Revealing the Evanescent Components in Kronecker Product-based Codebooks: Insights and Applications

Kronecker product-based codewords, constructed from 2D DFT bases, are fundamental to constructing Type I, Type II, and enhanced Type II codebooks in 5G New Radio (NR). While these codewords are conventionally interpreted as directed orthogonal beams, this paper reveals that a significant portion of these codebooks is associated with evanescent waves, rendering them redundant for practical array beamforming and channel representation. This redundancy is rigorously proven using mathematical and electromagnetic models and validated by full-waveform and system-level simulations. Leveraging this redundancy, we propose a method to compress these codebooks, typically reducing their size by 21.5%. This compression significantly decreases signaling and pilot overhead, enhancing the efficiency of channel state information feedback and beam training without adding algorithmic complexity. We also propose codebooks for irregular arrays that are compatible with existing NR feedback frameworks, potentially accelerating the standardization of irregular array deployment. Inspired by the revelation of codebook redundancy, we extend the discussions to the properties of near-field channel and classical Rayleigh channels, and offer practical suggestions for future standard designs.