Antennas without phase center (AWPC) have been used for Direction-of-Arrival estimation. However, these structures, being symmetric, always face the whole-space ambiguity problem. This paper proposes a new asymmetric AWPC structure for DOA estimation that is able to resolve the ambiguity in the whole space. In addition, the structure is optimized in such a way that it is compact and isotropic. Simulated results indicate the effectiveness of the proposed structure.