Correlation-Aware Optimal Antenna Spacing for HAPS Massive MIMO With Uniform Planar Arrays

Abstract

High-altitude platform stations (HAPS) have received significant attention in recent years due to their inherent advantages, including wide-area line-of-sight connectivity, rapid deployment, and the ability to provide a flexible aerial layer between terrestrial and satellite networks. These characteristics position HAPS as a promising component of integrated space–air–ground architectures for sixth-generation (6G) communication systems. However, the strong line-of-sight (LoS) propagation that benefits the link budget can also lead to highly correlated multiuser channels, particularly when users have limited angular separation as observed from the HAPS. To mitigate this effect, this paper develops a correlation-aware HAPS massive multi-input multi-output (MIMO) framework with uniform planar array (UPA) in which the inter-element spacing is treated as an optimization variable rather than being fixed at the conventional half-wavelength spacing. A closed-form LoS correlation coefficient is derived for an $M_{x} \times M_{y}$ UPA, and the probability that the correlation magnitude exceeds a prescribed threshold is obtained by accounting for the corresponding main-lobe and grating-lobe regions. The spacing is selected to minimize the excessive-correlation probability. Monte Carlo evaluations compare half-wavelength and optimized arrays in terms of excessive-correlation probability, the probability of at least one correlated user pair, and the lower tail of zero-forcing sum-rate under max–min power control. The results demonstrate that the proposed UPA spacing optimization enhances the robustness of multiuser HAPS transmission while explicitly characterizing the tradeoff between increased array aperture and grating-lobe ambiguity.