Geosynchronous Orbit Research Articles

An Accurate and Efficient BP Algorithm Based on Precise Slant Range Model and Rapid Range History Construction Method for GEO SAR

The Geosynchronous Satellite Synthetic Aperture Radar (GEO SAR) operates at a high orbital altitude, resulting in an extended imaging time and substantial variations in slant range. Additionally, the GEO SAR satellite orbit experiences a bending effect, and the target’s movement, caused by the Earth’s rotation, is influenced by the Earth’s curvature. The back-projection (BP) algorithm has been proven to be a highly effective technique for precise imaging with GEO SAR by processing these specific echo signals. However, this approach necessitates considerable computational resources. Existing BP algorithms, such as the fast BP algorithm, do not consider the “Stop-and-Go” error present in GEO SAR. Consequently, we developed a Precise Slant Range Model that considers the motion of both the satellite and targets. The model incorporates velocity and acceleration factors to accurately represent the signal transmission from transmission to reception. Additionally, we propose a Rapid Range History Construction Method to lessen the computational burden of generating the three-dimensional range history array. By utilizing the Precise Slant Range Model and the Rapid Range History Construction Method, and employing parallel processing through aperture segmentation, we propose an Accurate and Efficient BP imaging algorithm suitable for GEO SAR applications. To validate its effectiveness, simulations were conducted using the parameters of a GEO SAR system. The results indicated that the proposed algorithm enhances the imaging quality of GEO SAR, reduces the processing time, and achieves high-precision rapid imaging, thereby improving operational efficiency.

Design and Instrument Characterization of the High‐Energy Resolution Relativistic Electron Telescope (HERT) Using Geant4 Simulation

AbstractEarth's outer radiation belt is filled with relativistic (∼100s of keV–3 MeV) and ultrarelativistic (∼>3 MeV) electrons. The acceleration of electrons to these high energies are believed to be caused by inward radial transport and local acceleration, but the relative importance of the two mechanisms to electrons with different energies are still under considerate debate. In the post Van Allen Probes era, measurements of radiation belt populations must rely on small space missions such as CubeSats and SmallSats. The Miniaturized High‐Energy‐Resolution relativistic electron Telescope (HERT) is a compact (≤3U) telescope designed for a CubeSat mission in geosynchronous transfer orbit (GTO). HERT's main objective is to provide high‐energy‐resolution measurements of outer belt electrons in an energy range of ∼1–7 MeV to help differentiate the contribution of inward radial transport and local acceleration. Geant4 simulations were conducted to characterize the instrument responses. A novel method of using a spherical cap particle source in Geant4 simulation was developed for more efficient instrument characterization. Combined with Bow tie analysis, it is demonstrated that HERT will have an energy resolution of 5% for ∼1.5–3 MeV electrons and 12% for ∼3–7 MeV with current electronics design. In addition, using the AE9 model, we showed the instrument would have statistically sufficient count rates in the outer belt while not saturating the electronics. With a compact configuration and higher energy resolution in comparison to previous instruments, HERT will significantly contribute to the quantitative understanding of the radiation belt electron dynamics.

An optimization framework with improved auction-based initialization for highly constrained on-orbit servicing mission planning

The on-orbit servicing (OOS) mission planning problem for multiple geosynchronous earth orbit (GSO) satellites is a critical issue due to its huge economic value. However, given the complexity of the space scenario and the subjective nature of the formulation process, the problem is highly constrained in actual use, and the performance of conventional optimization algorithms decreases due to fuel or mission deadline constraints. With the goal of enhancing solution quality and speeding up the solution process, this paper proposes a novel optimization framework. The problem is decomposed into three sub-problems and then solved using the proposed three-level algorithm to lessen its complexity. In addition, a new initialization method is embedded to improve global search capabilities. Notably, considering the high computation efficiency of the auction algorithm (AA), an improved version is designed to generate primary solutions, which introduces the grouping and reallocation mechanism. Then, several variations of the primary solutions are used as the initial variables in the optimization. Numerical simulations demonstrate that the proposed methodology has higher computational efficiency and convergence performance than conventional strategies.

Building the Space Elevator Tether

A simple Earth-based space elevator consists of a cable or tether extending from the surface to well beyond geosynchronous orbit. A climber grips the tether, pulling itself upward and delivering payload to space. For a space elevator to be feasible, the material from which the tether is built must be strong enough that the tether can support itself and any climbers that ascend it. Three such materials exist today and their industrial-scale production seems near at hand. These materials are compared and, based on previous studies, required improvements for each are listed. The material properties, along with the load, determine the shape and mass of the tether. Two example tether shapes are shown: one using the constant stress model and another which takes into account atmospheric winds and orbital debris. Options for tether construction are discussed. These are influenced by the material fabrication process, the way in which materials are combined and arranged in the tether and how much of the fabrication takes place on Earth or in space. Keywords: Space Elevators, Strong Materials, Tether Construction

A station-keeping maneuver detection method of non-cooperative geosynchronous satellites

Orbit maneuver detection is one of the major concerns for the work of Space Situation Awareness of GEO protected region. In this study, we propose a non-cooperative GEO satellites station-keeping maneuver detection approach based on the two-dimensional Convolutional Neural Network (CNN) and the public Two-Line Element (TLE). The proposed method focuses on identifying “station-keeping categories” using the time series segments of TLE data. The time series TLE of the selected objects are converted into several equal-sized segments using a window slicing method. These segments are then used to train a two-dimensional CNN classification model that can divide the input data into three categories of maneuver. The applicability of the proposed method on satellites in the same orbital region were further tested using other objects that had not been included during the modeling process. Experimental results demonstrated the feasibility and robustness of the proposed method, with a classification macro F1-score of 94.45%, macro precision of 94.48%, and macro recall of 94.46%. The results suggest that the proposed method provides a promising solution for detecting GEO station-keeping maneuvers.

Multi-agent reinforcement learning satellite guidance for triangulation of a moving object in a relative orbit frame

Multi-agent systems are of ever-increasing importance in a contested space environment—use of multiple, cooperative satellites potentially increases positive mission outcomes on orbit, while autonomy becomes an ever-increasing requirement to increase reaction time to dynamic situations and lower the burden on space operators. This research explores multi-agent satellite swarm Guidance, Navigation, and Control (GNC) using deep reinforcement learning (DRL). DRL policies are trained to provide guidance inputs to agents in multi-agent swarm environments for completing complex, teamwork-focused objectives in geosynchronous orbit. An example scenario is explored for a group of satellite agents maneuvering to triangulate an object that is non-stationary in the relative orbit frame. Reward shaping is used to encourage learning guidance that positions swarm members to maximize triangulation accuracy, using angles-only observations for navigation relative to the target. Results show the policies successfully learn guidance through reward shaping to improve triangulation accuracy by a significant factor.

Design of VO2-based spacecraft smart radiator with low solar absorptance

Thermochromic film with the ability to self-adaptively switch emittance is important for spacecraft missions experiencing rapidly increasing demand. Current research on thermochromic films primarily focuses on optimizing emittance tunability, while the solar absorptance of these films remains high, limiting their practical application in spacecraft thermal control. In this work, a VO2-based spacecraft smart radiator with low solar absorptance and high emittance tunability is proposed. The smart radiator is a multilayer structured film composed of a switchable resonator (i.e., a superposed Fabry-Perot cavity) and a solar reflector (i.e., a Distributed Bragg Reflector). The performance of the smart radiator is optimized by combining the Rigorous Coupled Wave Analysis method and Genetic Algorithm, achieving a normal solar absorptance of 0.121 and emittance tunability of 0.825. The solar absorptance and emittance tunability of the smart radiator remain excellent even at large incident angles. The underlying mechanisms involved in the smart radiator are attributed to the combination of superposed Fabry-Perot resonance and multiple solar reflectance. In addition, we provide a numerical example using a geosynchronous orbit satellite to demonstrate that the regulation range of the net heat dissipation flux density can increase from 146.5–463.9 W/m2 by using Optical Solar Reflector to 0–494.6 W/m2 when using the proposed smart radiator within the permissible temperature range (263.15–318.15 K) of spacecraft. This VO2-based spacecraft smart radiator with outstanding properties which outperform the existing thermochromic films reveals the promising potential of thermochromic films for spacecraft intelligent thermal control applications.

A Study of Solar Radiation Pressure Model in BDS-3 Precise Orbit Determination

For the BDS (BeiDou Navigation Satellite System) satellites, the solar radiation pressure is the major non-gravitational perturbation the satellites suffer. Due to the influence of multiple factors, accurate modeling the solar radiation pressure acting on these satellites is difficult to accomplish. The solar radiation pressure perturbation is an essential source of error in the precise orbit determination (POD) and orbit prediction processes of the BDS satellites. As the ECOMC (Empirical CODE Orbit Model 1 and 2 Combined) model adopts the advantageous features of the ECOM1 (Empirical CODE Orbit Model 1) model and the ECOM2 (Empirical CODE Orbit Model 2) model, a greater number of parameters have been introduced into the model, leading to strong correlation between the ECOMC model parameters. In response to the deficiency of the ECOMC model, the authors collected the BDS-3 satellite precise ephemeris data that were provided by Wuhan University (WHU) from January 2019 to April 2022. And by these ephemeris data, the ECOMC model’s 13 parameters were obtained through the dynamic orbit fitting method. By conducting these time sequence diagrams analysis of the ECOMC model parameters, this thesis affords the selection strategies of the solar radiation pressure parameters of the ECOMC model for BDS-3 inclined geosynchronous orbit (IGSO) and medium earth orbit (MEO) satellite. And the rationality of the selection strategies of the solar radiation pressure parameters for the ECOMC model was verified by orbit fitting and orbit prediction experiments. The results show that using the improved ECOMC model gains the best orbit fitting effects for BDS-3 IGSO and MEO satellite, and can also enhance the accuracy of medium and long-term orbit prediction of BDS-3 IGSO and MEO satellite.

Multiobjective Mission Planning for Multiple Geosynchronous Spacecraft Refueling

This paper studies the multiple geosynchronous spacecraft refueling problem (MGSRP) with multiple servicing spacecraft (Ssc) and fuel depots (FDs). In the mission scenario, multiple Ssc and FDs are parked in the geosynchronous Earth orbit (GEO) initially. Ssc start from FDs and maneuver to visit and refuel multiple GEO targets with known demands. These capacitated Ssc are expected to rendezvous with fuel-deficient GEO targets and FDs for the purpose of delivering the fuel stored in FDs to GEO targets. The objective is to find a set of Pareto-optimal solutions with minimum fuel cost and mission duration. The MGSRP is a much more complex variant of multidepot vehicle routing problems mixing discrete and continuous variables. A two-nested optimization model is built. We propose a new multiobjective hybrid particle swarm optimization to solve the outer-loop problem, and the design variables are the refueling sequence, task assignment, time distribution, and locations of FDs. In the inner-loop problem, branch and bound method is used to find the optimal decision variable for a given outer-loop solution. Finally, numerical simulations are presented to illustrate the effectiveness and validity of the proposed approach.

An improved satellite-induced code bias correction model for BDS un-GEO satellites in consideration of elevation and azimuth angles

The satellite-induced code bias (SICB) resulting in code-phase divergences of nearly 1.0 m has been observed in the code measurements of BeiDou navigation satellite system (BDS). Since the SICB is proved to be elevation- and frequency-dependent, several SICB correction models have been proposed to remove the systematic bias, but most of them only consider elevation angles, overlooking the influence of azimuth angles, which would limit the accuracy of the correction models, especially for Medium Earth Orbit (MEO) satellites. To deal with this problem, we proposed an improved SICB piecewise correction model as a function of elevation and azimuth angles and estimated parameters for each BDS un-GEO (Geostationary Earth Orbit) satellite and each available frequency with node-separation of 1°. The epoch-difference method is employed to remove the effect of stable terms, such as phase-ambiguities, receiver- and satellite-dependent hardware delays. Moreover, to reduce the effect of code noise and multipath at low-elevation conditions, the threshold of elevation angle for the improved model is determined based on the statistics of Multipath (MP) combinations. Besides, weight-average algorithm is used to obtain the optimal MP deviations and improve the accuracy of proposed correction model in consideration of signal-to-noise (SNR). The experiment results with real GNSS data show that the SICB models are more suitable for BDS-2 MEO satellites than Inclined Geosynchronous Orbit (IGSO) satellites. The code measurements on B1 signal are more susceptible to the SICB than that on B3 signal. After applying the improved SICB correction models, the RMS errors of MP series are significantly reduced for BDS-2 un-GEO satellites. However, for BDS-3 satellites, only centimeter-level SICB deviations can be detected for all frequency-bands, and the RMS of MP variations have slight changes after applying the SICB corrections, indicating that the systematic bias in MP combinations is not obvious, especially for BDS-3 MEO satellites.

Satellite Clustering for Non-Terrestrial Networks: Concept, Architectures, and Applications

Recently, megaconstellations with a massive number of low Earth orbit (LEO) satellites are being considered as a possible solution for providing global coverage due to relatively low latency and high throughput compared to geosynchronous orbit (GEO) satellites. However, as the number of satellites and operators participating in the LEO constellation increases, inter-satellite interference will become more severe, which may yield marginal improvement or even decrement in network throughput. In this article, we introduce the concept of satellite clusters that can enhance network performance through satellites’ cooperative transmissions. The characteristics, formation types, and transmission schemes for the satellite clusters are highlighted. Simulation results evaluate the impact of clustering from coverage and capacity perspectives, showing that when the number of satellites is large, the performance of clustered networks outperforms the unclustered ones. The viable network architectures of the satellite cluster are proposed based on the 3rd Generation Partnership Project (3GPP) standard. Finally, the future applications of clustered satellite networks are discussed.

A Nonlinear Dependence on the Geomagnetic Activity of the Ratio of the Maximum Stream Flux of Charged Particles in a Geostationary Orbit to the Minimum Stream Flux

A new mathematical model was proposed using an ordinary differential equation that analytically(when the index of geomagnetic activity Kp = const or Kp ≈ const) or numerically (if Kp(t) ≠ const) describesperpendicular (for a pitch angle of 90°) differential or integral fluxes of relativistic electrons in a geostationary(geosynchronous) orbit, as well as in any circular orbit in the Earth’s magnetosphere. The model assumes thatthe fluxes depend on the local time LT in orbit, the Kp, MacIlvwaine parameter and L, and the perpendiculardifferential flux or integral flux of relativistic electrons taken at 0000:00 LT. We use observations of relativistic(2 MeV) electron fluxes averaged over the local time hour along the orbit of the GOES spacecraft from 1995to 2009. The model is compared with these data. Almost perfect agreement was obtained for observationswith the model, where the prediction efficiency of predicting the accuracy of the model at PE = 0.9989. Usingsimilar data from the GOES 10 allows one to obtain PE = 0.9924. The proposed formulas make it possible tofind, for example, the average value of the perpendicular integral flux of relativistic electrons per day and topredict the maximum perpendicular integral flux of relativistic electrons in the geostationary orbit approximately1 day ahead. The nonlinear effect is theoretically predicted in the form of a nonlinear dependence ofthe ratio of the maximum perpendicular integral flux to the minimum flux of charged particles in the geostationaryorbit from the Kp-index of geomagnetic activity. Thus far, comparison of the model has been madewith the averaged integral relativistic electron flows fluxes produced for the 0 ≤ Kp 6 range with a predictedmaximum flow flux ratio of 24.4139 times at Kp = 8 and with the prediction efficiency of predicting the accuracyof the nonlinear effect PE = 0.8678.

Atlas of historical and proposed nuclear devices and power systems in the Earth-Moon System and wider Solar System

The 2010s witnessed a renewal in international interest of space operations extending outside geosynchronous orbit to encompass the cislunar environment and beyond with invigorated U.S., Chinese, and Russian lunar mission initiatives; planned commercial lunar projects; and coalescing international efforts to reach Mars and push deeper into the Solar System. With the space beyond the near-Earth orbital regimes likely to become competitive and congested in the coming decades, reliable and high-yield means of generating power and propulsion will be needed to enhance mission assurance and operational responsiveness. Nuclear systems represent a promising technology with a rich heritage and provenance of space-based applications to satisfy emerging requirements for electrical power and propulsive impulse for long-term human development of the Earth-Moon system and its planetary neighbors. In this work, an atlas for defining the varying historical or proposed uses of nuclear power in space operations and exploration is presented according to spatial zone within the Earth-Moon and wider Solar System. Depending on the spatial zone, nuclear power will be discussed with respect to applications such as electrical power generation, propulsion, resource extraction, and weapon testing and employment for the space control and planetary defense missions.

Estimating inter-satellite link Ka-band antenna phase center offsets to improve BDS-3 satellite orbit determination

Satellite antenna phase center offset (PCO) correction is essential not noly for L-band ground-tracking GNSS high-precision data processing, but also for Ka-band inter-satellite link (ISL) observations. The Ka-band ISL and L-band satellite-ground observations of 90 days from 25 November 2020 to 23 February 2021 are used for the Ka-band PCO estimation and precise orbit determination (POD) validation for BDS-3 satellites. The results show that the standard deviations of the estimated Ka-band PCOs for 29 BDS-3 satellites are 1.73, 2.63 and 3.58 cm in the X, Y and Z components, respectively. The accuracy of the Ka-band PCO estimates for medium Earth orbit satellites (MEO) is better than those of inclined geosynchronous orbit (IGSO) and geostationary Earth orbit (GEO) satellites due to a better observation geometry. The POD validation results indicate that using the estimated Ka-band PCOs can improve the ISL-based orbit determination performance. Using Ka-band ISL and L-band satellite-ground observations with 40 global stations for combined POD, the orbit overlap comparison shows that the average three-dimensional (3D) root mean square (RMS) error for 29 BDS-3 satellites is decreased from 12.6 to 6.6 cm with a reduction of 47.6%, and satellite laser ranging (SLR) validation for 4 BDS-3 satellites shows an accuracy improvement from 6 to 5 cm in RMS. When using ISL and only 7 regional ground stations are used, the average 3D RMS of orbit overlap errors is decreased from 15.9 to 10.9 cm with a reduction of 31.6%, and the RMS of SLR residuals for 4 BDS-3 satellites is decreased from 6.7 to 5.6 cm. For ISL-only POD, the average 3D RMS of orbit overlap errors is decreased from 18.0 to 12.4 cm with a reduction of 31.1%, and the RMS of SLR residuals for 4 BDS-3 satellites is decreased from 7.1 to 6.9 cm.

An on‐orbit calibration method for time delay of inter‐satellite link transponder in tracking and data relay satellite

AbstractThe tracking and data relay satellite (TDRS) in geosynchronous orbit (GEO) can provide ranging and communication services for user spacecraft in low Earth orbit (LEO) through the inter‐satellite link (ISL). The time delay of TDRS ISL transponder in orbit differs from its pre‐launch state and changes due to the complex space environment, adding significant errors to the user spacecraft's orbit determination based on four‐way ranging data. The authors have developed a calibration system and proposed an efficient on‐orbit calibration method for the ISL transponder's time delay in TDRS. Experimental results demonstrate the effectiveness of the authors’ method, and the RMS of calibration residuals is less than 0.5 m.

Wave optics approach to solar cell BRDF modeling with experimental results.

Light curve analysis is often used to discern information about satellites in geosynchronous orbits. Solar panels, comprising a large part of the satellite's body, contribute significantly to these light curves. Historically, theoretical bidirectional reflectance distribution functions (BRDFs) have failed to capture key features in the scattered light from solar panels. In recently published work, a new solar cell BRDF was developed by combining specular microfacet and "two-slit" diffraction terms to capture specular and periodic/array scattering, respectively. This BRDF was experimentally motivated and predicted many features of the solar cell scattered irradiance. However, the experiments that informed the BRDF were limited to a single laser wavelength, single beam size, and single solar cell sample. In addition, the BRDF was not physics based and therefore, physical insight into what causes certain features in the scattered irradiance was not evident. In this work, we examine solar cell scattering from first principles and derive a simple physics-based expression for the scattered irradiance. We analyze this expression and physically link terms to important scattering features, e.g., out-of-plane phenomena. In addition, we compare our model with experimental data and find good agreement in the locations and behaviors of these features. Our new model, being more predictive by nature, will allow for greater flexibility and accuracy when modeling reflection from solar cells in both real-world and experimental situations.

A Method for Measuring Gravitational Potential of Satellite’s Orbit Using Frequency Signal Transfer Technique between Satellites

We introduce an approach for the direct measurement of the gravitational potential (GP) along the trajectory of a satellite, with a specific focus on Low-Earth Orbit (LEO) satellites. A LEO satellite communicates with several Geosynchronous Equatorial Orbit (GEO) satellites via frequency signal links. The GP difference can be measured in real-time using the gravitational frequency shift approach by equipping both LEO and GEO satellites with precise atomic clocks. Since the GP at the high orbits of the GEO satellites can be precisely determined by the present gravitational field model EGM2008, the GP along the LEO satellite’s trajectory can be determined. In this study, simulation experiments were conducted, featuring a GRACE-type satellite as the LEO satellite in communication with three equidistant GEO satellites. The results indicated that the accuracy of the GP measurements along the LEO satellite’s trajectory primarily depends on the precision of the onboard atomic clocks. Supposing optical atomic clocks attain an instability level of 1×10−17τ−1/2 (τ in seconds), we determined the GP distribution covered by the LEO satellite’s trajectories with 30-day observations. Then, we determined a gravitational field at the centimeter level based on the GP distribution. The GP data derived from the trajectory of a LEO satellite can be utilized to establish temporal gravitational fields, which have broad applications in different disciplines.

A hybrid grey wolf optimizer using opposition-based learning, sine cosine algorithm and reinforcement learning for reliable scheduling and resource allocation

As the number of space debris in geosynchronous Earth orbits continues to grow, the threat posed by space debris to satellites surveillance is increasing, and the available orbital resources are also decreasing. Thus, reasonably scheduling and allocating the resources for space object tracking has become vital. This paper establishes an optimization model for the resource allocation and scheduling problem for space debris tracking. A fusion algorithm that combines the grey wolf optimizer, opposition-based learning, sine cosine search strategy, and reinforcement learning was proposed and used to solve the problem. Six groups of realistic data were selected based on the relevant background information of space debris tracking to test the validity and effectiveness of the proposed algorithm. The performance of the state-of-the-art optimization algorithms was compared with that of the proposed algorithms. The result of the experiment indicates that the proposed algorithm effectively solves the resource allocation and scheduling problem for space debris tracking.

The Extraction and Characterization of Pseudorange Multipath Based on BDS-3 Multi-Frequency Observations.

Global Navigation Satellite System (GNSS) observations are subject to various errors during their propagation process. A reasonable correction of these errors can improve the positioning, navigation, and timing (PNT) service capability. The impact of multipaths on pseudorange observations can reach a decimeters or even meters level. However, their mechanism is complex and there is currently no universally accepted high-precision correction model. The correlation between the pseudorange multipaths (MP) of BDS-2 satellites and satellite elevation has been confirmed, while there have been fewer analyses of the MP characteristics for different frequencies of BDS-3 satellites. The broadcasting of multi-frequency observations in BDS-3 should theoretically make the extracted MP more accurate compared to traditional methods. Based on this, in this contribution, a multi-frequency MP extraction algorithm based on the least squares principle is proposed, which can simultaneously eliminate the influence of higher-order ionospheric delay. The analytical expression for only eliminating first-order ionospheric delay is successfully derived. Subsequently, the characteristics of the MPs extracted from different frequency combinations and the impact of combination noise on the extraction accuracy are discussed. The influence of second-order ionospheric delay on the MPs for each frequency under different combination noises, as well as the periodic behavior exhibited in long-term observations of the BDS-3 medium earth orbit (MEO) and inclined geosynchronous orbit (IGSO) satellites, are also analyzed. Finally, the correlations between the MPs of each frequency of BDS satellite and elevation are quantitatively analyzed based on observations from 35 stations. Overall, this work has positive implications for the study of the MP characteristics of BDS-3 and subsequent modeling efforts.

Quantum-limited optical time transfer for future geosynchronous links.

The combination of optical time transfer and optical clocks opens up the possibility of large-scale free-space networks that connect both ground-based optical clocks and future space-based optical clocks. Such networks promise better tests of general relativity1-3, dark-matter searches4 and gravitational-wave detection5. The ability to connect optical clocks to a distant satellite could enable space-based very long baseline interferometry6,7, advanced satellite navigation8, clock-based geodesy2,9,10 and thousandfold improvements in intercontinental time dissemination11,12. Thus far, only optical clocks have pushed towards quantum-limited performance13. By contrast, optical time transfer has not operated at the analogous quantum limit set by the number of received photons. Here we demonstrate time transfer with near quantum-limited acquisition and timing at 10,000 times lower received power than previous approaches14-24. Over 300 km between mountaintops in Hawaii with launched powers as low as 40 µW, distant sites are synchronized to 320 attoseconds. This nearly quantum-limited operation is critical for long-distance free-space links in which photons are few and amplification costly: at 4.0 mW transmit power, this approach can support 102 dB link loss, more than sufficient for future time transfer to geosynchronous orbits.