Extremely Large-scale Array Systems: Near-Field Codebook Design and Performance Analysis

Extremely Large-scale Array (ELAA) promises to deliver ultra-high data rates with increased antenna elements. However, increasing antenna elements leads to a wider realm of near-field, which challenges the traditional design of codebooks. In this paper, we propose novel near-field codebook schemes based on the fitting formula of codewords' quantization performance. First, we analyze the quantization performance properties of uniform linear array (ULA) and uniform planar array (UPA) codewords. Our findings reveal an intriguing property: the correlation formula for ULA codewords can be represented by the elliptic formula, while the correlation formula for UPA codewords can be approximated using the ellipsoid formula. Building on this insight, we propose a ULA uniform codebook that maximizes the minimum correlation based on the derived formula. Moreover, we introduce a ULA dislocation codebook to further reduce quantization overhead. Continuing our exploration, we propose UPA uniform and dislocation codebook schemes. Our investigation demonstrates that oversampling in the angular domain offers distinct advantages, achieving heightened accuracy while minimizing overhead in quantifying near-field channels. Numerical results demonstrate the appealing advantages of the proposed codebook over existing methods in decreasing quantization overhead and increasing quantization accuracy.