ALM Based Manifold Optimization for Wireless Beamforming

This book introduces a powerful new approach to solving complex optimization problems in wireless communication: the Augmented Lagrangian Method (ALM)-based Manifold Optimization (MO) framework. Modern wireless systems such as 5G and beyond must meet demanding requirements for speed, reliability, sensing, and energy efficiency, all while operating under strict physical and hardware constraints. Traditional optimization methods often fall short when faced with the nonconvex, high-dimensional nature of these problems. By combining MO, which respects the underlying geometric structure of feasible solutions, with the ALM, which robustly handles constraints, this book provides a unified solution strategy for many of the most challenging wireless design problems. Readers will find clear explanations of the mathematical foundations, detailed algorithms, and illustrative examples that connect theory to practice. Special features include step-by-step treatments of beamforming for integrated sensing and communication (ISAC), simultaneous wireless information and power transfer (SWIPT), backscatter communication, and reconfigurable intelligent surfaces (RIS). Simulation results, tables, and illustrations further enhance understanding. The book’s most important contribution is its ability to bridge theory and real-world application, equipping researchers, engineers, and graduate students with the tools to design next-generation communication systems that are efficient, reliable, and future-ready.