Learning on a Grassmann Manifold: CSI Quantization for Massive MIMO Systems

TL;DR

This paper introduces a data-driven, machine learning-based method for designing beamforming codebooks in massive MIMO systems by formulating the problem as an unsupervised clustering task on a Grassmann manifold, leading to improved beamforming gains.

Contribution

It presents a novel model-free approach using K-means clustering on Grassmann manifolds for CSI quantization, extending to product codebooks for full-dimension MIMO systems.

Findings

Achieves higher beamforming gains than existing techniques.

Reduces codebook size while maintaining performance.

Demonstrates effectiveness through simulation results.

Abstract

This paper focuses on the design of beamforming codebooks that maximize the average normalized beamforming gain for any underlying channel distribution. While the existing techniques use statistical channel models, we utilize a model-free data-driven approach with foundations in machine learning to generate beamforming codebooks that adapt to the surrounding propagation conditions. The key technical contribution lies in reducing the codebook design problem to an unsupervised clustering problem on a Grassmann manifold where the cluster centroids form the finite-sized beamforming codebook for the channel state information (CSI), which can be efficiently solved using K-means clustering. This approach is extended to develop a remarkably efficient procedure for designing product codebooks for full-dimension (FD) multiple-input multiple-output (MIMO) systems with uniform planar array (UPA) antennas. Simulation results demonstrate the capability of the proposed design criterion in learning the codebooks, reducing the codebook size and producing noticeably higher beamforming gains compared to the existing state-of-the-art CSI quantization techniques.