Modeling the Doppler Shift in Cislunar Environment with Gaussian Mixture Models

This study investigates the RF-based Doppler shift distribution characterization of the Lunar South Pole (LSP) based inter-satellite link (ISL) in varying inclination. Doppler shift in parts per million (ppm) is determined and analyzed, as it provides an independence from the carrier frequency. Due to unknown relative velocity states duration, the Gaussian Mixture Model (GMM) is found to be the best fitting distribution for ISLs with $1^\circ$ inclination interval Doppler shift with respect to a predetermined satellite. Goodness-of-fit is investigated and quantified with Kullback-Leibler (KL) divergence and weighted mean relative difference (WMRD) error metrics. Simulation results show that ISL Doppler shifts reach up to $\pm1.89$ ppm as the inclination of the other orbit deviates higher from the reference orbit, inclining $80^\circ$. Regarding the error measurements of GMM fitting, the WMRD and KL divergence metrics for ISL take values up to 0.6575 and 2.2963, respectively.

Multi-Orbiter Continuous Lunar Beaming

In this work, free-space optics-based continuous wireless power transmission between multiple low lunar orbit satellites and a solar panel on the lunar rover located at the lunar south pole are investigated based on the time-varying harvested power and overall system efficiency metrics. The performances are compared between a solar panel with the tracking ability and a fixed solar panel that induces \textit{the cosine effect} due to the time-dependent angle of incidence (AoI). In our work, the Systems Tool Kit (STK) high-precision orbit propagator, which calculates the ephemeris data precisely, is utilized. Interestingly, orbiter deployments in constellations change significantly during a Moon revolution; thus, short-duration simulations cannot be used straightforwardly. In our work, many satellite configurations are assessed to be able to find a Cislunar constellation that establishes a continuous line-of-sight (LoS) between the solar panel and at least a single LLO satellite. It is found that 40-satellite schemes enable the establishment of a continuous WPT system model. Besides, a satellite selection method (SSM) is introduced so that only the best LoS link among multiple simultaneous links from multiple satellites will be active for optimum efficiency. Our benchmark system of a 40-satellite quadruple orbit scheme is compared with 30-satellite and a single satellite schemes based on the average harvested powers and overall system efficiencies 27.3 days so the trade-off options can be assessed from the multiple Cislunar models. The outcomes show that the average system efficiencies of single, 30-satellite, and 40-satellite schemes are 2.84%, 32.33%, and 33.29%, respectively, for the tracking panel and 0.97%, 18.33%, and 20.44%, respectively, for the fixed solar panel case.

Hybrid FSO and RF Lunar Wireless Power Transfer

This study focuses on the feasibility analyses of the hybrid FSO and RF-based WPT system used in the realistic Cislunar environment, which is established by using STK HPOP software in which many external forces are incorporated. In our proposed multi-hop scheme, a solar-powered satellite (SPS) beams the laser power to the low lunar orbit (LLO) satellite in the first hop, then the harvested power is used as a relay power for RF-based WPT to two critical lunar regions, which are lunar south pole (LSP) (0{\deg}E,90{\deg}S) and Malapert Mountain (0{\deg}E,86{\deg}S), owing to the multi-point coverage feature of RF systems. The end-to-end system is analyzed for two cases, i) the perfect alignment, and ii) the misalignment fading due to the random mechanical vibrations in the optical inter-satellite link. It is found that the harvested power is maximized when the distance between the SPS and LLO satellite is minimized and it is calculated as 331.94 kW, however, when the random misalignment fading is considered, the mean of the harvested power reduces to 309.49 kW for the same distance. In the next hop, the power harvested by the solar array on the LLO satellite is consumed entirely as the relay power. Identical parabolic antennas are considered during the RF-based WPT system between the LLO satellite and the LSP, which utilizes a full-tracking module, and between the LLO satellite and the Malapert Mountain region, which uses a half-tracking module that executes the tracking on the receiver dish only. In the perfectly aligned hybrid WPT system, 19.80 W and 573.7 mW of maximum harvested powers are yielded at the LSP and Mountain Malapert, respectively. On the other hand, when the misalignment fading in the end-to-end system is considered, the mean of the maximum harvested powers degrades to 18.41 W and 534.4 mW for the former and latter hybrid WPT links.

Continuous Power Beaming to Lunar Far Side from EMLP-2 Halo Orbit

This paper focuses on FSO-based wireless power transmission (WPT) from Earth-Moon Lagrangian Point-2 (EMLP-2) to a receiver optical antenna equipped with solar cells that can be located anywhere on the lunar far side (LFS). Different solar-powered satellite (SPS) configurations which are EMLP-2 located single stable satellite and EMLP-2 halo orbit revolving single, double, and triple satellites are evaluated in terms of 100% LFS surface coverage percentage (SCP) and continuous Earth visibility. It is found that an equidistant triple satellite scheme on EMLP-2 halo orbit with a semi-major axis length of 15,000 km provides full SCP for LFS and it is essential for the continuous LFS wireless power transmission. In our proposed dynamic cislunar space model, geometric and temporal parameters of the Earth-Moon systems are used in affine transformations. Our dynamic model enables us to determine the full coverage time rate of a specific region such as the LFS southern pole. The outcomes show that the equidistant double satellite scheme provides SCP=100% during 88.60% time of these satellites' single revolution around the EMLP-2 halo orbit. Finally, the probability density function (PDF) of the random harvested power $P_H$ is determined and it validates the simulation data extracted from the stable EMLP-2 satellite and revolving satellite around EMLP-2 halo orbit for minimum and maximum LoS distances. Although the pointing devices to mitigate random misalignment errors are considered for the stable and revolving SPSs, better pointing accuracy is considered for the stable satellite. Our simulations show that the probability of $P_H\le$41.6 W is around 0.5 for the stable satellite whereas the CDF=0.99 for the revolving satellite case for a transmit power of 1 kW.

Mitigation of Misalignment Error Over Inter-Satellite FSO Energy Harvesting

In this paper, the impact of the acquisition, tracking, and pointing (ATP) module utilization on inter-satellite energy harvesting in low-earth orbit (LEO) is investigated for various beam divergence angles. Random elevation and azimuth misalignment error angles at both the transmitter and the receiver are modeled with Gaussian distribution hence the radial pointing error angle can be modeled with Rayleigh distribution statistically. Then, the misalignment loss factors at the transmitter and receiver are obtained independently. The harvested power as a function of the transmit power and inter-satellite distance is analyzed along with the maximum achievable range that satisfies the 1U (i.e., 0.1$\times$0.1$\times$0.1 m) small satellite power requirement on space tasks. Our simulation results show that in a free space optics (FSO) link without the ATP module, a laser with a wider beam divergence angle $\theta$ puts an effort to compensate for the loss of misalignment and hence provides higher harvested power than narrow ones. However, when the ATP module is in use, the laser with narrower $\theta$ outperforms the laser with wider $\theta$ in harvested power. Furthermore, the utilization of the ATP module leads to a significant improvement in the maximum achievable range.