基于逐次凸逼近的多用户MIMO收发机设计非凸优化理论与算法

The joint optimization of transmitters and receivers has huge potentials in improving the transmission performance of MIMO networks. However, the classical convex optimization techniques face huge obstacles when they are used to optimize the transceiver designs for future multiuser MIMO systems, which are typically formulated as nonconvex optimization problems with nonconvex constraints and nonconvex objectives. As a consequence, it may be hindered to further improve the transmission performance of wireless communication networks with traditional optimization techniques. In this project, aiming at improving the transmission performance of the wireless communication systems, we will study the methods and schemes to solve the nonconvex optimization problems for multiuser MIMO transceiver designs based on the novel idea of successive convex approximation (SCA). We will focus our research on how to solve the complex transceiver design problems with nonconvex constraints and/or nonconvex objectives. Specifically, our research will be composed of the following two aspects. One the one hand, we will study the basic SCA-based nonconvex optimization theory and algorithms by considering the special architectures of MIMO transceivers. On the other hand, we will apply the SCA frameworks for designing the centralized and decentralized multiuser MIMO transceiver optimization schemes as well as enhancing the robustness of the system. The potential innovations of this project rest in the following three folds. Fist, we will extend the area of SCA framework by solving the optimization problems with both nonconvex objectives and nonconvex constraints. Second, we intend to applying the SCA framework to avoid the high complexity incurred by the traditional transceiver designs when solving the transceiver design sub-problems. Third, we will develop effective parallelization methods for decentralized applications by combining the SCA with the alternating direction multiplier (ADMM) procedures. The research of this project can provide feasible technical supports and solutions for future multiuser MIMO communication system designs.

收发机联合优化是改善MIMO网络传输性能的重要手段。然而，经典凸优化技术难以有效求解未来多用户MIMO系统中的非凸约束、非凸目标收发机优化问题，进而限制了无线网络传输性能的改进。本项目拟基于逐次凸逼近（SCA）这一新型的非凸优化思想，围绕“如何更加有效地求解多用户MIMO通信系统中高度非凸的复杂收发机设计优化问题以实现无线通信系统传输能的提升”这一核心科学问题，研究非凸收发机优化问题的有效求解方法。具体研究内容包括考虑MIMO收发机特征的SCA优化基本理论和算法以及基于SCA框架的多用户MIMO收发机设计中心式、分布式求解方案和鲁棒性增强方法等。本项目的创新点包括将SCA框架扩展至非凸约束非凸目标优化问题的求解、利用SCA框架规避传统收发机设计中复杂度高的子问题、将SCA与交替方向乘子法（ADMM）结合构建并行化方法等。本研究可为未来多用户MIMO通信系统设计提供可行的技术支持与解决方案。

多用户干扰是限制密集覆盖MIMO网络传输性能提升的瓶颈。用户间协作预编码和接收滤波是抑制MIMO用户间干扰、提升系统传输效率的重要手段。然而，多用户MIMO系统中多元变量参数的耦合所带来的高度非凸性为其收发机联合优化带来巨大挑战。围绕“如何更加有效地求解多用户MIMO通信系统中高度非凸的复杂收发机设计优化问题以实现无线通信系统传输性能提升”这一核心科学问题，本项目探索了基于逐次凸逼近（SCA）的高度非凸问题的有效求解方法和MIMO收发机高效优化算法。主要研究内容主要包括：1）面向收发机优化的非凸优化问题SCA求解理论和方法研究。主要研究结合MIMO 收发机特征的替代函数构建方法、非凸约束的处理方法、多变量的解耦方法。2）基于新型非凸优化理论的MIMO多用户网络收发机联合优化算法研究。主要关注可直接体现系统性能指标和用户需求的收发机设计方案建模及基于SCA技术的有效优化算法设计。3）机器学习技术在MIMO系统和多用户网络中的应用。主要研究基于机器学习的智能无线传输与资源管理方法。通过对上述内容的研究，项目取得的进展包括：探索了基于一阶泰勒级数近似、二阶泰勒级数近似、半定规划放松等技术的替代函数构建方法，为利用逐次凸逼近技术求解非凸目标和非凸约束优化问题提供了理论基础。2）基于所研究的非凸优化理论和方法，面向多种多用户MIMO场景，包括MIMO干扰信道、MIMO广播信道、MISO干扰信道和智能反射表面（IRS）辅助MISO干扰信道等，结合交替优化框架、半定规划放松等，开发了多种基于SCA的多用户MIMO收发机优化算法，为多用户MIMO系统以和速率、均方误差（MSE）和信号与干扰噪声比（SINR）等为准则的收发机联合设计提供了一系列有效的优化方案。提出了发射端预编码神经网络和接收端无线变换网络（RTN）相结合的新型MIMO端到端深度学习传输结构，设计了基于强化学习的认知无线电干扰信道网络频谱接入算法，展示了通过机器学习技术改善通信系统性能的有效性和可行性。本项目的开展为多用户MIMO收发机联合优化提供了新方法，对下一代无线通信系统设计提供了理论和方法支撑。