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

TL;DR

This work tackles the CSI feedback bottleneck in near-field XL-MIMO frequency-division duplexing systems by proposing a distribution-aware codebook framework. It introduces a three-phase CSI-feedback protocol and a polar-domain Phase-1 codebook paired with an RVQ Phase-2 codebook, featuring a novel geometric range-sampling strategy guided by Voronoi partitioning to maximize received power. The authors prove that angle sampling should be uniform and that range sampling should adopt a geometric progression, extend the approach to nonuniform user distributions, and provide bit-allocation insights showing $B_1= ext{O}( ext{log} M)$ and $B_2= ext{O}(K)$. Numerical results reveal significant rate gains over polar-domain baselines, especially with limited feedback and larger arrays, and demonstrate robustness to distribution mismatches and multi-path settings.

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 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 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 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.

Figures (20)

• Figure 1: An XL-MIMO near-field communication system.
• Figure 2: Comparison of FDD transmission protocols.
• Figure 3: $f$ vs. $\varepsilon_{r}$ (given $\varepsilon_\theta=0$) and $\varepsilon_\theta$ (given $\varepsilon_{r} = 0$) with $\vartheta=1$ (other parameters refer to Section \ref{['sec:number_sim']}).
• Figure 4: Accuracy verification of Lemma \ref{['lemma:Gamma_approximation']} with $p=11$ (other parameters refer to Section \ref{['sec:number_sim']}).
• Figure 5: An example of uniform partitioning of the angle domain $\mathcal{Q}$ with $3$ angle samples $\{\hat{\theta}_1,\hat{\theta}_2,\hat{\theta}_3\}$. The blue region is the Voronoi cell $\mathcal{C}_2$. The boundaries of Voronoi cells $\dot{\theta}_i$ are represented by black lines. Red dots denote the angle samples. The black dot denotes an arbitrary angle $\theta$ that falls into the Voronoi cell $\mathcal{C}_2$, whose optimal angle sample is $\hat{\theta}_2$.

Theorems & Definitions (16)

• Lemma 1
• proof
• Lemma 2
• proof
• Lemma 3
• proof
• Lemma 4
• proof
• Proposition 1
• proof