A compact impedance-matched W-shaped antenna is presented that can radiate a perfect circular polarization (CP) at its boresight and distinct polarization states at different propagating directions in the far-field. The antenna structure consists of a horizontal dipole, a vertical dipole, and two elliptical loops connecting the adjacent arms of the dipole elements. The arc length and geometry of the loops are designed to produce the perfect CP at the boresight of the antenna. Using a single feed point, the antenna has an isotropic radiation pattern and is capable of producing distinct polarization states in different directions except for the plane of the antenna. Also, the symmetrical polarization characteristics with respect to the axes of the antenna symmetry are shown in the same propagating direction. This ambiguity of polarization can be resolved by using a pair of the proposed antennas operating at slightly different frequencies as a transmitter and triad dipoles to realize an azimuth-polar direction finding system. To demonstrate the validity of the antenna design, an antenna structure operating at 2.58 GHz is fabricated over a ground plane and measured. The measured radiation pattern shows the perfect CP at the boresight and 6.2% for the 3 dB axial ratio bandwidth.