Up to now, conventional compact antennas have been designed to acquire as much gain as an ideal 6-port polarimetric antenna can obtain. It was recently shown that an achievable number of degrees of freedom (DOF) can be increased regardless of given antenna space. Here, we propose a compact directional 16-port antenna, with a size of about (0.5 lambda)(3) and a radiation frequency of 2 GHz, which allows more than a six-DOF gain to be achieved using pattern gain. We analyze the far field of the proposed 16-port antenna using spherical vector-wave modes and show that the ergodic capacity of the proposed 16-port antenna is close to that of an ideal 16-port antenna.