In this paper, a two-step codeword design approach for millimeter wave (mmWave) massive MIMO systems is presented. Ideal codewords are first designed, which ignores the hardware constraints in terms of phase shifter resolution and the number of RF chains. Based on the ideal codewords, practical codewords are then obtained taking the hardware constraints into consideration. For the ideal codeword design in the first step, additional phase is introduced to the beam gain to provide extra degree of freedom. We develop a phase-shifted ideal codeword design (PS-ICD) method, which is based on alternative minimization with each iteration having a closed-form solution and can be extended to design more general beamforming vectors with different beam patterns. Once the ideal codewords are obtained in the first step, the practical codeword design problem in the second step is to approach the ideal codewords by considering the hardware constraints of the hybrid precoding structure in terms of phase shifter resolution and the number of RF chains. We propose a fast search based alternative minimization (FS-AltMin) algorithm that alternatively designs the analog precoder and digital precoder. Simulation results verify the effectiveness of the proposed methods and show that the codewords designed based on the two-step approach outperform those designed by the existing approaches.

中文翻译：

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具有量化移相器的毫米波大规模 MIMO 系统的两步码字设计

在本文中，提出了一种用于毫米波 (mmWave) 大规模 MIMO 系统的两步码字设计方法。首先设计理想的码字，忽略移相器分辨率和射频链数量方面的硬件限制。基于理想码字，然后考虑硬件约束获得实际码字。对于第一步中的理想码字设计，将附加相位引入波束增益以提供额外的自由度。我们开发了一种相移理想码字设计 (PS-ICD) 方法，该方法基于替代最小化，每次迭代都有一个封闭形式的解决方案，并且可以扩展到设计具有不同波束模式的更通用的波束成形向量。一旦在第一步中获得了理想的码字，第二步中的实际码字设计问题是通过考虑混合预编码结构在移相器分辨率和射频链数量方面的硬件约束来接近理想码字。我们提出了一种基于快速搜索的替代最小化（FS-AltMin）算法，该算法交替设计模拟预编码器和数字预编码器。仿真结果验证了所提出方法的有效性，并表明基于两步法设计的码字优于现有方法设计的码字。我们提出了一种基于快速搜索的替代最小化（FS-AltMin）算法，该算法交替设计模拟预编码器和数字预编码器。仿真结果验证了所提出方法的有效性，并表明基于两步法设计的码字优于现有方法设计的码字。我们提出了一种基于快速搜索的替代最小化（FS-AltMin）算法，该算法交替设计模拟预编码器和数字预编码器。仿真结果验证了所提出方法的有效性，并表明基于两步法设计的码字优于现有方法设计的码字。