Capacity Analysis and Optimal Spacing Design for Regular Hexagonal Array MIMO Systems

This letter delves into determining the optimal antenna element spacing for the regular hexagonal array (HA) within a constrained spatial aperture to maximize multi-input multi-output (MIMO) system capacity. Towards this end, a precise mathematical relation between the system capacity with deploying HAs and the antenna element spacing is meticulously established. Given that the element spacing is implicitly interwoven with the coupling matrix, radiation efficiency, and correlation matrix, we employ the Marcenko-Pastur law, polynomial graph fitting (PGF), and considering logarithmic correction to the Hannan limit to address complex mathematical challenges. These techniques enable the explicit modeling of coupling effects, radiation efficiency, and channel eigenvalues as functions of antenna spacing, thereby facilitating the solving of the optimization problem. Remarkably, using the derived optimal spacing of 0.606261-wavelength for HA configuration yields capacity improvements of 46.04% compared to that of half-wavelength spacing and 48.55% over traditional uniform planar array (UPA). Furthermore, this methodology demonstrates exceptional adaptability, offering a robust framework that can be effectively extended to other planar array structures operating under similar constraints.