This paper bridges this critical gap by providing a systematic examination of the beamforming codebook technology, i.e., precoding matrix indicator (PMI), in the 5G NR from theoretical, standardization, and implementation perspectives. We begin by introducing the background of beamforming in multiple-input multiple-output (MIMO) systems and the signaling procedures for codebook-based beamforming in practical 5G systems. Then, we establish the fundamentals of regular codebooks and port-selection codebooks in 3GPP standards. Next, we provide rigorous technical analysis of 3GPP codebook evolution spanning Releases 15-18, with particular focus on: 1) We elucidate the core principles underlying codebook design, 2) provide clear physical interpretations for each symbolic variable in the codebook formulas, summarized in tabular form, and 3) offer intuitive visual illustrations to explain how codebook parameters convey information. These essential pedagogical elements are almost entirely absent in the often-obscure standardization documents. Through mathematical modeling, performance benchmarking, feedback comparisons, and scenario-dependent applicability analysis, we provide researchers and engineers with a unified understanding of beamforming codebooks in real-world systems. Furthermore, we identify future directions and other beamforming scenarios for ongoing research and development efforts. This work serves as both an informative tutorial and a guidance for future research, facilitating more effective collaboration between academia and industry in advancing wireless communication technologies.

翻译：本文从理论、标准化与实现三个维度，对5G NR中的波束赋形码本技术（即预编码矩阵指示，PMI）进行了系统性梳理，填补了该领域的关键空白。首先介绍了多输入多输出（MIMO）系统中波束赋形的背景知识，以及实际5G系统中基于码本的波束赋形信令流程。随后，阐述了3GPP标准中常规码本与端口选择码本的基本原理。接着，对3GPP第15至18版本中的码本演进进行了严谨的技术分析，重点包括：1）阐明码本设计的核心原则；2）以表格形式总结码本公式中各符号变量的明确物理含义；3）通过直观的可视化图示解释码本参数如何传递信息。这些关键的教学要素在通常晦涩难懂的标准化文档中几乎完全缺失。通过数学模型构建、性能基准测试、反馈机制比较以及场景适用性分析，本研究为科研人员和工程师提供了对实际系统中波束赋形码本的统一认知。此外，本文指出了未来研究方向及其他波束赋形应用场景，为持续研发工作提供参考。本成果兼具指导性教程与前瞻研究指南的双重作用，有助于学术界与工业界更高效地协作推进无线通信技术发展。