Neighbor discovery in wireless networks with multipacket reception

Neighbor discovery is one of the first steps in configuring and managing a wireless network. Most existing studies on neighbor discovery assume a single-packet reception model where only a single packet can be received successfully at a receiver. In this paper, motivated by the increasing prevalence of multipacket reception (MPR) technologies such as CDMA and MIMO, we study neighbor discovery in MPR networks that allow multiple packets to be received successfully at a receiver. More specifically, we design and analyze a series of randomized algorithms for neighbor discovery in MPR networks. We start with a simple Aloha-like algorithm that assumes synchronous node transmissions and the number of neighbors, n, is known. We show that the time for all the nodes to discover their respective neighbors is Θ(ln n) in an idealized MPR network that allows an arbitrary number of nodes to transmit simultaneously. In a more realistic scenario, in which no more than k nodes can transmit simultaneously, we show that the time to discover all neighbors is Θ(n ln n/k). When a node knows whether its transmission is successful or not (e.g., based on feedbacks from other nodes), we design an adaptive Aloha-like algorithm that dynamically determines the transmission probability for each node, and show that it yields a ln n improvement over the simple Aloha-like scheme. Last, we extend our schemes to take into account a number of practical considerations, such as lack of knowledge of the number of neighbors and asynchronous algorithm operation, while resulting in only a constant or log n factor slowdown in algorithm performance.