A Framework on Order-Reduction Optimization for Array-Assisted Communication Networks

Antenna arrays are the fundamental component of modern high-throughput wireless networks. The diversity of array structures and system functionalities results in strong non-convexity of the related optimization problems, making it difficult to derive optimal solutions and thereby limiting network performance. To address this issue, the order-reduction optimization plays an important role, providing a trade-off between system performance and computational complexity. In this paper, we propose a comprehensive and systematic framework on order-reduction optimization, which has a wide range of application scenarios and satisfactory performance. We first discuss the construction of order-reduction inequalities and related properties in terms of three mathematical paradigms: the log-trace-based identity, the positive definite identity, and the tangent identity. Then we propose order-reduction algorithms applied to constant-modulus (CM) constrained optimization problems. Specifically, the hybrid digital-analog system, the reconfigurable intelligent surface (RIS)-aided system, and the holographic metasurface antenna (HMA)-aided system are investigated, respectively. In addition, we consider the application of the proposed order-reduction algorithms to different functional systems, where integrated sensing and communication (ISAC) and the physical layer security (PLS) are included.