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

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.

A Literature Survey on AI-Aided Beamforming and Beam Management for 5G and 6G Systems

“…With progressive phase weights applied to each element of each codeword, the DFT codebook steers the beams around the angular space according to these weights and the antenna elements. Despite being simple and robust, this codebook has some limitations: although it may cover all directions, many of them may not have direct use and increase the time of the beam training [150]. Because they are generic, these codebooks may have their performance compromised by imperfections in the hardware of the transceiver [149].…”

“…Based on the pilots received in an uplink transmission, with the proposed architecture, the codewords that generate the highest gain for the received pilot are chosen and adjusted according to the back-propagation algorithm. To maximize the normalized average gain of beamforming, Bhogi et al [150] propose a beamforming codebook generation model where learning adapts to propagation conditions. Using the K-means model, the results showed improvements in beamforming compared to CSI quantization techniques and still managed to reduce the codebook size.…”

“…Reduces the codebook design problem to an unattended clustering problem in a Grassmann collector. [150] Limited feedback…”

A Literature Survey on AI-Aided Beamforming and Beam Management for 5G and 6G Systems

“…With progressive phase weights applied to each element of each codeword, the DFT codebook steers the beams around the angular space according to these weights and the antenna elements. Despite being simple and robust, this codebook has some limitations: although it may cover all directions, many of them may not have direct use and increase the time of the beam training [146]. Because they are generic, these codebooks may have their performance compromised by imperfections in the hardware of the transceiver [145].…”

“…Based on the pilots received in an uplink transmission, with the proposed architecture, the codewords that generate the highest gain for the received pilot are chosen and adjusted according to the back-propagation algorithm. To maximize the normalized average gain of beamforming, Bhogi et al [146] proposed a beamforming codebook generation model where learning adapts to propagation conditions. Using the k-means model, the results showed improvements in beamforming compared to CSI quantization techniques and still managed to reduce the codebook size.…”