大规模多输入多输出（Massive Multiple-Input Multiple-Output，Massive MIMO）技术可以显著提高无线传输的空间自由度、抗干扰能力、频谱效率等。它作为第五代移动通信（The 5th Generation Mobile Communication，5G）系统关键技术之一，也将在未来移动通信系统中发挥重要作用。Massive MIMO技术是通过在基站部署大规模天线阵列来实现的，然而由于物理空间的制约，阵列中的阵元高密度排布，导致阵元间产生电磁互耦合效应，引起波束方向图畸变，使系统性能变差。因此，本文在紧致平面阵列 Massive MIMO系统下，采用优化算法，解决波束方向图畸变问题。

（1）在获知信道状态信息的前提下，以波束方向图畸变最小为目标，提出一种互耦抑制波束赋形算法。首先基于信道状态信息得到理想忽略互耦影响情况下的波束方向图，然后采用感应电动势方法，建模互耦矩阵表征互耦合效应，进而得到考虑耦合后的波束方向图。以考虑耦合前后方向图畸变最小为目标，同时增加基站功率约束和用户间干扰功率约束，建立优化问题。通过卡鲁什-库恩-塔克条件和拉格朗日乘子法求解优化问题，得到互耦抑制波束赋形。仿真结果表明，在信噪比（Signal to Noise Ratio，SNR）为-5dB至30dB范围内，该算法的平均频谱效率分别比迫零算法、最小均方误差算法、块对角化算法提高了14.16%、13.27%、12.41%。即，考虑耦合时所提算法性能优于传统波束赋形算法的性能，且能逼近理想忽略互耦影响情况下的性能，有效解决了波束方向图畸变问题，提高了系统频谱效率。

（2）由于Massive MIMO系统获知信道状态信息的开销很大，进一步在固定阵列面积和阵元数的前提下，以阵列方向图主瓣增益差异最小为目标，在无需获知信道状态信息的条件下，提出一种非均匀阵列拓扑和激励幅值联合优化的算法，并设计匹配的非均匀阵列码本。首先得到相同阵列孔径和阵元数且忽略耦合效应的均匀阵列方向图，然后采用感应电动势方法，建模互耦矩阵表征互耦合效应，进而推导得到考虑耦合效应的非均匀阵列方向图。以非均匀阵列方向图主瓣增益逼近均匀阵列方向图主瓣增益为目标，同时增加非均匀阵列峰值旁瓣电平约束、阵元位置不重叠约束以及阵列孔径约束，建立优化问题。通过非精确块坐标下降法将复杂优化问题分解为多个子问题，进行迭代求解，得到非均匀阵列拓扑和激励幅值。然后根据上述优化结果设计非均匀阵列码本。仿真结果显示在所考虑的SNR范围内，所设计的非均匀阵列匹配所设计码本的平均频谱效率相比于均匀阵列使用经典商用离散傅里叶变换码本情况下提升了62.67%。相同阵列面积下的非均匀互质平面阵列和互质L型阵列的平均频谱效率分别是所设计阵列的46.99%和35.45%。即，所设计阵列和码本能够在低系统开销情况下有效解决波束方向图畸变问题，实现了更高的系统性能。

Massive multiple-input multiple-output (MIMO) technology can significantly improve the spatial freedom, anti-interference capability, and spectral efficiency of wireless transmission. It is one of the key technologies of The 5th generation mobile communication (5G) system and will also play an important role in the future mobile communication system. Massive MIMO technology is realized by deploying massive antenna arrays at base stations, however, due to physical space constraints, the array elements in the array are arranged in high density, resulting in electromagnetic mutual coupling effects between the array elements, causing distortion of the beampattern and deteriorating the system performance. Therefore, in this paper, an optimization algorithm is used to solve the beampattern distortion problem under the tight planar array massive MIMO system.

(1)A mutual coupling suppression beamforming algorithm is proposed with the objective of minimizing the distortion of the beampattern under the premise of obtaining the channel state information. Firstly, the beampattern with the neglect of mutual coupling influence under ideal condition is obtained based on the channel state information, and then the mutual coupling effect is characterized by modeling the mutual coupling matrix using the induced electromotive force method, and then the beampattern after considering the coupling is obtained. With the objective of minimizing distortion of the beampattern before and after considering the coupling, the optimization problem is established by adding both the base station power constraint and the inter-user interference power constraint. The mutual coupling suppression beam beamforming is obtained by solving the optimization problem with the Karush-Kuhn-Tucker condition and the lagrange multiplier method. The simulation results show that the average spectral efficiency of this algorithm is improved by 14.16%, 13.27%, and 12.41% compared to the zero forcing algorithm, minimum mean square error algorithm, and block diagonalization algorithm, respectively， in the signal to noise ratio (SNR) range of -5dB to 30dB. That is, the performance of the proposed algorithm is better than that of theconventional beamforming algorithm when coupling is considered, and it can approximate the performance in the ideal case of neglecting the influence of mutual coupling, effectively solving the beampattern distortion problem and improving the system spectral efficiency.

(2)Due to the high overhead of obtaining channel state information in Massive MIMO systems, under the premise of fixed array area and array element number，we further propose an algorithm without obtaining channel state information for joint optimization of nonuniform array topology and excitation amplitude and design matching nonuniform array codebook, with the objective of minimizing the difference in the main lobe gain of the array pattern. Firstly, the uniform array pattern with the same array aperture and array element number and neglecting the coupling effect is obtained, and then the mutual coupling effect is characterized by modeling the mutual coupling matrix using the induced electromotive force method, and then the non-uniform array pattern with considering the coupling effect is deduced. The main lobe gain of the non-uniform array pattern approximates the main lobe gain of the uniform array pattern as the target, while adding the non-uniform array peak sidelobe level constraint, the array element position non-overlap constraint and the array aperture constraint to establish the optimization problem. The complex optimization problem is decomposed into multiple subproblems by the inexact block coordinate descent method and solved iteratively to obtain the nonuniform array topology and excitation amplitude. Then the non-uniform array codebook is designed based on the above optimization results. The simulation results show that the average spectral efficiency of the designed non-uniform array matching the designed codebook is improved by 62.67% compared to the uniform array using the classical commercial discrete fourier transform codebook in the considered SNR range. The average spectral efficiencies of the non-uniform coprime planar array and coprime L-shaped array with the same array area are 46.99% and 35.45% of the designed arrays, respectively. That is, the designed array and codebook can effectively solve the beampattern distortion problem with low system overhead and achieve higher system performance.

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