集成感知与通信：面向6G的数学基础、信号处理与系统设计教程
Integrated Sensing and Communications: A Tutorial on Mathematical Foundations, Signal Processing and System Design for 6G
- Texas A&M University（德克萨斯A&M大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本教程系统梳理ISAC的数学基础与信号处理，统一雷达与通信工具包，推导感知-通信性能极限，并覆盖波形设计、网络架构及安全等关键议题，为6G ISAC研究提供入门指南。
AI中文摘要：
集成感知与通信（ISAC）是6G无线网络的基石技术，它利用单一波形、孔径和硬件平台同时传输信息并感知物理环境。尽管该领域已迅速成熟，但其文献分散于雷达信号处理、估计与信息理论以及无线通信等领域，这使得新入门者难以拼凑出完整的数学图景。本教程旨在填补这一空白。从复基带信号模型出发，我们构建了进入ISAC领域的研究者所需的数学基础。我们发展了雷达感知工具包（匹配滤波器、模糊函数、最大似然参数估计、Fisher信息矩阵、Cramer-Rao界和Neyman-Pearson检测）、通信工具包（Shannon和MIMO容量、注水算法和多用户预编码），然后将它们统一起来推导ISAC的基本极限：Cramer-Rao界-速率区域、容量-失真函数和确定性-随机权衡。我们基于这些基础来解决波形设计（采用2D-FFT距离-多普勒处理的OFDM雷达、OTFS和联合波形优化）、发射波束成形优化以及接收端估计与检测。随后，我们综述了将ISAC扩展到网络级别的架构（毫米波和太赫兹操作、可重构智能表面和无小区网络）以及主要应用、标准化工作和安全考虑。一个完整实现的MIMO-OFDM设计示例将这些数学知识串联起来。全文统一并列表呈现符号，推导关键结果，并将开创性贡献置于背景中，使读者在完成阅读后既具备数学流畅性，又拥有开始ISAC研究所需的文献地图。
英文摘要：
Integrated sensing and communications (ISAC) is a cornerstone of sixth-generation (6G) wireless networks: a single waveform, aperture, and hardware platform simultaneously conveys information and senses the physical environment. Its literature, however, is spread across radar signal processing, estimation and information theory, and wireless communications, which makes it difficult for a newcomer to assemble the full mathematical picture. This tutorial fills that gap. Starting from complex-baseband signal models, we build the required foundations step by step, with self-contained derivations. We develop the sensing toolkit (matched filter, ambiguity function, maximum-likelihood estimation, Fisher information, the Cramér-Rao bound (CRB), and Neyman-Pearson detection) and the communication toolkit (Shannon and MIMO capacity, water-filling, and multiuser precoding), and then unify them into the fundamental limits of ISAC: the CRB-rate region, the capacity-distortion function, and the deterministic-random tradeoff. On these foundations we treat waveform design (OFDM radar with two-dimensional FFT processing, OTFS, and jointly optimized waveforms), transmit beamforming as explicit optimization, including semidefinite relaxation, and receiver-side estimation and detection. We then survey the architectures that scale ISAC to the network level (millimeter-wave and terahertz operation, reconfigurable intelligent surfaces, and cell-free networks), together with applications, standardization, and security. A worked MIMO-OFDM design example with concrete numerology ties the mathematics together. Throughout, notation is unified and tabulated, key results are derived rather than merely cited, and seminal contributions are placed in context, so that the reader finishes with both the mathematical fluency and the literature map required to begin research in ISAC.
