Directional ZigZag: Neighbor Discovery with Directional Antennas

We introduce a new neighbor discovery method for wireless nodes with adaptive antennas, called "directional ZigZag." Adaptive antennas are capable of electronically changing their gain pattern and in particular form beams and steer them in arbitrary directions. Despite improving range, this makes neighbor discovery more difficult. We consider three cases; namely, nodes transmit with beamsteering and receive in omni-directional mode (DTOR), transmit with omni-directional antenna and receive with beam- steering (OTDR), and use beamsteering (directional antennas) for both transmitting and receiving (DTDR). We show that directional ZigZag detects the neighbors with vanishing probability of error. Furthermore, it is the first algorithm that requires a discovery period that scales on linearly with the average number of neighbors. This is proven through establishing a connection between ZigZag and message passing decoding.