This paper proposes a simple, low-cost multi-mode patch antenna combining good MIMO performance with precise Angle of Arrival (AoA) estimation. The AoA is based on the monopulse antenna concept, however, unlike in radar applications, the necessity for complex circuitry is replaced by the intrinsic properties of even and odd resonant patch modes. This capability is advantageous for future "Internet of Things" antennas, embedded into low-cost and size-constrained devices. The envelope correlation coefficient, measured in an anechoic chamber, is below 1.5 %, ensuring good MIMO performance. An exemplary addition to localization algorithm exploiting antenna properties is demonstrated.