Tetrahedral array for constant gain hemispherical coverage

A system for monitoring a hemispherical space, comprising:

• a system for monitoring the hemispherical space, the system including a first sensor array configured to provide a substantially constant gain across nearly an entirety of the hemispherical space, the first sensor array having a trirectangular tetrahedron configuration including:
• a first face having a plurality of first elements arranged in a first aperiodic lattice;
• a second face disposed orthogonal to the first face, the second face having a plurality of second elements arranged in a second aperiodic lattice;
• and
• a third face disposed orthogonal to the first face and the second face, the third face having a plurality of third elements arranged in a third aperiodic lattice;
• wherein each of the first elements, the second elements, and the third elements have an antenna pattern which can be expressed in terms of a first polar angle θ and a second polar angle ϕ, whereby θ is viewing zenith angle and ϕ is azimuth, and
• wherein each of the first elements have a cos2(θ) power pattern and each of the second elements have a
• cos
• 2
• 
• (
• θ
• -
• π
• 2
• )
• power pattern relative to the first face.