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LAURA Users Manual: 5.7

This users manual provides in-depth information concerning installation and execution of Laura, version 5. Laura is a structured, multi-block, compu- tational aerothermodynamic simulation code. Version 5 represents a major refactoring of the original Fortran 77 Laura code toward a modular structure afforded by Fortran 2003. The refactoring improved usability and maintain- ability by eliminating the requirement for problem-dependent re-compilations, providing more intuitive distribution of functionality, and simplifying inter- faces required for multi-physics coupling. As a result, Laura now shares gas-physics modules, MPI modules, and other low-level modules with the Fun3D unstructured-grid code. In addition to internal refactoring, several new features and capabilities have been added, e.g., a GNU-standard instal- lation process, parallel load balancing, automatic trajectory point sequencing, free-energy minimization, and coupled ablation and flowfield radiation.

CFD hypersonics reentry↗

Particle Swarm Optimisation for group structure optimization for radiotherapy shielding

Neutron transport simulations are ubiquitous in nuclear engineering because they allow one to model experimental systems and render a model platform for easy perturbation of experimental designs. In addition, simulations allow one to gain experimental insight without actually having to go through the trouble of building a physical experiment. Neutron transport simulations can be stochastic or deterministic based. Stochastic neutron transport simulations are typically simulated using the Monte Carlo method and yield very accurate solutions but are computationally expensive, while deterministic methods are typically faster but can be less accurate. Here we focus on optimizing the accuracy of deterministic neutron transport simulations for radiotherapy simulations. Deterministic neutron transport requires discretization of angle, energy, and space to appropriately analyze the system one is trying to model. Discretization of energy is challenging because of the highly variable neutron flux at certain neutron energies. Improper discretization of energy in the transport model can lead to erroneous results and therefore inaccurate interpretations of the solution. In this study, we evaluate Particle Swarm Optimization (PSO) as a mechanism for selecting optimal group structures for radiotherapy shielding. We tested the particle swarm optimization algorithm on radiotherapy shielding problems using Los Alamos National Laboratory's (LANL) main deterministic transport code PARTISN. Results show that the optimized energy group structures generated from the optimization algorithm outperformed LANL's standard energy group structures, and therefore demonstrate utility in using PSO to expedite computation times due to the increased accuracy obtained with a smaller but optimized group structure. (authors)

43 PARTICLE ACCELERATORS↗

Energy Credits—A New Way to Save in ASHRAE/IES Standard 90.1-2022

This article discusses a new Section 11 that has been added to Standard 90.1-2022 to increase energy savings by requiring additional energy credit measures beyond the base prescriptive requirements. This new requirement targets a 5% reduction in overall building energy cost using a broad range of additional measures. Allowing designers to choose measures that are particularly suited to a particular project provides flexibility in increasing energy savings. There are resources available to help designers implement this new requirement in Standard 90.1.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

The spatial correlation properties of dark galaxy halos in a CDM universe

We use the Hierarchical Particle Mesh (HPM) N-body code written by J. V. Villumsen (Villumsen, 1989) to investigate the two-point spatial correlation function, xi(r), of dark galaxy halos as a function of halo mass and local environment (i.e. high, low, or average mass density). We assume a standard cold dark matter (CDM) universe (omega = 1, delta = 0, H sub 0 = 50,km/sec/Mpc). Because of the large dynamic ranges in mass and length that can be obtained with the HPM code, it is well-suited to an investigation of this sort.

Brainerd, Tereasa G.↗

Precision gamma-ray constraints for sub-GeV dark matter models

The indirect detection of dark matter particles with mass below the GeV scale has recently received significant attention. Future space-borne gamma-ray telescopes, including All-Sky-ASTROGAM, AMEGO, and GECCO, will probe the MeV gamma-ray sky with unprecedented precision, offering an exciting test of particle dark matter in the MeV-GeV mass range. While it is typically assumed that dark matter annihilates into only one Standard Model final state, this is not the case for realistic dark matter models. Here we analyze existing indirect detection constraints and the discovery reach of future detectors for the well-motivated Higgs and vector-portal models using our publicly-available code Hazma. In particular, we show how to leverage chiral perturbation theory to compute the dark matter self-annihilation cross sections into final states containing mesons, the strongly-interacting Standard Model dynamical degrees of freedom below the GeV scale. We find that future telescopes could probe dark matter self-annihilation cross sections orders of magnitude smaller than those presently constrained by cosmic microwave background, gamma-ray and terrestrial observations.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Performance Test Code for Determining and Reporting Annual Heat Rate and CO2 for Coal Fueled EGUs

This material is based upon work supported by the Department of Energy under Award Number DEFE0031933. The US Department of Energy (DOE) has retained the services of ASME Standards Technology LLC (ASME ST-LLC) to develop a standardized test method and calculation protocol for determining and reporting annual/long-term heat rate for coal-fueled plants electricity generating units. ASME ST-LLC has retained the services of McHale & Associates, Inc. and Licata Energy & Environmental Consultants, Inc. to provide the technical input to this study. This code applies to hydrocarbon fueled Rankine cycle power generating facilities of any size. It is intended to be used for the determination of continuous power output and heat rate of a generating facility in its operating load cycle and in its operational lineup during the reporting period.

01 COAL, LIGNITE, AND PEAT↗

Review of Experimental Data for Validating Computer Codes Used in Shielding Calculations for Spent Fuel Storage and Transportation Systems

This report presents a review of available radiochemical assay data and shielding benchmarks applicable to spent nuclear fuel (SNF) shielding calculations. The relevant information reviewed herein includes the Spent Fuel Composition (SFCOMPO) database, the Shielding Integral Benchmark Archive and Database (SINBAD), the International Handbook of Evaluated Criticality Safety Benchmark Experiments, and published measurements of external dose rates of casks loaded with SNF. The relevant experimental data identified in this report may be used to support verification and validation of computer codes used in SNF cask/transport shielding applications, as well as development of calculation uncertainties. It should be noted that a relatively small subset of the identified experimental data (e.g., criticality alarm experiments) is available in a standard format established by the international community participating in experimental isotopic and shielding data evaluations. An effort of the SFCOMPO Technical Review Group (TRG) is underway to publish first isotopic evaluations of individual assay data using a standard data evaluation format. The SINBAD TRG has recently initiated benchmark evaluations and modernization of the database. Therefore, more relevant information is expected in the future that will enable users to select quality experimental data in depletion code and shielding code validations for SNF applications.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

The Automatic Parallelisation of Scientific Application Codes Using a Computer Aided Parallelisation Toolkit

The shared-memory programming model is a very effective way to achieve parallelism on shared memory parallel computers. Historically, the lack of a programming standard for using directives and the rather limited performance due to scalability have affected the take-up of this programming model approach. Significant progress has been made in hardware and software technologies, as a result the performance of parallel programs with compiler directives has also made improvements. The introduction of an industrial standard for shared-memory programming with directives, OpenMP, has also addressed the issue of portability. In this study, we have extended the computer aided parallelization toolkit (developed at the University of Greenwich), to automatically generate OpenMP based parallel programs with nominal user assistance. We outline the way in which loop types are categorized and how efficient OpenMP directives can be defined and placed using the in-depth interprocedural analysis that is carried out by the toolkit. We also discuss the application of the toolkit on the NAS Parallel Benchmarks and a number of real-world application codes. This work not only demonstrates the great potential of using the toolkit to quickly parallelize serial programs but also the good performance achievable on up to 300 processors for hybrid message passing and directive-based parallelizations.

Ierotheou, C.↗

A New Appraisal- Lessons from the History of Efforts to Value Green and High-Performance Home Attributes in the United States

Rigorous consideration of green and high-performance (“green/HP”) features is rarely included in the property valuation process._ To help illuminate why this is the case, this report takes stock of the history of efforts to improve practices, and identifies barriers that have emerged and opportunities for overcoming them. Particular emphasis is placed on what energy and environmental policymakers and other stakeholders outside the appraisal community can contribute to the broader effort to advance professional practices. The history has unfolded in parallel with turbulent periods in the housing market for which appraisers and their customers are deemed to share responsibility, followed by cycles of regulations, siloing of appraisers in the name of professional integrity, and commoditization of the valuation process itself. This pattern has important ramifications for aspirations that appraisers engage more fully in identifying and valuing the green/HP characteristics of homes. On the one hand, it is legally and ethically incumbent on appraisers to do so, yet on the other hand it is perceived as a risky avenue to follow. Risks arise where findings can be challenged as either over- or under-stating value, together with a market environment in which the complexity of their assignments increases despite downward pressure on appraiser fees. While efforts to address green/HP considerations date back to the early 1980s, the vast majority of activity has taken place within the past five years. Many players have engaged in the efforts to promote improved valuation practices. These include the Appraisal Foundation, The Appraisal Institute, Colorado Energy Office, Earth Advantage, EcoBroker, Elevate Energy, Fannie Mae, Federal Housing Administration, Home Innovation Research Labs, The Institute for Market Transformation, Northwest Energy Efficiency Alliance, National Association of Homebuilders, National Association of State Energy Officials, National Association of Appraisers, RESNET, USEPA, USDOE and its National Laboratories, the U.S. Green Buildings Council, and the Vermont Green Homes Alliance. Many activities have resulted, ranging from trainings, to data-gathering instruments, and the emergence of a literature attempting to statistically isolate the effects of green/HP characteristics on home values. In some cases, the results of studies have been overgeneralized and oversold, and embodied flawed methods. Although the green/HP community has encouraged appraisers to focus on exemplary buildings (e.g., LEED or ENERGY STAR Certified), any level of green or energy performance can in fact influence value, including below-average performance (a.k.a. “brown discount”), irrespective of whether or not the building has been formally rated. This overly narrow focus represents a significant missed opportunity. Other surmountable challenges include limitations to non-appraisers’ understanding of the appraisal process (and practical constraints therein). A byproduct of this can be unrealistic expectations of what appraisers can and will do in the marketplace. These challenges notwithstanding, the environment for moving forward has improved. There is better data today (a critical need); expanded efforts to disclose energy use information (characteristics, consumption, bills); improved and more pervasive building energy codes, building rating and labeling initiatives; and a host of federal, state, and local policies that have collectively brought green/HP practices much more into the mainstream. Meanwhile, a renewed focus on professional standards of care and competency for assessing green/HP homes make it increasingly important for appraisers to consider these factors in their assignments. Despite the past four decades of studies, there is little if any discernible uptake of these practices by the appraisal practice at large. It would behoove interested parties to step back and consider what new strategies might be productive. A key element of any new plan should be to reset the nature of interactions with the industry, with the goal a more collaborative, two-way discussion to help improve outsiders’ understanding of the valuation process. It is not only the appraiser that needs to be engaged and could benefit from awareness raising. Homeowners, builders, lenders, utilities, insurance companies should also provide input on how green/HP factors impact property valuations and ways to accurately reflect these considerations in appraisals and real estate transactions more broadly. Given extensive inertia within the appraisal industry and a mixed history of interactions with the non-appraisal stakeholders, it is unlikely that the status quo will achieve much unless followed with more coordinated and persistent efforts. Workshops, studies, and memoranda of understanding will not on their own have much impact, and do not address deeper structural issues. Expectations are often unrealistic and not attentive to real-world constraints faced by appraisers. The report identifies key barriers impeding more thorough consideration of green/HP factors in residential real estate appraisals, and solutions for mitigating them. Barriers • Although industry standards of practice caution against bias of any sort, a skeptical predisposition towards “green” is reinforced by information deficiencies. • Information deficiencies result from the lack or difficulty of obtaining usable data on green/HP features in subject properties as well as valid sales comparisons or cashflow analyses. • Competency deficiencies, such as lack of conversancy in relevant technical topics, leads to oversights, and disjointed treatment of relevant information. • Time/cost pressure and process commoditization (e.g., template-based approaches) result from highly constrained budgets, quick turn-around times expected of appraisers, and standardized practices that were not developed with green/HP considerations in mind. • Professional differences between appraisers and sustainability professionals include divergent objectives, the former being market observers and the latter market influencers. • Risk aversion arises from multiple concerns including veracity, accuracy, and persistence of energy data, impacts of operational choices, new sources of appraiser liability associated with green/HP assessments, industry pressures not to over-value buildings or suggestion of bias, and concern about spending non-billable time on complex assignments. • A public policy vacuum has been created by disjointed and uncoordinated efforts from public-sector stakeholders, insufficient efforts to discuss and understand the appraisal industry and process, and a perception by some valuation professionals that green/HP is oversold. Opportunities • Elevating the competency of appraisers can be achieved through a combination of improved industry standards of care and equal-access training and professional development offerings. • Development of better information resources must focus on building-level information that provides robust documentation as well as aggregate sales-comparison data and other contextual information such as local codes, typical upgrade costs, energy prices, etc. • Improved energy benchmarking and rating tools could provide appraisers with information more well-adapted to their particular needs, which differ from those of typical audiences such as energy managers. • Better characterizing and managing risk will enable appraisers to cope with uncertainties in performance information, and help identify where risks may be introduced or mitigated by green/HP features, including higher costs or obsolescence of poorly-performing buildings. • Integrating disaster resilience and sustainability in appraisals would recognize important synergisms among these features, including durability and ability of green/HP buildings to better withstand external hazards. • Mitigating the problem of additional time/cost for performing assignments is an essential need that can be addressed by providing easier access to information and analytic procedures, perhaps coupled with new resources to defray the associated costs. • Enhancing demand for improved appraisals is a fundamental need, and depends on owners, developers, lenders, and others soliciting competent appraisers to perform scopes that expressly call out green/HP considerations, and to critically review the work product for compliance before acceptance. • Engaging new market participants, such as energy utilities and insurance companies can ensure fuller representation and participation of market stakeholders already engaged in green/HP activities and capable of furnishing valuable data and managing associated risks. Cutting across these individual activities, there is a need for outside stakeholders to formulate and follow a roadmap instead of piecemeal initiatives, bridging the professional/cultural divide between appraisers and green/HP communities, and tracking progress in order to know what is working. A more coherent communication and training strategy is needed, as the appraisal industry is highly fragmented, with two-thirds of appraisers opting out of membership in trade associations. In sum, while there is no silver bullet for advancing the practice of valuing green/HP features, there are concrete opportunities. Parties seeking solutions must identify barriers they wish to address and select from among potential initiatives that map to those barriers. Close collaboration with the appraisal community is critical, as non-appraisers have historically obtained limited traction with this industry due to lack of understanding of the nuances involved in the valuation profession. Large organizations and agencies should have a united approach; the perception or reality of a fragmented and uncoordinated strategy is unsettling for prospective partners in the appraisal industry. This requires improved communication and education within and among these communities.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Whole core analysis of OECD/NEA TVA-WB1 benchmark exercise 1 using continuous-energy Monte Carlo code MVP with JENDL-4.0u and ENDF/B-VII.0

The TVA WB1 benchmark problem was precisely modeled in accordance with the geometry and material specifications, and benchmark exercise 1 was solved with the MVP code and the nuclear data libraries based on JENDL-4.0u (JENDL-4.0 updated file) and ENDF/B-VII.0. The criticality, the control rod bank worth, the isothermal temperature coefficient (ITC), the integral rod worth of bank D, and differential soluble boron worth (DBW) were obtained. The criticality and the control rod bank worth were compared with the measured data and published calculation results with other codes, Serpent and KENO. The criticality and the control rod bank worth calculated by MVP and the libraries agree with the measured and the published calculation results within the criteria specified in the ANSI/ANS standard. From these results, the calculation model for the MVP and the libraries was verified. The other parameters such as ITC, the integral rod worth, and DBW were also compared between JENDL-4.0u and ENDF/B-VII.0. The comparison of the results shows JENDL-4.0u and ENDF/B-VII.0 give comparable results within the standard deviation, the difference between libraries is small. (author)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Implementing Superresolution of Nonstationary Tides with Wavelets: An Introduction to CWT_Multi

Abstract Tides are often nonstationary due to nonastronomical influences. Investigating variable tidal properties implies a trade-off between separating adjacent frequencies (using long analysis windows) and resolving their time variations (short analysis windows). Previous continuous wavelet transform (CWT) tidal methods resolved tidal species. Here, we present CWT_Multi, a MATLAB code that 1) uses CWT linearity (via the “response coefficient method”) to implement superresolution, i.e., resolving tidal constituents beyond the Rayleigh criterion; 2) provides a Munk–Hasselmann constituent selection criterion appropriate for superresolution; and 3) introduces an objective, time-variable form of inference (“dynamic inference”) based on time-varying data properties. CWT_Multi resolves tidal species on time scales of days, and multiple constituents per species with fortnightly filters. It outputs astronomical phase lags and admittances, analyzes multiple records, and provides power spectra of the signal(s), residual(s), and reconstruction(s); confidence limits; and signal-to-noise ratios. Artificial data and water levels from the Lower Columbia River Estuary (LCRE) and San Francisco Bay Delta (SFBD) are used to test CWT_Multi and compare it to harmonic analysis programs NS_Tide and UTide. CWT_Multi provides superior reconstruction, detiding, dynamic analysis utility, and time resolution of constituents (but with broader confidence limits). Dynamic inference resolves closely spaced constituents (like K 1 , S 1 , and P 1 ) on fortnightly time scales, quantifying impacts of diel power peaking (with a 24-h period, like S 1 ) on water levels in the LCRE. CWT_Multi also helps quantify the impacts of high flows and a salt barrier closing on tidal properties in the SFBD. On the other hand, CWT_Multi does not excel at prediction, and results depend on analysis details, as for any method applied to nonstationary data. Significance Statement Ocean tides, especially in coastal and estuarine systems, are often nonstationary, in the sense that the mean and standard deviation of tidal properties vary over time, usually in response to some nontidal process. We introduce here a MATLAB code, CWT_Multi, that uses wavelet transforms to resolve both tidal species and constituents on time scales from a few days to months. Our code accommodates multiple scalar time series and has typical tidal analysis features like constituent selection and inference, plus two forms of uncertainty analyses. It is flexible, allowing the user to adapt analysis properties to diverse datasets. CWT_Multi is applicable to many problems involving time-variable tides, including sea level rise, compound flooding, sediment transport, and wetland habitat analyses. Application to vector data is a straightforward extension, but further development of our uncertainty analysis is merited. Because nonstationary tidal analysis is rapidly advancing, we also define the features of a “well-formed” analysis code.

Lobo, Matthew↗

Modernising ATLAS Software Build Infrastructure

In the last year ATLAS has radically updated its software development infrastructure hugely reducing the complexity of building releases and greatly improving build speed, flexibility and code testing. The first step in this transition was the adoption of CMake as the software build system over the older CMT. This required the development of an automated translation from the old system to the new, followed by extensive testing and improvements. This resulted in a far more standard build process that was married to the method of building ATLAS software as a series of 12 separate projects from Subversion. We then proceeded with a migration of the code base from Subversion to Git. As the Subversion repository had been structured to manage each package more or less independently there was no simple mapping that could be used to manage the migration into Git. Instead a specialist set of scripts that captured the software changes across official software releases was developed. With some clean up of the repository and the policy of only migrating packages in production releases, we managed to reduce the repository size from 62 GiB to 220 MiB. After moving to Git we took the opportunity to introduce continuous integration so that now each code change from developers is built and tested before being approved. With both CMake and Git in place we also dramatically simplified the build management of ATLAS software. Many heavyweight homegrown tools were dropped and the build procedure was reduced to a single bootstrap of some external packages, followed by a full build of the rest of the stack. This has reduced the time for a build by a factor of 2. It is now easy to build ATLAS software, freeing developers to test compile intrusive changes or new platform ports with ease. We have also developed a system to build lightweight ATLAS releases, for simulation, analysis or physics derivations which can be built from the same branch.

97 MATHEMATICS AND COMPUTING↗

Numerical Simulation of Ion Thruster Optics

A three-dimensional simulation code (ffx) designed to analyze ion thruster optics is described. It is an extension of an earlier code and includes special features like the ability to model a wide range of grid geometries, cusp details, and mis-aligned aperture pairs to name a few. However, the principle reason for advancing the code was in the study of ion optics erosion. Ground based testing of ion thruster optics, essential to the understanding of the processes of grid erosion, can be time consuming and costly. Simulation codes that can accurately predict grid lifetimes and the physical mechanisms of grid erosion can be of great utility in the development of future ion thruster optics designed for more ambitious applications. Results of simulations are presented that describe wear profiles for several standard and nonstandard aperture geometries, such as those grid sets with square- or slotted-hole layout patterns. The goal of this paper will be to introduce the methods employed in the ffx code and to briefly demonstrate their use.

Rawlin, Vincent K.↗

Development of an algebraic turbulence model for analysis of propulsion flows

A simple turbulence model that will be applicable to propulsion flows having both wall bounded and unbounded regions was developed and installed within the PARC Navier-Stokes code by linking two existing algebraic turbulence models. The first is the Modified Mixing Length (MML) model which is optimized for wall bounded flows. The second is the Thomas model, the standard algebraic turbulence model in PARC which has been used to calculate both bounded and unbounded turbulent flows but was optimized for the latter. This paper discusses both models and the method employed to link them into one model (referred to as the MMLT model). The PARC code with the MMLT model was applied to two dimensional turbulent flows over a flat plate and over a backward facing step to validate and optimize the model and to compare its predictions to those obtained with the three turbulence models already available in PARC.

Georgiadis, N. J.↗

Development of an algebraic turbulence model for analysis of propulsion flows

A simple turbulence model that will be applicable to propulsion flows having both wall bounded and unbounded regions was developed and installed within the PARC Navier-Stokes code by linking two existing algebraic turbulence models. The first is the Modified Mixing Length (MML) model which is optimized for wall bounded flows. The second is the Thomas model, the standard algebraic turbulence model in PARC which has been used to calculate both bounded and unbounded turbulent flows but was optimized for the latter. This paper discusses both models and the method employed to link them into one model (referred to as the MMLT model). The PARC code with the MMLT model was applied to two dimensional turbulent flows over a flat plate and over a backward facing step to validate and optimize the model and to compare its predictions to those obtained with the three turbulence models already available in PARC.

Georgiadis, N. J.↗

Standard Component Commodity Usage Guides (CUGs) for Charge-Coupled Devices (CCDs)

Communicating risk and reliability information within NASA Goddard’s missions is crucial to continuing the development of new technology and ensuring GSFC missions achieve their science objectives. The Reliability and Risk Assessment Branch (Code 371) within the SMA directorate is one of GSFC’s leaders in communicating this information to missions, and one tool 371 engineers use to provide this information is the Commodity Usage Guides (CUGs). CUGs are helpful in compiling various critical parameters and heritage information for standard payload components, ensuring project personnel inherit the lessons learned from previous experiences. The purpose of this project was to create CUGs for CCDs used within GSFC missions. To formulate a CUG applicable data was aggregated into the CUG template for Charge-Coupled Devices (CCDs)--electro-optical components used to convert photons into digital images and data. CCDs can easily be adapted to a variety of mission requirements making them widely used at GSFC, and therefore suitable for CUGs. Once the CUGs for CCDs are completed the information can be distributed to engineers, scientists and other project members to ensure the lessons learned are passed on to the next mission.

Christman, Jerika H.↗

GMSK Modulation for Deep Space Applications

Due to scarcity of spectrum at 8.42 GHz deep space Xband allocation, many deep space missions are now considering the use of higher order modulation schemes instead of the traditional binary phase shift keying (BPSK). One such scheme is pre-coded Gaussian minimum shift keying (GMSK). GMSK is an excellent candidate for deep space missions. GMSK is a constant envelope, bandwidth efficien modulation whose frame error rate (FER) performance with perfect carrier tracking and proper receiver structure is nearly identical to that of BPSK. There are several issues that need to be addressed with GMSK however. Specificall, we are interested in the combined effects of spectrum limitations and receiver structure on the coded performance of the X-band link using GMSK. The receivers that are typically used for GMSK demodulations are variations on offset quadrature phase shift keying (OQPSK) receivers. In this paper we consider three receivers: the standard DSN OQPSK receiver, DSN OQPSK receiver with filte ed input, and an optimum OQPSK receiver with filte ed input. For the DSN OQPSK receiver we show experimental results with (8920, 1/2), (8920, 1/3) and (8920, 1/6) turbo codes in terms of their error rate performance. We also consider the tracking performance of this receiver as a function of data rate, channel code and the carrier loop signal-to-noise ratio (SNR). For the other two receivers we derive theoretical results that will show that for a given loop bandwidth, a receiver structure, and a channel code, there is a lower data rate limit on the GMSK below which a higher SNR than what is required to achieve the required FER on the link is needed. These limits stem from the minimum loop signal-to-noise ratio requirements on the receivers for achieving lock. As a result of this, for a given channel code and a given FER, there could be a gap between the maximum data rate that BPSK can support without violating the spectrum limits and the minimum data rate that GMSK can support with the required FER depending on the type of GMSK receiver that is used.

Communications↗