召集人：罗智泉（香港中文大学.深圳）、张瑞（香港中文大学.深圳）、刘亚锋（中国科学院数学与系统科学研究院）

时间：2024.09.15—2024.09.21

“通信中的数学问题研讨会”日程

9月16日

9月17日 

9月18日 

9月19日 

报告人及报告摘要

Finite Horizon Optimization

罗智泉

香港中文大学（深圳）

摘要：In practical scenarios, there is often a strict upper bound on the number of algorithm iterations that can be performed within a given time limit. This raises the question of optimal step size and hyperparameter design for a fixed iteration budget. We present recent advances in effectively addressing this highly non-convex problem for gradient descent and other algorithms. Additionally, we extend the DeepMind work on AlphaTensor and introduce new reductions in the number of operations required for computation of more general matrix expressions. This provides further acceleration of calculations in linear algebra.

Separation-free spectral super-resolution via convex optimization

杨在

西安交通大学

摘要：Atomic norm methods have recently been proposed for spectral super-resolution with flexibility in dealing with missing data and miscellaneous noises. A notorious drawback of these convex optimization methods however is their lower resolution in the high signal-to-noise regime as compared to conventional methods such as ESPRIT. In this paper, we devise a simple weighting scheme in existing atomic norm methods and show that in theory the resolution of the resulting convex optimization method can be made arbitrarily high in the absence of noise, achieving the so-called separation-free super-resolution. This is proved by a novel, kernel-free construction of the dual certificate whose existence guarantees exact super-resolution using the proposed method. Numerical results corroborating our analysis are provided.

智能超表面辅助下的感知：一些数学问题的探讨

刘亮

香港理工大学

摘要：通信感知一体化被认为是第六代（6G）蜂窝网路标准的一个重要组成部分。考虑到当下智能超表面在通信领域吸引到的广泛关注，一个自然而然的问题是：在将来6G通信感知一体化网络中，智能超表面在感知领域将起到何种作用。在这个讲座中，我们将探讨利用智能超表面充当被动锚点以定位那些与基站没有视距信道的目标物体的可能性。由于传统的锚点都是主动锚点，我们将首先介绍“被动”锚点的概念，即利用基站通过目标物体-智能反射面-基站路径接收到的信号，而不是智能反射面接收到的信号（被动属性），估计目标物体到智能反射面的距离和入射角（锚点属性）。接下来，我们将阐述利用智能反射面充当被动锚点的所面临的数学问题，并且提出一些创新的信号处理方法解决以上挑战。我们希望这个讲座可以为智能反射表面在6G领域的研究带来一些新的视角。

OFDM Achieves the Lowest Ranging Sidelobe Under Random ISAC Signaling

刘凡

南方科技大学

摘要：This talk aims to answer a fundamental question in the area of Integrated Sensing and Communications (ISAC): What is the optimal communication-centric ISAC waveform for ranging? Towards that end, we shall first establish a generic framework to analyze the sensing performance of communication-centric ISAC waveforms built upon orthonormal signaling bases and random data symbols. Then, we evaluate their ranging performance by adopting both the periodic and aperiodic auto-correlation functions (P-ACF and A-ACF), and defined the expectation of the integrated sidelobe level (EISL) as a sensing performance metric. On top of that, we prove that among all communication waveforms with cyclic prefix (CP), the orthogonal frequency division multiplexing (OFDM) modulation is the only globally optimal waveform that achieves the lowest ranging sidelobe for quadrature amplitude modulation (QAM) and phase shift keying (PSK) constellations, in terms of both the EISL and the sidelobe level at each individual lag of the P-ACF. As a step forward, we prove that among all communication waveforms without CP, OFDM is a locally optimal waveform for QAM/PSK in the sense that it achieves a local minimum of the EISL of the A-ACF. Finally, we demonstrate by numerical results that under QAM/PSK constellations, there is no other orthogonal communication-centric waveform that achieves a lower ranging sidelobe level than that of the OFDM, in terms of both P-ACF and A-ACF cases.

网络编码的快速解码解密

李碩彥

电子科技大学

摘要：A major theme in commutative algebra and ring theory revolves around the question: What can be done in the absence of division? The same question applies to engineering efficiency in network coding together with cryptography. 电子书《数学之窗》第 9.4 节 deals with the problem for network coding with private-key encryption. It would be nice to see a public-key version.

Low-complexity Bit-embedding Decoder for Non-binary LDPC Codes in $\mathbb{F}_{2^q}$

王勇超

西安电子科技大学

摘要：In this talk, a new decoder  based on a bit-embedding technique for non-binary low-density parity-check (LDPC) codes over Galois fields of characteristic two ($\mathbb{F}_{2^q}$) is presented. The main content of this work is summarized in the following: first, we derive the equivalent binary codeword and binary parity-check matrix for non-binary LDPC codes in $\mathbb{F}_{2^q}$; second, a customized belief propagation algorithm utilizing bit-embedding technique is proposed based on the formulated binary-check matrix; in the end, simulations results demonstrate that both error-correction performance and decoding efficiency of the proposed approach are very competitive in comparison with the state-of-the-art non-binary LDPC decoders.

Radar Anti-jamming Strategy Learning via Domain-knowledge Enhanced Online Convex Optimization

蒲文强

深圳市大数据研究院

摘要：The dynamic competition between radar and jammer systems presents a significant challenge for modern Electronic Warfare (EW), as current active learning approaches still lack sample efficiency and fail to exploit jammer's characteristics. In this paper, the competition between a frequency agile radar and a Digital Radio Frequency Memory (DRFM)-based intelligent jammer is considered. We introduce an Online Convex Optimization (OCO) framework designed to illustrate this adversarial interaction. Notably, traditional OCO algorithms exhibit suboptimal sample efficiency due to the limited information obtained per round. To address the limitations, two refined algorithms are proposed, utilizing unbiased gradient estimators that leverage the unique attributes of the jammer system. Sub-linear theoretical results on both static regret and universal regret are provided, marking a significant improvement in OCO performance. Furthermore, simulation results reveal that the proposed algorithms outperform common OCO baselines, suggesting the potential for effective deployment in real-world scenarios.

时变星地融合网络切片

刘伟

西安电子科技大学

摘要：泛在连接是6G的六大应用场景之一，星地融合网络为泛在连接提供服务保障。星地融合网络切片可以打通异构资源壁垒，实现多维资源融合共享，保障不同类型任务的QoS需求。 在本次报告中，介绍时变星地融合网络的时变图建模方法，以及时变星地融合网络切片相关的虚拟网络功能部署和流路由联合优化策略。

Extreme Point Pursuit: A Framework for Constant Modulus Optimization

Wing-Kin Ma

The Chinese University of Hong Kong

摘要：This talk describes an optimization framework for a class of constant modulus (CM) problems, which covers binary constraints, discrete phase constraints, semi-orthogonal matrix constraints, non-negative semi-orthogonal matrix constraints, and several types of binary assignment constraints. Capitalizing on the basic principles of concave minimization and error bounds, we study a convex-constrained penalized formulation for general CM problems. The advantage of such formulation is that it allows us to leverage non-convex optimization techniques, such as the simple projected gradient method, to build algorithms. We will explore the theory of this framework, particularly, conditions under which the formulation provides exact penalization results. We will also examine practical aspects, such as computational aspects and applications.

Efficient Global Algorithms for Transmit Beamforming Design in ISAC Systems

王治国

四川大学

摘要：In this paper, we propose a multi-input multi-output transmit beamforming optimization model for joint radar sensing and multi-user communications, where the design of the beamformers is formulated as an optimization problem whose objective is a weighted combination of the sum rate and the Cramer-Rao bound, subject to the transmit power budget. Obtaining the global solution for the formulated nonconvex problem is a challenging task, since the sum-rate maximization problem itself (even without considering the sensing metric) is known to be NP-hard. The main contributions of this paper are threefold. Firstly, we derive an optimal closed-form   solution to the formulated problem in the single-user case and the multi-user case where the channel vectors of different users are orthogonal. Secondly, for the general multi-user case, we propose a novel branch and bound (B\&B) algorithm based on the McCormick envelope relaxation. The proposed algorithm is guaranteed to find the globally optimal solution to the formulated problem.  Thirdly, we design a graph neural network (GNN) based pruning policy to determine irrelevant nodes that can be directly pruned in the proposed B\&B algorithm, thereby significantly reducing the number of unnecessary enumerations in it and improving its computational efficiency.  Simulation results show the efficiency of the proposed vanilla and GNN-based accelerated B\&B algorithms.

时延-多普勒域调制波形与多天线传输体制

魏志强

西安交通大学

摘要：随着部署场景和新型产业生态的不断扩展，统筹地面蜂窝网与卫星、高空平台、无人机等空间网络相互融合，是补齐信息普惠短板、实现全域覆盖的关键。高移动场景中的高速、高效和可靠通信能力长期制约着无线通信性能。高移动通信信道衰落变化快、多普勒扩展严重，破坏了传统OFDM波形的正交性，引入了严重的子载波干扰，降低了OFDM调制的效率和可靠性。与OFDM调制波形不同，将信息调制在时延多普勒域，为信息提供了“时频变载波”，简化了信息与信道之间的耦合方式，可有效地对抗信道的时变性。本报告将回答时延-多普勒通信的一些基础问题，介绍时延-多普勒通信中的挑战和技术方案，包括信道估计和MIMO-OTFS，展望时延-多普勒通信的应用前景。

Quadratic Transform for Fractional Programming in Signal Processing and Machine Learning

Kaiming Shen

The Chinese University of Hong Kong, Shenzhen

摘要：Fractional programming (FP) is an invaluable optimization tool for communications and signal processing because many problems in these areas are fractionally structured, e.g., the signal-to-interference-plus-noise ratio (SINR) maximization for wireless transmission, the normalized cut maximization for graph clustering, the Cram\'{e}r-Rao bound (CRB) minimization for radar signal processing, the mean squared error minimization for pilot signal design, the margin maximization for support vector machine (SVM), and the age of information (AoI) minimization for sensor networks, etc. This feature article aims at a general introduction to the commonly used FP techniques upon which some latest advances in communications and signal processing are based. After briefly reviewing the classic FP theory, the article focuses on a recently developed method called the quadratic transform. We begin with the basic version of the quadratic transform considering the sum-of-ratios max FP, which the classic methods of Charnes-Cooper and Dinkelbach fail to address. The quadratic transform is further extended to a variety of other FP scenarios. For every FP method, in a top-down manner, we first present its general math framework and then specialize it to specific application. The article also gives insights into the quadratic transform by connecting it to other fundamental methods, such as the fixed-point iteration, weighted minimum mean squared error (WMMSE), majorization-minimization (MM), and gradient projection. Moreover, the convergence condition and the convergence rate are examined when we then turn our attention to the theoretical basis of the quadratic transform.

Rotation Group Synchronization via Quotient Manifold

Anthony Man-Cho So

The Chinese University of Hong Kong

摘要：Rotation group synchronization is a fundamental inverse problem that arises in applications such as graph realization, computer vision, and robotics. In this talk, we focus on the least-squares estimator of rotation group synchronization with general additive noise. Departing from the standard approach of utilizing the geometry of the ambient Euclidean space to study phase/orthogonal group synchronization, we adopt an intrinsic Riemannian approach to study rotation group synchronization. Benefiting from a quotient geometric view, we prove the negative definiteness of the quotient Riemannian Hessian around the optimal solution to the orthogonal group synchronization problem. Consequently, the Riemannian local error bound property holds and can be applied to analyze the convergence properties of various Riemannian algorithms. Furthermore, improved estimation results of the spectral and least-squares estimator are derived, which guarantee the tightness of orthogonal group synchronization for solving the rotation group version under certain noise level.

This is joint work with Linglingzhi Zhu and Chong Li.

无人机连续轨迹设计低复杂度算法

胡钰林

武汉大学

摘要：无人机轨迹在时间和空间上都具有连续性，包含无穷多个时间点所对应的无人机位置信息，这种需要优化无穷多个变量的连续轨迹设计问题挑战大且求解复杂度高。本报告拟介绍“基于间续悬飞结构的轨迹设计”以及“基于机械等效的轨迹设计”两种方案，在大幅降低复杂度的同时提升无人机连续轨迹设计的性能。

An Efficient Benders Decomposition Approach for Optimal Large-Scale Network Slicing

陈伟坤

北京理工大学

摘要：In this talk, we consider the network slicing (NS) problem which attempts to map multiple customized virtual network requests to a common shared network infrastructure and allocate network resources to meet diverse service requirements. We propose an efficient customized Benders decomposition algorithm for globally solving the large-scale NP-hard NS problem. The proposed algorithm decomposes the hard NS problem into two relatively easy function placement (FP) and traffic routing (TR) subproblems and iteratively solves them enabling the information feedback between each other, which makes it particularly suitable to solve large-scale problems. Specifically, the FP subproblem is to place service functions into cloud nodes in the network, and solving it can return a function placement strategy based on which the TR subproblem is defined; and the TR subproblem is to find paths connecting two nodes hosting two adjacent functions in the network, and solving it can either verify that the solution of the FP subproblem is an optimal solution of the original problem, or return a valid inequality to the FP subproblem that cuts off the current infeasible solution. The proposed algorithm is guaranteed to find the globally optimal solution of the NS problem. By taking the special structure of the NS problem into consideration, we successfully develop two families of valid inequalities that render the proposed algorithm converge much more quickly and thus much more efficient. Numerical results demonstrate that the proposed valid inequalities effectively accelerate the convergence of the decomposition algorithm, and the proposed algorithm significantly outperforms the existing algorithms in terms of both solution efficiency and quality.

基于硬件约束的矩阵计算问题

郭成军

华为技术有限公司

摘要：在无线通信算法中，矩阵计算扮演者核心角色；在硬件实现中，矩阵算子的重要性也尤为突出。面对日益增长的数据量和问题规模，如何在有限的硬件条件约束下，设计出既能满足通信系统高效运行，又能充分利用硬件特性的最优矩阵，已成为亟待解决的关键问题，本次报告将介绍该类问题的工程背景和范例。

QCQP问题的SDP紧松弛的新进展及S引理推广

艾文宝

北京邮电大学

摘要：如何判别带有不多于四个约束的复数齐次QCQP问题的经典SDP松弛是不是紧松弛？该问题一直是一个没有完全解决的悬疑问题。本报告将介绍最新的充分必要的判别条件，以及在满足判别条件时如何获得原问题最优解的算法。在此基础上，我们将介绍著名的S引理和袁氏引理在三个矩阵上何时成立的充分必要条件。最后，我们还将介绍对角矩阵下任意多个约束的QCQP问题SDP紧松弛的一个充分条件，以及它与前面的判别条件之间的相互关系。

面向在地化传输的环境感知

Tsung-Hui Chang

The Chinese University of Hong Kong, Shenzhen

摘要：This talk will discuss the potential of using local environment knowledge to achieve efficient transmission designs in wireless networks. Some examples like CSI feedback, pilot selection and multi-BS coordination are presented.

基于大语言模型的自适应云计算调度方法设计

王祥丰

华东师范大学

摘要：云计算调度问题通常被数学建模为在线向量装箱问题。以混合整数规划建模并借助求解器可以有效求解批量调度问题，而启发式方法是求解在线调度问题的核心。云计算调度的关键难点在于请求序列的不确定性，通常一种调度方法不可能一直表现优异，因此如何设计自适应动态调度方法成为核心关键问题。以CodeX、DeepSeek Coder等为代表的代码大模型表现出优异的代码编写能力，这也为我们设计新的云计算调度方法提供了新的技术路径。在本报告中，我们会介绍如何利用大模型设计面向云计算调度的运筹优化新方法。

Semantic Guided Diffusion Empowered Ultra-High-Definition Video Transmission over Wireless Networks

朱光旭

深圳市大数据研究院

摘要：With the growing popularity of immersive VR applications and increasing demands for higher video quality, the need for ultra-high-definition wireless video transmission is rising and will be a key application for future 6G networks. However, current transmission technologies struggle to achieve the high compression rates and low decoding delays necessary for real-time ultra-HD video. Semantic communication (SemCom) offers a promising avenue for enhancing transmission efficiency, especially as traditional bit-level communication approaches its theoretical limits. A key enabling technology in SemCom is deep learning-based joint source and channel coding (DeepJSCC). However, existing DeepJSCC methods lack interpretability because they transmit semantic information implicitly by mapping data to latent features. Additionally, the black-box nature of neural networks makes it challenging to ensure the reliable transmission of critical semantics. To address these challenges, we propose advancing DeepJSCC towards a more "semantic" approach. Specifically, we suggest transmitting interpretable and lightweight semantics as side information alongside JSCC latent features. At the receiver end, we introduce a novel latent diffusion model designed for wireless communication, trained from scratch to integrate seamlessly with DeepJSCC. Using the semantic side information, the receiver employs the proposed semantics-guided latent diffusion for denoising. Furthermore, since accurate channel state information (CSI) is essential in practice, we propose estimating CSI directly from the channel output. The estimated CSI is then used for step matching in the denoising diffusion process, enabling CSI-free transmission. Finally, the denoised feature is fed into the JSCC decoder to reconstruct the image. Numerical results demonstrate that our proposed scheme can achieve comparable performance without accurate CSI. Additionally, guided by semantic information and leveraging the powerful diffusion model, our method surpasses current DeepJSCC schemes, delivering satisfactory reconstruction performance even at SNR = -5 dB. This proposed scheme highlights the potential of incorporating diffusion models in future SemCom systems and suggests several promising applications.

Bayesian automatic model order determination in wireless communications

Yik-Chung Wu

The University of Hong Kong

摘要：In wireless communications, there are many estimation problems require the information of model order. For example, the number of propagation paths in channel estimation, the number of active users in grant-free access, and the number of interference sources in radio map reconstruction. While it is common to assume the model orders are known in wireless communication research, in practice, this information is hardly known precisely. This talk will introduce how Bayesian method could solve this problem without exhaustive tuning. Examples would focus on channel estimation in massive MIMO communication, and activity detection and channel estimation in cell-free networks.

Accelerated and Deep Expecation-Maximization Method for Quantized Linear Regression

邵明杰

山东大学

摘要：In this talk, we delve into the realm of parameter estimation from quantized data, with a particular focus on quantized linear regression (QLR). QLR finds its applications in various domains, including signal processing, data analysis, and wireless communication. Our primary objective is to explore the maximum-likelihood (ML) estimation for QLR and its solving algorithm: the expectation maximization (EM) algorithm. To begin, we investigate the convergence rate of the EM algorithm for the QLR problem. By establishing a link between EM and the proximal gradient method, we gain valuable insights into the convergence analysis. Notably, we uncover how system parameters influence the rate at which EM converges. This understanding paves the way for developing novel accelerated and/or inexact EM schemes. We present convergence rate results to validate the efficacy of these new schemes. Furthermore, we introduce a deep EM algorithm. This novel algorithm leverages an efficient structured deep neural network that is based on the principles of EM. By integrating deep learning techniques into the EM framework, we aim to enhance the algorithm's performance and computational efficiency. Simulation results unequivocally demonstrate that our algorithms outperform the standard EM counterpart in terms of speed and efficiency.

多节点通信感知一体化系统的信息论性能限

李旻

浙江大学

摘要：通信感知一体化技术通过对通信和感知系统进行硬件和频谱共享的联合设计，可大大提高系统的频谱效率并降低硬件成本，是未来网络的核心技术之一。传统信息论是针对纯通信系统的容量估计理论，无法适应一体化系统复杂通感协同和多样化性能目标。因此，亟需将现有的通信容量单一性能限扩展到通信-感知多维性能界，探究系统资源制约通信容量和感知性能的规律。本报告围绕多节点通感一体化系统的典型场景，探讨通感一体化多址接入、中继辅助的双站通感一体化等信道的数学建模、通信-感知折中性能限推导和逼近性能限的编码传输方法构造，揭示一体化设计的性能增益。

非线性信道建模与预测

薛江

西安交通大学

摘要：针对移动信道非线性展开研究，通过多种机器学习方法研究信道非线性建模与预测算法，实现移动条件下信道的精确建模。同时，探讨大模型在信道估计问题中的应用前景与面临的困难。

Optimal Adaptive Beamforming with Robust Sidelobe Level Control Against the Mismatches of the Steering Vectorss

黄永伟

广东工业大学

摘要：An optimal adaptive  beamforming problem in the form of the worst-case interference-plus-noise power (INP) minimization under the constraints on sufficiently high robust mainlobe level and sufficiently low robust sidelobe levels is considered. In the context of robust sidelobe level control, the estimation of the steering vector around grid points in the sidelobe region is assumed to contain bounded errors, because of imperfect array calibration, modeling errors, undesired signal propagation effects, environmental changes, etc. The optimal adaptive beamforming problem is then reformulated into a second-order cone programming (SOCP) problem, and solved efficiently, where the computational burden is significantly reduced because of only one half number of second-order cone constraints of the non-robust beamforming optimization problem enforcing the same sidelobe level control in the robust beamforming problems). In addition, the worst-case signal-to-interference-plus-noise ratio (SINR) maximization with the robust sidelobe level control constraints is established and recast into another SOCP; however, the solution for the SOCP often exhibits excessively low mainlobe and sidelobe levels. To manage that, we propose a one-step SOCP approximation approach via properly selecting the value of one parameter, outputting a suboptimal beamvector, which leads to lower sidelobe levels in the normalized beampattern as well as higher array output SINRs. Simulation examples are presented to demonstrate the improved performance of the two proposed beamformers in terms of the normalized beampattern and the array output SINR.

Single-loop primal dual method for sum rate maximization of RIS aided MIMO network

孙聪

北京邮电大学

摘要：Reconfigurable intelligent surface aided multiple input multiple output interference network is considered. The precoding beamforming matrices and RIS parameters are jointly designed for sum rate maximization. The approximation explores the upper bound of the sum rate, and the optimization problem is reformulated as a minimax saddle point problem through the approximated Lagrangian function. The single-loop primal dual method is designed for the saddle point problem, where the primal variable is updated through one projected gradient step and the dual variable is solved through quadratic interpolation. The proposed algorithm converges to an \epsilon-KKT point under mild assumptions. Its complexity grows only linearly in the RIS element number. Numerically the proposed method performs well compared to the benchmark methods, which achieves promising sum rate with very little computational cost.

Optimality of Approximate Message Passing Algorithms for Rank-one Matrix Estimation with Rotationally Invariant Noise

马俊杰

中国科学院数学与系统科学研究院

摘要：We study the problem of estimating a rank-one signal matrix from an observed matrix generated by corrupting the signal with additive rotationally invariant noise. We develop a new class of approximate message-passing algorithms for this problem and provide a simple and concise characterization of their dynamics in the high-dimensional limit. At each iteration, these algorithms exploit prior knowledge about the noise structure by applying a non-linear matrix denoiser to the eigenvalues of the observed matrix and prior information regarding the signal structure by applying a non-linear iterate denoiser to the previous iterates generated by the algorithm. We exploit our result on the dynamics of these algorithms to derive the optimal choices for the matrix and iterate denoisers. We show that the resulting algorithm achieves the smallest possible asymptotic estimation error among a broad class of iterative algorithms under a fixed iteration budget.

Covariance-Based Activity Detection in Cooperative Multi-Cell Massive MIMO: Scaling Law and Efficient Algorithms

王子岳

中国科学院数学与系统科学研究院

摘要：Device activity detection is an important task in massive machine-type communication (mMTC) in 5G and beyond wireless networks. In this talk, we will present recent results on the covariance-based activity detection problem in a multi-cell massive multi-input multi-output (MIMO) system. We will focus on both theoretical analysis and algorithm design. In particular, for theoretical analysis, we demonstrate a quadratic scaling law in the multi-cell system. This result shows that, the maximum number of active devices that can be correctly detected in each cell increases quadratically with the length of the signature sequence and decreases logarithmically with the number of cells. For algorithm design, we introduce two efficient accelerated coordinate descent (CD) algorithms with a convergence guarantee for solving the device activity detection problem. The first algorithm reduces the complexity of CD by using an inexact coordinate update strategy. The second algorithm avoids unnecessary computations of CD by using an active set selection strategy. Simulation results show that the proposed algorithms exhibit excellent performance in terms of computational efficiency and detection error probability.

参会人员信息表