Cross-Correlation of Large-Scale Parameters in Multi-Link Systems: Analysis Using the Box-Cox Transformation

Spatially distributed transmission points connected to the same source, known as distributed antenna systems, can improve system performance compared with single-link traditional systems. However, the anticipated gain depends heavily on the cross-correlation properties of the large-scale parameters (LSPs) of the different links. Usually, measured LSPs - except the large-scale fading-have non-Gaussian distributions. Therefore, in order to study their multi-link cross-correlation properties, scenario- and parameter-specific ad-hoc transformations are applied, such that the LSPs have Gaussian distributions in the transform domain [1], [2]. In this paper, we propose using the Box-Cox transformation as a general framework for homogenizing this conversion step. The Box-Cox transformation is, by nature, not distribution specific; therefore, it can be used regardless of the empirical distributions of the studied LSPs. We demonstrate the applicability of the proposed framework by studying multi-link fully-coherent propagation measurements of four base stations and one mobile station in a suburban microcell environment at 2.6 GHz. The inter- and intra-link cross-correlation of four LSPs - the large-scale fading, the delay, azimuth, and elevation spreads-are analyzed and their distributions are modeled. Based on our analysis, it is found that for the investigated environment: 1) the LSPs of the different links can be modeled using unimodal and bimodal Gaussian distributions; and 2) the inter- and intra-link cross-correlation coefficients of the different studied LSPs can be modeled using the Truncated Gaussian distribution. The proposed models are validated using the Kolmogorov-Smirnov test, and their parameters are provided.