毫米波大规模多输入多输出（Massive Multiple-Input Multiple-Output, Massive MIMO）技术作为移动通信系统的关键使能技术之一，拥有大带宽、高频谱效率以及高可靠性等显著优势。在毫米波Massive MIMO系统中，天线阵列的优化部署是一项至关重要的研究课题。与传统均匀阵列相比，非均匀天线阵列可以平衡信道特征值，进而获得可观的性能增益。由于Massive MIMO系统需要部署大规模天线阵列，因而在固定孔径情况下采用非均匀平面阵列（Non-uniform Planar Array, NUPA）已成为一种发展趋势。然而，如何从理论层面优化设计NUPA拓扑仍然是一个具有挑战性的开放问题。本文基于毫米波Massive MIMO系统，优化设计出了在单用户和多用户两种场景中拓扑排布特点恰好相反的两种NUPA拓扑。具体研究内容如下：

（1）针对近场球面波（Spherical Wave, SW）传播条件下的单用户MIMO（Single User MIMO, SU-MIMO）视距（Line-of-Sight, LOS）场景，在收发端阵列沿不同轴旋转的一般情况下建立阵列的几何模型；对有效自由度（Effective Degree of Freedom, EDoF）进行表征，同时借助克罗内克乘积特性以及特征值渐近分析法，来构建水平和垂直维度分量上的信道特征值与阵元位置、阵列旋转角之间的理论关系，进而直观反映出阵元位置与EDoF之间的数学解析关系；以EDoF最大化为优化目标，以阵元位置为优化变量，以空间资源受限与相邻阵元间距不小于半波长为约束，建立NUPA拓扑优化问题；采用自适应梯度下降法求解该优化问题，最终设计出具有四周密集、中间稀疏且中心对称排布特点的NUPA拓扑。此外，我们还讨论了阵列旋转角对系统性能的本质影响。研究表明，在阵列孔径相同的情况下，所设计的NUPA拓扑在整个信噪比（Signal-Noise Ratio, SNR）范围内均能提供比其他对比阵列拓扑更高的性能增益，仿真结果还验证了理论分析的正确性，从而在理论层面为非均匀阵列拓扑优化设计提供了有效的指导准则。

（2）为了更加符合实际传输场景的需求，在SU-MIMO系统的基础上进一步扩展到多用户MIMO（Multi-User MIMO, MU-MIMO）系统。具体来说，在近场SW传播条件下的MU-MIMO莱斯信道中构建收发端阵列的几何结构关系；借助詹森不等式、大数定律等推导遍历和速率的近似表达式，以此作为优化问题的目标函数；随后利用克罗内克混合乘积、高阶泰勒展开以及迭代凸近似方法，求解了以阵元位置作为变量的优化问题；特别地，我们讨论了所设计的NUPA拓扑的排布特征，并对不同系统配置下的拓扑排布特点进行了相应分析。需要强调的是，在MU-MIMO系统中设计的NUPA拓扑呈现出四周稀疏、中间密集且中心对称的排布特点，这与SU-MIMO系统中设计的NUPA拓扑排布特点恰好相反。此外，我们还发现随着用户终端天线数的减少，阵列各单元将向中心聚拢，并从电磁波传播角度进一步分析了不同阵列拓扑的排布特征与通信场景之间的关系；仿真结果验证了所设计的具有强鲁棒性的NUPA拓扑相比于其他对比阵列拓扑的显著性能优势，其中在SNR为-5dB至20dB时，所设计的NUPA拓扑的遍历和速率比均匀平面阵列（Uniform Planar Array, UPA）平均提升约13.6%，从而为Massive MU-MIMO系统提供了一种有效的阵列拓扑设计准则。

As one of the key enabling technologies for mobile communication systems, millimeter-wave massive multiple-input multiple-output (Massive MIMO) technology offers significant advantages such as large bandwidth, high spectral efficiency, and high reliability. In millimeter-wave Massive MIMO systems, the optimal deployment of antenna arrays is a crucial research topic. Compared with the traditional uniform array, the non-uniform antenna array can balance the channel eigenvalues and obtain considerable performance gain. Since massive MIMO systems require the deployment of large-scale antenna arrays, the use of non-uniform planar arrays (NUPAs) in the fixed apertures has become a trend. However, how to optimize the design of NUPA topology from the theoretical level remains a challenging open problem. In this paper, based on the millimeter-wave Massive MIMO system, we optimize and design two NUPA topologies with exactly opposite topological arrangement characteristics in both single-user and multi-user scenarios. The specific research contents are as follows:

(1) For the single-user MIMO (SU-MIMO) line-of-sight (LOS) scenario with near-field spherical wave (SW) propagation, a geometric model of the array is established under the general condition that the transceiver array rotates along different axes. The effective degree of freedom (EDoF) is characterized, and theoretical relations between the channel eigenvalues of the horizontal and vertical dimensions and the array element positions and array rotation angles are constructed using Kronecker product and eigenvalue asymptotic analysis, so as to intuitively reflect the mathematical analytical relation between array element positions and EDoF. The NUPA topology optimization problem is formulated with EDoF maximization as the optimization objective, array element positions as the optimization variable, and spatial resource limitation and adjacent array element spacing not less than half wavelength as constraints. Adaptive gradient descent is used to solve the optimization problem. Finally, the NUPA topology with dense surrounding, sparse middle, and symmetric center is designed. In addition, we discuss the essential effect of the array rotation angle on the system performance. It has been shown that for the same array aperture, the designed NUPA topology can provide a higher performance gain than other compared array topologies over the entire signal-noise ratio (SNR) range. The simulation results also verify the correctness of the theoretical analysis and thus provide effective guidance for the optimization design of non-uniform array topologies at the theoretical level.

(2) To meet the requirements of practical transmission scenarios, the SU-MIMO system is further extended to the multi-user MIMO (MU-MIMO) system. Specifically, the geometric structure relations of the transceiver array are constructed in the MU-MIMO Rician channel with near-field SW propagation. The approximate expression for the ergodic sum-rate, which is used as the objective function of the optimization problem, are derived using Jensen's inequality and the law of large numbers. Then, the optimization problem with array element positions as variables is solved by using the Kronecker mixture product, higher-order Taylor expansion, and iterative convex approximation. In particular, we discuss the arrangement properties of the designed NUPA and analyze the topological arrangement properties under different system configurations. It should be emphasized that the NUPA topology designed in the MU-MIMO system exhibits the feature of sparsity around, dense in the middle, and center-symmetry, which is the opposite of the NUPA topology designed in the SU-MIMO system. Moreover, we find that the elements of the array converge towards the center as the number of antennas at the user terminals decreases, and further analyze the relationship between the arrangement properties of different array topologies and the communication scenario from the perspective of electromagnetic wave propagation. Simulation results show that the designed robust NUPA topology has a significant performance advantage over other compared array topologies. When the SNR is from -5dB to 20dB, the ergodic sum-rate of the designed NUPA topology is approximately 13.6% higher than that of the uniform planar array (UPA), which provides an effective array topology design criterion for Massive MU-MIMO systems.

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