The orthogonal bases of discrete Fourier transform (DFT) has been recognized as the standard spatial-domain bases for Type I, Type II and enhanced Type II codewords by the 3rd Generation Partnership Project (3GPP). For uniform planar arrays, these spatial-domain bases are derived as the Kronecker product of one-dimensional DFT bases. Theoretically, each spatial basis corresponds to a beam directed towards a specific angle of departure and the set of bases represent the orthogonal beams that cover the front hemisphere of an array. While the Kronecker-product based precoding scheme facilitates the concise indexing of a codeword in the codebooks through precoding matrix indicators (PMIs) in channel state information feedback, it introduces redundant spatial beams characterized by high spatial-frequency components. This paper investigates the presence of codewords representing high spatial-frequency components within the Kronecker-product based codebooks. Through theoretical analysis and simulations, we confirm the redundancy of these codewords in MIMO communications, advocating for their removal from the codebooks to enhance system performance. Several topics relevant to the high spatial components are also involved in the discussion. Practical suggestions regarding future standard design are provided based on our theoretical analysis and simulation results.

翻译：离散傅里叶变换（DFT）的正交基已被第三代合作伙伴计划（3GPP）确立为Type I、Type II及增强型Type II码字的标准空间域基。对于均匀平面阵列，这些空间域基由一维DFT基的Kronecker积导出。理论上，每个空间基对应一个指向特定离开角的波束，而基集合代表了覆盖阵列前半球的正交波束。虽然基于Kronecker积的预编码方案通过信道状态信息反馈中的预编码矩阵指示符（PMI）实现了码本中码字的简洁索引，但它引入了以高空间频率分量为特征的冗余空间波束。本文研究了基于Kronecker积的码本中表征高空间频率分量的码字的存在性。通过理论分析与仿真，我们证实了这些码字在多输入多输出（MIMO）通信中的冗余性，主张将其从码本中移除以提升系统性能。讨论还涉及与高空间分量相关的若干议题。基于理论分析和仿真结果，我们为未来标准设计提供了实用建议。