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The New Jersey Board of Public Utilities (BPU) requested technical assistance from Berkeley Lab to inform its strategy for advancing demand response through its demand-side program planning process. Berkeley Lab developed this roadmap to delineate milestones for the portfolio's development and to identify the utility investments and BPU actions that achieve those milestones.
Estimating the energy yield of a wind plant during the preconstruction phase is a historically difficult task, even with industry improvements in these estimations. We build on prior research comparing the realized energy production of wind plants and their estimated annual energy production P50 values (median energy production), using owner-provided energy production and losses. We produced similar results to prior studies but with a slightly increasing bias of overestimating median energy production (a bias between realized and estimated energy production of −7.4 % to −6.6 %, depending on the scenario, as opposed to −6.7 % to −5.5 % from earlier studies). In addition to assessing annual energy production P50 bias, we compared both the 1-year and the long-term annual energy production P90 and uncertainty energy yield assessment estimates to the observed long-term-corrected energy production. We found that neither the energy yield assessment uncertainty nor the P90 is conservative enough compared to the observed distribution of prediction errors, suggesting significant room for improvement in the energy yield assessment process.
DeePMD-kit is a powerful open-source software package that facilitates molecular dynamics simulations using machine learning potentials known as Deep Potential (DP) models. This package, which was released in 2017, has been widely used in the fields of physics, chemistry, biology, and material science for studying atomistic systems. The current version of DeePMD-kit offers numerous advanced features, such as DeepPot-SE, attention-based and hybrid descriptors, the ability to fit tensile properties, type embedding, model deviation, DP-range correction, DP long range, graphics processing unit support for customized operators, model compression, non-von Neumann molecular dynamics, and improved usability, including documentation, compiled binary packages, graphical user interfaces, and application programming interfaces. This article presents an overview of the current major version of the DeePMD-kit package, highlighting its features and technical details. Additionally, this article presents a comprehensive procedure for conducting molecular dynamics as a representative application, benchmarks the accuracy and efficiency of different models, and discusses ongoing developments.
In this work, we performed an initial design space exploration of an accelerated processing unit (APU)—a hybrid CPU+GPU architecture that integrates both compute units (CUs) and memory into a unified system. This integration aims to reduce data movement, enhance memory locality, and improve energy efficiency by enabling the CPU and GPU to share memory directly. This effort focused on the interplay of key design components—cache line size, the number of CUs, and main memory technology—and the trade-offs of each configuration were analyzed. This paper highlights the various configurations’ impact on memory accesses, data reuse, and power utilization. The results provide valuable insights that can be leveraged to optimize APU architectures for high-performance and energy-efficient computing and thus create a balanced architecture. This optimization can be achieved by adopting dynamic cache management, runtime CU scaling, and advanced memory integration, highlighting the potential of APUs to address critical challenges in compute, data movement, and memory power consumption.
Radio telescopes that employ arrays of many antennas are in operation, and ever larger ones are being designed and proposed. Signals from the antennas are combined by cross-correlation. While the cost of most components of the telescope is proportional to the number of antennas N, the cost and power consumption of cross-correlationare proportional to N2 and dominate at sufficiently large N. Here we report the design of an integrated circuit (IC) that performs digital cross-correlations for arbitrarily many antennas in a power-efficient way. It uses an intrinsically low-power architecture in which the movement of data between devices is minimized. In a large system, each IC performs correlations for all pairs of antennas but for a portion of the telescope's bandwidth (the so-called "FX" structure). In our design, the correlations are performed in an array of 4096 complex multiply-accumulate (CMAC) units. This is sufficient to perform all correlations in parallel for 64 signals (N=32 antennas with 2 opposite-polarization signals per antenna). When N is larger, the input data are buffered in an on-chipmemory and the CMACs are re-used as many times as needed to compute all correlations. The design has been synthesized and simulated so as to obtain accurate estimates of the IC's size and power consumption. It isintended for fabrication in a 32 nm silicon-on-insulator process, where it will require less than 12mm2 of silicon area and achieve an energy efficiency of 1.76 to 3.3 pJ per CMAC operation, depending on the number of antennas. Operation has been analyzed in detail up to N = 4096. The system-level energy efficiency, including board-levelI/O, power supplies, and controls, is expected to be 5 to 7 pJ per CMAC operation. Existing correlators for the JVLA (N = 32) and ALMA (N = 64) telescopes achieve about 5000 pJ and 1000 pJ respectively usingapplication-specific ICs in older technologies. To our knowledge, the largest-N existing correlator is LEDA atN = 256; it uses GPUs built in 28 nm technology and achieves about 1000 pJ. Correlators being designed for the SKA telescopes (N = 128 and N = 512) using FPGAs in 16nm technology are predicted to achieve about 100 pJ.
The Crew Launch Vehicle (CLV), a key component of NASA's blueprint for the next generation of spacecraft to take humans back to the moon, is being designed and built by engineers at NASA s Marshall Space Flight Center (MSFC). The vehicle s design is based on the results of NASA's 2005 Exploration Systems Architecture Study (ESAS), which called for development of a crew-launch system to reduce the gap between Shuttle retirement and Crew Exploration Vehicle (CEV) Initial Operating Capability, identification of key technologies required to enable and significantly enhance these reference exploration systems, and a reprioritization of near- and far-term technology investments. The Upper Stage Element (USE) of the CLV is a clean-sheet approach that is being designed and developed in-house, with element management at MSFC. The USE concept is a self-supporting cylindrical structure, approximately 115' long and 216" in diameter, consisting of the following subsystems: Primary Structures (LOX Tank, LH2 Tank, Intertank, Thrust Structure, Spacecraft Payload Adaptor, Interstage, Forward and Aft Skirts), Secondary Structures (Systems Tunnel), Avionics and Software, Main Propulsion System, Reaction Control System, Thrust Vector Control, Auxiliary Power Unit, and Hydraulic Systems. The ESAS originally recommended a CEV to be launched atop a four-segment Space Shuttle Main Engine (SSME) CLV, utilizing an RS-25 engine-powered upper stage. However, Agency decisions to utilize fewer CLV development steps to lunar missions, reduce the overall risk for the lunar program, and provide a more balanced engine production rate requirement prompted engineers to switch to a five-segment design with a single Saturn-derived J-2X engine. This approach provides for single upper stage engine development for the CLV and an Earth Departure Stage, single Reusable Solid Rocket Booster (RSRB) development for the CLV and a Cargo Launch Vehicle, and single core SSME development. While the RSRB design has changed since the CLV Project's inception, the USE design has remained essentially a clean-sheet approach. Although a clean-sheet upper stage design inherently carries more risk than a modified design, it does offer many advantages: a design for increased reliability; built-in extensibility to allow for commonality/growth without major redesign; and incorporation of state-of-the-art materials, hardware, and design, fabrication, and test techniques and processes to facilitate a potentially better, more reliable system. Because consideration was given in the ESAS to both clean-sheet and modified USE designs, this paper will highlight the advantages and disadvantages of both approaches and provide a detailed discussion of trades/selections made that led to the final upper stage configuration.
This study presents the first model intercomparison of aerosol‐cloud‐turbulence interactions in a controlled cloudy Rayleigh‐Bénard Convection chamber environment, utilizing the Pi Chamber at Michigan Technological University. We analyzed simulated cloud chamber‐averaged statistics of microphysics and thermodynamics in a warm‐phase, cloudy environment under steady‐state conditions at varying aerosol injection rates. Simulation results from seven distinct models (DNS, LES, and a 1D turbulence model) were compared. Our findings demonstrate that while all models qualitatively capture observed trends in droplet number concentration, mean radius, and droplet size distributions at both high and low aerosol injection rates, significant quantitative differences were observed. Notably, droplet number concentrations varied by over two orders of magnitude between models for the same injection rates, indicating sensitivities to the model treatments in droplet activation and removal and wall fluxes. Furthermore, inconsistencies in vertical relative humidity profiles and in achieving steady‐state liquid water content suggest the need for further investigation into the mechanisms driving these variations. Despite these discrepancies, the models generally reproduced consistent power‐law relationships between the microphysical variables. This model intercomparison underscores the importance of controlled cloud chamber experiments for validating and improving cloud microphysical parameterizations. Recommendations for future modeling studies are also highlighted, including constraining wall conditions and processes, investigating droplet/aerosol removal (including sidewall losses), and conducting simplified experiments to isolate specific processes contributing to model divergence and reduce model uncertainties.
The work described in this report is responsive to the Office of Fossil Energy program ‘Energy Storage for Fossil Power Generation.’ This Phase I report has been prepared by Pintail Power LLC, with support from Nexant ECA, Electric Power Research Institute (EPRI) and Southern Company Services as a deliverable for the U.S. Department of Energy for NETL Award DE-FE-00320016. The Liquid Salt Combined Cycle™ (LSCC™) technology provides large-scale energy storage integrated with Fossil Electric Generating Units (FEGUs) to meet critical needs in the energy transition by providing: • the lowest cost large-scale storage for time-shifting of renewable energy, • superior fuel efficiency to reduce GHGs from dispatchable resources, • flexible capacity and ramping to balance variability of wind and solar resources, • essential grid stability services to assure reliability of a low-carbon grid. The LSCC approach: • employs equipment that has already been proven in utility service, • uses safe, non-toxic, non-degrading, perpetual-life storage medium, • leverages and repurposes existing FEGU assets, • expands the value stack of energy storage to reduce market, financing, and commodity risks. Pintail Power has developed the LSCC technology to meet the need for reliable, efficient, and cost-effective integration of Variable Renewable Energy (VRE) into a low-carbon electric grid by coupling proven thermal energy storage with proven gas turbines, steam turbines, and heat transfer equipment. This novel approach is intended to address the key issues facing the grid and operators of renewable and fossil generating units including: • Overgeneration and curtailment of renewables, • Need for fast ramping dispatchable resources, • Improved efficiency and flexibility of fossil units, • Additional peaking capacity to support electrification of transportation and heating, • Provision of reliability services to support high penetration of VRE, especially synchronous inertia and fast frequency response. A Technology Readiness assessment by EPRI confirmed that LSCC technology consists of commercially proven hardware used in industrial and utility applications. Although the novel LSCC approach has not yet been demonstrated as a complete system, interfaces between major components have been conservatively specified. A Phase III pilot is planned to demonstrate equipment integration and operation. The patented innovation is removal of the evaporator section from the exhaust heat recovery system, with the evaporation performed by stored energy in a separate steam generator. This arrangement couples renewable and fossil power generation via long-duration energy storage to deliver cost, performance, and operational synergies, including superior charging and discharging flexibility, reduced fuel consumption and lower CO 2 emissions compared to conventional Combined Cycle Power Plants, and low-cost, large-scale energy storage. The LSCC technology is composed of proven equipment integrated with gas turbine exhaust heat in a novel system. During charging, electric heaters raise the salt temperature as it flows from the Cold Salt Tank to the Hot Salt Tank. During discharging, hot salt produces steam from feedwater that is heated with gas turbine exhaust, which also superheats steam to drive a steam turbine. LSCC technology can be added to any combustion-turbine to integrate renewable energy, provide needed grid services, and increase the value of fossil electric generating units based on the technology’s following attributes: • Long-duration storage enables time-shifting of VRE to avoid curtailment and impairment of renewable assets. • Long storage duration combined with fast-charging capability increases arbitrage opportunities by storing more energy when the price is low and discharging more hours when the price is high. • Long storage duration allows resource adequacy to be supplied across multiple days to increase reliability and reduce risk. • The stored energy reduces fuel heat rate and GHG emissions, and increases merit, so the LSCC dispatches earlier and longer to increase the plant’s capacity factor and asset value. • The stored energy enables pre-heating and startup of the steam cycle, without operating the gas turbine, to enable fast startup and ramping when dispatched for discharge. • The steam turbine can operate without the gas turbine so it can provide valuable synchronous inertia during charging without consuming fuel. • Fast frequency response and regulation services can be provided during charging using solid-state heater and pump controls to vary the charge power input in response to grid signals. • The LSCC system can be configured for resilience including black start, islanded/micro-grid operation, and even self-recharging of storage using either gas turbine power or gas turbine exhaust heat. The commercialization plan is to add LSCC technology to existing simple cycle gas turbine power plants with the 50MW GE LM6000 aero-derivative gas turbine as the reference design basis. A Techno-economic assessment of the reference design evaluated the benefits (Levelized Avoided Cost of Energy) and costs (Levelized Cost of Energy). The plant definition included all major systems and budgetary vendor quotes. Pintail Power and NexantECA developed the overall cost estimate for the LSCC plant up to the total plant cost level, following the DOE-NETL cost estimate guidelines at AACE Class 3 (-20%/+30%). This includes the equipment cost, bulk material, direct and indirect labor costs to arrive at the bare erected cost. Engineering costs are factored from the BEC and added to it to arrive at the EPC cost. Process and project contingencies were then factored from the EPC cost and rolled-up to yield the total plant cost of $\$$184 million for 1746 MWh of discharge electricity. • At $\$$105/kWh, the reference plant costs less than any of the Energy Storage Systems evaluated by PNNL in 2020 for the Energy Storage Grand Challenge. Operations and Maintenance cost estimates were scaled from combined cycle practice, assuming that the LSCC unit was co-located with and sharing some labor expense with other units, to arrive at $\$$2.2 million per year. Plant economics were evaluated using prices from the ERCOT Day-Ahead Market for calendar year 2019 (excluding the market disruptions from the COVID pandemic and the February 2020 deep freeze event). Assuming economic dispatch in the ERCOT Day-Ahead market, the reference plant capacity factor would have discharged for 2777 hours at 91.9 MW, a 31.66% capacity factor, with a marginal cost of $\$$25.59/MWh, and a LACE of $\$$82.41/MWh. Fixed charges were calculated according to EIA guidelines to arrive at an LCOE of $\$$83.48. The benefit-to-cost ratio of 0.99 suggests that the reference plant would have been cost-effective and competitive in the market. EPRI interviewed selected utilities to gauge the need for, applicability of and interest in the LSCC system. Several utilities are currently managing increased load growth along with the inclusion of increasing levels of renewable generation, putting pressure on conventional generation by requiring increased turndown requirements and ultimately lower capacity factors. All of the utilities interviewed have CO 2 reduction targets in the 2030-2050 timeframe that will severely limit the participation of fossil generation and require better utilization of carbon free generation. While there is limited opportunity for storage in the current markets, the utilities interviewed stated that there will be a substantial need for long duration energy storage in the future given the expected trends. Utilizing an energy storage system will generally be preferred over new gas capacity in some cases, with the capabilities of the LSCC system being a potential option for retrofit to existing simple cycle gas turbine units, allowing them to deliver greater participation in the market with lower carbon intensity. A technology gap assessment and technology maturation plan identified a pilot-scale demonstration as the final step before commercialization. Key gaps to be addressed during the Phase II FEED (Front-End Engineering Design) are component selection and design, commissioning procedures, and operational procedures and the control system for LSCC charging and discharging. The project team has been expanded to include Wood Group PLC as EPC. The proposed Phase II work leads to a pilot-scale engineering demonstration (TRL 6) to be conducted at Southern Company’s Plant Rowan, where the prototype system will perform “all the functions that will be required of the operational system.” The proposed pilot will facilitate commercialization (TRL-9) by scale-up to utility-scale systems integrated with peaking GTs or directly to facility scale systems using industrial GTs. The conceptual design for the pilot plant focuses on the novel integration aspects of LSCC technology. A slipstream of gas turbine exhaust will feed a waste heat recovery unit coupled to a molten salt steam generator heated by stored energy. The pilot is intended to demonstrate all key operating modes of the LSCC technology during charging, discharging and standby. The pilot equipment will be approximately one-seventh scale of the LM6000 commercial target and is expected to have commercial off-ramp potential for facility-scale applications.
Laser Powder Bed Fusion (LPBF) enables the additive manufacturing of complex lattice structures. However, the fabrication of lattice structures via LPBF poses challenges in achieving the intended geometrical accuracy due to their inherent complexity. This study investigates the effects of LPBF processing parameters, specifically laser power and scanning speed, on the geometrical characteristics, surface quality, and mechanical behavior of Inconel 718 lattices structures. The results reveal that processing parameters required for the fabrication of near-full dense structures do not translate effectively to lattice configurations, as variations in energy input influence lattice geometry and surface quality. In this work, strut thickness, open-pore size, open-cell porosity, and surface roughness were measured, and the mechanical properties of the lattices were evaluated under shear loading. The findings indicate that lower energy inputs, achieved by reducing laser power and increasing scanning speed, yield porous structures but lead to mechanical degradation. In contrast, high energy inputs lead to lattices with enhanced strength but result in undesirable open-pore blockage and dimensional inaccuracies. These findings provide insights into tailoring LPBF parameters for dimensional accuracy in lattices and correlating the processing parameters to mechanical performance and surface roughness.
High-fidelity electromagnetic transient (EMT) simulation plays a critical role in understanding the dynamic behavior and fast transients involved in operation, control, and protection of Multi-Terminal dc (MTdc) grids. Here, this paper proposes a cost-effective high-performance real-time EMT simulation platform for large-scale cross-continental MTdc grids based on graphics processing unit (GPU). The proposed simulation platform: i) assembles detailed EMT models of all components within an MTdc-ac grid into a single platform. This setup provides a complete simulation solution to capture fast transient signals required for high-bandwidth controller design and protection studies without any compromise; ii) implements the first GPU-based simulation architecture and corresponding algorithms for MTdc-ac grids with real-time performance at scales of 1s; iii) is highly-efficient and balances the high utilization of GPU resources and low latency required for the simulation; and iv) outperforms the existing central processing unit (CPU)- or digital signal processor (DSP)/field-programmable gate array (FPGA)-based simulators in terms of its higher scalability on large-scale MTdc-ac grids and superior price-performance ratio on the hardware. Accuracy and performance of the proposed platform are evaluated with respect to the reference results from PSCAD/EMTDC environment.
This report presents the design of system interfaces enabling flexible thermal power extraction from two advanced nuclear reactor concepts: a sodium-cooled fast reactor (SFR) operating on a Rankine cycle, and a gas-cooled reactor (GCR) utilizing a Brayton cycle. The study addresses the dual challenge of ensuring reliable base-load electricity generation while meeting the variable high-temperature steam demands of industrial processes (IPs).
Electric transmission system operators (ISOs, RTOs, or utilities) require proposed power plants seeking to connect to the transmission grid to undergo a series of impact studies before they can be built. This process establishes what new transmission equipment or upgrades may be needed before a project can connect to the system and assigns the costs of that equipment. The lists of projects in this process are known as “interconnection queues”. In collaboration with https://www.interconnection.fyi. Berkeley Lab compiled, aggregated, and cleaned interconnection queue data from >50 transmission grid operators (7 ISO/RTOs and 50 non-ISO balancing areas), which collectively represent ~98% of currently installed U.S. electric generating capacity.
Increasing the fuel discharge burnup of current light water reactors (LWRs) promises reductions in fuel cycle and/or operations costs. By assuming a constant core power density, the economic gain is enabled by better fuel utilization and/or an increased capacity factor. In this effort to investigate greater than 62 MWd/kgU maximum rod average burnup for 110+ kW/l core power density, two core designs have been developed for a standard 17x17, 193 fuel assemblies pressurized water reactor (PWR). The levelized unit cost methodology is employed to evaluate fuel cycle, operation and maintenance, and capital cost impacts and to examine the economic viability of both core design pathways. Core design and optimization are performed using the commercial STUDSVIK code package. Fuel performance analysis is realized in full core configuration via auditing FRAPCON4.1, FAST1.2, and the high-fidelity code BISON. To provide a realistic assessment, the core design process takes into consideration best practices in current PWR core design. It features acceptable performance in terms of various core design constraints on maximum allowable peaking and boron concentration. Gadolinia (Gd2O3) is used as a burnable poison with a maximum of 9 wt% concentration while feeding 89 or 77 fuel assemblies in a 3-batch refueling scheme. Full core fuel performance simulation, which allows for characterization of relevant fuel temperatures, plenum pressures, stresses, and strains, is performed with respect to two bounding burnup levels. Such performance is potentially licensable for the 18-month high burnup core (<68 MWd/kgU peak pin), while it is more challenging for the 24-month high burnup core design pathway (<75 MWd/kgU peak pin). Maximum rod plenum pressure is identified as the most limiting fuel performance parameter. Here, while the scope of the present study focuses on the steady-state plus overpower conditions, the acceptability of the new discharge burnup has to be further assessed by considering uncertainties and impacts under accident scenarios in the future.
The United States has pledged to develop a 100% carbon-free electric power system by 2035 and a net-zero-emissions economy by 2050. While important advancements have been made in the scale, performance, and economics of clean energy technologies, meeting the nation's ambitious goals will not only require their deployment at scale, but also additional innovation and effective integration of different solutions. Technological developments across the broad suite of low-carbon energy solutions are advancing rapidly, with ongoing innovations in renewable electricity generation, industrial processes, and energy-saving technologies and services, including LED lighting, induction heating, electric vehicles, energy storage solutions, and mobility as a service, plus smart devices, controls, and more efficient and smart buildings. Combining renewable electricity with biotic and abiotic pathways to produce chemicals, fuels, and materials promises to deliver new solutions. Grid-interactive buildings and communities, integrating transportation infrastructure and vehicles, are likely to be significant components of any zero-carbon energy strategy. Low-carbon industrial manufacturing will also make strong contributions to a net-zero economy. While the technical prospects appear promising, variations in the state of infrastructure, jurisdictional and social equity, pollution, economic and socio-cultural constraints, energy resource availability, and supply chain dynamics found in different locations present a range of challenges and demand customized solutions. This paper provides a critical review and offers new insights into the technical, infrastructure, analytic, political, and economic challenges faced in translating the nation's ambitious net-zero-emissions goals into feasible and reliable implementation action plans.
Rapid increases in distributed energy resources on distribution systems are prompting research efforts to improve and evaluate electric power distribution algorithms; however, there is a shortage of realistic, large-scale, U.S.-style test systems for the evaluation of such advanced algorithms. Some available tools to build large-scale test systems are of European style, and their application to studies focused on the United States might not be desirable given very different characteristics between the European and U.S. distribution designs. Motivated by this need, this paper develops detailed algorithms to build large-scale U.S. distribution systems and incorporates them in a new Reference Network Model, RNM-US. The approach starts with information from street maps and a catalog with electric equipment that includes power lines, transformers, voltage regulators, capacitors, and switching devices. The paper presents the algorithms through an illustrative case study of the different steps that comprise the process of building a synthetic distribution grid. Finally, the paper presents a medium- and a large-scale data set covering 10 million electrical nodes and 120,000 km of power lines, demonstrating the applicability of the proposed method to build very large-scale synthetic distribution systems.
Chemical separations are a cornerstone of industrial manufacturing processes that generate products and services that have improved the standard of living for humans across the globe. To give some context as to how ubiquitous separations are in the modern world, they are involved in the production of fuels, medicines, clean water, fertilizers, materials used in semiconductor chip manufacturing, and other goods. A 2019 report by the National Academies of Sciences, Engineering, and Medicine highlights that chemical separations account for about 10 to 15% of energy use in the United States. Of the four broad sectors (residential, transportation, industry, and commerce) that use energy in the United States, industry has the largest use at 32% and about half of the energy use in industry hails from separations. It is likely that the transportation and residential sectors will experience significant decarbonization in the next 25 years with the proliferation of wind and solar energy sources coupled with electrochemical energy storage and electrification of vehicles. Finally, industrial decarbonization, on the other hand, is far more complex and challenging and it is imperative that future engineers and scientists work hard to devise alternative processes that can be powered on renewable electrons while generating little waste to produce the goods and services that make up our modern lives.
The major elements of the NASA manned space station are described, and science activities it could be used for are suggested. The core facilities include at least two major laboratory modules with supporting utilities, including habitation accommodations, docking facilities, power and heat rejection units, and external space and support for attached payloads. A vertically oriented structure, called the Power Tower, is being studied. Scientific accommodations inside the modules include major facility instrumentation for a variety of microgravity research projects, with initial emphasis upon materials research and life sciences. The second element is composed of free-flying satellites operating in orbits near the core station. The third element consists of satellites in polar orbits. One or more large, multi-instrument platforms are planned for Earth observation and solar-terrestrial processes research.
Proposed modifications of an offset-quadri-phase-shift keying (offset-QPSK) transmitter and receiver would reduce the amount of signal processing that must be done in the receiver to resolve the QPSK fourfold phase ambiguity. Resolution of the phase ambiguity is necessary in order to synchronize, with the received carrier signal, the signal generated by a local oscillator in a carrier-tracking loop in the receiver. Without resolution of the fourfold phase ambiguity, the loop could lock to any of four possible phase points, only one of which has the proper phase relationship with the carrier. The proposal applies, more specifically, to an offset-QPSK receiver that contains a carrier-tracking loop like that shown in Figure 1. This carrier-tracking loop does not resolve or reduce the phase ambiguity. A carrier-tracking loop of a different design optimized for the reception of offset QPSK could reduce the phase ambiguity from fourfold to twofold, but would be more complex. Alternatively, one could resolve the fourfold phase ambiguity by use of differential coding in the transmitter, at a cost of reduced power efficiency. The proposed modifications would make it possible to reduce the fourfold phase ambiguity to twofold, with no loss in power efficiency and only relatively simple additional signal-processing steps in the transmitter and receiver. The twofold phase ambiguity would then be resolved by use of a unique synchronization word, as is commonly done in binary phase-shift keying (BPSK). Although the mathematical and signal-processing principles underlying the modifications are too complex to explain in detail here, the modifications themselves would be relatively simple and are best described with the help of simple block diagrams (see Figure 2). In the transmitter, one would add a unit that would periodically invert bits going into the QPSK modulator; in the receiver, one would add a unit that would effect different but corresponding inversions of bits coming out of the QPSK demodulator. The net effect of all the inversions would be that depending on which lock point the carrier-tracking loop had selected, all the output bits would be either inverted or non-inverted together; hence, the ambiguity would be reduced from fourfold to twofold, as desired.