Neighbor discovery is a first step in the initialization of wireless networks in large-scale ad hoc networks. In this paper, we propose a randomized neighbor discovery scheme for wireless networks with a multi-packet reception (MPR) capability. We let the nodes to have different advertisement probabilities. The node gradually adjusts its probability according to its operation phases: greedy or slow-start. In the greedy phase, the node advertises aggressively while it does moderately in the slow-start phase. Initial phase and advertisement probability are determined randomly. Then, the nodes change the probability adaptively according to advertisements the reception state from the other nodes. In order to decide the reception state precisely, the exact number of nodes in the network is necessary. To make our proposed scheme work in case of no prior knowledge of the population, we propose a population estimation method based on a maximum likelihood estimation. We evaluate our proposed scheme through numerical analysis and simulation. Through the numerical analysis, we show that the discovery completion time is lower bounded in [Formula presented] and upper bounded in [Formula presented] when there exists N nodes with MPR-k capability. The bounds are the same as those of previous studies that propose static optimal advertisement probability. Through the simulation, we evaluate that our adaptive scheme outperforms in terms of discovery completion time, advertisement efficiency, and wasted time slot ratio than a scheme with static advertisement probability when the population of the network is unknown.
