Low-Complexity and Power-Efficient Precoding Codebook Design on Sparse Grassmannian

TL;DR

This paper introduces a sparse Grassmannian precoding codebook design that reduces complexity and power consumption while maintaining performance, outperforming current 5G codebooks in achievable rate and PAPR.

Contribution

It presents a novel sparse codebook construction method based on Schubert cell decomposition, significantly reducing computational complexity and storage compared to existing designs.

Findings

Achieves low PAPR and low complexity with performance comparable to optimal codebooks.

Outperforms 5G NR codebooks in achievable rate under Rayleigh fading.

Asymptotically approaches optimal performance in simulations.

Abstract

We propose a sparse Grassmannian design for precoding codebooks. Due to their sparse structure, our proposed codebooks achieve low peak-to-average power ratio (PAPR), low complexity of precoder multiplication, and low storage cost, while demonstrating performance comparable to the optimal codebook. Specifically, we introduce a method for constructing codebooks based on Schubert cell decomposition on the Grassmann manifold. Designing an optimal Grassmannian precoding codebook generally requires high computational complexity. In the proposed approach, by exploiting its sparsity, the objective function can be simplified, and the search space can also be significantly reduced compared to state-of-the-art codebooks. Numerical simulations in uplink systems demonstrate that the proposed sparse codebook asymptotically approaches the optimal codebook and outperforms the codebook currently adopted in 5G NR, in terms of achievable rate under uncorrelated Rayleigh fading channels, while maintaining substantially lower PAPR than conventional dense designs. These results confirm that the proposed sparse codebook can be a practical and power-efficient alternative to conventional codebooks for a wide range of uplink transmission scenarios.