This paper has established a new theoretical framework that allows us to analyze the ultra-wideband system performance using the closed form formulations. A new generalized time-domain multipath channel based on the geometric theory of diffraction/uniform theory of diffraction (GTD/UTD) framework is incorporated into the system bit-error rate and signal-to-noise ratio by modifying the existing system model. Closed form expressions for important geometric configurations are derived in the time domain for the first time. Some interesting insights into the physical mechanisms and system analysis are observed through explicit expressions and numerical results.

A generalized time domain multipath channel and its application in ultra-wideband (UWB) wireless optimal receiver design-Part II: physics-based system analysis

The time-domain (TD) solution of the two-dimensional multiple-diffraction case is investigated. The proposed TD solution is based on the representation of the inverse Fourier transform of the corresponding frequency-domain (FD) solution in closed form, as it is given by the uniform theory of diffraction (UTD), and it incorporates the TD representation of the higher-order diffraction coefficients. An algorithm to predict the TD diffracted field after an arbitrary number of objects is also presented. In the proposed algorithm, different types of objects along the propagation path can be applied as well, such as absorbing knife-edges and metallic or nonperfectly conducting wedges. The comparison between the TD solution and the numerical inverse fast Fourier transform of the FD solution proves the validity of the proposed solution.

Multiple Time-Domain Diffraction for UWB Signals

The authors point out that modeling of interfaces between two media, using time-domain surface impedances, permits one to reduce the discretization volume in the finite-difference-time-domain (FDTD) technique. The method presented here is based on an exact formulation of surface impedances, starting from Fresnel reflection coefficients for oblique incidence of the incident wave. The concept, valid for homogeneous and frequency-independent media, is then introduced into an FDTD algorithm where it is converted into a surface-impedance boundary condition (SIBC) for vertical or horizontal polarizations of locally plane waves. Two- and three-dimensional results are compared to those computed with classical FDTD or Fresnel reflection coefficients involving a Fourier transform. >

Implementation of a surface impedance formalism at oblique incidence in FDTD method

In this paper, we develop a deterministic UWB multipath channel model based on time-domain uniform geometrical theory of diffraction (TD-UTD) technique. The solution includes the three basic ray mechanisms of geometrical optics (GO) and UTD, i.e., directed ray, multireflected rays from lossy surfaces, and diffracted ray from lossy edge. Since the analysis is conducted in time-domain electromagnetic field, unlike statistical model, the approach for UWB channel model can determine not only signal attenuation, but also waveform distortion in terms of pulse shape and pulse duration when the UWB signal propagates in multipath environments. Here, a generic impulse response model by taking into account channel impulse response as well as transmitter and receiver antenna impulse responses is given. Then, the analytical description of time-domain single reflected ray and reflection coefficients of horizontal polarization and vertical polarization is provided. The time-domain multiple reflected rays are expressed by the convolution of individual reflection coefficient from lossy surfaces with different electromagnetic properties. The time-domain diffraction ray is described as time-domain diffraction coefficients and reflection coefficient. Finally, the simulation results in a typical office room are presented.

UWB multipath channel model based on time-domain UTD technique

We develop a method for the analytical evaluation of the inverse Laplace transform representations for transient transverse magnetic (TM) plane wave obliquely incident on a conductive half-space. We assume that the permittivity and conductivity of the dispersive half-space are independent of frequency. The time-domain expressions for the reflected and transmitted waves are first represented as inverse Laplace transforms. The transient fields are then shown to consist of two canonical integrals. The canonical integrals, in turn, are solved analytically, thereby yielding close-form solutions involving incomplete Lipschitz-Hankel integrals (ILHIs). The ILHIs are computed numerically using efficient convergent and asymptotic series expansions, thus enabling the efficient computation of the transient fields. The exact, closed-form expressions are verified by comparing with previously published results and with results obtained using standard numerical integration and fast Fourier transform (FFT) algorithms. An asymptotic series representation for the ILHIs is also employed to obtain a relatively simple late-time approximation for the transient fields. This approximate late-time expression is shown to accurately model the fields over a large portion of its time history.

An accurate and efficient analysis for transient plane waves obliquely incident on a conductive half space (TE case)

An approach to the computation of the electromagnetic field reflected from a lossy half-space directly in the time domain is discussed. This approach requires first evaluating the impulse response of the half-space and then convolving it with the specified incident field waveform. To obtain the impulsive reflected field, either for vertical or horizontal polarization, approximations to the Fresnel reflection coefficients are made, thereby permitting an analytical expression in the time domain. Several different numerical examples using this technique are presented to illustrate the use of the method and the error contained in the solution. >

F.M. Tesche

Papers

On the direct calculation of a transient plane wave reflected from a finitely conducting half space