Approximation of Correlation Matrix for High Altitude Platform Stations

A High Altitude Platform Station (HAPS) is a new and promising technology with different uses like wireless communication services, traffic monitoring, navigation applications and Internet of Things (IoT) applications. Since it is positioned much higher than ground-level users, line-of-sight (LOS) is more common in HAPS systems. Especially in HAPS systems that include multiple antennas, the effect of correlation between antennas is an important factor limiting the performance. The effect of correlation is strongly influenced by the spacing between the antenna elements and environmental factors. This effect can be reduced by the effect of rich scattering environment in terrestrial Multi-Input/Multi-Output (MIMO) systems, yet this observation is not applicable to HAPS systems. In this study, a tight bound expression for the correlation matrix which does not have an expression in closed form and has a significant place in the performance of HAPS systems has been obtained. Comprehensive numerical values have been obtained under different system parameters to demonstrate the convergence performance of the approximate expression to the real value, and the results have been compared.