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Wave Propagation in Underground Tunnels
Prediction of the mechanisms of propagation of electromagnetic waves in a variety of environments including underground tunnels is important in the planning and deployment of wireless and sensor networks. Our overall goal is to develop numerical techniques for wave propagation in underground tunnels that will address the challenges of irregular boundary shapes, non-smooth boundaries, curved tunnels, and bifurcating tunnels, Fig. 1. We are exploring the use ADI technique parabolic equation technique together with the A successful numerical technique will allow accurate predictions of path loss, angular spread and time dispersion of the field. Figs. 2a and 2b show the comparison between analytical (top) and computed (bottom) fields inside a circular and semicircular tunnel with Neumann boundary conditions. A Gaussian source is imposed at zero range and the field is shown at a distance of 100 m away from the source at the operating frequency of 1 GHz.
Wave Propagation Over Rough Ocean Surfaces
When radio waves propagate over the surface of sea, they are affected by its surface roughness as well as the radio refractive index of the atmosphere through which they pass. These effects are very pronounced at microwave frequencies and are of utmost importance to Navy in ship-ship communication and detection, http://sunspot.spawar.navy.mil/.
We are developing numerical schemes to study radio waves propagating at low grazing angles over a rough ocean surface by considering both the full wave Helmholtz equation as well as the approximate parabolic equation. Over rough surfaces the propagated power is divided between the coherent power, which contributes in the specular direction and the diffuse power which contributes in all other directions as well. Fig. 3a and 3b show the fraction of the coherent power to the total power over a rough surface with Gaussian height statistics and Pierson-Moskowitz roughness spectrum. The latter relates the standard deviation of the roughness height to wind-speed. In the figures, the wind speed varies from 1-16 m/s, the grazing angle varies from 0.1-8 degrees and the frequency is kept constant at 3 GHz. A plane wave with a grazing angle of is assumed to be incident on the rough surface and the scattered power is observed as a function of height above the mean surface level. The figures demonstrate at what point the propagation phenomenon switches from purely coherent to diffuse type of behavior
Electromagnetic Modeling of MIMO Systems
Multiple Input Multiple Output (MIMO) systems are very attractive for increasing the information carrying capacity of wireless systems operating with limited bandwidth. Employing electromagnetic methods we are making studies on the available degrees of freedom of MIMO systems in a rich multipath environment when the receiving signals are corrupted by noise. The degrees of freedom approximately give a sense of the number of modes that can be utilized for MIMO communications. Fig. 4a shows the average number of degrees of freedom as a function of transmit antenna power. Fig. 4b shows the average number of degrees of freedom as a function of the receive volume size.
Another related topic is to use non-exact methods to model path loss in rich scattering environments. We are exploring the use of diffusion equation to model mean path loss as a function of distance from the transmitter. Fig. 5a and 5b show the received power as a function of distance from transmitter using a full-wave integral equation model together with the analytical one predicted by diffusion equation. A mixture of lossy objects with cross-sectional shapes chosen from circular, square, and elongated elliptical shapes were included in the full-wave approach. The cylinders were scattered with random locations and orientations within the scattering volume.
