论文标题
矩阵单音优化第二部分:多变量优化
Matrix-Monotonic Optimization Part II: Multi-Variable Optimization
论文作者
论文摘要
与本论文的第一部分相反,该论文[1]的重点是与单个矩阵变量相关的优化问题,在本文中,我们研究了矩阵单调优化框架在与多个矩阵变量相关的优化问题中的应用。据揭示,只要满足某些条件,矩阵单音优化即使对于多个基于基于矩阵变化的优化问题仍然有效。使用此框架,可以得出矩阵变量的最佳结构,并且可以实质上简化关联的多个矩阵变差优化问题。在本文中,给出了几个特定的示例,这些示例本质上是开放的问题。首先,我们研究了各种功率约束下的多用户多用户多输入多输出(MU-MIMO)上行链路通信。使用所提出的框架,可以得出每个用户在各种功率约束下对预编码矩阵的最佳结构。其次,我们考虑了分布式传感器网络中各种功率约束下在每个传感器处的信号压缩矩阵的优化。最后,我们研究了在各种功率约束下使用不完美的通道状态信息(CSI)的多跳扩增和前向(AF)MIMO继电器网络的收发器优化。在本文的最后,给出了几个模拟结果,以证明所提出的理论结果的准确性。
In contrast to Part I of this treatise [1] that focuses on the optimization problems associated with single matrix variables, in this paper, we investigate the application of the matrix-monotonic optimization framework in the optimization problems associated with multiple matrix variables. It is revealed that matrix-monotonic optimization still works even for multiple matrix-variate based optimization problems, provided that certain conditions are satisfied. Using this framework, the optimal structures of the matrix variables can be derived and the associated multiple matrix-variate optimization problems can be substantially simplified. In this paper, several specific examples are given, which are essentially open problems. Firstly, we investigate multi-user multiple-input multiple-output (MU- MIMO) uplink communications under various power constraints. Using the proposed framework, the optimal structures of the precoding matrices at each user under various power constraints can be derived. Secondly, we considered the optimization of the signal compression matrices at each sensor under various power constraints in distributed sensor networks. Finally, we investigate the transceiver optimization for multi-hop amplify-and-forward (AF) MIMO relaying networks with imperfect channel state information (CSI) under various power constraints. At the end of this paper, several simulation results are given to demonstrate the accuracy of the proposed theoretical results.