Optimal Elevation of Phased Array Antennas in Pyramidal Configurations Using a Minimax-Based Approach

Hemispherical scan coverage is required in many communications applications such as satellite communications and surveillance and tracking systems. Phased array antennas in pyramidal configurations are used to provide hemispherical scan coverage since they provide a significant reduction in scan losses compared to a single planar array. This paper presents a novel approach based on minimax optimization for determining the elevation angle of the individual planar arrays in a pyramidal configuration, given a general hemispherical coverage requirement. This approach always returns an optimal solution, unlike the equalization-based methods traditionally used in the literature. The analysis demonstrates the significant design improvement offered by the minimax-based approach for a small number of arrays and for narrow coverage ranges. It also demonstrates how the advantage of this approach becomes less pronounced at and near full hemispherical coverage and for a large number of arrays.