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211 records · Page 12
All sourcesNASA NTRSDOE OSTI
NASA NTRS2000

Measurements and Calculations of Microwave Radiance and Reflectivity for Storm-Associated Frozen Hydrometeors

During the TEFLUN-B (Texas-Florida under-flights for the Tropical Rainfall Measuring Mission (TRMM)) field experiment of August-September, 1998, a number of ER-2 aircraft flights with a host of microwave instruments were conducted over many convective storms, including some hurricanes, in the coastal region of Florida and Texas. These instruments include MIR (Millimeter-wave Imaging Radiometer), AMPR (Advanced Microwave Precipitation Radiometer), and EDOP (ER-2 Doppler Radar). EDOP is operated at the frequency of 9.7 GHz, while the AMPR and the MIR together give eleven channels of radiometric measurements in the frequency range of 10-340 GHz. The concurrent measurements from these instruments provide unique data sets for studying the details of the microphysics of hydrometeors. Preliminary examination of these data sets shows features that are generally well understood; i.e., radiometric measurements at frequencies <= 37 GHz mainly respond to rain, while those at frequencies >= 150 GHz, to snow and ice clouds above the freezing level. In this paper we present results of comparisons between these measurements and model calculations of brightness temperature and radar reflectivity. For simplicity the analysis is limited to the anvil region of the storms where only frozen hydrometeors are present. Various models of particle size distribution (e.g., Gunn-Marshall, Sekhon-Srivastava, and the Central Equatorial Pacific Experiment (CEPEX)) are examined in the calculations of brightness temperatures at the MIR frequencies and radar reflectivity at the EDOP frequency. Estimation of ice water path is made based on the best agreement between the measurements and calculations of brightness temperature and reflectivity. Problems associated with these analyses and measurement accuracy will be discussed.

Wang, James R.↗
NASA NTRS2008

Linear FMCW Laser Radar for Precision Range and Vector Velocity Measurements

An all fiber linear frequency modulated continuous wave (FMCW) coherent laser radar system is under development with a goal to aide NASA s new Space Exploration initiative for manned and robotic missions to the Moon and Mars. By employing a combination of optical heterodyne and linear frequency modulation techniques and utilizing state-of-the-art fiber optic technologies, highly efficient, compact and reliable laser radar suitable for operation in a space environment is being developed. Linear FMCW lidar has the capability of high-resolution range measurements, and when configured into a multi-channel receiver system it has the capability of obtaining high precision horizontal and vertical velocity measurements. Precision range and vector velocity data are beneficial to navigating planetary landing pods to the preselected site and achieving autonomous, safe soft-landing. The all-fiber coherent laser radar has several important advantages over more conventional pulsed laser altimeters or range finders. One of the advantages of the coherent laser radar is its ability to measure directly the platform velocity by extracting the Doppler shift generated from the motion, as opposed to time of flight range finders where terrain features such as hills, cliffs, or slopes add error to the velocity measurement. Doppler measurements are about two orders of magnitude more accurate than the velocity estimates obtained by pulsed laser altimeters. In addition, most of the components of the device are efficient and reliable commercial off-the-shelf fiber optic telecommunication components. This paper discusses the design and performance of a second-generation brassboard system under development at NASA Langley Research Center as part of the Autonomous Landing and Hazard Avoidance (ALHAT) project.

Pierrottet, Diego↗
NASA NTRS1983

Variability in the power spectrum of solar five-minute oscillations

It is noted that two-dimensional power spectra of solar five-minute oscillations exhibit prominent ridge structures in (k, omega) space, k being the horizontal wavenumber and omega the temporal frequency. The positions of these ridges in k and omega can be used in probing temperature and velocity structures in the subphotosphere. The progress made in a program to establish whether power spectra taken on separate days show shifts in ridge locations is surveyed, noting that these may arise from different velocity and temperature patterns having been brought into the sampling region by solar rotation. Power spectra are obtained for six days of observations of Doppler velocities using the Mg I 5173 A and Fe I 5434 A spectral lines. Each data set encompasses 8 to 11 hr in time and samples a region 256 x 1024 arcsec in spatial extent, with a spatial resolution of 2 arcsec and temporal sampling of 65 s. Statistically significant shifts are detected in ridge locations between certain data sets. When analyzed in terms of eastward and westward propagating waves, the character of these displacements is seen as implying that changes have occurred in both temperature and horizontal velocity fields underlying the observing window. The velocity changes are estimated to be of the order of 100 m/s.

Hill, F.↗
NASA NTRS1985

A comparison of Doppler lidar wind sensors for Earth-orbit global measurement applications

Now, there are four Doppler lidar configurations which are being promoted for the measurement of tropospheric winds: (1) the coherent CO2 Lidar, operating in the 9 micrometer region using a pulsed, atmospheric pressure CO2 gas discharge laser transmitter, and heterodyne detection; (2) the coherent Neodymium doped YAG or Glass Lidar, operating at 1.06 micrometers, using flashlamp or diode laser optical pumping of the solid state laser medium, and heterodyne detection; (3) the Neodymium doped YAG/Glass Lidar, operating at the doubled frequency (at 530 nm wavelength), again using flashlamp or diode laser pumping of the laser transmitter, and using a high resolution tandem Fabry-Perot filter and direct detection; and (4) the Raman shifted Xenon Chloride Lidar, operating at 350 nm wavelength, using a pulsed, atmospheric pressure XeCl gas discharge laser transmitter at 308 nm, Raman shifted in a high pressure hydrogen cell to 350 nm in order to avoid strong stratospheric ozone absorption, also using a high resolution tandem Fabry-Perot filter and direct detection. Comparisons of these four systems can include many factors and tradeoffs. The major portion of this comparison is devoted to efficiency. Efficiency comparisons are made by estimating the number of transmitted photons required for a single pulse wind velocity estimate of + or - 1 m/s accuracy in the middle troposphere, from an altitude of 800 km, which is assured to be reasonable for a polar orbiting platform.

Menzies, Robert T.↗
NASA NTRS1994

Correlated environmental corrections in TOPEX/POSEIDON, with a note on ionospheric accuracy

Estimates of the effectiveness of an altimetric correction, and interpretation of sea level variability as a response to atmospheric forcing, both depend upon assuming that residual errors in altimetric corrections are uncorrelated among themselves and with residual sea level, or knowing the correlations. Not surprisingly, many corrections are highly correlated since they involve atmospheric properties and the ocean surface's response to them. The full corrections (including their geographically varying time mean values), show correlations between electromagnetic bias (mostly the height of wind waves) and either atmospheric pressure or water vapor of -40%, and between atmospheric pressure and water vapor of 28%. In the more commonly used collinear differences (after removal of the geographically varying time mean), atmospheric pressure and wave height show a -30% correlation, atmospheric pressure and water vapor a -10% correlation, both pressure and water vapor a 7% correlation with residual sea level, and a bit surprisingly, ionospheric electron content and wave height a 15% correlation. Only the ocean tide is totally uncorrelated with other corrections or residual sea level. The effectiveness of three ionospheric corrections (TOPEX dual-frequency, a smoothed version of the TOPEX dual-frequency, and Doppler orbitography and radiopositioning integrated by satellite (DORIS) is also evaluated in terms of their reduction in variance of residual sea level. Smooth (90-200 km along-track) versions of the dual-frequency altimeter ionosphere perform best both globally and within 20 deg in latitude from the equator. The noise variance in the 1/s TOPEX inospheric samples is approximately (11 mm) squared, about the same as noise in the DORIS-based correction; however, the latter has its error over scales of order 10(exp 3) km. Within 20 deg of the equator, the DORIS-based correction adds (14 mm) squared to the residual sea level variance.

Zlotnicki, V.↗
NASA NTRS1999

Investigation of Point Doppler Velocimetry (PDV) for Transition Detection in Boundary Layers

A two component Point Doppler Velocimetry (PDV) system has been developed and tested. Improvements were made to an earlier PDV system, in terms of experimental techniques, as well as the data acquisition and reduction software. Measurements of the streamwise and spanwise mean and fluctuating velocities for flows from a rectangular channel and over an NACA 0012 airfoil were made, and the data were compared against hot wire data. The closest to the airfoil surface that PDV measurements could be made was on the order of 0.005 m(0.2", z/c = 0.0169). When the PDV and hot wire data were compared, the time traces for each appeared similar. The mean velocities agreed to within plus or minus 2 m/sec, while the RMS velocities agreed to plus or minus 0.4 m/sec. While the PDV time autocorrelations agreed with those of the hot wire data, the PDV power spectral densities were noisier above 750 Hz. A major source of error in these experiments was determined to be the drifting of the iodine cell stem temperatures. While the stem temperatures were controlled to within plus or minus 0.1 C, this could lead to a frequency shift of as much as 6 MHz, which translates into an error of 1.6 m/sec for the back scatter channel, and up to 6.9 m/sec for the forward scatter channel. These error estimates are consistent with the observed error magnitudes.

Kuhlman, John M.↗
NASA NTRS1996

Radar Observations of Asteroids 1 Ceres, 2 Pallas, and 4 Vesta

Asteroids 1 Ceres, 2 Pallas, and 4 Vesta were observed with the 13-cm Arecibo radar and the 3.5-cm Goldstone radar during several apparitions between 1981 and 1995. These observations help to characterize the objects' surface properties. Echoes from Ceres and Pallas are approximately 95% polarized (muon(sub C) = sigm(sub SC)/sigma(sub OC) equivalent to 0.05) in the sense expected for specular (mirror) reflection yet broadly distributed in Doppler frequency, thus revealing surfaces that are smoother than the Moon at decimeter scales but much rougher (rms slopes > 20 deg) on larger scales. Slopes on Ceres appear to be somewhat higher when viewed with the 3.5-cm wavelength, a trend that is observed for the terrestrial planets and the Moon. In contrast, echoes from Vesta are significantly depolarized, indicating substantial near-surface complexity at scales near 13 cm (muon(sub C) = 0.24 +/- 0.04) and 3.5 cm (muon(sub C) = 0.32 +/- 0.04), which is probably a consequence of Vesta's relatively strong basaltic surface material and may be a signature of large impact features inferred to be present on the surface. The low radar albedos of Ceres (circumflex-sigma(sub C) = 0.042 +/- 0.006) and Pallas (circumfle-sigma(sub C) = 0.075 +/- 0.011) are in the range expected for surfaces with a carbonaceous chondrite mineralogy. Pallas' distinctly higher albedo implies a approximately 35% higher surface density, which could result from a lower regolith porosity and/or a higher specific gravity (zero-porosity density). Given a porosity of 45%, the specific gravities of the surface materials on Ceres and Pallas would be approximately 2.3 and approximately 3.0 g/cc, respectively, which would be consistent with (1) the presence of an additional silicate component on Pallas' surface (as inferred from spectroscopic observations) and (2) recent mass estimates, which suggest a higher mean (volume-averaged) density for Pallas than for Ceres.

Mitchell, David L.↗
NASA NTRS2001

Modeling Wave Driven Non-linear Flow Oscillations: The Terrestrial QBO and a Solar Analog

The Quasi Biennial Oscillation (QBO) of the zonal circulation observed in the terrestrial atmosphere at low latitudes is driven by wave mean flow interaction as was demonstrated first by Lindzen and Holton (1968), shown in a laboratory experiment by Plumb and McEwan (1978), and modeled by others (e.g., Plumb, Dunkerton). Although influenced by the seasonal cycle of solar forcing, the QBO, in principle, represents a nonlinear flow oscillation that can be maintained by a steady source of upward propagating waves. The wave driven non-linearity is of third or odd order in the flow velocity, which regenerates the fundamental harmonic itself to keep the oscillation going - the fluid dynamical analog of the displacement mechanism in the mechanical clock. Applying Hines' Doppler Spread Parameterization (DSP) for gravity waves (GW), we discuss with a global-scale spectral model numerical experiments that elucidate some properties of the QBO and its possible effects on the climatology of the atmosphere. Depending on the period of the QBO, wave filtering can cause interaction with the seasonal variations to produce pronounced oscillations with beat periods around 10 years. Since the seasonal cycle and its variability influence the period of the QBO, it may also be a potent conduit of solar activity variations to lower altitudes. Analogous to the terrestrial QBO, we propose that a flow oscillation may account for the 22-year periodicity of the solar magnetic cycle, potentially answering Dicke (1978) who asked, "Is there a chronometer hidden deep inside the Sun?" The oscillation would occur below the convection region, where gravity waves can propagate. Employing a simplified, analytic model, Hines' DSP is applied to estimate the flow oscillation. Depending on the adopted horizontal wavelengths of GW's, wave amplitudes less than 10 m/s can be made to produce oscillating zonal flows of about 20 m/s that should be large enough to generate a significant oscillation in the magnetic field. For the large length scales of the Sun, the flow cycle period tends to be very long. The period, however, can be made to be 22 years, provided the buoyancy frequency (stability) is sufficiently small, thus placing the proposed flow near the base of the convection zone where a dynamo is now believed to operate.

Mayr, Hans G.↗
NASA NTRS2010

Prospects for Habitable World Detections Using James Webb Space Telescope (JWST)

Doppler and transit surveys are finding extrasolar planets of ever smaller mass and radius, and are now sampling the domain of superEarths. Recent results from the Doppler surveys suggest that discovery of a transiting superEarth in the habitable zone of a lower main sequence star may be possible. We evaluate the prospects for an all-sky transit survey targeted to the brightest stars I that would find the most favorable cases for photometric and spectroscopic characterization using the James Webb Space Telescope. We use the proposed Transiting Exoplanet Survey Satellite (TESS) as representative of an all-sky survey. We couple the simulated TESS yield to a sensitivity model for the MIRI and NIRSpec instruments on JWST. Our sensitivity model includes all currently known and anticipated sources of random and systematic error for these instruments. We focus on the TESS planets with radii between Earth and Neptune. Our simulations consider secondary eclipse filter photometry using JWST/MIRI, comparing the 11- and 15- micron bands to measure carbon dioxide absorption in superEarths, as well as JWST!NIRSpec spectroscopy of water absorption from 1.7-3.0 microns, and carbon dioxide absorption at 4.3 microns. We find that JWST will be capable of characterizing dozens of TESS superEarths with temperatures above the habitable range, using both MIRI and NIRspec. We project that TESS will discover about eight nearby habitable transiting superEarths, all orbiting lower main sequence stars. The principal sources of uncertainty in the prospects for JWST characterization of habitable superEarths are superEarth frequency and the nature of superEarth atmospheres. Based on our estimates of these uncertainties, we project that JWST will be able to measure the temperature, and identify molecular absorptions (water, carbon dioxide) in one to four nearby habitable TESS superEarths orbiting lower main sequence stars.

Deming, Drake↗
NASA NTRS1994

Computer modeling of the sensitivity of a laser water vapor sensor to variations in temperature and air speed

Currently, there is disagreement among existing methods of determining atmospheric water vapor concentration at dew-points below -40 C. A major source of error is wall effects which result from the necessity of bringing samples into the instruments. All of these instruments also have response times on the order of seconds. NASA Langley is developing a water vapor sensor which utilizes the absorption of the infrared radiation produced by a diode laser to estimate water vapor concentration. The laser beam is directed through an aircraft window to a retroreflector located on an engine. The reflected beam is detected by an infrared detector located near the laser. To maximize signal to noise, derivative signals are analyzed. By measuring the 2f/DC signal and correcting for ambient temperature, atmospheric pressure and air speed (which results in a Doppler shifting of the laser beam), the water vapor concentration can be retrieved. Since this is an in situ measurement there are no wall effects and measurements can be made at a rate of more than 20 per second. This allows small spatial variations of water vapor to be studied. In order to study the sensitivity of the instrument to variations in temperature and air speed, a computer program which generated the 2f, 3f, 4f, DC and 2f/DC signals of the instrument as a function of temperature, pressure and air speed was written. This model was used to determine the effect of errors in measurement of the temperature and air speed on the measured water vapor concentration. Future studies will quantify the effect of pressure measurement errors, which are expected to be very small. As a result of these studied, a retrieval algorithm has been formulated, and will be applied to data taken during the PEM-West atmospheric science field mission. Spectroscopic studies of the water vapor line used by the instrument will be used to refine this algorithm. To prepare for these studies, several lasers have been studied to determine their output frequency range and power.

Tucker, George F.↗
NASA NTRS1996

Jet Evolution Visualized and Quantified Using Filtered Rayleigh Scattering

Filtered Rayleigh scattering was utilized as a flow diagnostic in an investigation of a method for enhancing mixing in supersonic jets. The primary objectives of the study were to visualize the effect of vortex generating tabs on supersonic jets, to exact quantitative data from these planar visualizations, and to detect the presence of secondary flows (i.e., streamwise vorticity) generated by the tabs. An injection seeded frequency-doubled Nd:YAG was the light source and a 14 bit Princeton Instruments iodine charge coupled display (ICCD) camera recorded the image through an iodine cell. The incident wave length of the laser was held constant for each flow case so that the filter absorbed unwanted background light, but permitted part of the thermally broadened Rayleigh scattering light to pas through. The visualizations were performed for axisymmetric jets (D=1.9 cm) operated at perfectly expanded conditions for Mach 1.0, 1.5, and 2.0. All data were recorded for the jet cross section at x/D=3. One hundred instantaneous images were recorded and averaged for each case, with a threshold set to eliminate unavoidable particulate scattering. A key factor in these experiments was that the stagnation air was heated such that the expansion of the flow in the nozzle resulted in the static temperature in the jet being equal to the ambient temperature, assuming isentropic flow. Since the thermodynamic conditions of the flow were approximately the same for each case, increases in the intensity recorded by the ICCD camera could be directly attributed to the Doppler shift, and hence velocity. Visualizations were performed for Mach 1.5 and Mach 2.0 jets with tabs inserted at the nozzle exit. The distortion of the jet was readily apparent and was consistent with Mie scattering-based visualizations. Asymmetry in the intensities of the images indicate the presence of secondary flow patterns which are consistent with the streamwise vortices measured using more traditional diagnostics in subsonic jets with the same tab configurations. Because each tab causes shocks to form, the assumption of isentropic flow is not valid for these cases. However, within a reasonable first-order estimation,the intensity across the illuminated plane for these cases can be related to a value combining density and velocity.

Reeder, Mark F.↗
NASA NTRS2000

Nozomi Cis-Lunar Phase Orbit Determination

Japan's Institute of Space and Astronautical Science (ISAS) launched Nozomi, its first mission to the planet Mars using the newly developed M-V launch vehicle on July 3, 1998. Scientific objectives of the mission are to study the structure and dynamics of the Martian upper atmosphere and its interaction with the solar wind. Nozomi is a cooperative mission between ISAS and the National Aeronautics and Space Administration (NASA). The NASA contribution includes navigation and tracking services provided by the Jet Propulsion Laboratory (JPL). The spacecraft also serves as an engineering demonstration of basic technology for planetary exploration. One of the new technologies was a unique trajectory, developed by ISAS, which used solar gravitational perturbations at the weak stability boundary as an aid to achieve an Earth-Mars transfer orbit. This trajectory saves approximately 120 m/s of Delta V compared to direct hyperbolic insertion and is considered an enabling technology for the mission. Nozomi was the first spacecraft to employ this trajectory and provided on-orbit validation of the technique. The trajectory was achieved by initially placing the spacecraft in a highly elliptical cis-lunar phasing orbit. Six maneuvers were performed during this period to correct injection errors and target an outbound lunar swingby in September 1998. The gravity assist from the lunar swingby raised apogee to the vicinity of the weak stability boundary. After three more targeting maneuvers, Nozomi performed an inbound lunar swingby followed immediately by a powered Earth swingby in late December 1998. A 420 m/s Trans Mars Insertion (TMI) burn at the final Earth periapsis was intended to place the spacecraft on a heliocentric trajectory leading to Mars orbit insertion in October 1999. Orbit determination for Nozomi is performed in parallel by both ISAS and the Multi-Mission Navigation (MMNAV) group at JPL. This was an advantage for the mission because each group would generate solutions based on data collected from their respective tracking networks. Spacecraft events, such as sequence uplinks and maneuvers, were generally scheduled during passes at the Usuda tracking station in Japan. As a result, maneuver design and reconstruction was derived from MMNAV solutions based on JPL tracking data obtained immediately prior to or following maneuvers. Data was also exchanged between ISAS and MMNAV so orbit determination could be performed on joint data sets in support of critical targeting late in the cis-lunar phase. In this paper, information regarding the MMNAV orbit determination effort for the first six months of the mission is presented. The spacecraft trajectory is characterized first, followed by a discussion of the orbit determination estimation procedure and models. Results from selected orbit solutions are presented and compared against reconstructed trajectories. One area of emphasis in this paper is orbit determination in the vicinity of the weak stability boundary. Precise navigation was necessary to target the second lunar swingby and the powered Earth swingby. Delivery accuracy of 150 m was required for these critical encounters, but a number of factors contributed to the general degradation of orbit determination accuracy. This included the fact that the spacecraft was at apogee, at a range of 1.7 million km and moving at less than I km/sec perpendicular to the line of sight. Nozomi was also close to zero degrees declination where there are known limitations on orbit determination performance. Finally, S-band tracking data was acquired through the Nozomi backup low gain antenna. This antenna is offset from the axis of this spin stabilized spacecraft and superimposed large signatures in the Doppler and range data. These difficulties were overcome by combining long data arcs, spanning several maneuvers, with a high fidelity solar pressure model. The model included a physically accurate representation of the spacecraft structure and a high time resolution orientation model. Observation modeling included the removal of the spin induced Doppler bias, spin signature and per pass correction of range calibration errors applied for data leading up to critical events. As a result, all orbit determination goals were met. A second area of emphasis in this paper is the JPL tracking and orbit determination effort in support of the TMI maneuver. TMI occurred out of contact with ground stations and the JPL Goldstone tracking complex had the first pass following the bum. As a result, MMNAV had the responsibility to make a rapid assessment of the maneuver performance. MMNAV made the determination that a 100 m/s under bum had occurred and promptly informed ISAS via voice lines. ISAS immediately began preparations for a correction maneuver (TMIc), which had to be performed during the next Usuda pass. The near real time assessment by MMNAV provided accurate antenna frequency and pointing updates for the spacecraft acquisition at Usuda and the close coordination between the two agencies enabled the design and successful execution of the TMc maneuver. Propellant consumption during the correction burn dictated that the mission be redesigned. ISAS developed a new plan which adds 3 full solar orbits, two Earth swingbys and one lunar swingby with arrival at Mars in January 2004. The final Mars orbit will still enable the mission to achieve all of its science objectives.

Ryne, Mark↗
NASA NTRS2008

Using LDPC Code Constraints to Aid Recovery of Symbol Timing

A method of utilizing information available in the constraints imposed by a low-density parity-check (LDPC) code has been proposed as a means of aiding the recovery of symbol timing in the reception of a binary-phase-shift-keying (BPSK) signal representing such a code in the presence of noise, timing error, and/or Doppler shift between the transmitter and the receiver. This method and the receiver architecture in which it would be implemented belong to a class of timing-recovery methods and corresponding receiver architectures characterized as pilotless in that they do not require transmission and reception of pilot signals. Acquisition and tracking of a signal of the type described above have traditionally been performed upstream of, and independently of, decoding and have typically involved utilization of a phase-locked loop (PLL). However, the LDPC decoding process, which is iterative, provides information that can be fed back to the timing-recovery receiver circuits to improve performance significantly over that attainable in the absence of such feedback. Prior methods of coupling LDPC decoding with timing recovery had focused on the use of output code words produced as the iterations progress. In contrast, in the present method, one exploits the information available from the metrics computed for the constraint nodes of an LDPC code during the decoding process. In addition, the method involves the use of a waveform model that captures, better than do the waveform models of the prior methods, distortions introduced by receiver timing errors and transmitter/ receiver motions. An LDPC code is commonly represented by use of a bipartite graph containing two sets of nodes. In the graph corresponding to an (n,k) code, the n variable nodes correspond to the code word symbols and the n-k constraint nodes represent the constraints that the code places on the variable nodes in order for them to form a valid code word. The decoding procedure involves iterative computation of values associated with these nodes. A constraint node represents a parity-check equation using a set of variable nodes as inputs. A valid decoded code word is obtained if all parity-check equations are satisfied. After each iteration, the metrics associated with each constraint node can be evaluated to determine the status of the associated parity check. Heretofore, normally, these metrics would be utilized only within the LDPC decoding process to assess whether or not variable nodes had converged to a codeword. In the present method, it is recognized that these metrics can be used to determine accuracy of the timing estimates used in acquiring the sampled data that constitute the input to the LDPC decoder. In fact, the number of constraints that are satisfied exhibits a peak near the optimal timing estimate. Coarse timing estimation (or first-stage estimation as described below) is found via a parametric search for this peak. The present method calls for a two-stage receiver architecture illustrated in the figure. The first stage would correct large time delays and frequency offsets; the second stage would track random walks and correct residual time and frequency offsets. In the first stage, constraint-node feedback from the LDPC decoder would be employed in a search algorithm in which the searches would be performed in successively narrower windows to find the correct time delay and/or frequency offset. The second stage would include a conventional first-order PLL with a decision-aided timing-error detector that would utilize, as its decision aid, decoded symbols from the LDPC decoder. The method has been tested by means of computational simulations in cases involving various timing and frequency errors. The results of the simulations ined in the ideal case of perfect timing in the receiver.

Jones, Christopher↗