Abstract
The diffusion and Schr¨odinger propagators have been known to coexist on a lattice when a particle undergoing random walk is endowed with two states of spin in addition to the two states of direction in a 1+1 spacetime dimension. In this paper we derive explicit expressions for the various transitional probabilities by employing generating functions and transform methods. The transitional probabilities are all expressed in terms of a one-dimensional integral involving trigonometric functions and/or Chebyshev polynomials of the first and second kind from which the spacetime continuum limits of the diffusion equation and Schr¨odinger equation follow directly.
Abstract
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
Topology control problems are associated with assignment of power levels to nodes of a wireless network so that the resulting graph topology satisfies certain properties. In this paper we consider the problem of power-efficient topology control with switched beam directional antennas taking into account their non-uniform radiation pattern within the beamwidth. Previous work in the area have all assumed a uniform gain model with these antennas which renders antenna orientation insignificant as a parameter in topology control algorithms. We present algorithms that take into account a model of non-uniform gain with the objectives of minimizing the total power and maximum power to keep the network connected. We consider two cases: one where the antenna orientation is assumed given and another where the antenna orientation needs to be derived as well. For the first case, we present optimal and approximation algorithms for constructing power-efficient topologies . For the second case, we prove the problem to be NP-complete and present heuristic solutions along with approximation bounds. Through comparison of the two cases by simulation, significant reductions are shown in the maximum as well as total power required to keep the network connected for the second case, thus demonstrating the benefits of using antenna orientation as parameter in topology construction.
Abstract
The electromagnetic (EM) degrees of freedom (DOF) of a noise limited system in two dimensions with random multiple scattering is evaluated numerically following a rigorous DOF theory first developed by Miller and Piestun for optical systems. The received EM fields are efficiently calculated by fast multipole method (FMM), and the ensemble average of the DOF number is obtained through Monte Carlo simulation technique. The results show that the average EM DOF number is strongly dependent on the sizes of the transmit volume, the receive volume, and the scattering region. In particular, the average number of DOF generally increases with both the transmit and receive volumes. However this increase is a non-linear process and will not continue indefinitely. As the transmit volume or the receive volume expands, an upper-bound of the average DOF number is expected due to noise effects. Due to the lack of criteria for choosing a critical parameter involved in Miller and Piestun's original DOF definition, a modified definition is also considered. Even though the modified definition is SNR dependent, it provides a clearer physical meaning of the DOF. In addition, the simulations also suggest that it might not be appropriate to ignore the influence of the SNR on the DOF number when the system concerned is of general form and relative small, where no critical point of the channel quality can be identified. A logarithmic dependence of the DOF number on the total source power is demonstrated for such systems.
Abstract
New analytical shadow loss model is presented that takes into account absorption and scattering of incident waves by obstacles. The input parameters for the model are the obstacle occupational density, obstacle number density, and mean geometric cross section of the obstacles. The model yields a closed form expression for the mean excess loss in a typical office environment. Comparison with measured excess loss in NLOS situations is shown to demonstrate the utility of the model. The model is expected to be valid when the density of obstacles is sufficiently large.
Abstract
The purpose of this paper is to numerically evaluate the effectiveness and accuracy of Uscinski and Stanek's mean Green's function technique for computing the mean field of a wave scattered by a rough surface. We present here a direct comparison of this technique with a rigorous numerical method, the forward scattering integral equation method, and another analytical method, the first-order smoothing approximation. Furthermore, we compare the roughness generated equivalent admittance using the three methods. Numerical computations reveal that the scattered field calculated by this technique is not accurate particularly for the equivalent admittance at low grazing angles, even though the mean surface current density is recovered when the wave has traversed several correlation lengths on the surface..
Abstract
The effect of mutual coupling on the capacity of the multiple-input–multiple output (MIMO) cube antenna is demonstrated using numerical simulations. The twelve edges of the cube constitute center-fed electrical dipole antennas. A simple double bouncing scattering model is used to form the MIMO channel matrix. Mutual coupling between the elements that has impact on both the spatial correlation and the received signal-to-noise ratio (SNR) is taken into account using the mutual impedance matrix of the cube. Results of Monte Carlo simulations show that the theoretical capacity due to mutual coupling is lower than without mutual coupling for cube side lengths less than about 0 3 but the results roughly match those for higher side lengths.
Abstract
Recently, there has been significant interest in the capacity of multiple element antenna (MEA) wireless systems. Previous authors have shown that the asymptotic capacity of a system with N transmit and N receive antennas (termed an (N,N) MEA) grows linearly with N if, for all l, the correlation of the fading for two antenna elements whose indices differ by l remains fixed as antennas are added to the array. However, in practice, the total size of the array is often fixed, and thus the correlation of the fading for two elements separated in index by some value l will change as the number of antenna elements is increased. In this paper, under the condition that the length of a linear array of antennas is fixed, the asymptotic properties of the instantaneous mutual information IN,N of an (N,N) MEA wireless system are derived analytically and tested for accuracy for finite N through simulations. Two different cases are considered: (1) when the fixed array size constraint is imposed at the mobile unit, and (2) when the fixed array size constraint is imposed at both the base station and the mobile unit. For the first case, simulation results indicate that the analytical approximations are very accurate for moderate values of N, especially at high signal-to-noise-ratios (SNR). For the second case, the predicted non-convergence of IN,N is observed in simulations, as well.
Abstract
Conditions on the metric coefficients are derived in order for a three-dimensional electromagnetic field in a source free homogeneous space to be decomposed into transverse electric (TE) and transverse magnetic (TM) parts. The relationship between scalar and vector potentials and the equation satisfied by the vector potential component are also given.
Abstract
Starting from a parabolic approximation to the Helmholtz equation, a three–dimensional (3-D) vector parabolic equation technique for calculating path loss in an urban environment is presented. The buildings are assumed to be polygonal in cross section with vertical sides and flat rooftops and the terrain is assumed to be flat. Both buildings and ground are allowed to be lossy and present impedance-type boundary condition to the electromagnetic field. Vector fields are represented in terms of the two components of Hertzian potentials and depolarization of the fields is automatically included in the formulation. A split-step algorithm is presented for marching the aperture fields along the range. Boundary conditions on the building surfaces are treated by using a local Fourier representation of the aperture fields. Several test cases are considered to check the boundary treatment used in the technique as well as to validate the overall approach. Comparison is shown with uniform theory of diffraction (UTD), exact solutions, as well as with measurements.
Abstract
The paper demonstrates the use of Mellin transforms in the analytical evaluation of the mean capacity of multiple-input-multiple-output (MIMO) systems in various fading environments. Results are derived for the mean capacity for the following systems: a single-input-multiple-output (SIMO) system with Rayleigh fading, an (N, N) MIMO system with Rayleigh fading, an (N, N) MIMO system with a keyhole. A general asymptotic formula is derived that is valid for a wide variety of fading environments..
Abstract
The effect of element mutual coupling on the capacity of multiple-input–multiple-output (MIMO) antenna systems is demonstrated by considering a fixed-length linear array of half-wave dipoles. Mutual coupling between elements, which influences both the spatial correlation and the received signal-to-noise ratio (SNR), is taken into account by means of the impedance matrix. Monte Carlo simulations are performed for both single-sided (i.e., transmitting end or receiving end) and double-sided fading correlations. It is shown that mutual coupling results in substantially lower capacity and, hence, in reduced degrees of freedom.
Abstract
Starting from a Gaussian distribution of scatterers around a mobile station, expressions are provided for the probability density function (pdf) in the angle of arrival, the power azimuth spectrum, the pdf in the time of arrival, and the time delay spectrum, all as seen from a base station. Expressions are also provided for some of the quantities of practical interest such as the root-mean-square (rms) angular spread, the rms delay spread, and the spatial cross-correlation function. Results for the Gaussian scatter density model are compared with those for the circular scattering model and the elliptical scattering model as well as with experimental results available for outdoor and indoor environments. Comparison is shown for the pdfs as well as for the power spectra in angle and delay. It is shown that the present model, in contrast to the previous models, produces results that closely agree with experimental results.With an appropriate choice of the standard deviation of the scattering region, the Gaussian density model can be made suitable both for environments with very small angular spreads as well as those with very large angular spreads. Consequently, the results provided in the paper are applicable to both macrocellular as well as picocellular environments.