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A data representation technique dubbed Kolmogorov model (KM), has been applied to the beam alignment problem in large-dimensional antenna systems. The previous learning-based beam alignment solely focused on utilizing the predictive power of KM, i.e., the capability of predicting the outcome of random variables that are outside the training set, to reduce the beam training overhead. However, a distinctive feature of KM, namely, the interpretability which enables the capability of extracting additional information hidden inside the data, has not yet been exploited. Moreover, the prohibitively high computational complexity of the existing KM learning algorithm offsets the benefits brought by KM and hampers its application to large-scale problems. In this paper, we propose a joint beam alignment and tracking framework by incorporating the predictability and interpretability of KM. Especially, our proposed scheme enables a novel interpretable beam tracking that reveals insights on relations among the sounded observations to alleviate the beam sounding overhead after the initial beam alignment. To reduce the computational complexity of KM learning, two enhancement approaches, based on discrete monotonic optimization (DMO) and dual optimization, respectively, are proffered. Numerical results demonstrate that the proposed methods can reduce the computational cost of the existing KM learning algorithm by up to three orders of magnitude. Furthermore, the proposed methods show superior beam alignment and tracking performance over other state-of-the-art techniques, notably in the low signal-to-noise ratio (SNR) regime.

KM Learning for Millimeter-Wave Beam Alignment and Tracking: Predictability and Interpretability