Downtilt Optimization of Array Antennas Based on Envelope Radiation Patterns for HAPS Service Links With Massive MIMO

High-altitude platform stations (HAPSs) are gaining traction as a promising technology for significantly expanding coverage to aerial, maritime, and mountainous areas in 6G communication. Service links with a single HAPS are expected to provide extensive coverage ranging from 50 km to 100 km, making the design of suitable array antenna configurations for different coverage sizes a critical challenge. In multi-user multiple-input multiple-output (MU-MIMO) systems, communication capacity depends not only on the array antenna configuration but also on user distribution and precoding schemes. Consequently, optimizing antenna configurations while considering all these factors is practically complex. This paper proposes antenna configuration optimization method capable of maximizing any given percentile value of signal-to-noise ratio (SNR) to suit the coverage size of HAPS by isolating the geometric configuration of the antennas from other variables. Specifically, by utilizing the rotational symmetry of the HAPS service area, we model arbitrary array antennas as multi-tier circular arrays. We introduce an evaluation metric based on the beam envelope and formulate the antenna configuration optimization problem as a downtilt optimization problem. The joint optimization problem of downtilt angles can be reduced to individual optimization problems for each circular array, and we demonstrate the downtilt optimization using the gradient descent method. Based on the optimization results, we propose a tilted cylindrical array, comprising side elements of a traditional cylindrical array antenna tilted at optimal angles, and compare its performance with conventional planar, hemispherical, and cylindrical arrays. Consequently, the proposed tilted cylindrical array demonstrates the highest performance, improving the 50-th percentile and 5-th percentile SNR values by approximately 3.5 dB in a coverage radius of 50 km compared to its non-tilted counterpart. Improvement effects were observed in both single-user MIMO and MU-MIMO scenarios, confirming the effectiveness of the proposed antenna configuration optimization method.