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 5 G and beyond systems.

中文翻译：

---

使用无限维希尔伯特空间的通道协方差转换和建模


本研究考虑了信道协方差转换问题，其中包括通过利用在不同载波频率上获得的测量值以及在足够接近的频带内传播环境的平稳性特性来估计无线信道的空间协方差矩阵。本研究的第一个贡献是基于无限维希尔伯特空间的建模框架，该框架统一了大量具有不同复杂度和通用性的经典和新颖的协方差模型，同时仍然有效地捕获传播环境和天线阵列的重要属性。在这个框架下，本研究通过提出两种基于集合论方法的简单而有效的算法来解决通道协方差转换问题，这些算法在准确性和复杂性方面均优于现有的基于模型的方法。具体地，第一算法可实现为简单的矩阵向量乘法。此外，与上述方法相比，这两种算法都可以应用于通用传播和阵列模型，例如双极化天线阵列，使其适用于现代 5G 及更高版本的系统。