Antenna array calibration is necessary to maintain the high fidelity of beam patterns across a wide range of advanced antenna systems and to ensure channel reciprocity in time division duplexing schemes. Despite the continuous development in this area, most existing solutions are optimised for specific radio architectures, require standardised over-the-air data transmission, or serve as extensions of conventional methods. The diversity of communication protocols and hardware creates a problematic case, since this diversity requires to design or update the calibration procedures for each new advanced antenna system. In this study, we formulate antenna calibration in an alternative way, namely as a task of functional approximation, and address it via Bayesian machine learning. Our contributions are three-fold. Firstly, we define a parameter space, based on near-field measurements, that captures the underlying hardware impairments corresponding to each radiating element, their positional offsets, as well as the mutual coupling effects between antenna elements. Secondly, Gaussian process regression is used to form models from a sparse set of the aforementioned near-field data. Once deployed, the learned non-parametric models effectively serve to continuously transform the beamforming weights of the system, resulting in corrected beam patterns. Lastly, we demonstrate the viability of the described methodology for both digital and analog beamforming antenna arrays of different scales and discuss its further extension to support real-time operation with dynamic hardware impairments.

翻译：天线阵列校准对于维持先进天线系统中波束方向图的高保真度以及确保时分双工方案中的信道互易性至关重要。尽管该领域持续发展，但现有多数解决方案针对特定无线电架构进行了优化、需要标准化的空中数据传输，或是作为传统方法的扩展。通信协议和硬件的多样性构成了问题性案例，因为这种多样性要求为每个新型先进天线系统设计或更新校准程序。本研究采用替代性方式将天线校准表述为函数逼近任务，并通过贝叶斯机器学习加以解决。我们的贡献包含三个方面。首先，基于近场测量定义参数空间，该空间捕获了与每个辐射单元相关的底层硬件缺陷、其位置偏移以及天线单元间的互耦效应。其次，采用高斯过程回归从稀疏近场数据集中构建模型。部署后，学习到的非参数模型可有效持续转换系统的波束赋形权重，从而生成修正后的波束方向图。最后，我们论证了所述方法在不同规模数字与模拟波束赋形天线阵列中的可行性，并讨论了其扩展至支持动态硬件缺陷实时运行的进一步方向。