## 2 Lunar Surface Propagation Path Loss Models  
To enhance surface exploration, multi-robot systems are being extensively researched. Accordingly, understanding the operational environment is crucial for accurate radio propagation modeling due to differences between lunar and terrestrial conditions. While propagation models for signal strength are well-established on Earth, their suitability for lunar sites requires careful evaluation due to the unique lunar conditions [19]. Different approaches to propagation modeling can be seen in the literature. The very well-known approach is that of NASA [20], which presented the application of an adapted Longley-Rice model for irregular terrains along with digital elevation data that accurately represent a real lunar location. This model is well suited to estimating path loss deviation from theoretical attenuation over a reflecting surface. This model also validated the field data collected during the Apollo project. This approach also enables the estimation of radio frequency (RF) path loss across the lunar landscape. Another approach was to introduce lunar propagation models that take inspiration from various established terrestrial communication models such as Fresnel zones, the free-space path loss model, and the irregular terrain model including reflection and diffraction due to irregular terrains [19]. This approach was used to formulate a radio propagation model tailored to the lunar environment, specifically designed for micro-rovers equipped with low-height antennas. By utilizing this newly developed model alongside the Digital Elevation Model of the Apollo 15 Mission's landing site, a series of simulations were conducted to forecast the feasible communication range and the quality of links for three different micro-rovers. Another approach is to utilize the free-space model, two-ray model, and spherical diffraction model to estimate radio attenuation on the lunar surface [21]. This model can accurately predict the link budget in lunar surface communication. The results were close to that of the model predicted in [20]. In [22], a solution for predicting path loss in lunar communication when encountering obstacles is outlined. This method simplifies transmission loss across the lunar surface into four typical scenarios based on lunar surface irregularities and obstacle shapes. The analysis accounts for free-space transmission loss, ground proximity loss, diffraction loss, and antenna gain. Additionally, data from the Apollo project were incorporated into this study, demonstrating that their accuracies align well with the model presented in [20]. Moreover, a lunar wireless model was developed in [23]. In this proposed model, the Digital Elevation Model from four distinct lunar sites is employed. These models were generated through measurements taken by the Terrain Mapping Camera, which was part of Chandrayaan-1, a recent lunar mission conducted by India. A lunar wireless mode examines all potential occurrences and signal degradations relevant to the wireless sensor network deployed on the lunar surface and anticipates minimal diffraction loss compared to the primary factors of direct path attenuation and multipath signal reflections for the specific intended usage. Given the primary objective of establishing unobstructed line-of-sight communication between transmitting and receiving units, this level of loss was disregarded. In [24], there was an attempt to develop a propagation analysis incorporating terrain characteristics, frequency considerations, and antenna height. The aforementioned models did not directly account for these factors. Given that reflections and diffractionsare the dominant mechanisms in terrain-specific effects at higher frequencies, it becomes crucial to realistically incorporate these effects. In this context, the geometrical theory of diffraction (GTD) was employed, allowing for the consideration of reflections and diffractions from three-dimensional (3-D) lunar terrain, including craters.