Compound antennas are disclosed, as are aircraft comprising compound antennas and methods to use compound antennas. In one embodiment, a compound antenna comprises a ground plane, a helix antenna element comprising a first dielectric core having a first end and a second end and coupled to the ground plane at the first end, the helix antenna element exhibiting a normal mode polarization pattern, and a conical spiral antenna element disposed proximate the helix antenna element, the conical spiral antenna element exhibiting an axial mode polarization pattern, wherein both the normal-mode and the axial mode patterns are circular polarization patterns and have the same sense. Other embodiments may be described.