⚡ electrical engineering

Parallax-aware and MAB-empowered Beam Training for Modular XL-MIMO Systems

This paper proposes a parallax-aware and multi-armed bandit-empowered beam training scheme for modular XL-MIMO systems that synergistically combines adaptive codebook updates with a greedy exponential Thompson sampling strategy to dynamically compress the action space and optimize beam selection, thereby achieving substantial effective spectral efficiency gains with significantly reduced training overhead in hybrid near- and far-field environments.

Original authors: Chuanpeng Xu, Huibin Liang, Yunchao Song, Chen Liu, Yusong Wang

Published 2026-10-27

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CC BY 4.0

Original authors: Chuanpeng Xu, Huibin Liang, Yunchao Song, Chen Liu, Yusong Wang

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

In the race to build the next generation of wireless networks, engineers are pushing antennas to become larger and more powerful than ever before. Imagine a wall of radio antennas stretching for meters, packed with hundreds of tiny elements. This massive scale allows signals to travel further and carry more data, but it creates a tricky problem: the environment around these antennas is not uniform. Some signals bounce off nearby objects, behaving like ripples spreading out from a stone dropped in a pond, while others travel from far away, arriving as flat, parallel waves. Because the antenna wall is so wide, it sees these two types of waves at the same time, and the best way to catch a signal changes depending on exactly where the user is standing. If the system tries to guess the right direction by testing every single possibility, it wastes so much time and energy that the actual data transmission slows to a crawl.

To solve this, researchers at Nanjing University of Posts and Telecommunications have developed a smarter way to find the best signal path without wasting time on dead ends. They created a system that acts like a seasoned guide who learns the terrain as they walk. Instead of blindly checking every corner of the antenna wall, the system first builds a map based on the physical layout of the hardware. It understands that because the antenna wall is so large, the angle needed to hit a nearby object looks different from one end of the wall to the other, a phenomenon known as parallax. By accounting for this shift, the system creates a starting list of likely directions that covers the area without leaving gaps.

Once this initial map is ready, the system begins to learn. It tests a few directions and listens to the feedback from the user's device. If a direction yields a strong signal, the system remembers it. If a direction is just noise, it marks it as useless. The researchers used a learning method inspired by how a gambler might choose which slot machine to play, balancing the need to try new options with the desire to stick with what is already known to work well. As the system gathers more data, it detects when it has found a stable pattern. At that point, it performs a clever trick: it takes the successful directions found on one part of the antenna wall and projects them onto the other parts, adjusting for the physical distance between them. This allows the system to instantly know which directions are promising for the entire wall, rather than testing them one by one.

To ensure it does not waste time on empty space, the system also runs a statistical check to confirm whether a signal is real or just random static. If a direction is confirmed to be empty, the system removes it from its list of options entirely. This process of pruning the list of possibilities happens continuously, shrinking the search space until the system is only looking at the most promising paths. In computer simulations, this approach proved to be highly efficient. The system reached its best performance much faster than older methods and maintained a high rate of data transfer even when the signal had to travel through complex environments with many bouncing paths. By combining a physical understanding of the antenna's shape with a learning algorithm that adapts in real time, the researchers showed that it is possible to get the full power of these massive antenna arrays without the heavy cost of constant, exhaustive searching.

Technical Summary: Parallax-aware and MAB-empowered Beam Training for Modular XL-MIMO Systems

Problem Statement
The paper addresses the challenge of beam training in Modular Extremely Large-Scale MIMO (XL-MIMO) systems operating in hybrid near- and far-field environments. As array apertures increase, the Rayleigh distance extends significantly, causing users and scatterers to exist simultaneously in both near-field (spherical wave) and far-field (plane wave) regions. This hybrid-field propagation introduces severe spatial non-stationarity and parallax effects, where optimal beam directions vary non-linearly across different subarrays.

Conventional centralized beam training relies on full-dimensional instantaneous Channel State Information (CSI), resulting in prohibitive pilot overhead and vulnerability to channel fluctuations. While statistical CSI (S-CSI) and partially-connected subarray architectures offer hardware and complexity relief, existing methods often rely on static codebooks or predefined activation patterns. These approaches struggle with dynamic, spatially non-stationary channels, leading to prolonged blind exploration and slow convergence. Furthermore, applying standard Multi-Armed Bandit (MAB) frameworks directly to XL-MIMO is hindered by the "curse of dimensionality," as static action spaces prevent efficient pruning of noise-only sectors.

Methodology
The authors propose a closed-loop synergy framework that integrates an Adaptive Codebook Update Mechanism with MAB-empowered online learning. The scheme operates within a modular Extremely Large Aperture Array (M-ELAA) consisting of $N$ subarrays, each with $M$ antennas.

Parallax-Aware (PA) Initial Codebook:
To address spatial non-stationarity, the authors derive a mathematical definition for beam index redundancy based on subarray displacement and the uniform power distance. This allows the construction of an initial codebook that ensures full spatial coverage by adding precise angular overlap between adjacent subarrays, eliminating blind spots caused by the parallax effect.
Steady-State Detection and Dynamic Codebook Update:
The system monitors the beam training process using an empirical Quantile-Quantile (Q-Q) correlation criterion to detect statistical steady states. Once convergence is reached, the system triggers a cross-subarray geometric projection.
- Geometric Projection: Validated high-gain beams from one subarray are projected onto other subarrays using spatial-frequency gradients. This accounts for both far-field (planar) and near-field (spherical) extremes to define a candidate interval.
- Likelihood Ratio (LR) Pruning: To prevent the candidate set from expanding with low-gain or noise-only codewords, a Likelihood Ratio test is applied for zero-power detection. Beams identified as pure noise are pruned, dynamically compressing the action space.
MAB-empowered Beam Training (G-Exp-TS):
Within the compressed, adaptive action space, the beam selection process is formulated as a MAB problem. The objective is to maximize long-term Effective Spectral Efficiency (ESE).
- Reward Modeling: The received signal power is modeled as following an exponential distribution.
- G-Exp-TS Strategy: The authors propose a Greedy Exponential Thompson Sampling (G-Exp-TS) strategy. This approach balances exploration and exploitation by sampling from the exponential posterior distribution of the received power.
- Optimization: The beam selection is cast as a 0-1 integer programming problem to select the optimal subset of codewords (super arm) that maximizes the long-term average ESE, subject to a training overhead budget.

Key Contributions

Closed-Loop Synergy Framework: The paper introduces a framework that fundamentally integrates adaptive codebook updating with MAB learning. Unlike static approaches, this scheme converts geometric priors into dynamic candidate search regions and uses statistical feedback to prune the codebook in real-time, avoiding redundant exploration in noise sectors.
Parallax-Aware Initialization and Dynamic Pruning: The authors derive a rigorous definition for beam index redundancy to construct a PA initial codebook. They further introduce a steady-state detection mechanism based on Q-Q correlation and a geometric projection method coupled with an LR test. This achieves substantial codebook dimensionality reduction by dynamically removing invalid sectors without requiring explicit CSI.
G-Exp-TS Optimization: The beam training process is transformed into a 0-1 integer programming problem. The proposed G-Exp-TS strategy leverages the exponential posterior distribution of signal power to optimally balance exploration and exploitation, maximizing long-term ESE.

Simulation Results
Numerical simulations were conducted for a system with $N=8$ modules, $M=32$ antennas per module, and a carrier frequency of 100 GHz. The proposed scheme (G-Exp-TS BT) was compared against TH BT, Dual-UCB BT, and Hybrid BT baselines.

Convergence: The proposed scheme demonstrated rapid convergence to a stable steady state. The ESE increased during the exploration phase and stabilized quickly due to effective pruning of noise-dominated candidates.
Performance vs. SNR: Across various Signal-to-Noise Ratio (SNR) levels and numbers of scattering clusters ( $L=1, 3$ ), the proposed scheme consistently achieved higher ESE than all baseline schemes.
Overhead Efficiency: Unlike baseline schemes that exhibited an inverted-U trend (where excessive overhead led to performance degradation due to over-exploration), the proposed scheme achieved peak ESE at a minimal overhead budget. The dynamic compression of the codebook ensured that even with a large allocated budget, the actual training overhead remained bounded by the number of valid codewords, preventing time-fraction penalties.
Robustness: The scheme maintained robust performance across different multipath conditions and SNR regimes, effectively identifying dominant hybrid-field paths.

Significance
The paper claims that the proposed scheme fundamentally improves the efficiency of beam training in modular XL-MIMO systems. By synergizing geometric priors with online learning, the method bypasses the prohibitive overhead of traditional exhaustive sweeping and the slow convergence of static MAB approaches. The ability to dynamically compress the action space without explicit CSI allows the system to significantly reduce pilot overhead while maximizing Effective Spectral Efficiency. The authors conclude that this approach provides a practical solution for the hybrid-field challenges inherent in future 6G networks, offering a robust alternative to rigid, pre-defined beam training strategies.

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