Extremely large-scale Array Systems: Near-Filed Codebook Design and Performance Analysis

Extremely large-scale Array (ELAA) promises to deliver ultra-high data rates with more antenna elements. Meanwhile, the increase of antenna elements leads to a wider realm of near-field, which challenges the traditional design of codebooks. In this paper, we propose novel codebook design schemes which provide better quantized correlation with limited overhead. First, we analyze the correlation between codewords and channel vectors uniform linear array (ULA) and uniform planar array (UPA). The correlation formula for the ULA channel can be expressed as an elliptic function, and the correlation formula for the UPA channel can be represented as an ellipsoid formula. Based on the analysis, we design a uniform sampling codebook to maximize the minimum quantized correlation and a dislocation ULA codebook to reduce the number of quantized bits further. Besides, we give a better sampling interval for the codebook of the UPA channel. Numerical results demonstrate the appealing advantages of the proposed codebook over existing methods in quantization bit number and quantization accuracy.