Radio Propagation Modelling for Coordination of Lunar Micro-Rovers

i-SAIRAS2020-Papers (2020) 5047.pdf

RADIO PROPAGATION MODELLING FOR COORDINATION OF LUNAR MICRO-ROVERS

Virtual Conference 19-23 October 2020

Shreya Santra1, Leonard Bryan Paet1, Emanuel Staudinger2 and Kazuya Yoshida1

1Department of Aerospace Engineering, Tohoku University, Aoba 6-6-01, Aramaki, Aoba-ku, Sendai, Miyagi 980-0879, Japan, Email: [email protected], [email protected], [email protected] 2Institute of Communications and Navigation, German Aerospace Center (DLR) e.V., Oberpfaffenhofen, Muenchener Str 20, Wessling 82234, Germany, Email: [email protected]

ABSTRACT link quality prediction is a crucial requirement for evaluating the design of wireless communication This paper focuses on radio propagation modelling channels and mission planning. A robust and reliable towards a coordinated path planning solution for communication architecture between the multiple micro-rovers on the lunar surface. Radio agents will enable better coordination and result in an communication scenarios on the Moon greatly differ effective collective behavior [1]. from those on Earth. We account for these differences Radio propagation modelling is primarily concerned by reviewing several existing terrestrial around the way radio waves travel between systems at communication models to devise a site-specific radio both ends of a wireless communications link. The goal propagation model that accommodates the lunar is to determine whether a signal from a transmitting conditions, particularly for micro-rovers with low- device can be successfully received by another device height antennas. Using the devised model and the in a different location. Large-scale propagation Digital Elevation Model (DEM) of Apollo 15 Mission modelling, which typically covers distances from landing site, simulations were performed for three hundreds to thousands of meters, predicts the micro-rovers to predict the viable communication combined path losses affecting the radio signal based range and link quality. Received signal strength on available knowledge about the prevailing indicator (RSSI) maps and path loss graphs were propagation environment [2]. generated taking into account the lunar regolith Various propagation phenomena occur during radio properties, terrain geometry, operating signal transmissions that determine the path loss. For frequency, and antenna properties. instance, the receiver may receive a direct attenuated The results presented in this paper enable reliable signal (also called as line-of-sight (LOS) signal) from point-to-point communication and maintain the transmitter and indirect signals (or non-line-of- continuous connectivity between the moving micro- sight (NLOS) signal) due to the physical and rovers exploring the lunar surface. environmental effects like reflection, refraction, diffraction, and scattering. Observations show that the Keywords: Radio Propagation, Lunar surface, Swarm propagation characteristics are significantly affected Robotics, Path Planning, Communication by the Fresnel zones, terrain geometry, surface materials, antenna properties, and operating signal 1. INTRODUCTION frequency [3], [4]. Therefore, knowledge of the operational environment Lunar exploration has recently gained momentum, and is necessary to accurately model the radio propagation. several lander missions are proposed for the coming Various propagation models exist to determine the decade. Multi-robot systems are now being signal strength and predict link quality for terrestrial extensively studied for surface exploration missions as scenarios. However, the conditions on the Moon are they allow flexibility and provide a cost-effective different compared to that on Earth, and these models solution offering a promising alternative to single need to be reviewed carefully for applicability at lunar large rovers for wide-area lunar operations, such as sites. [5]. resource prospecting for deposits of water ice and This paper presents site-specific radio propagation volatiles. Precise coordination between these rovers is modelling and path loss characterization for the a challenge that involves inter-agent communication traverse path of the Apollo 15 landing site. The to enable the exchange of information while objective is to enable information driven path- navigating through unknown environments. Radio planning and coordinated surface exploration. i-SAIRAS2020-Papers (2020) 5047.pdf

2. RADIO PROPAGATION BASICS 2.2 Free-Space Path Loss Model is used to model the LOS path loss incurred in a free-space environment, This section discusses selected basics of radio without any absorption, diffraction, reflections, or propagation and reviews the models related to the other characteristic-altering phenomena. The equation work described in the later sections of this paper. for the combined path loss in the absence of any obstructions in the Fresnel zones is given by Eq. 2 2.1 Fresnel zones are ellipsoid-shaped regions of 휆 space between two radio antennas that determine the 퐹푆푃퐿[푑퐵] = 20푙표푔 ( ) (2) ‘radio LOS’ between them. Fig. 1 shows an example 10 4휋푑 communications link with the relevant Fresnel zones. where 휆 is the wavelength of the radio signal and d is the separation distance between transmitter and receiver [6].

2.3 Reflections Due to Irregular Terrain starts to become significant when a portion of the terrain, mutually visible to both transmitter and receiver antennas, breaches the 2nd Fresnel zone boundary, as illustrated in Fig. 2.

Figure 1: Fresnel Zone Ellipsoids and Clearances

The radius of the n-th Fresnel zone boundary at any point between a transmitter and receiver can be approximated using Eq. 1:

푑 푑 퐹 ≈ √푛휆 1 2 (1) 푛 푑

where 휆 is the wavelength of the radio signal, and d1 and d2 are the distances of the transmitter and receiver respectively from the point where the Fresnel zone Figure 2: Reflection due to irregular terrain radius is being calculated [6]. The volume enclosed by the boundary defined by F1 is the ‘1st Fresnel zone’, When this happens, the first challenge is to ascertain if while the intermediate volume between the boundaries specular reflection is possible. This is done by finding of F1 and F2 is the ‘2nd Fresnel zone’. In theory, there potential specular reflection point/s along the mutually is an infinite number of Fresnel zones between visible terrain. If a candidate point is not found, then transmitters and receivers. In practice, however, the specular reflection is not possible and the excess path first two zones are sufficient for determining the loss due to reflections is set to 0 [7]. If a specular reflection and diffraction phenomena occurring in reflection point is found, then the excess path loss due long-distance communication links [6]. to reflections (in dB) can be calculated using Eq. 3: When the 1st and 2nd Fresnel zones are clear of obstacles (i.e., when the path clearance hc at any point 2 in the terrain profile in Fig. 1 is below the 2nd Fresnel 퐿푅 [푑퐵] = −10푙표푔10|1 + 훤푒푓푓 푐표푠(훥휑)| (3) zone boundary), then the propagation environment can be treated as ‘free-space.’ The combined propagation where 훥휑is the phase difference between the LOS path loss is equal to free-space path loss (FSPL) as signal and the reflected wave, given by Eq. 4: described in Sec. 2.2. Otherwise, the effects of reflection or diffraction become significant. The path 2휋 훥휑 = [(푑 + 푑 )− 푑 ] (4) loss in excess of FSPL due to these phenomena can be 휆 푖푛 푟푒 퐿푂푆 calculated using the methods outlined in Secs. 2.3 - 2.4. i-SAIRAS2020-Papers (2020) 5047.pdf

and 훤푒푓푓is the effective reflection coefficient, loss predictions. The advantage of such an approach is presented in Eq. 5: that it considers actual lunar terrain profiles to predict the communication link between agents. This is 훤 = (휌 퐷) ∗ 훤 (5) particularly important when multiple micro-rovers are 푒푓푓 푠 following given trajectories. The limitations of the existing models are considered and adapted to achieve where the reflection coefficient (훤) at the specular a valid communication network design at the chosen reflection point modified by a surface roughness location on Moon. parameter (휌푠) and a divergence factor due to curvature of the surface (D). The reflection coefficient 3.1 Lunar Terrain Modelling (훤) can be computed using standard equations based on the surface electrical properties, antenna Apollo 15 was one of the few lunar landing missions polarization, and grazing angle at the specular which conducted several important scientific activities reflection point [7]. The surface roughness parameter on the surface of the Moon. The Apollo 15 landing site (휌푆) and divergence factor (D) are computed based on was located at 26.132°N, 3.634°E at the foot of the standard equations found in [7]. Apennine mountain range, with the objectives of sampling material from the rim of the Imbrium basin 2.4 Diffractions due to Irregular Terrain becomes a and studying the volcanic processes that produced significant cause of path loss when any part of the Hadley Rille. The Hadley-Apennine region has rock terrain covers 55% or more of the 1st Fresnel boundary fragments, rounded hill formations, and expansive [8]. Given a defined terrain profile between transmitter craters [13]. Fig. 3 shows the traverse paths for the and receiver antennas, we used methods outlined in astronauts during which they covered a total of 27.9 Section 4.5 of Recommendation ITU-R P.526-15 [8] km. to calculate the excess path loss due to diffraction (LD, in dB).

2.5 Irregular Terrain Model (ITM), also known as the Longley-Rice Model [9], is a semi-empirical model that takes into account the irregular terrain profile and electromagnetic properties to predict the signal distribution in a given area for frequencies between 20MHz and 10GHz [9]. ITM with necessary modifications has the highest potential for application to planetary surface communication, particularly for moving rovers utilizing the path-specified 3D geometry [10].

3. LUNAR RADIO PROPAGATION MODELLING Figure 3: Apollo 15 map with traverse path. Credits: Lunar terrain features and conditions are very different United States Geological Survey (USGS) from those of Earth. Therefore, terrestrial data with vegetation, buildings, and atmospheric effects are not A high-resolution Digital Elevation Map (DEM) of the applicable for lunar operations. For this work, a site based on measurements taken by the Narrow- specific lunar site was chosen, and the terrain Angle Camera (NAC) onboard the Lunar information was acquired for the study. Reconnaissance Orbiter (LRO) were obtained from After reviewing terrestrial propagation models, a the NASA Planetary Data Systems (PDS) archives. deterministic model for the Apollo15 landing site was This map was pre-processed using the Geospatial Data developed based on Secs. 2.2 - 2.4. This was then Abstraction Library (GDAL) [14] routines and was compared to a semi-empirical modified ITM to then loaded into MATLAB for simulations. analyze and predict the quality of RF signal propagation with free-space loss, reflection, and Fig. 4 shows the 3D view of the Apollo 15 DEM, a diffraction losses. Compared to previous efforts on rectangular area measuring 6820 meters (W) x 7580 lunar radio propagation modelling [3], [5], [10], [11], meters (H) at 5 meters/pixel resolution. [12], this work uses high-resolution lunar terrain maps of 5meters/pixel to perform site-specific radio path i-SAIRAS2020-Papers (2020) 5047.pdf

The parameters taken into account for subsequent simulations are listed in Tab. 1.

Table 1: Parameters used for the deterministic model for lunar RF propagation simulation Parameter Value

Moon Radius: 1737.4km

Antenna Height 8 meters (LM) 2 meters (RV)

Transmitter and Receiver Dipole (Gain = 2 Antennas dBi) Figure 4: 3D DEM for Apollo 15 landing site Operating Frequencies 259.7 MHz (VHF) 3.2 Site-Specific Lunar Path Loss Prediction 2.4 GHz (UHF)

Using the high-resolution Apollo 15 landing site Transmitter Power 50 W DEM, we performed lunar radio propagation modelling via two site-specific path loss prediction Receiver Sensitivity -60 dBm models in MATLAB: a deterministic model based on the methods outlined in Secs. 2.2-2.4 and a semi- Lunar regolith permittivity(ε) 3 empirical model based on a modified ITM. Lunar regolith conductivity(σ) S/m For the deterministic model, we followed the Reflection Coefficient -1 (approx.) framework as shown in Fig. 5. First, we load the preprocessed Apollo 15 DEM file to MATLAB via Antenna Polarization Vertical Mapping Toolbox. Next, we set the location of the lunar module (LM) and rovers (RVs) on this map. We The electrical conductivity ranges from 10−14 S/m then extract 2D terrain profiles from LM to RVs and −9 determine the appropriate path loss mode to use based when sunlit to 10 S/m in darkness [15]. For this work, we assume that the rover antenna on Fresnel zone clearances for the terrain. heights are significantly smaller than the propagation distances covered, which results to grazing angles 휑 ≈ 0. Hence, the reflection coefficient 훤 is approximated to -1 and the rough surface scattering

factor휌푠 ≈ 1. 3.3 Evaluation of Lunar Propagation Scenarios

Three LM to RVs (LM⇔RV) radio links were simulated by setting up a single transmitter at the Apollo 15 LM location and three micro-rovers acting as receivers located at various distances away from the LM. Fig. 6 shows the exact coordinates of these micro- rovers.

Figure 5: Deterministic path loss prediction model

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3.4 Map of Lunar Propagation Scenarios at the Apollo 15 Landing Site

We applied the deterministic model to generate radio propagation scenarios and RSSI maps at the Apollo 15 landing site. These maps assume a single transmitter at the Apollo 15 LM location. Two sets of plots were generated: one set for 259.7 MHz, and another for 2.4 GHz, signal frequencies. Figs. 8 and 9 show the radio propagation scenario maps for these two frequencies. We observed that the propagation condition at 259.7 MHz is mostly dominated by diffraction, while free- space propagation is possible at 2.4 GHz for distances close to LM.

Figure 6: LM⇔ RV radio links

The three links were chosen to correspond to three different lunar radio propagation scenarios. The 2D terrain profile for each link was extracted, and Fresnel zone clearance evaluations were performed on each link. Fig. 7 shows the Fresnel zone clearance plots for the three links at 2.4 GHz.

Figure 8: Map of radio scenarios on Apollo 15 site for 259.7 MHz, generated via deterministic model

Figure 7: Fresnel zone clearance plots @ 2.4 GHz (top) LM⇔ RV1, 200m (mid) LM⇔ RV2, 600m (bottom) LM⇔ RV3, 900m

Based on Fig. 7, it was observed that LM⇔RV1, which is the shortest link of the three, exhibits the free- space propagation scenario. Meanwhile, LM⇔RV2 matches to the diffraction propagation scenario. Lastly, LM⇔RV3 corresponds to the reflection Figure 9: Map of radio scenarios on Apollo 15 site propagation scenario. for 2.4 GHz, generated via deterministic model i-SAIRAS2020-Papers (2020) 5047.pdf

Figs. 10 and 11 show the corresponding received resemble a lunar-like environment. The rovers are signal strength maps. We noticed that while diffraction placed at the same locations as in Sec 3.3. This gives is more prevalent at 259.7 MHz compared to 2.4 GHz, an estimate of how the signals are affected by the the received signal strength levels are generally reflections and diffractions by including the terrain higher. This is due to an overall lower free-space path information and lunar conditions. loss at lower frequencies. 4.1 Antenna Patterns

To show the effects of lunar ground materials on a vertically polarized dipole antenna on the LM at a height of 8 meters, the radiation patterns for signals of two frequencies 259.7 MHz VHF and 2.4 GHz UHF are investigated at the site. Fig. 12 shows the comparison of radiation patterns for both the frequencies. The lunar ground acts as a partial reflector and partial absorber to the RF signals, causing changes in the antenna radiation patterns compared to an ideal dipole [3]. Such mechanisms are observed to be more prominent for 259.7 MHz frequency.

Figure 10: RSSI map for Apollo 15 landing site for 259.7 MHz, generated via deterministic model

Figure 12: Antenna pattern under lunar conditions at Apollo 15 site for 259.7 MHz (top) and 2.4 GHz (bottom) respectively

4.2 Signal Strength maps

To analyze the communication quality along the paths Figure 11: RSSI map for Apollo 15 landing site of the rovers, signal strength maps were generated for 2.4 GHz, generated via deterministic model using the modified ITM. The model has been parameterized to desert-like conditions minimizing the 4. COMPARISON WITH MODIFIED ITM effects of foliage. This model estimates higher loss values at longer distances as reflections and To validate the theoretical model with already diffractions become significant with distance and established models, simulations were conducted on interferes with the first Fresnel zone. MATLAB by modifying the existing ITM [16] to i-SAIRAS2020-Papers (2020) 5047.pdf

Figs. 13 and 14 show the RSSI maps of the coverage Table 2: Comparison of signal strength at each of the area for the LM with antenna height 8 meters from the rover locations for Deterministic Model and ground. Modified ITM

4.3 Transmission Path Loss

The point-to-point combined path loss between the LM (transmitter) and the rovers (receivers) over an irregular terrain is calculated by Eq. 6:

푃퐿[푑퐵] = 퐹푆푃퐿[푑퐵] + 푃퐿푒푥푐푒푠푠[푑퐵] (6)

where, PL[dB] is the combined path loss, FSPL[dB]

Figure 13: RSSI map for Apollo 15 landing site is free-space path loss, and 푃퐿푒푥푐푒푠푠[푑퐵] is excess for 259.7 MHz, generated via modified ITM path loss due to reflection (LR) or excess path loss due to diffraction (LD), whichever is appropriate. The RF path loss for the rover traverses during the signal transmission for both the models are shown in Fig. 15.

Figure 15: Transmission losses predicted along the rovers’ traverses with respect to the distance from LM for Deterministic and modified ITM Figure 14: RSSI map for Apollo 15 landing site for 2.4 GHz, generated via modified ITM As seen in Fig. 15, the transmission loss is higher at 2.4 GHz. It is also observed that the path loss estimates from the deterministic model are in close agreement with the estimates from the modified ITM, with the The signal strength at the location of the rovers for latter giving a slightly higher estimate at longer both the models are listed in Tab. 2 distances. It should be noted that these results are specific to the Apollo 15 site, while other sites with more sharp features would induce path loss different from that presented here.

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5. CONCLUSION [5] Pabari, J. P. et al. (2010) ‘Radio Frequency Modelling for Future Wireless Sensor Network on Site-specific radio propagation modelling will enable Surface of the Moon’, International Journal of accurate estimation of the communication link quality Communications, Network and System Sciences, on the lunar surface by accounting for the different 3(04), pp. 395–401. doi: propagation scenarios and terrain geometries along the doi:10.4236/ijcns.2010.34050. trajectory of a rover. A deterministic model based on theoretical constructions was developed and [6] Parsons, J. D. (2001) The Mobile Radio simulated, then compared with the existing semi- Propagation Channel (2nd e.d.). John Wiley & Sons. empirical ITM. The devised model is easily applicable if the elevation data and receiver path geometry for [7] Boithias, L. (1987) Radiowave Propagation. any chosen site is known. McGraw Hill, NewYork. Future work involves enabling the micro-rovers to coordinate with each other while they explore a target [8] ITU-R (2019) Propagation by diffraction. ITU-R area, such that they share positional information P.526-15. through the communication channel that can be applied in path planning. The next step is to perform [9] Rice, P. L. et al. (1965) Transmission Loss practical range-test experiments with rovers equipped Predictions for Tropospheric Communication with advanced radio systems to determine the Circuits. Technical Note 101. Boulder, Colorado. received-signal strength. This will establish the [10] Foore, L. and Ida, N. (2007) ‘Path Loss Prediction validity of the theoretical analysis and simulations to Over the Lunar Surface Utilizing a Modified Longley- evaluate the proposed communication solution in Rice Irregular Terrain Model’, in. Wireless for Space practical applications. Workshop, Colorado Springs: NASA.

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