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 packets from multiple simultaneous transmitters to be received successfully at a receiver. Starting with a clique of n nodes, we first analyze a simple Aloha-like algorithm and show that it takes Θ((n ln n)/k) time to discover all neighbors with high probability when allowing up to k simultaneous transmissions. We then design two adaptive neighbor discovery algorithms that dynamically adjust the transmission probability for each node. We show that the adaptive algorithms yield a Θ(ln n) improvement over the Aloha-like scheme for a clique with n nodes and are thus order-optimal. Finally, we analyze our algorithms in a general multi-hop network setting. We show an upper bound of O((Δ ln n)/k) for the Aloha-like algorithm when the maximum node degree is Δ, which is at most a factor ln n worse than the optimal. In addition, when Δ is large, we show that the adaptive algorithms are orderoptimal, i.e., have a running time of O(Δ/k) which matches the lower bound for the problem.