  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.
