Il Suek Koh

Efficient Calculation of the Fields of a Dipole Radiating Above an Impedance Surface

The classic problem of field computation for an infinitesimal dipole radiating above an impedance half-space is revisited. The expressions for the traditional solution consist of integrals of the Sommerfeld type that cannot be evaluated in closed form and due to their highly oscillatory nature are difficult to evaluate numerically. The exact image theory, which has previously been applied to vertical electric and magnetic dipoles, is used to derive explicit expressions for dipoles of arbitrary orientation above impedance surfaces. Starting from the spectral representation of the field, the reflection coefficients are cast in the form of exact Laplace transforms and then by changing the order of integrations field expressions in terms of rapidly converging integrals are obtained. These expressions are exact, and valid for any arbitrary source alignment or observation position. It is shown that the formulation for a horizontal dipole contains an image in the conjugate complex plane resulting in a diverging exponential term not previously addressed in the literature. It is shown through further mathematical manipulations, that the diverging term is a contribution of the mirror image which can be extracted. Comparison of numerical results from exact image theory and the original Somm~rfeld-type expressions shows good agreement as well as a speedup in computation time of many orders of magnitude, which depends on the distance between the transmitter and the receiver. This formulation can effectively replace the approximate asymptotic expressions used for predicting wave propagation over a smooth planar ground (having different regions of validity). The exact image formulation is also of practical use in evaluation of the Greens function for various applications in scattering problems where approximate solutions are not sufficient.

Effect of canopy-air interface roughness on HF-VHF wave propagation in forest

The problem of electromagnetic wave propagation in a realistic forest environment in the high-frequency and very high-frequency bands is considered. In particular, the effect of the nonplanar interface between the air and the canopy, which has been ignored in previous models, is examined. An analytical formulation is obtained for the mean field when both the transmitter and the receiver are within the foliage. This formulation is based on distorted Born approximation and accounts for the surface roughness that exists between the canopy and air interface. It is shown that the surface roughness attenuates the so-called lateral wave slightly, which is the dominant source of the field at receiver locations far from the transmitter. It is also shown that this attenuation rate increases when the RMS height of the surface roughness is increased.

Polarimetric channel characterization of foliage for performance assessment of GPS receivers under tree canopies

The attenuation, depolarization, and fluctuation of a microwave signal going through a tree canopy are investigated by developing a Monte Carlo based coherent scattering model. In particular, the model is used to analyze the performance of Global Positioning System (GPS) receivers under tree canopies. Also the frequency and time-domain channel characteristics of a forest are investigated when a transmitter is outside and a receiver is inside a forest. A fractal algorithm (Lindenmayer system) is used to generate the structure of coniferous or deciduous trees whose basic building blocks are arbitrarily oriented finite cylinders, thin dielectric needles, and thin dielectric disks. Attenuation and phase change of the mean field through foliage is accounted for using Foldys approximation. Scattering of the mean field from individual tree components and their images in the underlying ground plane are computed analytically and added coherently. Since tree trunks and some branches are large compared to the wavelength and may be in the close proximity of the receiver, a closed-form and uniform expression for the scattered near-field from dielectric cylinders is also developed. Monte Carlo simulation of field calculation is applied to a cluster of trees in order to estimate the statistics of the channel parameters, such as the probability density function (pdf) of the polarization state of the transmitted field, path loss, and the incoherent scattered power (the second moment of the scattered field), as a function of the observation point above the ground.

Estimation of coherent field attenuation through dense foliage including multiple scattering

Single-scattering theory is shown to be insufficient for the estimation of effective propagation constant in foliage at high microwave and millimetre-wave frequencies. Clusters of broad leaves and needles are treated as a unit scatterer whose ensemble forward scattering is used in Foldys approximation to estimate attenuation rate in foliage. It is shown that single-scattering approximation overestimates forward scattering as high as 3-4 dB at 35 GHz.

Demonstration of time reversal methods in a multi-path environment

Time reversal methods (TRM) offer a unique opportunity for solving the problem of electromagnetic (EM) wave propagation and focusing in a spatially varying (inhomogeneous) medium. While the concept of time reversal is new to the field of EM wave propagation, it has been applied in the area of acoustics and ultrasonics for several years (Fink, M. and Prada, C., Inverse Problems, vol.17, p.R1-38, 2001). In any finite size array that occupies a limited spatial area, the system is diffraction limited; however in acoustics, it has been shown that, in an inhomogeneous medium, a time reversal array is not always diffraction limited and can achieve super-resolution. Basically, scatterers near the transmitting array and/or focal point act as an extension of the array in the focusing process. The paper shows that the same phenomenon exists for EM waves. While the feasibility of applying TRM to EM problems has been demonstrated, many issues must be investigated and resolved before TRM can be implemented practically in a communications or radar imaging system.

A complete physics-based channel parameter simulation for wave propagation in a forest environment

At HF through UHF frequencies, wave propagation in a forest environment is mainly attributed to a lateral wave which propagates at the canopy-air interface. Due to the existence of tree trunks, significant multiple scattering also occurs which is the dominant source of field fluctuations. Basically, the current induced in the tree trunks by the source and the lateral wave reradiate and generate higher order lateral waves and direct scattered waves. Using a full-wave analysis based on the method of moments in conjunction with Monte Carlo simulations, the effect of multiple scattering among a very large number of tree trunks is studied. It is shown that only scatterers near the source and the observation points contribute to the field fluctuations significantly. This result drastically simplifies the numerical complexity of the problem. Keeping about 200 tree trunks in the vicinity of the transmitter dipole and the receiver point, a Monte Carlo simulation is used to evaluate the statistics of the spatial and spectral behavior of the field at the receiver. Using a wide-band simulation, the temporal behavior (impulse response) is also studied as is performance of antenna arrays and the effects of different spatial diversity combining schemes in such a multipath environment.

Fast multipole representation of Green's function for an impedance half-space

In this paper, exact and approximate multipole representations for fields of a horizontal or a vertical infinitesimal dipole above impedance surfaces are derived from the exact image formulation. These multipole expansions are appropriate for applications in the method of moments through a formulation known as the fast multipole method. Unlike the existing approximate formulations, these new multipole representations of the Greens function for the half-space impedance surface problem do not impose any restrictions on the location of source or observation points and are computationally very efficient.

Full-wave simulation of propagation channel parameters for a forest environment

Scattering from tree trunks is the dominant source to the field fluctuations in a forest environment. Using full-wave analysis based on the method of moments in conjunction with Monte Carlo simulations the effect of multiple scattering among a large number of tree trunks and their interaction with the lateral waves are studied. It is shown that only scatterers near the source and the observation points contribute to the field fluctuations significantly. Keeping about 200 tree trunks in the vicinity of the transmitter dipole and the receiver point, Monte Carlo simulation is used to evaluate the statistics of the spatial and spectral behavior of the field at the receiver. Using a wide bandwidth simulation, the temporal behavior is also studied and the performance of antenna arrays is investigated.

Physics based ray-tracing propagation model for suburban areas

In this paper a hybrid model has been developed based on a physics-based model for the forest and a ray-tracing algorithm. Using the physical model of the forest, effective dielectric constant is found and applied to the raytracing algorithm. This 3-D modeler can consider objects with different shape and position, and therefore the simulator can be used for any arbitrary scenario.

Long distance path-loss estimation for wave propagation through a forested environment

Accurate modeling of wave propagation behavior through forested environments is of great interest for civilian and military communication applications. Existing foliage propagation models treat the forest as an effective lossy dielectric medium and predict an exponential increase of path-loss with respect to the propagation distance within the forest. Such a model captures only the coherent power of the signal and neglects the incoherent power from the field fluctuation due to the random distribution of scatterers, such as brranches and leaves, within th forest. For long distance communication, such incoherent power tends to dominate the overall received power after a certain distance. Experimental results show that the simple models grossly overestimate the path-loss. A new Statistical WAve Propagation (SWAP) model, based on coherent wave theory and a renormalization approach, is presented and is shown to provide a reasonably accurate and computationally efficient solution for the estimation of path-loss in a forested environment over long distances.