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NASA NTRS2018

Development of a Ground Test and Analysis Protocol to Support NASA's NextSTEP Phase 2 Habitation Concepts

Beaton, Kara H.↗

NASA NTRS2018

Development of a Ground Test and Analysis Protocol for NASA's NextSTEP Phase 2 Habitation Concepts

The NASA Next Space Technologies for Exploration Partnerships (NextSTEP) program is a public-private partnership model that seeks commercial development of deep space exploration capabilities to support human spaceflight missions around and beyond cislunar space. NASA first issued the Phase 1 NextSTEP Broad Agency Announcement to U.S. industries in 2014, which called for innovative cislunar habitation concepts that leveraged commercialization plans for low-Earth orbit. These habitats will be part of the Deep Space Gateway (DSG), the cislunar space station planned by NASA for construction in the 2020s. In 2016, Phase 2 of the NextSTEP program selected five commercial partners to develop ground prototypes. A team of NASA research engineers and subject matter experts (SMEs) have been tasked with developing the ground-test protocol that will serve as the primary means by which these Phase 2 prototypes will be evaluated. Since 2008, this core test team has successfully conducted multiple spaceflight analog mission evaluations utilizing a consistent set of operational tools, methods, and metrics to enable the iterative development, testing, analysis, and validation of evolving exploration architectures, operations concepts, and vehicle designs. The purpose of implementing a similar evaluation process for the Phase 2 Habitation Concepts is to consistently evaluate different commercial partner ground prototypes to provide data-driven, actionable recommendations for Phase 3. This paper describes the process by which the ground test protocol was developed and the objectives, methods, and metrics by which the NextSTEP Phase 2 Habitation Concepts will be rigorously and systematically evaluated. The protocol has been developed using both a top-down and bottom-up approach. Top-down development began with the Human Exploration and Operations Mission Directorate (HEOMD) exploration objectives and ISS Exploration Capability Study Team (IECST) candidate flight objectives. Strategic questions and associated rationales, derived from these candidate architectural objectives, provide the framework by which the ground-test protocol will address the DSG stack elements and configurations, systems and subsystems, and habitation, science, and EVA functions. From these strategic questions, high-level functional requirements for the DSG were drafted and associated ground-test objectives and analysis protocols were established. Bottom-up development incorporated objectives from NASA SMEs in autonomy, avionics and software, communication, environmental control and life support systems, exercise, extravehicular activity, exploration medical operations, guidance navigation and control, human factors and behavioral performance, human factors and habitability, logistics, Mission Control Center operations, power, radiation, robotics, safety and mission assurance, science, simulation, structures, thermal, trash management, and vehicle health. Top-down and bottom-up objectives were integrated to form overall functional requirements - ground-test objectives and analysis mapping. From this mapping, ground-test objectives were organized into those that will be evaluated through inspection, demonstration, analysis, subsystem standalone testing, and human-in-the-loop (HITL) testing. For the HITL tests, mission-like timelines, procedures, and flight rules have been developed to directly meet ground test objectives and evaluate specific functional requirements. Data collected from these assessments will be analyzed to determine the acceptability of habitation element configurations and the combinations of capabilities that will result in the best habitation platform to be recommended by the test team for Phase 3.

Gernhardt, Michael L.↗

NASA NTRS2014

Development of a Route Crossing Tool for Shared Airspace Environments

In current-day Terminal Radar Approach Control (TRACON) operations, departure and arrival controllers maintain separate and dedicated airspace for their respective traffic flows. Although this practice has obvious safety features, it also leads to inefficiencies; for example, departure aircraft may be routinely capped beneath arrival airspace. With the right decision-support and coordination tools, departures could continue to climb through arrival airspace when sufficient gaps exist. Previous studies of ‘shared airspace’ have examined pre-arranged coordination procedures, as well as tools that gave feedback to the controllers on where gaps between arrivals were located and whether the departure aircraft could be scheduled to fly through those gaps [1, 2, 3, 4]. Since then, the Route Crossing Tool (RCT) has been developed to allow controllers to assess multiple pre-defined route options at points where the arrivals and departures cross, thereby increasing the possibility of climbing a departure through an arrival gap.The RCT aids in ensuring lateral separation between departure and arrival aircraft that pass through the same altitude. Since the RCT can be applied tactically, it can enable aircraft to fly through arrival flows even if these aircraft depart outside scheduled times. The RCT makes use of a set of predefined parallel departure routes crossing the arrival flow at equidistant intersecting points on the arrival route. The RCT uses the Estimated Time of Arrival (ETA) of the departure aircraft at each intersecting point to calculate the lateral separation with the neighboring arrivals when it crosses that point; this information is graphically displayed to the controller. Additionally, the RCT incorporates forecast winds in its ETA predictions.Multiple prototypes of the RCT have been iteratively developed with feedback from Subject Matter Experts (SMEs). This paper presents the final design, the design process, and lessons learned. Initial results from a simulation suggest that the tool was successful in helping controllers to safely climb more aircraft. Controller feedback on the tool was also positive.

shared airspace↗

NASA NTRS2008

Sensor Selection and Data Validation for Reliable Integrated System Health Management

For new access to space systems with challenging mission requirements, effective implementation of integrated system health management (ISHM) must be available early in the program to support the design of systems that are safe, reliable, highly autonomous. Early ISHM availability is also needed to promote design for affordable operations; increased knowledge of functional health provided by ISHM supports construction of more efficient operations infrastructure. Lack of early ISHM inclusion in the system design process could result in retrofitting health management systems to augment and expand operational and safety requirements; thereby increasing program cost and risk due to increased instrumentation and computational complexity. Having the right sensors generating the required data to perform condition assessment, such as fault detection and isolation, with a high degree of confidence is critical to reliable operation of ISHM. Also, the data being generated by the sensors needs to be qualified to ensure that the assessments made by the ISHM is not based on faulty data. NASA Glenn Research Center has been developing technologies for sensor selection and data validation as part of the FDDR (Fault Detection, Diagnosis, and Response) element of the Upper Stage project of the Ares 1 launch vehicle development. This presentation will provide an overview of the GRC approach to sensor selection and data quality validation and will present recent results from applications that are representative of the complexity of propulsion systems for access to space vehicles. A brief overview of the sensor selection and data quality validation approaches is provided below. The NASA GRC developed Systematic Sensor Selection Strategy (S4) is a model-based procedure for systematically and quantitatively selecting an optimal sensor suite to provide overall health assessment of a host system. S4 can be logically partitioned into three major subdivisions: the knowledge base, the down-select iteration, and the final selection analysis. The knowledge base required for productive use of S4 consists of system design information and heritage experience together with a focus on components with health implications. The sensor suite down-selection is an iterative process for identifying a group of sensors that provide good fault detection and isolation for targeted fault scenarios. In the final selection analysis, a statistical evaluation algorithm provides the final robustness test for each down-selected sensor suite. NASA GRC has developed an approach to sensor data qualification that applies empirical relationships, threshold detection techniques, and Bayesian belief theory to a network of sensors related by physics (i.e., analytical redundancy) in order to identify the failure of a given sensor within the network. This data quality validation approach extends the state-of-the-art, from red-lines and reasonableness checks that flag a sensor after it fails, to include analytical redundancy-based methods that can identify a sensor in the process of failing. The focus of this effort is on understanding the proper application of analytical redundancy-based data qualification methods for onboard use in monitoring Upper Stage sensors.

Garg, Sanjay↗

NASA NTRS1976

Transonic airfoil design using Cartesian coordinates

A numerical technique for designing transonic airfoils having a prescribed pressure distribution (the inverse problem) is presented. The method employs the basic features of Jameson's iterative solution for the full potential equation, except that inverse boundary conditions and Cartesian coordinates are used. The method is a direct-inverse approach that controls trailing-edge closure. Examples show the application of the method to design aft-cambered and other airfoils specifically for transonic flight.

Carlson, L. A.↗

DOE OSTI2024

Accelerating the design of lattice structures using machine learning

Lattices remain an attractive class of structures due to their design versatility; however, rapidly designing lattice structures with tailored or optimal mechanical properties remains a significant challenge. With each added design variable, the design space quickly becomes intractable. To address this challenge, research efforts have sought to combine computational approaches with machine learning (ML)-based approaches to reduce the computational cost of the design process and accelerate mechanical design. While these efforts have made substantial progress, significant challenges remain in (1) building and interpreting the ML-based surrogate models and (2) iteratively and efficiently curating training datasets for optimization tasks. Here, we address the first challenge by combining ML-based surrogate modeling and Shapley additive explanation (SHAP) analysis to interpret the impact of each design variable. We find that our ML-based surrogate models achieve excellent prediction capabilities (R 2 > 0.95) and SHAP values aid in uncovering design variables influencing performance. We address the second challenge by utilizing active learning-based methods, such as Bayesian optimization, to explore the design space and report a 5 × reduction in simulations relative to grid-based search. Collectively, these results underscore the value of building intelligent design systems that leverage ML-based methods for uncovering key design variables and accelerating design.

36 MATERIALS SCIENCE↗

NASA NTRSDate not supplied

History and Status of the CDISC Aerodynamic Design Method

This paper will review the development and application of the CDISC aerodynamic design method that began in the early 1980s and continues in active use today. The method uses an iterative, knowledge-based approach that has been coupled with numerous flow solvers utilizing a variety of grid types and levels of flow physics. It has been applied to configurations varying in complexity from 2-D airfoils to full 3-D aircraft at flow conditions ranging from low-speed, high-lift to supersonic cruise. The knowledge-based approach provides a very rapid design process, with designs typically completed in approximately 1-2x the time required for an initial converged analysis of the baseline. The evolution of the method as it tracked the expansive growth of grid and flow solver technology, along with some major applications over 5 decades, are given, followed by a description of the philosophy and process used in design. Finally, an example of its use in a preliminary design environment is given.

CDISC↗

NASA NTRSDate not supplied

History and Status of the CDISC Aerodynamic Design Method

CDISC↗

DOE OSTI2023

Ultrasonic Measurements of Temperature Profile and Heat Fluxes in Coal-Fired Power Plants (Final Report)

Many industrial processes are inaccessible or inhospitable to characterization by traditional temperature measurement methods, such as thermocouples, especially over prolonged exposure to harsh environments. Ultrasound is an established characterization technology with diverse applications ranging from medical imaging to therapies to flaw detection to nondestructive evaluation. Ultrasound may characterize solid materials and components noninvasively as a nondestructive evaluation modality and obtain internal measurements of material properties. For example, the speed of ultrasound propagation changes with Young’s modulus and Poisson’s ratio, which can be found from its measurements. Traditional ultrasonic characterization assumes all material properties remain constant with the position. When this assumption holds, a property of interest may be measured by relating it to the speed of ultrasound propagation (or a speed of sound, SOS) and measuring the SOS by timing the ultrasound propagation through a known distance. However, when a property of interest is spatially distributed, the propagation time depends on the SOS changing with the position along the ultrasound propagation path. The multiple temperature distributions may lead to an identical time of flight (TOF). Temperature is one property that impacts the speed of ultrasound and often cannot be assumed to remain constant with the position. Previously, in the context of temperature, we addressed the challenge of ultrasonic characterization of spatially distributed properties by developing a method for measuring segmental temperature distributions (MSTD). This method divides the ultrasonic propagation into segments bound by echogenic features. These features provide ultrasonic interfaces where some energy is reflected toward the receiving transducer, and the rest continues through the medium. The time-of-flight between the echoes reflected from echogenic features characterizes the spatial distribution in the properties of interest in the corresponding segment of the ultrasonic propagation path. This project demonstrated the application of the MSTD method in industrial conditions of the coal-fired power plant. We implemented the MSTD using metals and alloys waveguides, which may be the existing structure for which the temperature distribution is characterized or purposefully designed waveguides added to the structure by welding or other means specifically to quantify thermal properties using the MSTD method. Previous iterations of the MSTD method used ceramic and cementitious waveguides, which significantly attenuate ultrasound. On the other hand, low attenuation in metallic waveguides creates interactions between echogenic features which compilates the signal analysis in the segmental TOF measurements. We have established the WG design principles that minimize the interferences between trailing and primary echoes and, in some cases, eliminate them. The waveguides in which echoes do not interfere improve the timing accuracy and the robustness of ultrasonic measurements of the spatial distributions in material properties. Our emphasis remained on the estimation of the temperature distributions. We have developed general recommendations for designing ultrasonically segmented waveguides with the reduced influence of trailing echoes. Two of our waveguide designs were tested in the industry. The first waveguide was designed for insertion into a combustion zone of the utility-scale coal-fired power plant boiler. The second design allows the characterization of temperature distribution in the direction normal to the boiler’s water wall, a large heat exchanger converting the chemical energy released during combustion to the steam driving the electrical power generation turbines. These waveguides were designed to operate within a restrictive space of thermally insulated water wall and incorporate densely located echogenic features while combatting the influence of trailing echoes. The project has successfully demonstrated the feasibility of using the developed method for accurate, continuous, and robust temperature measurements in extreme environments of power generation and other industrial processes. It, therefore, has achieved its overarching goal of advancing the technology readiness level of the novel Ultrasound Measurements of Segmental Temperature Distribution (US-MSTD) method for real-time measurements of the temperature distribution and heat fluxes closer to commercial availability, developing a prototype multipoint measurement system, and validating its performance on coal-fired utility boilers. The success of this project was achieved in collaboration with the power generator, Rocky Mountain Power, and set the stage for the transfer of this technology from the laboratory to the industry.

01 COAL, LIGNITE, AND PEAT↗

DOE OSTI2024

FPGA-Accelerated Range-Limited Molecular Dynamics

Long timescale Molecular Dynamics (MD) simulation of small molecules is crucial in drug design and basic science. To accelerate a small data set that is executed for a large number of iterations, high-efficiency is required. Recent work in this domain has demonstrated that among COTS devices only FPGA-centric clusters can scale beyond a few processors. The problem addressed here is that, as the number of on-chip processors has increased from fewer than 10 into the hundreds, previous intra-chip routing solutions are no longer viable. We find, however, that through various design innovations, high efficiency can be maintained. These include replacing the previous broadcast networks with ring-routing and then augmenting the rings with out-of-order and caching mechanisms. Others are adding a level of hierarchical filtering and memory recycling. Two novel optimized architectures emerge, together with a number of variations. These are validated, analyzed, and evaluated. We find that in the domain of interest speed-ups over GPUs are achieved. Finally, the potential impact is that this system promises to be the basis for scalable long timescale MD with commodity clusters.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1987

Controller synthesis for flexible spacecraft using multivariable loop-shaping and factorization methods

The problem of designing fine-pointing controllers is considered for large, flexible space structures using modern multivariable synthesis methods. The first method is an iterative procedure which utilizes frequency-domain singular-value techniques, and is found to yield satisfactory performance and robustness. For the second method, which is based on coprime factorizations, a particular bicoprime is obtained, and the steps in the design process are described. This method is still under development.

Joshi, Suresh M.↗

DOE OSTI2024

LAMP DTL Scoping Studies (Technical Report)

The present studies are based on the preliminary design efforts, and on the Scoping Studies of the “Strawman” design of LAMP front-end upgrade, referred in the text below to as “Feb.2024 Iteration”, presented in. The main accomplishment of present studies was substantial increase of the fidelity of the beam dynamics simulations in the proposed drift tube linac (DTL). The main accent was on development of the methodology for calculation of the longitudinal (synchrotron) and transverse (betatron) oscillations frequencies (phase advance per focusing period) values and providing the accelerating structure focusing lattice that has safe parameters of such oscillations to avoid unwanted emittance growth and possible beam halo formation. The resulting values of the oscillations phase advances are presented in Table 1, and in Figure 5 in the main body of the report. Special efforts were made to achieve the RF power consumption within limits of the existing RF power system and make sure that DTL fits in the existing tunnel. The LAMP scope does not suggest any additional building and/or tunnel construction. Table 1 summarizes some of these results, as well as Table 3 in the main body of the report.

43 PARTICLE ACCELERATORS↗

NASA NTRS1979

Low speed airfoil design and analysis

A low speed airfoil design and analysis program was developed which contains several unique features. In the design mode, the velocity distribution is not specified for one but many different angles of attack. Several iteration options are included which allow the trailing edge angle to be specified while other parameters are iterated. For airfoil analysis, a panel method is available which uses third-order panels having parabolic vorticity distributions. The flow condition is satisfied at the end points of the panels. Both sharp and blunt trailing edges can be analyzed. The integral boundary layer method with its laminar separation bubble analog, empirical transition criterion, and precise turbulent boundary layer equations compares very favorably with other methods, both integral and finite difference. Comparisons with experiment for several airfoils over a very wide Reynolds number range are discussed. Applications to high lift airfoil design are also demonstrated.

Eppler, R.↗

DOE OSTI2021

Coupled Microbial-Conversion and Computational-Fluid-Dynamics (CFD) Models for Butanediol Production in Micro-Aerated Reactors

Microbial conversion of substrates to macromolecules has been widely used in the synthesis of value-added products in pharmaceutical and biotechnology industries. These bioreactions are also being investigated in the production of low-value commodities such as biofuels [1]. Gas-liquid mass-transfer and transport-reaction coupling are important challenges when designing and scaling up these reactor systems. Experiments in wellmixed small-scale reactors have enabled characterization of microbial reactivity, while their coupling with macroscale transport remains relatively unexplored. In this work, we use a coupled metabolic-CFD model to study the action of a genetically engineered microbe Zymomonas mobilis [2] on sugars to produce 2,3-Butanediol (BDO). BDO is an important hydrocarbon intermediate that can be catalytically upgraded to several fuels and chemicals [3]. An important aspect to this particular microbial conversion is the need for micro-aerated environments as opposed to traditional aerobic fermentation. Slight variations in oxygen concentration can result in competing reaction pathways that disable BDO production. Hence, gas-liquid mass transfer and transport need to be optimized in large-scale reactors to maximize BDO production, for which CFD is a valuable tool. The aerobic-fermentation CFD model previously developed by the authors [5] for simulating bubble-column and airlift reactors at scale was used in this study. The Reynolds-averaged mass, momentum and energy transport equations for interpenetrating gas and liquid phase are solved in this model along with the transport and interphase mass transfer of oxygen. Our previous work used a phenomenological model for microbial oxygen uptake that neglected microbial growth and other reaction pathways. In this work, a detailed metabolic model enabled prediction of product formation and inhibition pathways. In order to manage computational cost, we used a subcycling technique [6] that takes advantage of the clear separation in transport (~ 200 sec) and reaction (~ 2-3 hours) timescales. The CFD model is first solved to steady state, after which the metabolic model is advanced at every cell in the computational domain using the local oxygen concentration. The CFD model is then run to achieve a new steady state that provides a new oxygen distribution for the metabolic model. This process, where reaction and fluid updates are interleaved together, is iterated until reactants are completely exhausted. This work will examine the performance of different reactor designs such as bubble column and airlift reactors at scale (250-500 m3). Oxygen mass-transfer coefficient and distribution are critically analyzed among reactors, and optimization studies pertaining to aeration is presented. Furthermore, it has been observed in experiments that high BDO production may be achieved by manipulating the aerobic environment over the course of reaction, such that oxygen concentration is high during the growth phase, and very low as sugar is depleted. This characteristic will be addressed by our simulations for which a timedependent scheduling strategy for aeration is presented that maximizes BDO production. [1] Humbird, D., Davis, R., and McMillan, J., Aeration costs in stirred-tank and bubble column bioreactors, Biochemical Engineering Journal, 127, 161—166, 2017 [2] Yang, S., Mohagheghi, A., Franden, M. A., Chou, Y.-C., Chen, X., Dowe, N., Himmel, M. E., and Zhang, M., Metabolic engineering of zymomonas mobilis for 2, 3-butanediol production from lignocellulosic biomass sugars. Biotechnology for biofuels, 9(1):189, 2016 [3] Kim, S. J., Sim, H. J., Kim, J. W., Lee, Y. G., Park, Y. C., and Seo, J. H., Enhanced production of 2,3-butanediol from xylose by combinatorial engineering of xylose metabolic pathway and cofactor regeneration in pyruvate decarboxylase-deficient Saccharomyces cerevisiae. Bioresource Technology, 245:1551–1557, 2017 [4] Weller, H., Tabor, G., Jasak, H. and Fureby, C., A tensorial approach to computational continuum mechanics using object-oriented techniques, Computers in physics, 12, 6, 620--631, 1998

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

DOE OSTI2021

Conceptual Design of High Field Central Solenoid for Fusion Nuclear Science Facility

Fusion Nuclear Science Facility (FNSF) is a critical fusion nuclear step in the US beyond ITER before proceeding to a larger and electricity producing fusion power plant. Although FNSF is a steady state machine to be operated at high duty cycle, a high field and high current density central solenoid magnet is needed for plasma startups. Due to space constraints in the FNSF in-board radial build, the magnetic field and coil current density required exceed conventional low temperature superconductor (LTS) performance limits and the design can only be achieved by high temperature superconductors (HTS). The design for the central solenoid, also called the ohmic heating (OH) magnet for FNSF shall meet the 100 Weber double flux swing requirement for plasma startups. Finally, the stresses at such a high field and high current density coil may require a bucked and wedged TF-OH design to accommodate space for coil winding support structures in in-board system radial build for high field FNSF operations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

Assessment of the burning-plasma operational space in ITER by using a control-oriented core-SOL-divertor model

In future tokamaks, the control of burning plasmas will require careful regulation of the plasma density and temperature. Along with the design of effective burn-control systems, understanding how the fusion power varies in the density-temperature space is vital for the operation of fusion power plants. Here in this work, the steady-state operational space of ITER is studied using a control-oriented core-plasma model coupled to a two-point model of the scrape-off-layer (SOL) and divertor regions. The two models are coupled through the exchange of input-output parameters. The deuterium and tritium recycling from the wall are output parameters of the SOL-divertor model that are used as input parameters in the core-plasma density balance. Furthermore, the separatrix temperature, which is an output parameter of the SOL-divertor model, is incorporated into the radial core-plasma temperature profiles. Therefore, the temperature-dependent power balance of the plasma core is intimately linked to the SOL-divertor model. Both the power entering the SOL from the core, as determined by the core-plasma power balance, and the separatrix density, as dictated by the core-plasma density balance, are input parameters to the SOL-divertor model. They are control knobs in the SOL-divertor model that can be regulated using the core-plasma actuators: auxiliary power and pellet injection. There are various operational limitations, such as the saturation of the aforementioned actuators, that will prevent ITER from accessing certain high-fusion plasma regimes. The achievable tritium concentration in the fueling lines and the maximum sustainable heat load on the divertor will impose further restrictions. By accounting for these limitations, the ITER operational space is computed based on the coupled core-SOL-divertor model and visualized using Plasma Operation Contour (POPCON) plots that map performance metrics, such as the fusion to auxiliary power ratio, over the density-temperature space. Comparisons are drawn between plasmas with different recycling, confinement, and SOL-divertor conditions.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2023

Reinforcement Learning of Structured Stabilizing Control for Linear Systems With Unknown State Matrix

This paper delves into designing feedback control gains for a continuous-time linear quadratic regulator (LQR) problem that is constrained to certain predefined structure with unknown state matrix. We bring forth the ideas from reinforcement learning (RL) in conjunction with sufficient stability and performance guarantees in order to design these structured gains using the trajectory measurements of states and controls. Here we first formulate a model-based framework using dynamic programming (DP) to embed the structural constraint to the LQR gain computation in the continuous-time setting, and then subsequently, formulate a policy iteration RL algorithm that can alleviate the requirement of known state matrix in conjunction with maintaining the feedback gain structure. The design enables a distributed learning control design which is necessary for many large-scale cyber-physical systems. Theoretical guarantees are provided for stability and convergence of the structured reinforcement learning (SRL) algorithm. We validate our theoretical results with numerical simulations on a multi-agent networked linear time-invariant (LTI) dynamic system.

42 ENGINEERING↗

NASA NTRS1990

Modelling and computationally efficient time domain linear equalisation of nonlinear bandlimited QPSK satellite channels

The problem of modeling and equalization of a nonlinear satellite channel is considered. The channel is assumed to be bandlimited and exhibits both amplitude and phase nonlinearities. In traditional models, computations are usually performed in the frequency domain and solutions are based on complex numerical techniques. A discrete time model is used to represent the satellite link with both uplink and downlink white Gaussian noise. Under conditions of practical interest, a simple and computationally efficient time-domain design technique for the minimum mean square error linear equalizer is presented. The efficiency of this technique is enhanced by the use of a fast and simple iterative algorithm for the computation of the autocorrelation coefficients of the output of the nonlinear channel. Numerical results on the evaluations of bit error probability and other relevant parameters needed in the design and analysis of a nonlinear bandlimited QPSK system demonstrate the simplicity and computational efficiency of the proposed approach.

Konstantinides, K.↗