Cross-correlation based Approach for Counting Nodes of Undersea Communications Network Considering Limited Bandwidth

Background and Objectives: Node counting is undoubtedly an essential task since it is one of the important parameters to maintain proper functionality of any wireless communications network including undersea acoustic sensor networks (UASNs). In undersea communications networks, protocol-based node counting techniques suffer from poor performance due to the unique propagation characteristics of the medium. To solve the issue of counting nodes of an undersea network, an approach based on cross-correlation (CC) of Gaussian signals has been previously introduced. However, the limited bandwidth (BW) of undersea communication presents a significant challenge to the node counting technique based on CC, which traditionally uses Gaussian signals with infinite BW. This article aims to investigate this limitation. Methods: To tackle the infinite BW issue, a band-limited Gaussian signal is employed for counting nodes, impacting the cross-correlation function (CCF) and the derived estimation parameters. To correlate the estimation parameters for finite and infinite BW scenarios, a scaling factor (SF) is determined for a specific BW by averaging their ratios across different node counts. Results: Error-free estimation in a band-limited condition is reported in this work if the SF for that BW is known. Given the typical undersea BW range of 1–15 kHz, it is also important to establish a relationship between the SF and BW. This relationship, derived and validated through simulation, allows for determining the SF and achieving accurate node count under any band-limited condition within the 1–15 kHz range. Furthermore, an evaluation of node counting performance in terms of a statistical parameter called the coefficient of variation (CV) is performed for finite BW scenarios. As a side contribution, the effect of noise on the CC-based undersea node counting approach is also explored.Conclusion: This research reveals that successful node counting can be achieved using the CC-based technique in the presence of finite undersea BW constraints.