The path-loss exponent (PLE) is a key parameter in wireless propagation channels. Therefore, obtaining the knowledge of the PLE is rather significant for assisting wireless communications and networking to achieve a better performance. Most existing methods for estimating the PLE not only require nodes with known locations but also assume an omni-directional PLE. However, the location information might be unavailable or unreliable and, in practice, the PLE might change with the direction.

In this paper, we are the first to introduce two directional maximum likelihood (ML) self-estimators for the PLE in wireless networks. They can individually estimate the PLE in any direction merely by locally collecting the related received signal strength (RSS) measurements. The corresponding Cram´er-Rao lower bound (CRLB) is also obtained. Simulation results show that the performance of the proposed estimators is very close to the CRLB. Additionally, also for the first time, the RSSs based on only a geometric path loss are found to follow a truncated Pareto distribution in wireless random networks. This might be of great help in the analysis of wireless communications and networking.