Research on neighbor discovery algorithms in wireless ad hoc networks

Abstract

Neighbor discovery is of paramount importance in initialization of wireless ad hoc networks. In this paper, we deal with a variety of neighbor discovery algorithms. Vasudevan, Sudarshan, et al. (2013) designed non-feedback/feedback based neighbor discovery algorithms in single-hop networks having n nodes. They considered two cases where all nodes initially know the network size or not. They argue that the order of running time of feedback based algorithm is O(n) and that of non-feedback algorithm is O(n log n) regardless of the fact that initial network size is known to all nodes or not. However, we find that the order of running time of feedback-based algorithm when the initial network size is unknown to all nodes is indeed $(2^{\lceil \log_2 n \rceil} - n)O(ln n)$ + O(n). We propose two neighbor discovery algorithms for this case. The first algorithm uses maximum likelihood estimation and the other uses adaptive transmission probability. We simulated these algorithms and the simulation results showed great performance enhancement compared to the previous algorithms not using maximum likelihood estimation and adaptive transmission probability. In addition, we assume a simple packet error case and find that the order of running time of a feedback based neighbor discovery algorithm with initial network size n is $O(n(\log_{1/Pe} n+1))$ when the network has a positive packet error probability $P_e$. The order of running time of non-feedback neighbor discovery algorithm when the initial network size is known to all nodes in a packet error case is multiplied by a factor of $O(\log_{1/Pe}n+1)$ compared to no packet error case.