of potentially new APs with only AP location information. The generation of inferred CKMs across APs can help dense networks achieve convenient initial CKM generation, environment-aware AP deployment, and cost-effective CKM updates. Considering that different APs in the same region share the same physical environment, there exists a natural correlation between the channel knowledge of different APs. Therefore, by mining the implicit correlation between location-specific channel knowledge, cross-AP CKM inference can be realized using data from other APs. This paper proposes a cross-AP inference method to generate CKMs of potentially new APs with deep learning. The location of the target AP is fed into the UNet model in combination with the channel knowledge of other existing APs, and supervised learning is performed based on the channel knowledge of the target AP. Based on the trained UNet and the channel knowledge of the existing APs, the CKM inference of the potentially new AP can be generated across APs. The generation results of the inferred CKM validate the feasibility and effectiveness of cross-AP CKM inference with other APs' channel knowledge.

Double-Side Delay Alignment Modulation for Multi-User Millimeter Wave and TeraHertz Communications

Delay alignment modulation (DAM) is an innovative broadband modulation technique well suited for millimeter wave (mmWave) and terahertz (THz) massive multiple-input multiple-output (MIMO) communication systems. Leveraging the high spatial resolution and sparsity of multi-path channels, DAM mitigates inter-symbol interference (ISI) effectively, by aligning all multi-path components through a combination of delay pre/post-compensation and path-based beamforming. As such, ISI is eliminated while preserving multi-path power gains. In this paper, we explore multi-user double-side DAM with both delay pre-compensation at the transmitter and post-compensation at the receiver, contrasting with prior one-side DAM that primarily focuses on delay pre-compensation only. Firstly, we reveal the constraint for the introduced delays and the delay pre/post-compensation vectors tailored for multi-user double-side DAM, given a specific number of delay pre/post-compensations. Furthermore, we show that as long as the number of base station (BS)/user equipment (UE) antennas is sufficiently large, single-side DAM, where delay compensation is only performed at the BS/UE, is preferred than double-side DAM since the former results in less ISI to be spatially eliminated. Next, we propose two low-complexity path-based beamforming strategies based on the eigen-beamforming transmission and ISI-zero forcing (ZF) principles, respectively, based on which the achievable sum rates are studied. Simulation results verify that with sufficiently large BS/UE antennas, single-side DAM is sufficient. Furthermore, compared to the benchmark scheme of orthogonal frequency division multiplexing (OFDM), multi-user BS-side DAM achieves higher spectral efficiency and/or lower peak-to-average power ratio (PAPR).

Convolutional Beamspace Beamforming for Low-Complexity Far-Field and Near-Field MU-MIMO Communications

Inter-user interference (IUI) mitigation has been an essential issue for multi-user multiple-input multiple-output (MU-MIMO) communications. The commonly used linear processing schemes include the maximum-ratio combining (MRC), zero-forcing (ZF) and minimum mean squared error (MMSE) beamforming, which may result in the unfavorable performance or complexity as the antenna number grows. In this paper, we introduce a low-complexity linear beamforming solution for the IUI mitigation by using the convolutional beamspace (CBS) technique. Specifically, the dimension of channel matrix can be significantly reduced via the CBS preprocessing, thanks to its beamspace and spatial filtering effects. However, existing methods of the spatial filter design mainly benefit from the Vandermonde structure of channel matrix, which only holds for the far-field scenario with the uniform plane wave (UPW) model. As the antenna size increases, this characteristic may vanish in the near-field region of the array, where the uniform spherical wave (USW) propagation becomes dominant. To gain useful insights, we first investigate the beamforming design and performance analysis of the CBS-based beamforming based on the UPW model. Our results unveil that the proposed CBS-based MMSE beamforming is able to achieve a near-optimal performance but demands remarkably lower complexity than classical ZF and MMSE schemes. Furthermore, our analysis is also extended to the near-field case. To this end, a novel optimization-based CBS approach is proposed for preserving spatial filtering effects, thus rendering the compatibility of the CBS-based beamforming. Finally, numerical results are provided to demonstrate the effectiveness of our proposed CBS-based beamforming method.

Movable Antenna for Wireless Communications:Prototyping and Experimental Results

Movable antenna (MA), which can flexibly change the position of antenna in three-dimensional (3D) continuous space, is an emerging technology for achieving full spatial performance gains. In this paper, a prototype of MA communication system with ultra-accurate movement control is presented to verify the performance gain of MA in practical environments. The prototype utilizes the feedback control to ensure that each power measurement is performed after the MA moves to a designated position. The system operates at 3.5 GHz or 27.5 GHz, where the MA moves along a one-dimensional horizontal line with a step size of 0.01{\lambda} and in a two-dimensional square region with a step size of 0.05{\lambda}, respectively, with {\lambda} denoting the signal wavelength. The scenario with mixed line-of-sight (LoS) and non-LoS (NLoS) links is considered. Extensive experimental results are obtained with the designed prototype and compared with the simulation results, which validate the great potential of MA technology in improving wireless communication performance. For example, the maximum variation of measured power reaches over 40 dB and 23 dB at 3.5 GHz and 27.5 GHz, respectively, thanks to the flexible antenna movement. In addition, experimental results indicate that the power gain of MA system relies on the estimated path state information (PSI), including the number of paths, their delays, elevation and azimuth angles of arrival (AoAs), as well as the power ratio of each path.

Prototyping and Experimental Results for ISAC-based Channel Knowledge Map

Channel knowledge map (CKM) is a novel approach for achieving environment-aware communication and sensing. This paper presents an integrated sensing and communication (ISAC)-based CKM prototype system, demonstrating the mutualistic relationship between ISAC and CKM. The system consists of an ISAC base station (BS), a user equipment (UE), and a server. By using a shared orthogonal frequency division multiplexing (OFDM) waveform over the millimeter wave (mmWave) band, the ISAC BS is able to communicate with the UE while simultaneously sensing the environment and acquiring the UE's location. The prototype showcases the complete process of the construction and application of the ISAC-based CKM. For CKM construction phase, the BS stores the UE's channel feedback information in a database indexed by the UE's location, including beam indices and channel gain. For CKM application phase, the BS looks up the best beam index from the CKM based on the UE's location to achieve training-free mmWave beam alignment. The experimental results show that ISAC can be used to construct or update CKM while communicating with UEs, and the pre-learned CKM can assist ISAC for training-free beam alignment.