Signal Propagation Analysis and Optimization of 5G Communication Network Based on Complex Function Theory

While 5G networks have revolutionized daily life and industrial applications, their signal propagation mechanisms face persistent challenges that limit performance. This paper systematically investigates the application of complex function theory to address these challenges and enhance 5G signal propagation. With cases, it analyzes the theory, demonstrating its benefits in enhancing signal processing precision, optimizing network coverage, and ensuring system stability. However, practical implementation challenges are identified, including: ideal models dont match real hardware, analytical methods are too complex for real-time tasks, and theres a gap between math and algorithms. To solve these, solutions like model correction (to address hardware non-idealities), the adoption of high-precision hardware and robust algorithms (to reduce computational complexity), and machine learning techniques (to bridge the math-algorithm gap) are proposed. This research provides a comprehensive framework for leveraging complex function theory to optimize 5G signal propagation, while also highlighting the necessity for future studies to validate these findings with real-world data and testing under extreme conditions.