  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.
