Channel Covariance Conversion and Modelling Using Infinite Dimensional Hilbert Spaces

This study considers the channel covariance conversion problem, which consists in estimating the spatial covariance matrix of a wireless channel by exploiting measurements obtained on a different carrier frequency and stationarity properties of the propagation environment across sufficiently close frequency bands. The first contribution given in this study is a modelling framework based on infinite dimensional Hilbert spaces that unifies a plethora of classical and novel covariance models with different degrees of complexity and generality, while still effectively capturing important properties of the propagation environment and of the antenna array. Given this framework, this study addresses the channel covariance conversion problem by proposing two simple yet effective algorithms based on set-theoretic methods that outperform existing model-based approaches both in terms of accuracy and complexity. In particular, the first algorithm is implementable as a simple matrix -vector multiplication. Moreover, in contrast to the aforementioned approaches, both algorithms can be applied to general propagation and array models such as dual-polarized antenna arrays, making them suitable for modern 5G and beyond systems.