Codebook Design for Limited Feedback in Near-Field XL-MIMO Systems

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Abstract
In this paper, we study efficient codebook design for limited feedback in extremely large-scale multiple-input-multiple-output (XL-MIMO) frequency division duplexing (FDD) systems. It is worth noting that existing codebook designs for XL-MIMO, such as the polar-domain codebook, have not well taken into account user (location) distribution in practice, thereby incurring excessive feedback overhead. To address this issue, we propose in this paper a novel and efficient feedback codebook tailored to the user distribution. To this end, we first consider a typical scenario where users are uniformly distributed within a specific polar-region, based on which a sum-rate maximization problem is formulated to jointly optimize angle-range samples and bit allocation among angle/range feedback. This problem is challenging to solve due to the lack of a closed-form expression for the received power in terms of angle and range samples. By leveraging a Voronoi partitioning approach, we show that uniform angle sampling is optimal for received power maximization. For the more challenging range sampling design, we obtain a tight lower bound on the received power and show that geometric sampling, where the ratio between adjacent samples is constant, can maximize the lower bound and thus serves as a high-quality suboptimal solution. We then extend the proposed framework to accommodate more general non-uniform user distribution via an alternating sampling method. Furthermore, theoretical analysis reveals that as the array size increases, the optimal allocation of feedback bits increasingly favors range samples at the expense of angle samples. Finally, numerical results validate the superior rate performance and robustness of the proposed codebook design under various system setups, achieving significant gains over benchmark schemes, including the widely used polar-domain codebook.
Funding Information
  • National Key Research and Development Program Youth Scientist Project (2023YFB2905100)
  • National Natural Science Foundation of China (62571227)
  • National Natural Science Foundation of China (62331023)
  • Basic and Applied Basic Research Foundation of Guangdong Province (2024A1515010097)
  • Korean Dermatological Association (JCYJ20240813094212016)
  • Korean Dermatological Association (2023QN10X152)
  • Guangzhou Basic and Applied Basic Research Project (2025A04J4588)
  • Zhejiang Key R&D Program (2023C01021)
  • Young Elite Scientists Sponsorship Program by China Association for Science and Technology (2023QNRC001)
  • Fundamental Research Funds for the Central Universities (226-2024-00069)
  • National Natural Science Foundation of China (U25A20389)
  • Korean Dermatological Association (KJZD20240903095402004)
  • Korean Dermatological Association (JCYJ20241202124934046)
  • Young Elite Scientists Sponsorship Program by CAST (YESS20240364)

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