Near-field communication (NFC) system provides a plurality of transmit antennae. The transmit antennae of the plurality have at least two different polarizations. A plurality of receive antennae have polarizations arranged to receive signals from respective antennae of the transmit antennae, such that each polarization of the transmit antennae has a receive antennae with a corresponding polarization. The transmitters are tuned to a transmit frequency and each have a dimension. A distance between the receive and the transmit antennae is no greater than a greater of twice a maximum dimension squared of the transmit antennae divided by a wavelength of transmission and a wavelength of transmission divided by 2π.