Neighbor discovery represents a first step after the deployment of wireless ad hoc networks, since the nodes that form them are equipped with limited-range radio transceivers, and they typically do not know their neighbors. In this paper two randomized neighbor discovery approaches, called CDH and CDPRR, based on collision detection for static multi-hop wireless ad hoc networks, are presented. Castalia 3.2 simulator has been used to compare our proposed protocols against two protocols chosen from the literature and used as reference: the PRR, and the Hello protocol. For the experiments, we chose five metrics: the neighbor discovery time, the number of discovered neighbors, the energy consumption, the throughput and the number of discovered neighbors vs packets sent ratio. According to the results obtained through simulation, we can conclude that our randomized proposals outperform both Hello and PRR protocols in the presence of collisions regarding all five metrics, for both one-hop and multi-hop scenarios. As novelty compared to the reference protocols, both proposals allow nodes to discover all their neighbors with probability 1, they are based on collision detection and know when to terminate the neighbor discovery process. Furthermore, qualitative comparisons of the existing protocols and the proposals are available in this paper. Moreover, CDPRR presents better results in terms of time, energy consumption and number of discovered neighbors vs packets sent ratio. We found that both proposals achieve to operate under more realistic assumptions. Furthermore, CDH does not need to know the number of nodes in the network.