Continuous Aperture Array (CAPA)-Based Multi-Group Multicast Communications

2025-05-02

AI Summary

This paper addresses energy efficiency (EE) maximization for multi-group multicast transmission using continuous-aperture phased arrays (CAPAs), subject to per-group minimum spectral efficiency (SE) constraints and a total power budget. To solve this non-convex problem, we pioneer the integration of variational calculus with Lagrangian duality theory into CAPA-based multicast beamforming, rigorously deriving that the optimal beamformer admits a weighted superposition of group-specific channel responses. Building upon this structural insight, we propose a low-complexity zero-forcing closed-form solution and develop an efficient algorithm combining Dinkelbach’s method with block coordinate descent. Numerical results demonstrate that CAPAs substantially outperform conventional discrete antenna arrays in EE. However, the EE gain is non-monotonic with respect to aperture size and diminishes as user spatial distribution becomes more dispersed.

Technology Category

• Search and Optimization: Non-convex Optimization
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Energy management for devices in mobile Web and WoT environments
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

A continuous aperture array (CAPA)-based multi-group multicast communication system is investigated. An integral-based CAPA multi-group multicast beamforming design is formulated for the maximization of the system energy efficiency (EE), subject to a minimum multicast SE constraint of each user group and a total transmit power constraint. To address this non-econvex fractional programming problem, the Dinkelbach's method is employed. Within the Dinkelbach's framework, the non-convex group-wise multicast spectral efficiency (SE) constraint is first equivalently transformed into a tractable form with auxiliary variables. Then, an efficient block coordinate descent (BCD)-based algorithm is developed to solve the reformulated problem. The CAPA beamforming design subproblem can be optimally solved via the Lagrangian dual method and the calculus of variations (CoV) theory. It reveals that the optimal CAPA beamformer should be a combination of all the groups' user channels. To further reduce the computational complexity, a low-complexity zero-forcing (ZF)-based approach is proposed. The closed-form ZF CAPA beamformer is derived using each group's most representative user channel to mitigate the inter-group interference while ensuring the intra-group multicast performance. Then, the beamforming design subproblem in the BCD-based algorithm becomes a convex power allocation subproblem, which can be efficiently solved. Numerical results demonstrate that 1) the CAPA can significantly improve the EE compared to conventional spatially discrete arrays (SPDAs); 2) due to the enhanced spatial resolutions, increasing the aperture size of CAPA is not always beneficial for EE enhancement in multicast scenarios; and 3) wider user distributions of each group cause a significant EE degradation of CAPA compared to SPDA.

Problem

• Maximizing energy efficiency in CAPA-based multi-group multicast communications
• Transforming non-convex SE constraints into tractable forms with auxiliary variables
• Reducing computational complexity with low-complexity ZF-based beamforming approach

Innovation

• Uses Dinkelbach's method for energy efficiency maximization
• Employs block coordinate descent for beamforming design
• Proposes low-complexity zero-forcing to reduce computation