Neighbor discovery is an important first step after the deployment of ad hoc wireless networks since they are a type of network that do not provide a communications infrastructure right after their deployment, the devices have radio transceivers which provide a limited transmission range, and there is a lack of knowledge of the potential neighbors. In this work two proposals to overcome the neighbor discovery in static one-hop environments in the presence of collisions, are presented. We performed simulations through Castalia 3.2, to compare the performance of the proposals against that for two protocols from the literature, i.e. PRR and Hello, and evaluate them according to six metrics. According to simulation results, the Leader-based proposal (O(N)) outperforms the other protocols in terms of neighbor discovery time, throughput, discoveries vs packets sent ratio, and packets received vs sent ratio, and the TDMA-based proposal is the slowest ( O(N 2 ) ) and presents the worst results regarding energy consumption, and discoveries vs packets sent ratio. However, both proposals follow a predetermined transmission schedule that allows them to discover all the neighbors with probability 1, and use a feedback mechanism. We also performed an analytical study for both proposals according to several metrics. Moreover, the Leader-based solution can only properly operate in one-hop environments, whereas the TDMA-based proposal is appropriate for its use in multi-hop environments.