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The derivation of the probability density of irradiance for the received electromagnetic wave propagating through random inhomogeneities has applications in many diverse fields, such as optical wireless communications, radar, and imaging systems, to name few. The conventional approach in this regard is to combine distribution models, with each being found valid under different conditions, in a modulation process, e.g., the extended Rytov theory. However, in these techniques, the nature of the physical processes responsible for the randomness is not considered directly. Moreover, it is not clear how the model parameters are related to the physical environment. Recent research studies found that in random media, such as underwater, the exact physical processes in effect can significantly alter the distribution of the received signal intensity. In this article, a novel intensity distribution model is derived based on Rytov theory of propagation through weak turbulence. The physical parameters of the medium are directly included into the model parameters. Therefore, the resultant model is general enough to describe different physical environments. The utility of the model is validated by studying the effect of the medium parameters on the distribution through simulations. [ABSTRACT FROM AUTHOR]

In this article, we develop a hybrid method for studying wave scatterings and propagation in a vegetation field. The coherent multiple scatterings among the plants and the gaps in the vegetation field are considered through a two-step hybrid method. First, the T-matrix of a single plant is calculated using the Huygens principle and the vector cylindrical wave (VCW) expansion based on the full-wave solutions from the Ansys High Frequency Structure Simulator (HFSS). Second, the multiple scatterings between different plants are considered through the Foldy–Lax (FL) multiple-scattering equations using the calculated T-matrix and the translational addition theorem. The convergence and the accuracy of the hybrid method are verified with the HFSS by comparing the solutions of scatterings from four wheat plants. The full-wave Monte Carlo simulations of a field with 169 wheat plants at the $L$ -band are subsequently performed using the hybrid method. Numerical results show that the transmission in the gap region is significantly higher than that of the inner region with the difference given quantitatively. The transmissivity of microwave through the wheat field with a large vegetation water content (VWC) can be significantly underestimated by the classical radiative transfer equation (RTE) and distorted Born approximation (DBA) model. [ABSTRACT FROM AUTHOR]

This article presents a full-wave numerical method that, in conjunction with Monte Carlo simulation, is used to calculate the effective propagation constant of a random volume of conducting wires of arbitrary length and curvature. Bistatic scattering from many realizations of nonoverlapping metallic wires confined within a fictitious spherical enclosure is calculated to determine the mean electric field scattered by the random medium. This mean scattered field is then used to determine the effective permittivity of the random medium using an inverse scattering scheme. These values are then compared with the values given by the Foldy approximation for many particle sizes, geometries, and number densities within a given medium. An investigation into the results is undertaken to determine an expanded macromodel for 3-D electromagnetic propagation through such a random medium, and the applicability of Foldy’s approximation is determined using this model. [ABSTRACT FROM AUTHOR]

A partially coherent approach for computing the electromagnetic response of a layered medium having random rough interfaces and a random dielectric profile is presented as an alternative to the full-wave solution of the problem. The statistical nature of this problem, in particular, the random dielectric profile, introduces randomness in the phase of the electromagnetic field such that the field loses its phase coherency after traveling in the layered medium for a few correlation lengths of the permittivity. In this situation, there is a coherency length within which a coherent solution of Maxwell’s equation is required. For the distances beyond this coherency length, a combined coherent–incoherent cascading approach can be applied to reduce the computational complexity of the problem. The coherent response of each “block” within the medium (with a length approximately the coherency length) can be cascaded incoherently ignoring the phase response without losing accuracy. Cascading equations for block bistatic scattering are applied, and solutions of the equivalent block parameters are obtained by iteration up to the second order of multiple scattering. The proposed method is described in this article, and the numerical results are shown to compare the proposed cascading approach with the results obtained from the fully coherent solution. [ABSTRACT FROM AUTHOR]

The translation matrix ($T$ -matrix) solution to the 3-D problem of scattering of the electromagnetic waves from a dielectric layered medium with random rough interfaces is presented. The solution is based on the coupled vector integral equation of the electric field using the dyadic periodic Green’s function as a kernel. It is shown that the $T$ -matrix solution conserves energy, the bistatic scattering pattern is regular even in cases, where guided modes within the layered medium are excited, and also that the method’s results coincide with those of the second-order Small Perturbation Method (SPM2) in the small height limit. One of the advantages of the $T$ -matrix method compared to the SPM2 is the wide validity range of the solution, which is also studied. [ABSTRACT FROM AUTHOR]

We present a novel deterministic method capable of calculating statistical moments of transverse electric polarized fields scattered by perfect electric conductor gratings with small surface random perturbations. Based on a first-order shape Taylor expansion, the resulting electric field integral equations are solved via the method of moments with constant hierarchical basis or Haar wavelets. This allows for a sparse tensor approximation, significantly reducing the number of required unknowns and yielding a higher rate of convergence than a dense approximation. Moreover, the proposed approach converges faster than Monte Carlo simulations with significantly less computational effort. Validation of the proposed approach is performed for several cases, and realistic simulations applied to the calculation and prediction of grating efficiency reveal the applicability of the method. [ABSTRACT FROM PUBLISHER]

We present a novel beam summation (BS) formulation for tracking wavefields in fluctuating media. This formulation utilizes the ultrawideband phase-space BS method, which is structured upon a windowed Fourier transform (WFT) frame expansion of the sources and expresses the field as a discrete phase-space sum of beam propagators. This paper extends the frame concept, proving that this beam set constitutes a frame not only in the source domain, where it reduces to the conventional WFT, but everywhere in the propagation domain. This “beam frame” provides a self-consistent framework for tracking wavefields through scattering media in which the local interaction of the incident beams with the medium is expanded using the same set of beams. The resulting beam-to-beam (B2B) scattering coefficients depend on the local spectral properties of the medium. The overall B2B scattering matrix is therefore compact, coupling only beams that are adjacent in phase space, given the fluctuation properties. The new formulation expresses the entire scattering problem in terms of coefficients dynamics in the phase space. As demonstrated, the formulation is computationally efficient and captures all the relevant phenomenology. Part II extends this formulation for stochastic fields in random fluctuating medium characterized by the medium statistics. [ABSTRACT FROM PUBLISHER]

In Part I of this two-part sequence, we introduced a novel beam summation (BS) scheme for tracking waves through fluctuating media. A key step has been the proof that the set of beam propagators constitutes a frame everywhere in the propagation domain. This beam frame (BF) provides a self-consistent framework for wave tracking, where the field is expanded using the BF and the local scattering of each beam is reexpanded using the same beam-set and expressed as beam-to-beam (B2B) scattering coefficients. This theory is used here to derive a BS representation for the stochastic-field for cases where the medium fluctuations are random with a given statistics. The stochastic B2B scattering moments are therefore expressed in terms of the local spectral statistics of the medium projected onto a phase space window formed by the intersection of the excitation and the scattered beams. Since the medium statistics is typically smooth, unlike a single realization, the resulting stochastic B2B scattering matrix is compact and smooth and may actually be calculated analytically. It is demonstrated, via numerical examples and a comparison with Monte Carlo simulations, that the formulation is not only computationally efficient, but also provides a compact representation for the scattering phenomenology. [ABSTRACT FROM PUBLISHER]

This paper presents a feasibility study on extending the applicability of the discrete radiative energy transfer (dRET) model to the trunk layer of raised canopy forests. The framework herein presented, proposes a method to predict the scattered signal inside and around a formation of cylinders (mimicking thin tree trunks), which is based on the prior knowledge of the cylinder 2-D reradiation pattern as input parameters to the dRET model. The characterization and modeling of the cylinder 2-D reradiation patterns were performed in an anechoic chamber, so that frequency-dependent effects could be evaluated. The assessment of the proposed method was performed against measurements within a formation of both metallic and dielectric cylinders mimicking thin tree trunks, at micro- and millimeter-wave frequencies, i.e., 9.4, 18.8, and 37.6 GHz. [ABSTRACT FROM PUBLISHER]

Sparse grid collocation methods are used for uncertainty quantification in electromagnetic propagation problems. The first application here involves waves propagating in lossy media with uncertain permittivities and permeabilities, for which several cases with increasing random-space dimensionality are exemplified. The objective in the second application is to compute expected signal strength above flat Earth surface at ranges far from transmitter location, where randomness is present due to uncertain refractivity of the atmosphere. Two different sparse grid algorithms are demonstrated throughout the paper, and the deterministic evaluators are accessed as a black box by the sparse grid algorithms. The difficult task of a priori method adaption is overcome by a first order check that enforces the black box solver only a few times. Through the results considered, strengths of the two algorithms are differentiated depending on the characteristics of the randomness. The advantage of a new routine used in this work is emphasized by showing its numerical contribution to the field estimation problem in a specific example. By means of the sparse grid methods used, we quantitatively provide the relative importance of each RV in contributing to the changes in the field distribution received at the observation range. [ABSTRACT FROM PUBLISHER]

Study of synthetic aperture radar (SAR) resolution degradation in 2-D sparse random medium composed of electrically large dielectric cylinders with possibly high index of refraction is presented. This study is motivated by the need for better understanding of focusing capabilities of SAR systems through random media at submillimeter wave (sub-MMW) frequencies. Analytical recursive expressions are derived to predict the coherence of the transmitted wave as a function of the propagation distance due to different source locations as well as same source location but different operating frequencies. These expressions are directly related to the cross-range and range resolution of the SAR system operating in random media, respectively. Furthermore, by invoking the memory effect property of translational invariant random media, an efficient algorithm is developed to analytically evaluate the coherence functions. The formulations are based on a newly developed coherent wave propagation model, called Statistical S-matrix for wave propagation in spectral domain (SSWaP-SD). A full-wave numerical model in conjunction with Monte Carlo simulations is used to validate the analytical expressions for the coherence. Finally, full wave simulation of a SAR imaging scenario is presented, and a simple method is proposed to reduce the image speckle level without sacrificing the resolution. [ABSTRACT FROM PUBLISHER]

The ability of time-reversed signals in reproducing a given time-dependence of the electromagnetic field within random media is investigated. A general setup consisting of multiple sources cooperating in providing the best transmission is considered, where the constructive interference of their individual contributions is meant to improve the quality of the field generation with respect to a single-source setup. The medium response is described by means of tools from random-process theory, for the case of stationary media complex enough to ensure a large number of multi-path contributions. It is shown that even a very weak spatial coherence in the medium is sufficient to significantly hinder the improvement expected from the use of multiple-source scenarios. Experimental results obtained in a reverberation chamber support the validity of the proposed theory. Direct applications of these results can be found in recent proposals about the potential benefits of time-reversed signals used in wireless communications, imaging techniques, as well as in pulsed-field generation devices based on energy compression through dispersive media. [ABSTRACT FROM PUBLISHER]

The problem of long distance wave propagation in a sparse random medium is considered in this paper. A mathematical technique for modeling the behavior of electromagnetic wave propagation as a function of distance in a 2-D sparse random media at millimeter wave (MMW) regime is presented. The proposed model is a field method based on Maxwell's equation and, thus, the phase and magnitude of the field in the random medium can be tracked accurately. The random media is characterized by low volume fraction but electrically large scatterers having relatively high dielectric constant. The technique relies on discretizing the random media into thin slabs and relating the forward and backward scattered plane wave spectra from the individual slabs by an equivalent spectral bistatic scattering matrix. By cascading the scattering matrices of the individual slabs, the statistics of the overall scattered wave in both forward and backward directions are obtained. This technique will be referred to as statistical S-matrix approach in spectral domain, or SSWaP-SD. Using this method, it is shown that after propagation to a critical range inside the random media, the incoherent component of the forward propagating wave overcomes the mean-field component resulting in a dual-slope attenuation curve as a function of distance. The accuracy of the model is examined against a full wave Monte Carlo simulation and a very good agreement is observed. Finally, based on the proposed model, analytical expressions for predicting the forward path-loss as well as the back scattered power from a sparse, translational invariant discrete random media are derived. The analytical expressions are tested against Monte Carlo simulation for a very long random medium and very good agreements are demonstrated. [ABSTRACT FROM PUBLISHER]

This paper introduces an iterative scheme to overcome the unresolved issues presented in S-FDTD (stochastic finite-difference time-domain) for obtaining ensemble average field values recently reported by Smith and Furse in an attempt to replace the brute force multiple-realization also known as Monte-Carlo approach with a single-realization scheme. Our formulation is particularly useful for studying light interactions with biological cells and tissues having sub-wavelength scale features. Numerical results demonstrate that such a small scale variation can be effectively modeled with a random medium problem which when simulated with the proposed S-FDTD indeed produces a very accurate result. [ABSTRACT FROM PUBLISHER]

A generalized time-reversal (TR) technique for the generation of coherent wavefronts within complex media is presented in this paper. Although completely general, this method is primarily considered for testing purposes herein, where an equipment under test is submitted to a series of impinging wavefronts with varying features. Electromagnetic compatibility, antenna testing as well as telecommunications facilities where complex-wavefront schemes (e.g., multi-path configurations) are required, could benefit from the proposed approach. The main advantages and limitations of current standard TR approaches are reviewed in this respect, exposing their inadequacy for this particular context. The proposed alternative technique, named time-reversal electromagnetic chamber (TREC) is introduced and studied by means of a formal theoretical analysis, showing how a reverberation chamber (RC) supporting a diffused-field condition can be operated as a generator of deterministic pulsed wavefronts. The TREC is demonstrated to be capable of generating arbitrary wavefronts with a remarkable accuracy, allowing to revisit the RC as a deterministic facility: the main advantages of RCs and anechoic ones are merged, leading to a new facility capable of potentially generating in real-time pulsed wavefronts while using low input energies, without requiring neither mechanical displacements nor any special features of the sources. [ABSTRACT FROM PUBLISHER]

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. [ABSTRACT FROM AUTHOR]

The radiative transfer (RT) approach is widely used in applications involving scattering from layered random media with rough interfaces. Although it has been successful in several disciplines it is well known that this approach involves certain approximations. In this paper these assumptions and approximations are reexamined. To enable this a statistical wave approach is employed to this problem and the governing equations for the first and second moments of the wave functions are derived. A transition is hence made to arrive at a system of equations corresponding to that of the RT approach. It is hence found that more conditions are implicitly involved in the RT approach than generally believed to be sufficient. [ABSTRACT FROM AUTHOR]

A statistical multipath propagation model is developed in the double-angular domain to include effects of both angle of departure and angle of arrival. The model is characterized by a discrete stochastic double-angular spectrum of the Green's function between two volumes that communicate with each other in the presence of cluster scattering. The whole modeling process is a combination of theories, assumptions, and numerical verification by rigorous full wave electromagnetic simulations. Notably, an uncorrelated scattering assumption for received fields is extended to the double-angular domain, and the transport theory plays a key role defining the statistical properties of the spectrum of the Green's function. The spectrum is eventually modeled as a random matrix whose entries are uncorrelated zero-mean complex Laplacian random variables. The real and imaginary parts of the matrix entries are independent and identically distributed, and the variance profile follows the reduced incident intensity of the waves through random media. The parameters of the model are completely obtained from bulk statistical knowledge of the scattering environments, and the resulting model demonstrates good performance on EM DOF and MIMO capacity estimation. [ABSTRACT FROM AUTHOR]

The diffusion behavior of electromagnetic (EM) waves in two dimensional (2-D) multipath media is studied through integral equation based full wave Monte Carlo simulations. The influences of some physical factors are explored, among which the area density of the embedded obstacles manifests itself to be the most important one in determining wave diffusion. A lossy system starts to behave diffusively when the area density approximately exceeds 5%, and the diffusion equations are generally applicable for predicting power decay. At low densities, the power-distance relation of the waves appears to follow power laws. The sizes and shapes of the obstacles have a secondary effect on the diffusion of waves. Whenever a system contains small objects or objects with reflecting sides, the waves therein are more diffusive and the diffusion equation approximates the reality more accurately. Absorption loss decreases wave diffusion in general, but our results show that the diffusion equation for a system with very lossy but small obstacles can work very well for predicting power decay. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Coherent laser radar (ladar) deduces the shape, velocity and vibration of a remote target by measuring the round-trip optical phase or the Doppler shift of target-scattered light. Phase fluctuations from wind-driven atmospheric turbulence generate micro-Doppler or velocity error at μm/sec levels. The turbulence-induced noise spectra of all geometric phase components of the ladar, the average phase power spectral densities of arbitrary ladar receiver modes, and the resultant Doppler noise spectra, are derived in the Rytov approximation for any isotropic stationary turbulence, any wind velocity profile, any Fresnel number and any source illumination pattern. In Kolmogorov turbulence the piston phase noise spectrum, and the average phase shift over a time interval, are well-approximated by simple universal asymptotic forms dependent only on atmospheric coherence length, turbulence-weighted average wind speed ..., and aperture size D. The spectrum slope changes at a critical frequency of order .../D. The approximate results do not depend on the usually-unknown outer scale of turbulence. [ABSTRACT FROM AUTHOR]

This paper proposes various metrics to characterize space-time focusing resulting from application of time reversal techniques in richly scattering media. The concept and goals of time reversal are presented. Pertinent metrics describing both the time and space focusing effects are outlined. Two examples based on a model of discrete and continuous scattering media are used to illustrate how the proposed metrics vary as a function of various system and channel parameters, such as the bandwidth, delay and angle spreads, number of antennas, etc. [ABSTRACT FROM AUTHOR]