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NASA NTRS1993

Enhanced decoding for the Galileo S-band mission

A coding system under consideration for the Galileo S-band low-gain antenna mission is a concatenated system using a variable redundancy Reed-Solomon outer code and a (14,1/4) convolutional inner code. The 8-bit Reed-Solomon symbols are interleaved to depth 8, and the eight 255-symbol codewords in each interleaved block have redundancies 64, 20, 20, 20, 64, 20, 20, and 20, respectively (or equivalently, the codewords have 191, 235, 235, 235, 191, 235, 235, and 235 8-bit information symbols, respectively). This concatenated code is to be decoded by an enhanced decoder that utilizes a maximum likelihood (Viterbi) convolutional decoder; a Reed Solomon decoder capable of processing erasures; an algorithm for declaring erasures in undecoded codewords based on known erroneous symbols in neighboring decodable words; a second Viterbi decoding operation (redecoding) constrained to follow only paths consistent with the known symbols from previously decodable Reed-Solomon codewords; and a second Reed-Solomon decoding operation using the output from the Viterbi redecoder and additional erasure declarations to the extent possible. It is estimated that this code and decoder can achieve a decoded bit error rate of 1 x 10(exp 7) at a concatenated code signal-to-noise ratio of 0.76 dB. By comparison, a threshold of 1.17 dB is required for a baseline coding system consisting of the same (14,1/4) convolutional code, a (255,223) Reed-Solomon code with constant redundancy 32 also interleaved to depth 8, a one-pass Viterbi decoder, and a Reed Solomon decoder incapable of declaring or utilizing erasures. The relative gain of the enhanced system is thus 0.41 dB. It is predicted from analysis based on an assumption of infinite interleaving that the coding gain could be further improved by approximately 0.2 dB if four stages of Viterbi decoding and four levels of Reed-Solomon redundancy are permitted. Confirmation of this effect and specification of the optimum four-level redundancy profile for depth-8 interleaving is currently being done.

Dolinar, S.↗

NASA NTRS2010

The SMAP Level 4 Surface and Root-zone Soil Moisture (L4_SM) Product

The Soil Moisture Active and Passive (SMAP) mission is being developed by NASA for launch in 2013 as one of four first-tier missions recommended by the U.S. National Research Council Committee on Earth Science and Applications from Space in 2007. The primary science objectives of SMAP are to enhance understanding of land surface controls on the water, energy and carbon cycles, and to determine their linkages. Moreover, the high resolution soil moisture mapping provided by SMAP has practical applications in weather and seasonal climate prediction, agriculture, human health, drought and flood decision support. In this paper we describe the assimilation of SMAP observations for the generation of the planned SMAP Level 4 Surface and Root-zone Soil Moisture (L4_SM) product. The SMAP mission makes simultaneous active (radar) and passive (radiometer) measurements in the 1.26-1.43 GHz range (L-band) from a sun-synchronous low-earth orbit. Measurements will be obtained across a 1000 km wide swath using conical scanning at a constant incidence angle (40 deg). The radar resolution varies from 1-3 km over the outer 70% of the swath to about 30 km near the center of the swath. The radiometer resolution is 40 km across the entire swath. The radiometer measurements will allow high-accuracy but coarse resolution (40 km) measurements. The radar measurements will add significantly higher resolution information. The radar is however very sensitive to surface roughness and vegetation structure. The combination of the two measurements allows optimal blending of the advantages of each instrument. SMAP directly observes only surface soil moisture (in the top 5 cm of the soil column). Several of the key applications targeted by SMAP, however, require knowledge of root zone soil moisture (approximately top 1 m of the soil column), which is not directly measured by SMAP. The foremost objective of the SMAP L4_SM product is to fill this gap and provide estimates of root zone soil moisture that are informed by and consistent with SMAP observations. Such estimates are obtained by merging SMAP observations with estimates from a land surface model in a soil moisture data assimilation system. The land surface model component of the assimilation system is driven with observations-based surface meteorological forcing data, including precipitation, which is the most important driver for soil moisture. The model also encapsulates knowledge of key land surface processes, including the vertical transfer of soil moisture between the surface and root zone reservoirs. Finally, the model interpolates and extrapolates SMAP observations in time and in space. The L4_SM product thus provides a comprehensive and consistent picture of land surface hydrological conditions based on SMAP observations and complementary information from a variety of sources. The assimilation algorithm considers the respective uncertainties of each component and yields a product that is superior to satellite or model data alone. Error estimates for the L4_SM product are generated as a by-product of the data assimilation system.

Reichle, Rolf↗

NASA NTRS2017

New Global Electron Density Observations from GPS-RO in the D- and E-Region Ionosphere

A novel retrieval technique is developed for electron density (N(sub e)) in the D- and E-region (80-120 km) using the high-quality 50-Hz GPS radio occultation (GPS-RO) phase measurements. The new algorithm assumes a slow, linear variation in the F-region background when the GPS-RO passes through the D- and E-region, and extracts the N(sub e) profiles at 80-130 km from the phase advance signal caused by N(sub e). Unlike the conventional Abel function, the new approach produces a sharp N(sub e) weighting function in the lower ionosphere, and the N(sub e) retrievals are in good agreement with the IRI (International Reference Ionosphere) model in terms of monthly maps, zonal means and diurnal variations. The daytime GPS-RO N(sub e) profiles can be well characterized by the alpha-Chapman function of three parameters (N(sub mE), h(sub mE) and H), showing that the bottom of E-region is deepening and sharpening towards the summer pole. At high latitudes the monthly GPS-RO N(sub e) maps at 80-120 km reveal clear enhancement in the auroral zones, more prominent at night, as a result of energetic electron precipitation (EEP) from the outer radiation belt. The D-/E-region auroral N(sub e) is strongly correlated with K(sub p) on a daily basis. The new N(sub e) data allow further comprehensive analyses of the sporadic E (E(sub s)) phenomena in connection with the background N(sub e) in the E-region. The layered (2-10 km) and fluctuated (less than 2 km) E(sub s) components, namely N(sub e_Layer) than N(sub e_Pert), are extracted with respect to the background N( sub e_Region) on a profile-by-profile basis. The N(sub e_Layer) component has a strong but highly-refined peak at approximately 105 km, with an amplitude smaller than N(sub e_Region) approximately by an order of magnitude. The N(sub e_Pert) component, which was studied extensively in the past, is approximately 2 orders of magnitude weaker than N(sub e_Layer). Both N(sub e_Layer) and N(sub e_Pert) are subject to significant diurnal and semidiurnal variations, showing downward progression with local time in amplitude. The 11-year solar cycle dominates the N(sub e) interannual variations, showing larger N(sub e_Region) and N(sub e_Layer) but smaller N(sub e_Pert) amplitudes in the solar maximum years. Enhanced Ne profiles are often observed in the polar winter, showing good correlation with solar proton events (SPEs) and geomagnetic activity. The new methodology offers great potential for retrieving low N(sub e) in the D-region, where radio propagation and communication blackouts can occur due to enhanced ionization. For space weather applications it is recommended for GPSRO operations to raise the top of high-rate data acquisition to approximately 140 km in the future.

GSP-R↗

NASA NTRS1995

A 3D High-Order Unstructured Finite-Volume Algorithm for Solving Maxwell's Equations

A three-dimensional finite-volume algorithm based on arbitrary basis functions for time-dependent problems on general unstructured grids is developed. The method is applied to the time-domain Maxwell equations. Discrete unknowns are volume integrals or cell averages of the electric and magnetic field variables. Spatial terms are converted to surface integrals using the Gauss curl theorem. Polynomial basis functions are introduced in constructing local representations of the fields and evaluating the volume and surface integrals. Electric and magnetic fields are approximated by linear combinations of these basis functions. Unlike other unstructured formulations used in Computational Fluid Dynamics, the new formulation actually does not reconstruct the field variables at each time step. Instead, the spatial terms are calculated in terms of unknowns by precomputing weights at the beginning of the computation as functions of cell geometry and basis functions to retain efficiency. Since no assumption is made for cell geometry, this new formulation is suitable for arbitrarily defined grids, either smooth or unsmooth. However, to facilitate the volume and surface integrations, arbitrary polyhedral cells with polygonal faces are used in constructing grids. Both centered and upwind schemes are formulated. It is shown that conventional schemes (second order in Cartesian grids) are equivalent to the new schemes using first degree polynomials as the basis functions and the midpoint quadrature for the integrations. In the new formulation, higher orders of accuracy are achieved by using higher degree polynomial basis functions. Furthermore, all the surface and volume integrations are carried out exactly. Several model electromagnetic scattering problems are calculated and compared with analytical solutions. Examples are given for cases based on 0th to 3rd degree polynomial basis functions. In all calculations, a centered scheme is applied in the interior, while an upwind matching scheme is employed at material interfaces and the Engquist-Majda non-reflecting boundary condition is implemented at the numerical outer boundaries. The staggered leapfrog scheme and the Runge-Kutta methods are utilized for the time integration. Excellent agreements are found between the numerical and analytical solutions.

Liu, Yen↗