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We extend the 3-D numerical method of Maxwell's equation (NMM3D) for rough soil surface scattering from L-band to C-, X-, and Ku-bands. We illustrate the results for copolarization, cross-polarization, and polarization ratio (HH/VV). Copolarized and cross-polarized backscattering coefficients from NMM3D are analyzed for frequency dependence, incident angle dependence, and soil moisture dependence. We also cross compare results from analytical and empirical models. The 16 $\times$ 16 squared wavelength $(\lambda^2)$ of rough surface is applied for NMM3D using 256 processors on NSF Extreme Science and Engineering Discovery Environment clusters. Polarization ratio, HH/VV, is studied to address the feature of dependence on frequency for same fields (same physical parameters for the model). HH/VV is shown useful to provide additional information to study land surface. Results from NMM3D are also validated with POLARSCAT measurement data-1. NMM3D shows good agreement with data and better performance while considering copolarization, cross-polarization, and polarization ratio (HH/VV) together. The key advancement in computation efficiency in this paper is the implementation of a physically based near-field precondition algorithm in NMM3D to accelerate parallel computation. With precondition, the computation time is faster by ten times for larger root-mean-square height.

In this paper, we report on the performance of a semiempirical algorithm for the retrieval of soil moisture (SM) under dense tropical forests using ultrahigh frequency (UHF) polarimetric synthetic aperture radar (SAR) data. The algorithm is a simplification of a 3-D coherent model of forest canopy based on the distorted Born approximation (DBA). The simplified model reduces the number of parameters and preserves the three dominant scattering mechanisms of volume, volume-surface, and surface for three polarized backscattering coefficients, i.e., σ HH , σ HV , and σ VV , at UHF frequencies. The inversion process uses the Levenberg-Marquardt nonlinear least squares method to estimate the three model parameters: vegetation aboveground biomass, integrated SM up to a certain depth, and surface roughness. The performance of the inversion process is examined by first using simulation data where the initial values of the inversion process vary randomly and then using airborne UHF SAR data acquired in Costa Rica over La Selva Biological Station. The results with simulated data show that the inversion process is not significantly sensitive to initial values considering they are in the range of ±50% of the true value. A root-mean-square error (RMSE) of less than 4% can be achieved in retrieving the SM. The use of an alternate inversion approach without initial conditions using a genetic algorithm is less efficient (> 120 times longer time) and produces larger error with simulated data (RMSE = 11%) than the Levenberg-Marquardt estimation method. The inversion model simultaneously produces a biomass and SM distribution at 100-m spatial resolution. The RMSE of biomass estimation is 38 Mg/ha (15% relative error) when compared with 28 field plots. Over the plots where SM ground measurements are available, but not at the exact same day as the radar flight occurred, the total volumetric RMSE is 13.6%. However, only two ground measurements were very close to the flight day (three days apart), and for those, the SM estimate has about 3% absolute volumetric error. At the P-band, the SM sensing depth is inversely correlated with the SM allowing to map the spatial variations of SM close to the average root zone or hydrological active horizon of soils in tropical ecosystems.

This paper presents the procedure to perform cross-calibration of radar backscatter between the QuikSCAT and Oceansat-2 ocean wind scatterometers. Both QuikSCAT and Oceansat-2 are Ku-band dual pencil beam, rotating antenna scatterometers with similar design. There has been a joint effort by the Indian Space Research Organization, NASA, KNMI, and NOAA to perform calibration and validation of Oceansat-2 in order to extend the climate data record of ocean surface vector winds obtained by QuikSCAT. This has resulted in significant improvement in the quality of the normalized radar cross section (NRCS) data and the quality of the resultant winds produced using the Oceansat-2 NRCS measurements. An important aspect of this calibration is the reduction of the calibration bias between QuikSCAT and Oceansat-2. The nonspinning QuikSCAT scatterometer was repointed to achieve the same incidence angles for its two HH and VV polarized antenna beams as those utilized by Oceansat-2. The magnitudes of the NRCS (backscatter) measurements of the two scatterometers were then compared for two years in order to determine NRCS bias in decibels as a function of time. Biases for both antenna beams were computed. A wind speed/wind-relative azimuth angle histogram-matched method was applied to ocean data from the two scatterometers to determine the time series of the bias between the two. It has been determined that there was an $\sim$ 0.5 dB drop in Oceansat-2 radar backscatter on August 20, 2010. As a result, we compute cross-calibration adjustments to apply to Oceansat-2 data before and after this distinct drop in backscatter.

It has been well known that a few areas on the Earth's surface have a relatively constant backscattering coefficient and can serve as radar calibration targets. Examples include the Amazon rain forest, the Greenland ice sheet, parts of Antarctica, etc. However, there has not been any extensive investigation and quantitative evaluation of these targets in terms of their time variation, isotropy, and spatial variation. Here, we have analyzed a consistent set of Ku-band radar measurements for more than ten years from the QuikSCAT mission. This valuable set of data provides an unprecedented opportunity for us to study the long-term variability of observed backscattering from the Earth's surface at Ku-band. In this paper, we performed a global survey of potential constant land targets and evaluated their variability. Quantitative measurements of temporal and spatial variabilities (homogeneity) and isotropy are used to identify the locations of the best natural calibration targets. We also discuss annual and long-term trends in the data and offer potential explanations for these trends. We examine small regions with the least overall variation. By concentrating on low-variation areas, we can identify useful calibration targets for future radar missions and for intercalibration between existing radars. At the same time, by focusing on regions with little spatial or temporal heterogeneity, we can analyze the temporal variation on diurnal, seasonal, and decadal scales in homogenous natural terrain types including rain forest, dry brushy areas, and ice sheets. We found that rain forest targets in the Amazon and Congo are very stable in time and homogeneous. However, they are subjected to diurnal difference. On the other hand, the Antarctica ice sheet is another good candidate for stable target, but it has seasonal variability. The Greenland ice sheet shows a significant trend in backscatter in recent years, and therefore, may not be a suitable calibration site anymore. Another location for a good stable target is a dry brushy area in the Sahara, which shows comparable stability and isotropy with those of the Amazon, Congo, and Antarctica.

This study examines the potential of using bistatic radar reflections from the Global Navigation Satellite System (GNSS) to classify sea ice types in the Arctic Ocean during the sea ice formation period. For this study, we used data obtained from the United Kingdom (UK) TechDemoSat-1 (TDS-1) satellite mission. The main objective of the TDS-1 mission is to provide L-band radar reflections of the ocean surface in order to infer wind speed through an estimation of the ocean surface roughness. Given the orbit inclination of TDS-1, polar coverage is obtained providing datasets over the Arctic sea ice cover. Recent studies demonstrated the use of TDS-1 data for accurately deriving ocean-ice detection using the shape of the bistatic radar waveforms derived from delay-Doppler maps. We aim to advance this previous research by demonstrating the sensitivity of GNSS bistatic radar signals to sea ice types. The originality of the study presented in this manuscript is the classification of sea ice types, never implemented before with any GNSS-R mission. For this study, we examined the fall period of October 2015 in the Beaufort and Chukchi seas region, when considerable expanses of young ice, first-year ice (FYI), and multi-year ice (MYI) were present. We developed a sea ice multi-step classification approach based on bistatic radar reflections to generate not only an ocean-ice classification but to classify between the three dominant ice types present. The classification was done in multiple steps based on GNSS bistatic radar observations only and includes checks for spatio-temporal consistency with each dominant class. Validation results are based on the comparison of the GNSS classification against SAR-derived sea ice type maps produced at the US National Ice Center. First, we derived classifications of sea ice–open water samples with a success rate of 97%, comparable to previous studies. Next, the sea ice type classification results identified FYI, MYI and young ice with success rates of 70%, 82% and 81%, respectively, indicating a strong sensitivity of the L-band GNSS bistatic radar signals to the different surface scattering properties of these primary ice types. With this manuscript we demonstrate the potential of the GNSS bistatic radar signals to classify ice types during the sea ice formation period. GNSS bistatic radar signals provide unique forward scattered measurements at L-band, potentially on a daily temporal revisit, that can be used to produce enhanced information on sea ice characteristics, such as those currently generated by other sensors. In order to determine the use of GNSS-R measurements on an operational basis, further studies are needed over a year-long period of sea ice growth and melt to determine the full benefit of GNSS for improving and providing complementary information to that generated by both microwave and optical sensors.

Imaging of objects through complex environment is important in several applications, including imaging of hidden objects in obscuring media such as atmospheric and ocean turbulence, rough ocean surfaces, rain, fog, snow, and biological tissues. These media are often randomly varying in space and time, and statistical treatments are necessary to obtain images with useful spatial and temporal resolutions. In recent years, there has been increasing interest in using signal processing and correlation techniques to improve resolutions and to distinguish images from clutter. This paper presents several imaging techniques for objects in the presence of random media. Time-reversal MUSIC (multiple signal classification) imaging has excellent resolution when multiple scattering is small or moderate. Modified beamformer imaging has moderately high resolution even at large multiple scattering. We also include time reversal (TR) and synthetic aperture radar (SAR) imaging for comparison. The technique involves stochastic Green's function and mutual coherence function (MCF), eigenvectors of time-reversal matrix and pseudo spectrum. Numerical examples are given to show the effectiveness of these imaging techniques.

Multiple input-multiple output systems have received considerable attention because of their potential to achieve high channel capacity. This paper presents a study of the effects of a random scattering medium on channel capacity. Formulations are given including stochastic Green's functions and mutual coherence functions. Transmitter and receiver characteristics are included and analytical formulation for eigenvalues and channel capacities are given in terms of the medium scattering characteristics, optical depth, frequency, number of transmitter and receiver elements, transmitting power, and noise spectral power. As an example, we show 500 m link at 60 GHz through rain. The eigenvalues and the channel capacity are calculated in terms of SNR and the rain rate representing the optical depth. It is shown that as the rain rate increases, the correlation of waves at antennas decreases and the capacity increases. However, at high rain rate, the capacity tends to decrease due to the absorption and scattering.

In order to improve the performance of terrestrial free-space optical communication systems in adverse visibility conditions, we present a method for estimation of the atmospheric channel impulse response function which governs the optical intensity propagation. This method reduces run-time computational demands and system complexity in comparison to our previously proposed dual-wavelength channel estimation technique. We consider propagation of optical wavelengths in fog, where the droplet diameters are close to the wavelength and thus scattering and absorption effects are significant. A method for rapid calculation of a channel response function based on estimating the effective optical depth of the channel and curve-fitting is described. The channel response estimate can then be used to design a receiver-side equalizer (minimum mean-squared error linear equalizer) to correct the signal distortion due to propagation through the dispersive channel. The channel estimates are based on parametric curve-fitting functions which have been developed using the modified-vector radiative transfer theory to model the channel response. The optimal fit parameters are found using particle-swarm optimization to minimize the simulated bit-error rate of the received signal.

We analyse the problem of the estimation of the angle of arrival in discrete random scattering media. Assuming incidence of a plane wave, we derive the performance of the determination of the angle of arrival in terms of beamwidth, which reflects the ability to resolve the angle of arrival from several directions. The minimum variance beamformer or Capon beamformer is applied. We demonstrate that in random scattering media the signal arriving at the receiving array shows correlation and is modelled as a Gaussian function, and this correlation deteriorates the ability to determine the angle of arrival. A matrix compensation is introduced to improve the performance by correcting the correlation. The main parameter in compensation is the correlation length. We investigate the effect of the correlation length on the angle of arrival.

This paper presents the modeling of an underwater wireless optical communication channel using the vector radiative transfer theory. The vector radiative transfer equation captures the multiple scattering nature of natural water, and also includes the polarization behavior of light. Light propagation in an underwater environment encounters scattering effect creating dispersion which introduces inter-symbol-interference to the data communication. The attenuation effect further reduces the signal to noise ratio. Both scattering and absorption have adverse effects on underwater data communication. Using a channel model based on radiative transfer theory, we can quantify the scattering effect as a function of distance and bit rate by numerical Monte Carlo simulations. We also investigate the polarization behavior of light in the underwater environment, showing the significance of the cross-polarization component when the light encounters more scattering.

The time-reversal effects on super-resolution in random scattering media are analysed using numerical finite-difference time-domain (FDTD) simulations. The analytical solutions and results have been presented previously in the literature, which provide confirmation of spot-size reduction and also explanations of the shower curtain effects and backscattering enhancement. However, the analytical solutions are based on several approximations. Thus, validation of the analytical results against realistic scattering events is necessary. Two-dimensional FDTD Monte Carlo simulations have been employed for this investigation to simulate wave propagation and scattering in a random medium. The scattering environments are created by randomly locating cylindrical rods in the background medium. The simulation process involves a point source emitting a Gaussian pulse wave that propagates through the scattering medium, gets time-reversed, and then back-propagated into the same scattering medium. The focusing behaviours i...

A general formulation of a theory of imaging through random obscuring layers is described. Previously we presented a theory for the temporal behavior of a short pulse scattered from a random medium and from a point target. In this paper, we generalize our study to include the imaging of objects of finite size and the actual imaging pattern at the receiver. This involves the study of two-frequency fourth order moments. Numerical examples are given to illustrate several important features, including the optical depth, backscattering enhancement, shower curtain effects, aperture size, bandwidth and target size.

This paper presents a theory of imaging objects behind layers of scattering media. The transmitter is a focused array or an aperture emitting a short pulse. The scattered pulse is received by a focused array or aperture. The received signal consists of two components: the pulse scattered from a random medium and from the target, and these two components can be distinguished by the use of ultra wide band (UWB) pulse. The second moment of the received signal includes the fourth-order moments of stochastic Green's functions, which are reduced to the second moments by the use of the circular complex Gaussian assumption, and of the generalized two-frequency mutual coherence function. This imaging theory is a generalization of optical coherence tomography (OCT), SAR and confocal imaging. It clarifies the relationships among resolution, coherence length, shower curtain effects and backscattering enhancement.

Most electromagnetic problems deal with media with unit permeability. However, recent interest in metamaterials necessitated studies of wave characteristics in media with arbitrary permittivity and permeability whose real parts can be positive or negative. This paper presents analysis of wave characteristics on semiinfinite metamaterials. Waves are excited by electric or magnetic line sources, and the problem is separated into the p (TM) and the s (TE) polarization, showing symmetries. The Fourier spectra of the reflection and transmission coefficients are examined and the poles, branch points, and zeros are shown in the real /spl mu/-real /spl epsi/ diagram. We clarify the location of poles in proper and improper Riemann Surfaces, and the excitation of forward and backward surface waves, forward and backward Lateral waves, and Zenneck waves, and the relations between Brewster's angle and Sommerfeld poles. We include the behaviors of the backward surface waves and the temporal backward Lateral waves.

This paper presents a theory of the radar cross section (RCS) of objects in multiple scattering random media. The general formulation includes the fourthorder moments including the correlation between the forward and the backward waves. The fourth moments are reduced to the second-order moments by using the circular complex Gaussian assumption. The stochastic Green’s functions are expressed in parabolic approximation, and the objects are assumed to be large in terms of wavelength; therefore, Kirchhoff approximations are applicable. This theory includes the backscattering enhancement and the shower curtain effects, which are not normally considered in conventional theory. Numerical examples of a conducting object in a random medium characterized by the Gaussian and Henyey–Greenstein phase functions are shown to highlight the difference between the multiple scattering RCS and the conventional RCS in terms of optical depth, medium location and angular dependence. It shows the enhanced backscattering due to multiple scattering and the increased RCS if a random medium is closer to the transmitter.

The problem of polarized light propagating through scattering media can be explained using the vector radiative transfer equation. This equation is an integro-differential equation and is well-known to be unsolvable analytically. One of the approximate solutions is discrete ordinates method which is based on the discretization of the Stokes parameters and the Mueller matrix. Although it produces accurate results, it requires a lot of computational resources. In addition, there are limitations on the calculation for angles that are very close to the optical axis. The solutions at these angles are necessary for some applications such as atmospheric imaging. First-order scattering approximation has been applied to mitigate the computational resource situation. It can also be used to calculate the solution at the angles that are very close to optical axis. However, it lacks information about the cross-polarization and it is inaccurate when light encounters more scattering events. Second-order scattering approximation provides more accurate solutions and offers some information about cross-polarization. We develop the first-order and second-order scattering approximations and their solutions for the pulse wave case. We investigate the second-order approximation solutions and compare them to the solution from the complete vector radiative transfer equation in several cases.

The passage of a photon density wave through random media has been investigated extensively for medical imaging based on the diffusion approximation. In this paper, the photon density wave is studied based on the exact time-dependent vector radiative transfer theory. Both continuous and pulse photon density waves are analysed in a plane parallel medium using Mie scattering and the discrete ordinates method. The photon density wave shows superior properties over regular waves in several aspects. It has a narrower angular spectrum and maintains the original pulse shape. It also preserves the degree of polarization and increases the cross-polarization discrimination. These properties of a photon density wave suggest its potential for improving imaging. Thus, we apply the photon density wave to an imaging problem and show that it improves the quality of the images compared to other conventional imaging techniques.