Optimization Between Estimation Error and Transmit Energy in Cross-Correlation Based Underwater Network Cardinality Estimation

Network cardinality is a very crucial factor to ensure proper functionality of a communications network. Due to the harsh underwater environment, cardinality estimation of underwater wireless communications network using conventional protocol based methods of terrestrial networks is very challenging and inefficient. Hence, a cross-correlation based estimation approach using Gaussian signals is applied for this purpose. To obtain better performance using this estimation approach, it is assumed that the length of the signals is infinity, which is practically impossible because it implies infinite transmit energy. For this reason, it is required to investigate the effect of various signal length (N _s) on estimation performance. In process of achieving this goal, a relation between the N _s and estimation error is derived in this paper. Using this relationship, optimization between estimation error and transmit energy is obtained as N _s is an energy related term in the estimation process.