Fast and efficient discovery of all neighboring nodes by a node new to
a neighborhood is critical to the deployment of wireless ad hoc networks.
Unlike conventional ALOHA-type random access discovery schemes, this work
considers the paradigm where all nodes in the neighborhood simultaneously
send their unique on-off signature waveforms known to the receive node.
The receive node then identifies its neighbors among all possible nodes
in the network.  The received signal in time domain is regarded as the
outcome of a set of measurements, where the outcome of a measurement is
positive if there is energy at the corresponding time instance from at
least one neighbor, and negative otherwise.  The neighbor discovery
problem becomes thus a compressed sensing problem, which can be solved
efficiently, with or without noise.  Two practical, scalable algorithms
are developed, which are shown to be effective both analytically and
through numerical results.  Comparison with conventional random access
schemes shows that the schemes based on group testing require much shorter
transmission time overall for reliable discovery of the neighbors.