An antenna system which is capable of having omnidirectional transmitting and receiving capabilities is disclosed. The antenna system includes a plurality of directional antennas coupled to a transceiver, wherein the antennas are configured to have their main lobes extend in different directions. In a specific embodiment, there are six directional antennas configured to have their main lobes extend substantially along the positive and negative x-axes, the positive and negative y-axes, and the positive and negative z-axes of a three-dimensional Cartesian system. The six directional antennas may also be configured to transmit and receive signals to and from overlapping free space regions to give it omnidirectional coverage. Also disclosed are a network device which employs such antenna system, a wireless network system which employs a plurality of network devices each having such antenna system, and a method and software module to transmit and receive data using such antenna system.