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Next-Generation NASA Earth-Orbiting Relay Satellites: Fusing Optical and Microwave Communications

NASA is currently considering architectures and concepts for the generation of relay satellites that will replace the Tracking and Data Relay Satellite (TDRS) constellation, which has been flying since 1983. TDRS-M, the last of the second TDRS generation, launched in August 2017, extending the life of the TDRS constellation beyond 2030. However, opportunities exist to re-engineer the concepts of geosynchronous Earth relay satellites. The needs of the relay satellite customers have changed dramatically over the last 34 years since the first TDRS launch. There is a demand for greater bandwidth as the availability of the traditional RF spectrum for space communications diminishes and the demand for ground station access grows. The next generation of NASA relay satellites will provide for operations that have factored in these new constraints. In this paper, we describe a heterogeneous constellation of geosynchronous relay satellites employing optical and RF communications. The new constellation will enable new optical communications services formed by user-to-space relay, space relay-to-space relay and space relay-to-ground links. It will build upon the experience from the Lunar Laser Communications Demonstration from 2013 and the Laser Communications Relay Demonstration to be launched in 2019.Simultaneous to establishment of the optical communications space segment, spacecraft in the TDRS constellation will be replaced with RF relay satellites with targeted subsets of the TDRS capabilities. This disaggregation of the TDRS service model will allow for flexibility in replenishing the needs of legacy users as well as addition of new capabilities for future users. It will also permit the U.S. government access to launch capabilities such as rideshare and to hosted payloads that were not previously available.In this paper, we also explore how the next generation of Earth relay satellites provides a significant boost in the opportunities for commercial providers to the communications space segment. For optical communications, the backbone of this effort is adoption of commercial technologies from the terrestrial high-bandwidth telecommunications industry into optical payloads. For RF communications, the explosion of software-defined radio, high-speed digital signal processing technologies and networking from areas such as 5G multicarrier will be important. Future commercial providers will not be limited to a small set of large aerospace companies. Ultimately, entirely government-owned and -operated satellite communications will phase out and make way for commercial business models that satisfy NASA's satellite communications requirements. The competition being provided by new entrants in the space communications business may result in a future in which all NASA communications needs can be satisfied commercially.

Space Communications↗

Operational improvements of long-term predicted ephemerides of the Tracking and Data Relay Satellites (TDRSs)

Tracking and Data Relay Satellite (TDRS) orbit determination and prediction are supported by the Flight Dynamics Facility (FDF) of the Goddard Space Flight Center (GSFC) Flight Dynamics Division (FDD). TDRS System (TDRSS)-user satellites require predicted TDRS ephemerides that are up to 10 weeks in length. Previously, long-term ephemerides generated by the FDF included predictions from the White Sands Complex (WSC), which plans and executes TDRS maneuvers. TDRSs typically have monthly stationkeeping maneuvers, and predicted postmaneuver state vectors are received from WSC up to a month in advance. This paper presents the results of an analysis performed in the FDF to investigate more accurate and economical long-term ephemerides for the TDRSs. As a result of this analysis, two new methods for generating long-term TDRS ephemeris predictions have been implemented by the FDF. The Center-of-Box (COB) method models a TDRS as fixed at the center of its stationkeeping box. Using this method, long-term ephemeris updates are made semiannually instead of weekly. The impulse method is used to model more maneuvers. The impulse method yields better short-term accuracy than the COB method, especially for larger stationkeeping boxes. The accuracy of the impulse method depends primarily on the accuracy of maneuver date forecasting.

Kostoff, J. L.↗

Test report: Low cost access and efficient use of TDRSS

In order to develop new ways to increase the number of users taking advantage of NASA's Space Network for space-to-ground communications links, researchers at New Mexico State University (NMSU) developed a technique for using non-gimballed antennas for accessing a Tracking and Data Relay Satellite (TDRS) within the Space Network (SN). This concept would allow spin-stabilized satellites to access one of the TDRS spacecraft in the SN constellation as the user satellite sweeps past the TDRS position as the satellite approaches either its ascending or descending node if this node is relatively close to the TDRS subsatellite point. ne research team from NMSU developing this concept proposed to NASA the use of the Extreme Ultra Violet Explorer (EUVE) to test this concept on orbit. EUVE differs from the desired satellite configuration in that EUVE has a relatively high-gain parabolic antenna and, most importantly, EUVE has an inertially-stabilized attitude control system while the concept to be tested was for a spin-stabilized satellite. We believed that these limitations would not affect the basic proof-of-concept test we were trying to achieve. With the approval and coordination of NASA, a total of six satellite passes through the West TDRS were requested and the necessary equipment configured for data collection at the Second TDRS Ground Terminal (STGT), also known as Danzante, at the White Sands Complex.

Horan, S.↗

Preliminary Results from NASA/GSFC Ka-Band High Rate Demonstration for Near-Earth Communications

In early 2000, the National Aeronautics and Space Administration (NASA) commenced the Ka-Band Transition Project (KaTP) as another step towards satisfying wideband communication requirements of the space research and earth exploration-satellite services. The KaTP team upgraded the ground segment portion of NASA's Space Network (SN) in order to enable high data rate space science and earth science services communications. The SN ground segment is located at the White Sands Complex (WSC) in New Mexico. NASA conducted the SN ground segment upgrades in conjunction with space segment upgrades implemented via the Tracking and Data Relay Satellite (TDRS)-HIJ project. The three new geostationary data relay satellites developed under the TDRS-HIJ project support the use of the inter-satellite service (ISS) allocation in the 25.25-27.5 GHz band (the 26 GHz band) to receive high speed data from low earth-orbiting customer spacecraft. The TDRS H spacecraft (designated TDRS-8) is currently operational at a 171 degrees west longitude. TDRS I and J spacecraft on-orbit testing has been completed. These spacecraft support 650 MHz-wide Ka-band telemetry links that are referred to as return links. The 650 MHz-wide Ka-band telemetry links have the capability to support data rates up to at least 1.2 Gbps. Therefore, the TDRS-HIJ spacecraft will significantly enhance the existing data rate elements of the NASA Space Network that operate at S-band and Ku-band.

Wong, Yen↗

SIR-B coverage

The planned coverage with the Shuttle Imaging Radar-B (SIR-B) is described in detail. A total of about 60-million square km of coverage will be acquired including 50 h of Tracking and Data Relay Satellite (TDRS) data and 8 h of optically recorded data. In general, data will be acquired directly through TDRS whenever possible; however, because of certain constraints imposed by having just one TDRS in orbit during the time of this mission, many digitally taped data takes will be required. (Each separate SIR-B observation is designed as a data take). Optical data takes will be taken only over sites that cannot be acquired either directly through TDRS or on a digital tape. It is important to note that, although a digital data take may be acquired at any time during the mission, it will be necessary to dump that data take through TDRS at some later time, or replace the tape onboard the Shuttle with another blank tape.

Source record↗

JPL emergency support of TDRSS and compatible satellites

The Tracking and Data Relay Satellite System (TDRSS) will consist of three identical satellites in geosynchronous orbits and a dedicated ground receiving station. The first two satellites (TDRS East and TDRS West) will form the operational TDRS service network providing near-global real-time user satellite coverage. The third TDRS satellite will act as an in-orbit spare. Since the TDRSS satellite are supported by a single ground station, a method of providing emergency support for TDRS and user satellites is needed. The support to be provided by JPL's Deep Space Network is described.

Fanelli, N. A.↗

MOORE: A prototype expert system for diagnosing spacecraft problems

MOORE is a rule-based, prototype expert system that assists in diagnosing operational Tracking and Data Relay Satellite (TDRS) problems. It is intended to assist spacecraft engineers at the TDRS ground terminal in trouble shooting problems that are not readily solved with routine procedures, and without expert counsel. An additional goal of the prototype system is to develop in-house expert system and knowledge engineering skills. The prototype system diagnoses antenna pointing and earth pointing problems that may occur within the TDRS Attitude Control System (ACS). Plans include expansion to fault isolation of problems in the most critical subsystems of the TDRS spacecraft. Long term benefits are anticipated with use of an expert system during future TDRS programs with increased mission support time, reduced problem solving time, and retained expert knowledge and experience. Phase 2 of the project is intended to provide NASA the necessary expertise and capability to define requirements, evaluate proposals, and monitor the development progress of a highly competent expert system for NASA's Tracking Data Relay Satellite. Phase 2 also envisions addressing two unexplored applications for expert systems, spacecraft integration and tests (I and T) and support to launch activities. The concept, goals, domain, tools, knowledge acquisition, developmental approach, and design of the expert system. It will explain how NASA obtained the knowledge and capability to develop the system in-house without assistance from outside consultants. Future plans will also be presented.

Howlin, Katherine↗

Interference effects on Space Station Freedom and space shuttle orbiter Ku-band downlinks

The space shuttle orbiter (SSO) and Ku-band single access return (KSAR) link and the Space Station Freedom (SSF) KSAR link via the tracking and data relay satellite system (TDRSS) use the same carrier frequency. The interference between spacecraft is minimized by opposite antenna polarizations and by TDRSS antenna beam pointing, but if the SSF and SSO are in close proximity, it is expected that mutual interference will be significant. Recently, Tsang and Su (1988, 1989) simulated the mutual interference effects, using a practical nonlinear bandlimited channel. The purpose of this paper is to demonstrate that a simplified (i.e., linear band-limited channel) analytical approach will yield adequate accuracy for the expected range of operating conditions. Relative degradation in bit energy-to-thermal noise power spectral density ratio to achieve a 10 exp -5 coded bit-error-probability is determined to be 4 dB for the Ku-band SSO-to-TDRS I-channel return link with a 4.5 dB effective signal-to-interference total power ratio (S/I) when the Ku-band SSF-to-TDRS return link interferes, whereas Su's simulation yields approximately 5 dB degradation. For the Ku-band SSF-to-TDRS return link, both analysis and simulation results yield a relative signal degradation of 0.4 dB at the effective S/I = 21.6 dB. In conclusion, interference on the Ku-band SSO-to-TDRS I-channel return link is significant, but on the Ku-band SSF-to-TDRS return link it is negligible.

Kwon, Hyuck M.↗

Non-Gimbaled Antenna Pointing: Summary of Results and Analysis

There is considerable interest at this time in developing small satellites for quick-turnaround missions to investigate near-earth phenomena from space. One problem to be solved in mission planning is the means of communication between the control infrastructure in the ground segment and the satellite in the space segment. A nominal small-satellite mission design often includes an omni-directional or similar wide-pattern antenna on the satellite and a dedicated ground station for telemetry, tracking, and command support. These terminals typically provide up to 15 minutes of coverage during an orbit that is within the visibility of the ground station; however, not all orbits will pass over the ground station so that coverage gaps will exist in the data flow. To overcome this general limitation on data transmission for low-earth orbiting satellites, the Space Network (SN), operated by the National Aeronautics and Space Administration, (NASA) has been designed to transmit data to and from user satellites through the Tracking and Data Relay Satellites (TDRS) in geostationary orbit and interfacing to the White Sands Complex (WSC) in New Mexico for the data's ground entry point. The advantage of the SN over a fixed ground station is that all low-earth-satellite orbits will be within the visibility area of at least one TDRS within the SN for a large part of the orbit and the potential exists to establish a communications link if the user satellite can point an antenna in the direction of any one of the relay satellites. Within NASA, there is considerable interest in seeing that small satellite developers are aware of the advantages to the SN and that designs to include the SN are part of the satellite design. Small satellite users have not often considered using the SN because of: (1) The 26-dB link penalty differential between direct broadcast to a ground station and transmission through a TDRS to the ground; (2) The class of satellite is too small to support high-gain antennas and associated attitude control and drive electronics; (3) The class of satellites is severely weight and power limited; (4) There are perceived problems in scheduling communications for this class of user on the SN. This report addresses the potential for SN access using non-gimbaled, i.e. fixed-pointed, antennas in the design of the small satellite using modest transmission power to achieve the necessary space-to-ground transmissions. The advantage of using the SN is in the reduction of mission costs arising from using the SN infrastructure instead of a dedicated, proprietary ground station using a similar type of communications package. From the simulations and analysis presented, we will show that a modest satellite configuration can be used with the space network to achieve the data transmission goals of a number of users and thereby rival the performance achieved with proprietary ground stations. In this study, we will concentrate on the return data link (from the user satellite through a TDRS to the ground data entry point). The forward command link (from the ground data entry point through a TDRS to the user satellite) will usually be a lower data rate service and the data volume will also be considerably lower than the return link's requirement. Therefore, we assume that if the return link requirements are satisfied, then the forward link requirements can also be satisfied.

Horan, Stephen↗

Non-Gimbaled Antenna Pointing

The small satellite community has been interested in accessing fixed ground stations for means of space-to-ground transmissions, although a problem arises from the limited global coverage. There is a growing interest for using the Space Network (SN) or Tracking and Data Relay Satellites (TDRS) as the primary support for communications because of the coverage it provides. This thesis will address the potential for satellite access of the Space Network with a non-gimbaled antenna configuration and low-power, coded transmission. The non-gimbaled antenna and the TDRS satellites, TDRS-East, TDRS-West, and TDRS-Zone of Exclusion, were configured in an orbital analysis software package called Satellite Tool Kit to emulate the three-dimensional position of the satellites. The access potential, which is the average number of contacts per day and the average time per contact, were obtained through simulations run over a 30-day period to gain all the possible orientations. The orbital altitude was varied from 600 km through 1200 km with the results being a function of orbital inclination angles varying from 20 deg through 100 deg and pointing half-angles of I0 deg through 40 deg. To compare the validity of the simulations, Jet Propulsion Laboratory granted the use of the TOPEX satellite. The TOPEX satellite was configured to emulate a spin-stabilized antenna with its communications antenna stowed in the zenith-pointing direction. This mimicked the antenna pointing spin-stabilized satellite in the simulations. To make valid comparisons, the TOPEX orbital parameters were entered into Satellite Tool Kit and simulated over five test times provided by Jet Propulsion Laboratory.

Vigil, Jeannine S.↗

Space Communications Responsive to Events Across Missions (SCREAM): An Investigation of Network Solutions for Transient Science Space Systems

Space Communications Responsive to Events Across Missions (SCREAM): An Investigation of Network Solutions for Transient Science Space Systems The National Academies have prioritized the pursuit of new scientific discoveries using diverse and temporally coordinated measurements from multiple ground and space-based observatories. Networked communications can enable such measurements by connecting individual observatories and allowing them to operate as a cohesive and purposefully designed system. Timely data flows across terrestrial and space communications networks are required to observe transient scientific events and processes. Currently, communications to space-based observatories experience large latencies due to manual service reservation and scheduling procedures, intermittent signal coverage, and network capacity constraints. If space communications network latencies could be reduced, new discoveries about dynamic scientific processes could be realized. However, science mission and network planners lack a systematic framework for defining, quantifying and evaluating timely space data flow implementation options for transient scientific observation scenarios involving multiple ground and space-based observatories. This dissertation presents a model-based systems engineering approach to investigate and develop network solutions to meet the needs of transient science space systems. First, a systematic investigation of the current transient science operations of the National Aeronautics and Space Administration’s (NASA) Tracking and Data Relay Satellite (TDRS) space data network and the Neil Gehrels Swift Observatory resulted in a formal architectural model for transient science space systems. Two methods individual missions may use to achieve timely network services were defined, quantitatively modeled, and experimentally compared. Next, the architectural model was extended to describe two alternative ways to achieve timely and autonomous space data flows to multiple space-based observatories within the context of a purposefully designed transient science observation scenario. A quantitative multipoint space data flow modeling method based in queueing theory was defined. General system suitability metrics for timeliness, throughput, and capacity were specified to support the evaluation of alternative network data flow implementations. A hypothetical design study was performed to demonstrate the multipoint data flow modeling method and to evaluate alternative data flow implementations using TDRS. The merits of a proposed future TDRS broadcast service to implement multipoint data flows were quantified and compared to expected outcomes using the as-built TDRS network. Then, the architectural model was extended to incorporate commercial network service providers. Quantitative models for Globalstar and Iridium short messaging data services were developed based on publicly available sources. Financial cost was added to the set of system suitability metrics. The hypothetical design study was extended to compare the relative suitability of the as-built TDRS network with the commercial Globalstar and Iridium networks. Finally, results from this research are being applied by NASA missions and network planners. In 2020, Swift implemented the first automated command pipeline, increasing its expected gravitational wave follow-up detection rate by greater than 400%. Current NASA technology initiatives informed by this research will enable future space-based observatories to become interoperable sensing devices connected by a diverse ecosystem of network service providers.

Christopher J. Roberts↗

TDRSS multimode transponder program. Phase 2: Equipment development

This report contains a complete description of the TDRS Multimode Transponder and its associated ground support equipment. The transponder will demonstrate candidate modulation techniques to provide the required information for the design of an eventual VHF/UHF transponder suitable for installation in a user satellite, capable of operating as part of a Tracking and Data Relay Satellite (TDRS) systems. Use of geosynchronous TDRS which can serve both low data rate users at VHF and high data rate users at other frequencies has been considered. The effects of radio frequency interference from the earth and of multipath propagation due to reflections from the earth are expected to pose problems for the TDRS system at VHF. Investigations have suggested several modulation techniques that offer promise to overcome these problems.

Cnossen, R. S.↗

Navigation for IUS deployment. TDRSS navigation accuracy in support of IUS deployment, phase 1

The navigation accuracy for tracking the orbiter prior to interim upper stage (IUS) deployment using the tracking data relay satellite system (TDRSS) was studied. The orbiter navigation accuracy for both one and two TDRSS satellites, for short and long data arcs, and for Doppler-only and Doppler-plus range solutions was examined. All test cases were run with the orbiter in a 150-n. mi. circular orbit, 28.5 degree inclination, at the time interval from the completion of the orbital maneuvering system (OMS)-2 maneuver to OMS-2 plus 2 hours (approximate time for IUS deployment). The data used were simulated by the simulation navigation (SIMNAV) program. The software tool used to process the TDRS data was the Shuttle Navigation Analysis Program (SNAP), a Kalman filter tool used to solve for the orbiter position and velocity. Results summarize the expected navigation accuracy using the TDRS system. It was concluded that: (1) data from both TDRS satellites were essential for accurate navigation results: (2) range data were essential for the short arc test case but were not needed for the long arc test case; and (3) with Doppler and range data from both TDRS satellites, the results converged to a reasonable solution after 5 to 10 minutes of data.

Wylie, A. D.↗

AE-5 end of mission tests report

A spin up test and a TDRS tracking simulation were performed on the AE-5 spacecraft before its end of mission. the spin up test showed that the Body Horizon Scanner could be successfully used on other spacecraft with spin rates up to 10 RPM. the TDRS tracking simulation showed that an AE-5 type attitude control system could be successfully used to point the spacecraft towards a TDRS for the purpose of transmitting/relaying data via the TDRS.

Stengle, T. H.↗

TDRSS tracking data and orbit determination evaluation

TDRS-1 was launched on April 4, 1983. This paper presents preliminary results of TDRSS tracking data evaluation through September 1983. TDRSS tracking data evaluation is a summary of valid tracking data that characterizes data quality. TDRS-1 orbit accuracy is evaluated by using orbit consistency measured by comparing overlaps of TDRS-1 ephemerides produced from consecutive data arcs. TDRS-1 and user orbit accuracies and consistencies are also estimated. Orbit accuracy is estimated by comparing user orbits based on tracking data obtained both through the TDRSS and from ground-based tracking.

Campion, R. E.↗

The GRO remote terminal system

In March 1992, NASA HQ challenged GSFC/Code 531 to propose a fast, low-cost approach to close the Tracking Data Relay Satellite System (TDRSS) Zone-of-Exclusion (ZOE) over the Indian Ocean in order to provide global communications coverage for the Compton Gamma Ray Observatory (GRO) spacecraft. GRO had lost its tape recording capability which limited its valuable science data return to real-time contacts with the TDRS-E and TDRS-W synchronous data relay satellites, yielding only approximately 62 percent of the possible data obtainable. To achieve global coverage, a TDRS spacecraft would have to be moved over the Indian Ocean out of line-of-sight control of White Sands Ground Terminal (WSGT). To minimize operations life cycle costs, Headquarters also set a goal for remote control, from the WSGT, of the overseas ground station which was required for direct communications with TDRS-1. On August 27, 1992, Code 531 was given the go ahead to implement the proposed GRO Relay Terminal System (GRTS). This paper describes the Remote Ground Relay Terminal (RGRT) which went operational at the Canberra Deep Space Communications Complex (CDSCC) in Canberra, Australia in December 1993 and is currently augmenting the TDRSS constellation in returning between 80-100 percent of GRO science data under the control of a single operator at WSGT.

Zillig, David J.↗

NASA Hitchhiker Program Customer Payload Requirements (CPR)

The mission objective is to demonstrate each of the three types of technology intended for future small-satellite communications system design. Each experiment in the overall package is designed to exercise a different technology objective that may be found in the overall satellite communications and telemetry system design. The data communications through TORSS portion is designed to demonstrate that low-power communications systems with non-gimbaled antenna systems can transport significant quantities of data through TDRSS to the ground based on only transmitting through a TDRS when the experiment is near the TDRS subsatellite point. The remaining time. the payload communications system is not active. The demand access experiment is to demonstrate that the request for a demand access service can be transmitted through TDRS and received and decoded at the ground station. In this mode, the TDRS does not track the experiment but signal processing components at the White Sands Complex are used to detect and track the transmitted request. The laser communications experiment is designed to demonstrate passive transmission of telemetry data from the experiment. This mode uses a ground-based laser source to illuminate the experiment and modulate the beam with the data. Ground-based reception recovers the data from the reflected beam back to the ground station.

Horan, Stephen↗

Automated Antenna Design with Evolutionary Algorithms

Current methods of designing and optimizing antennas by hand are time and labor intensive, and limit complexity. Evolutionary design techniques can overcome these limitations by searching the design space and automatically finding effective solutions. In recent years, evolutionary algorithms have shown great promise in finding practical solutions in large, poorly understood design spaces. In particular, spacecraft antenna design has proven tractable to evolutionary design techniques. Researchers have been investigating evolutionary antenna design and optimization since the early 1990s, and the field has grown in recent years as computer speed has increased and electromagnetic simulators have improved. Two requirements-compliant antennas, one for ST5 and another for TDRS-C, have been automatically designed by evolutionary algorithms. The ST5 antenna is slated to fly this year, and a TDRS-C phased array element has been fabricated and tested. Such automated evolutionary design is enabled by medium-to-high quality simulators and fast modern computers to evaluate computer-generated designs. Evolutionary algorithms automate cut-and-try engineering, substituting automated search though millions of potential designs for intelligent search by engineers through a much smaller number of designs. For evolutionary design, the engineer chooses the evolutionary technique, parameters and the basic form of the antenna, e.g., single wire for ST5 and crossed-element Yagi for TDRS-C. Evolutionary algorithms then search for optimal configurations in the space defined by the engineer. NASA's Space Technology 5 (ST5) mission will launch three small spacecraft to test innovative concepts and technologies. Advanced evolutionary algorithms were used to automatically design antennas for ST5. The combination of wide beamwidth for a circularly-polarized wave and wide impedance bandwidth made for a challenging antenna design problem. From past experience in designing wire antennas, we chose to constrain the evolutionary design to a monopole wire antenna. The results of the runs produced requirements-compliant antennas that were subsequently fabricated and tested. The evolved antenna has a number of advantages with regard to power consumption, fabrication time and complexity, and performance. Lower power requirements result from achieving high gain across a wider range of elevation angles, thus allowing a broader range of angles over which maximum data throughput can be achieved. Since the evolved antenna does not require a phasing circuit, less design and fabrication work is required. In terms of overall work, the evolved antenna required approximately three person-months to design and fabricate whereas the conventional antenna required about five. Furthermore, when the mission was modified and new orbital parameters selected, a redesign of the antenna to new requirements was required. The evolutionary system was rapidly modified and a new antenna evolved in a few weeks. The evolved antenna was shown to be compliant to the ST5 mission requirements. It has an unusual organic looking structure, one that expert antenna designers would not likely produce. This antenna has been tested, baselined and is scheduled to fly this year. In addition to the ST5 antenna, our laboratory has evolved an S-band phased array antenna element design that meets the requirements for NASA's TDRS-C communications satellite scheduled for launch early next decade. A combination of fairly broad bandwidth, high efficiency and circular polarization at high gain made for another challenging design problem. We chose to constrain the evolutionary design to a crossed-element Yagi antenna. The specification called for two types of elements, one for receive only and one for transmit/receive. We were able to evolve a single element design that meets both specifications thereby simplifying the antenna and reducing testing and integration costs. The highest performance antenna found using a getic algorithm and stochastic hill-climbing has been fabricated and tested. Laboratory results correspond well with simulation. Aerospace component design is an expensive and important step in space development. Evolutionary design can make a significant contribution wherever sufficiently fast, accurate and capable software simulators are available. We have demonstrated successful real-world design in the spacecraft antenna domain; and there is good reason to believe that these results could be replicated in other design spaces.

Hornby, Gregory S.↗