An Introduction to Ultra Wideband Communication Systems

2.4. Electromagnetic Simulation of UWB Propagation in Indoor Environments

A communication propagation link starts from the feed point at the transmitting antenna and ends with the output terminals of the receiving antenna. Between the two antennas, electromagnetic waves propagate in the form of direct, refracted, reflected, and diffracted rays due to interactions with the surrounding media, which represent the channel. The characteristics of the channel are not independent from the properties of the transmitting and the receiving antennas, since received pulses depend on the direction of launched rays as well as the direction and the polarization of the received rays. Thus, the problem of simulating UWB propagation in indoor environments can be divided into two parts, one part dealing with transmitting and receiving antennas, and another part for the wave propagation in the channel.^[1]

^[1] Several sentences in the first two paragraphs of Sections 2.3 and 2.4.1 as well as (2.7)(2.12) are borrowed from [26] and reprinted here by permission of Wiley.

2.4.1. Simulation of Transmitting and Receiving Antennas

The simulation of a transmitting antenna should yield solutions for pulsed radiated electromagnetic fields in free space for all directions as a function of the input pulse and antenna characteristics. Assuming that a voltage signal v_TX (t) is the input to a transmitting antenna located at (x_s, y_s, z_s), then the radiated electric field at an observation point (x₀, y₀, z₀) can be described as

Equation 2.6

where h_TX (x₀,y₀,z₀;x_s, y_s, z_s;t)is the vector impulse response of the transmitting antenna at the observation point (x₀, y₀, z₀), and "*" represents convolution in the time domain. In the far field region, the dependence of radiated fields on the distance between the antenna and the observation point, r, includes the spherical spread factor 1/4pr, and the time delay c/r, where c is the wave velocity in free space. Thus, in the far field region, (2.6) can be expressed as

Equation 2.7

where

Equation 2.8

Equation 2.9

and f_TX (t) represents the impulse field pattern of the transmitting antenna. Also, in (2.9) , , and are unit vectors in the Cartesian coordinate system.

The simulation of a receiving antenna should result in the received output pulse due to incident pulsed plane waves arriving at the antenna from any direction and with any polarization. The received voltage signal v_RX (t) is

Equation 2.10

where e_inc (x_r, y_r, z_r; t) is a pulsed vector field incident on the receiving antenna located at (x_r, y_r, z_r), f_RX (t)is the impulse field pattern of the receiving antenna, and the symbol indicates a combination of time domain convolution and scalar product operations.

2.4.2. Simulation of the UWB Channel

Nearly all channel simulations for narrowband signals are based on high-frequency techniques, such as ray tracing, geometrical theory of diffraction (GTD), or uniform theory of diffraction (UTD) [14-22]. This is due to the fact that most dimensions are much larger than the wavelength of the signal. For UWB signals, the problem is somewhat different in that the signal occupies a wide spectrum, and thus there is no narrowly defined wavelength with which the dimensions can be compared. Different approaches can be used to describe the spatial dimensions pertaining to UWB signals. For example, dimensions may be compared to the wavelength of the central frequency of the spectrum of the pulse, the wavelength of the peak energy frequency in the spectrum of the pulse, or the spatial width of the pulsed signal. However, for high data rate UWB communication systems, all of these reference lengths are generally much smaller than the dimensions in indoor environments. With this view in mind, UWB indoor channels can be simulated using high-frequency techniques without a significant loss of accuracy in simulation results.

Wang et al [23] introduced a hybrid technique based on combining ray tracing and the finite difference time domain (FDTD) method to simulate narrowband communication links in indoor environments. Schiavone et al [24] proposed a similar approach for simulating indoor UWB propagation. However, these methods require huge computational resources to simulate UWB channels in relatively simple indoor environments. Furthermore, the computational requirements increase cubically with frequency. Thus, these techniques are limited to simple environments, such as a small room, and to UWB signals with restricted upper frequency limits. Here, the simulation of UWB propagation in realistic indoor environments is addressed in a comprehensive manner.

As a first step toward UWB channel simulation, one can begin with the simplest casewhen the propagation medium between transmitting and receiving antennas is free space. In this case, there are no reflected, refracted, and diffracted waves. The received signal is obtained from

Equation 2.11

For the case of indoor communications, various components contribute to the received signal, as schematically shown in Figure 2.21. The transmitting antenna radiates its energy as a collection of ray tubes distributed in all directions according to its impulse radiation pattern and the input pulse signal. The received signal due to the LOS ray depends mainly on the radiation characteristics of the transmitting and receiving antennas, and is slightly affected by the surroundings. Other rays can reach the receiving antenna upon multiple reflections from the walls, the floor, and the ceiling in the propagation environment. The received signal due to such multiple reflected rays depends on the number of reflections, the material of the reflecting surfaces, and the thickness and curvature of such surfaces. The thickness of each wall also causes internal multiple reflections inside the wall itself. The effect of these multiple internal reflections depends on the spatial length of the incident pulse and the thickness of the wall, and its complex dielectric constant. Diffraction at the edges of windows, door frames, and other scattering objects present in the medium gives rise to another group of rays, the diffracted rays. Each incident ray on an edge is diffracted as a cone of rays following Keller's diffraction cone [25]. The diffracted rays may directly reach the receiving antenna or undergo multiple reflections, and may even suffer multiple diffractions before reaching the receiving antenna.

The measured signal at the receiving antenna output can be formulated by combining the contributions from all types of rays,

Equation 2.12

where the summation over n accounts for all rays from the transmitting antenna. The first intersection point of the n^th ray along the x_0n, y_0n, z_0n), r_n is the path length for the n^th ray from the transmitting antenna to its first intersection point, defines the direction of the n^th ray upon reaching the receiving antenna, and Q_n (x_r, y_r, z_r; x_0n, y_0n, z_0n; t) is the channel dyadic impulse response at the receiving point due to the n^th ray. This dyadic impulse response accounts for all reflections, diffractions, spreading factors, time delays, and so on. For a LOS ray, the dyadic impulse response is simply a unity matrix. Thus, the contribution of a LOS ray to the received signal is the same as that in (2.11). Equation (2.12) shows how difficult it is to separate channel characterization from the radiation properties of the transmitting and receiving antennas. Changing the antennas may cause significant changes in the received UWB signal for the same channel environment. Thus, the channel simulation should be done in conjunction with the simulation of the specific antennas used. Here, simulation results will be presented for the case where TEM horns are used as transmitting and receiving antennas. These antennas were used for indoor UWB propagation measurements by the VT group as described in Section 2.3.

2.4.3. Organization of the Electromagnetic Simulator

In the previous section, the individual parts of the simulator were discussed in some detail. These parts are now integrated to construct the UWB propagation simulator. The simulation begins with a pulse fed to the transmitting antenna and ends with the received signal at the terminals of the receiving antenna. The input data for the simulator include the antenna parameters and the channel parameters. Channel parameters are divided into geometrical parameters and electrical parameters. The geometrical parameters include the dimensions and the orientations of all the wall segments constituting the channel. The thickness of each segment is one of its geometrical parameters. Also the locations of transmitting and receiving antennas constitute part of the geometrical parameters of the problem. The electrical parameters of the channel are the real and the imaginary parts of the dielectric constant of each segment as functions of frequency over the spectrum of the incident pulse.

The first step of the simulation is to trace all the rays transmitted from the location of the transmitting antenna to the plane where the receiving antenna is located. The required information for the ray tracing procedure includes the location of the phase center of the transmitting antenna, the geometry of the channel, and the plane of the receiving antenna. The outcome of this step is the location of the reflection, refraction, and diffraction points in the channel; the parallel and perpendicular polarization vectors for the reflection and refraction rays; the soft and hard polarization vectors for the diffracted rays; the total path length from the transmitting antenna to a point on the receiving plane; and the location and the direction of arrival at the receiving plane.

The second step is to determine the rays captured by the receiving antenna. It is assumed that a ray reaching the receiving plane is launched from a point source located at a distance equal to the total path length between the transmitting antenna and the receiving point. The location of this assumed point source should satisfy the direction of arrival at the corresponding receiving point. A ray is transmitted from this assumed point source to the location of the phase center of the receiving antenna.

The third step of the simulation is to determine the electric field and its polarization at the first intersection of each ray upon leaving the transmitting antenna. In this step, the simulation of the transmitting antenna provides such a field. For a LOS ray from the transmitting antenna to the receiving antenna, this is the field that is directly received by the receiving antenna. However, for other rays, this field should be transformed to the frequency domain where reflection, refraction, and/or diffraction of the wave is treated. Then, the frequency domain received fields are converted back to the time domain.

The fourth step of the simulation involves calculation of the reflection, refraction, and diffraction dyadics at each frequency. The total dyadic for a ray is the multiplication of the dyadics of different segments along the ray path.

The last step of the simulation is to obtain the total field at the receiving antenna. The amplitude, polarization, and direction of arrival of the received field on each ray are calculated using the data for the corresponding transmitted ray and the total dyadic of the ray. The Fourier Transform of the total dyadic gives the channel dyadic impulse response at the receiving point due to this ray. Finally, by combining the received signals due to all captured rays, the simulation of the UWB communication link is completed.

2.4.4. Comparisons of Measurement and Simulation Results

Now that the electromagnetic simulator has been developed, this section will validate the results by comparing them to some experimental data. To facilitate this comparison, the input signal to the transmitting antenna is assumed to be the actual Gaussian-like pulse (generated by Pico Second Pulse Labs Pulse Generator, Model 4100) used by the VT group in their UWB indoor propagation measurements. Figure 2.22 shows the voltage waveform of the input pulse normalized to its peak value. The simulation results are presented for transmitting and receiving antennas being the TEM horns used in the measurements. The two horns are essentially identical with the following parameters: electrode length l₀ = 36.4 cm, half separating angle A = 7.9º, and half apex angle B = 16.5°. The horn antennas are packaged inside a dielectric foam structure of very low dielectric constant e_r 1.07. This packaging has a negligible effect on the amplitude of the radiated fields. The simulation of TEM horn antennas is discussed in detail in [9]. The simulation results are compared with the time domain measurements (by the VT group) in the 2nd floor of Whittemore Hall at locations R x E, R x F, and R x G (see Fig. 2.10a). As mentioned before, the accuracy of the simulation is greatly affected by the details of the input data. Here we present a sample of the required details to develop the simulation. The width of the hallway is 2.83 m. The dropped ceiling is made largely of a low dielectric constant material at a height of 2.54 m, above which metallic pipes and cables are used for utilities. Through several trials it was found that an effective height of nearly 3 m for the ceiling yields a better agreement with the experimental results. The walls of the hallway are drywall supported by metallic studs. Metallic tiles coated with a ceramic layer cover the floor of the hallway. Thus, both the ceiling and the floor are assumed to be perfectly conducting surfaces. The overall thickness of a typical wall is nearly 0.1 m. The presented simulation is based on the assumption that the walls are completely composed of drywall. There are seventeen doors on the left side of the transmitter antenna and seven doors on the right. Almost all doors have the same dimensions and are made of the same materials. The height and the width of each door are 2.14 m and 0.9 m, respectively. The spacing between the centers of two successive doors is nearly 5.74 m. The distance between the transmitting antenna and the first door frame in the longitudinal direction is nearly 0.54 m. The distance between the starting point of the 10th frame and end point of the 9th frame in the longitudinal direction is nearly 1.7 m, and the distance between the starting point of the 11th frame and the end point of the 10th frame is nearly 3.4 m. The remaining doors on the right side are of the same periodic structure. The starting points of the right doorframes are at longitudinal distances of nearly 12.78 m, 17.95 m, 30.75 m, 33.02 m, 35.92 m, 41.13 m, and 44.03 m from the transmitting antenna. The door frames are perfectly conducting wedges of interior angle p/2.

Figures 2.23a to 2.23c compare the simulation results with the corresponding measured results at these three locations. As noted, there is generally good agreement between the measured and simulation results for all locations. The agreement for the first location, for which the distance between the transmitter and receiver is shortest, is best. The reasons may be due to internal multiple reflections in adjacent rooms and the presence of some tables and chairs in the hallway at larger distances. Ten multiple reflections were found to be adequate in the simulation. More multiple reflections do not increase the accuracy of simulation results.