Coded Beam Training

TL;DR

This work tackles the reliability-overhead tradeoff in beam training for XL-MIMO by embedding channel coding concepts into hierarchical beam training, forming a coded beam training framework. By establishing a duality between hierarchical beam training and channel coding, it enables the use of conventional codes (e.g., Hamming and convolutional codes) to protect the spatial-direction decisions against noise, thereby extending coverage to remote users with low $SNR$ while keeping pilot overhead small. The paper introduces two implementations: (i) a (7,4) Hamming-code based scheme with a seven-layer codebook and error-correcting beam encoding/decoding, and (ii) a convolutional-code based scheme with a $N=3,k=1,n=2$ encoder, GS-based codeword design, and a Viterbi-based decoder using an $LLR$ tailored to $\chi^2$-distributed beam training signals. Simulation results show substantial gains in success rate and achievable rate at low SNR and a significant reduction in training overhead (approximately 98% over exhaustive search), along with extended user coverage; the approach can extend to hybrid precoding and multi-user scenarios. Overall, coded beam training provides a practical, scalable path to reliable implicit CSI acquisition for next-generation XL-MIMO systems.

Abstract

In extremely large-scale multiple input multiple output (XL-MIMO) systems for future sixth-generation (6G) communications, codebook-based beam training stands out as a promising technology to acquire channel state information (CSI). Despite their effectiveness, when the pilot overhead is limited, existing beam training methods suffer from significant achievable rate degradation for remote users with low signal-to-noise ratio (SNR). To tackle this challenge, leveraging the error-correcting capability of channel codes, we introduce channel coding theory into hierarchical beam training to extend the coverage area. Specifically, we establish the duality between hierarchical beam training and channel coding, and the proposed coded beam training scheme serves as a general framework. Then, we present two specific implementations exemplified by coded beam training methods based on Hamming codes and convolutional codes, during which the beam encoding and decoding processes are refined respectively to better accommodate the beam training problem. Simulation results have demonstrated that the proposed coded beam training method can enable reliable beam training performance for remote users with low SNR while keeping training overhead low.

Figures (11)

• Figure 1: Illustration of the DFT codebook, $\mathcal{W}$, and the hierarchical codebook, $\mathcal{C}_{\rm hier}$, where the subscript "hier" in omitted in the figure.
• Figure 2: The codebook $\mathcal{C}_{\rm ham}$ designed by the (7,4) Hamming code (14 codewords in 7 layers in total), where the subscript is omitted in the figure.
• Figure 3: Space-time beam pattern: directions are encoded into $\bm x$ and then beam pattern $\mathcal{V}$ is constructed based on it.
• Figure 4: Overall framework of channel codes-aided hierarchical beam training with adaptive convolutional codes as an example.
• Figure 5: Illustration of the convolutional encoder.