**3. Hybrid deterministic-stochastic channel simulation**

In the framework of this project, a realistic UWB multi-path propagation simulation tool was developed in order to test and compare different algorithms and antenna arrangements for indoor UWB sensing and imaging. Multi-path propagation implies that the transmitted signal does not only arrive over the direct propagation path at the receiver, but also over paths which are dependent on the propagation environment in a complex manner. The received signal is then a combination of a multiplicity of reflected, diffracted and scattered electromagnetic waves. Wave propagation models, in general, can be classified into deterministic and stochastic ones. Deterministic models are based on the physical propagation characteristics of electromagnetic waves in a model of the propagation scenario. In contrast, stochastic models describe the behavior of the channel through stochastic processes.

By now, some statistical channel models have been established for the early design phase and for testing the ideas for possible applications. Statistical models randomly generate channel impulse responses of a channel based on the probability functions, which are usually obtained from measurements. However, if a system has to be tested in a specific environment, deterministic channel models are required, which approximate real physical phenomena.

One of the most popular deterministic channel modeling approaches is ray tracing (RT), based on geometrical optics and the uniform theory of diffraction. In outdoor areas ray tracing simulations emulate the propagation conditions very well [18]. Furthermore, it has been shown that ray tracing can be also easily extended to simulate ultra-wideband channels.

However, comparisons between the measurements and simulations with respect to UWB indoor channels show that the ray tracing results are often underestimated in terms of received power, mean delay and delay spread [26, 34, 42]. This is due to insufficient modeling or the complete neglect of diffuse scattering in the ray tracing model.

Diffuse scattering causes contributions to the power delay profile, which are not resolvable (dense multipath components). Through these contributions the power delay profile is smoother than in the scenarios with reflection and diffraction only.

#### 10 Will-be-set-by-IN-TECH 188 Ultra-Wideband Radio Technologies for Communications, Localization and Sensor Applications Cooperative Localization and Object Recognition in Autonomous UWB Sensor Networks <sup>11</sup>

In the model described in this section, a simple approach is proposed which combines the ray tracing method with statistically distributed scatterers. The approach is inspired by the diffuse scattering model for UWB channels presented in [33], by the spatiotemporal model for urban scenarios presented in [46] and by the geometrically-based stochastic channel model [40]. The scatterer placement and properties are bound to the geometry of the considered scenario. The parameters for the stochastic part of the model are derived from measurements. As only few additional scattering contributions per surface are added, the increase in computational effort is very little. The placement of scatterers ensures that part of the contributions are resolvable for the UWB system. Some preliminary results of this model were previously presented in [23], [24] and [25].

To get an impression of the sources of dense multipath components, the spatial behavior of the channel a stationary office scenario (scenario A), shown in Fig. 7, is analyzed.

(a) Schematic diagram of the measurement scenario

(b) Simulation environment

time dependent PDP is plotted along the *y*-axis. As the radiation pattern of the antenna array has a narrow main beam the directions of arrival of the propagation path, impinging on the

Cooperative Localization and Object Recognition in Autonomous UWB Sensor Networks 189

(a) Tx1 – Measurement (b) Tx1 – Simulation

**Figure 8.** Measured and simulated angle-dependent power delay profiles for the transmitter position

The comparison shows that most of the strong contributions are present in both measurements and simulations. Moreover, the amplitudes of the measured and simulated reflection

Nevertheless, a significant amount of power is missing in the simulations. Figure 9 shows the power delay profiles of Fig. 8 averaged over the delay time and over the angle. It can be observed that although some strong contributions such as the direct path and a reflection at *τ* = 25 ns is at the same level as that from the measurements, for most delay times the simulated power is considerably lower. From the PDP values averaged over the angle we may conclude that this effect is present for all observation angles. The dense components are not distributed evenly over the angle, but create *clusters* around the strong contributions. The observed dense contributions are not an effect of rough surfaces, as all surfaces in the room can be considered to be smooth within the frequency range used. Some contributions may arise from small objects such as doorknobs present in this scenario. Other contributions are most likely due to the scattering from the inhomogeneities within the walls or cabinets. In [44] it was shown that typical inhomogeneous building materials distort the transmitted signal significantly. Such distortions are expected to be present also in the reflected signal and are likely to cause dense components with delay times slightly larger than the delay time of the reflected signal. The amplitudes of such components are decreasing almost exponentially with the delay time.

This means that if the dense contributions are to be modeled, their delay times and angles of

To achieve the clustering effect, additional contributions are generated by placing point scatterers around the reflection points calculated by the ray tracing model, see Fig. 10. These scatterers represent small structures on the surface, which have not been considered in the

antenna can be directly identified in the picture.

contributions have been captured with good accuracy.

arrival should be grouped around the significant contributions.

**3.1. Scattering model**

Tx1.

**Figure 7.** Schematic diagram of the measurement (left) and simulation scenario (right, view from outside through the windows) for the DOA analysis of dense multipath components.

The measurement setup used consists of a vector network analyzer, low noise amplifier and of a set of step motor controlled positioners. The frequency range sampled by the analyzer is 2.5 - 12.5 GHz. For the measurements in scenario A, the motor controlled turntable is used to rotate the strongly directive antenna array described in [2] around its *z*-axis. This antenna is used as a receiver (Rx) and placed approximately in the middle of the room. The transmitter (Tx) is equipped with a UWB omnidirectional monocone antenna and placed at 5 positions marked in Fig. 7 (left).

In the same scenario, ray tracing simulations, as shown in Fig. 7 (right), with up to 5 reflections and up to 3 diffractions have been performed. At this point, no scattering is considered in the simulations. The transmission has not been considered here, earlier radar measurements in comparable rooms, [23], showed that no significant paths are to be expected from their side of the walls. On the other hand, objects inside the wooden cabinets may cause significant dense contributions. The patterns of the antennas used in the measurements have been measured in an anechoic chamber for the considered frequency band, and are considered in the simulations.

In Fig. 8 the measured and simulated power delay profiles (PDP) are depicted for the transmitter position 1, see Fig. 7 (left). For each rotation angle indicated on the *x*-axis, the time dependent PDP is plotted along the *y*-axis. As the radiation pattern of the antenna array has a narrow main beam the directions of arrival of the propagation path, impinging on the antenna can be directly identified in the picture.

**Figure 8.** Measured and simulated angle-dependent power delay profiles for the transmitter position Tx1.

The comparison shows that most of the strong contributions are present in both measurements and simulations. Moreover, the amplitudes of the measured and simulated reflection contributions have been captured with good accuracy.

Nevertheless, a significant amount of power is missing in the simulations. Figure 9 shows the power delay profiles of Fig. 8 averaged over the delay time and over the angle. It can be observed that although some strong contributions such as the direct path and a reflection at *τ* = 25 ns is at the same level as that from the measurements, for most delay times the simulated power is considerably lower. From the PDP values averaged over the angle we may conclude that this effect is present for all observation angles. The dense components are not distributed evenly over the angle, but create *clusters* around the strong contributions. The observed dense contributions are not an effect of rough surfaces, as all surfaces in the room can be considered to be smooth within the frequency range used. Some contributions may arise from small objects such as doorknobs present in this scenario. Other contributions are most likely due to the scattering from the inhomogeneities within the walls or cabinets. In [44] it was shown that typical inhomogeneous building materials distort the transmitted signal significantly. Such distortions are expected to be present also in the reflected signal and are likely to cause dense components with delay times slightly larger than the delay time of the reflected signal. The amplitudes of such components are decreasing almost exponentially with the delay time.

This means that if the dense contributions are to be modeled, their delay times and angles of arrival should be grouped around the significant contributions.

### **3.1. Scattering model**

10 Will-be-set-by-IN-TECH

In the model described in this section, a simple approach is proposed which combines the ray tracing method with statistically distributed scatterers. The approach is inspired by the diffuse scattering model for UWB channels presented in [33], by the spatiotemporal model for urban scenarios presented in [46] and by the geometrically-based stochastic channel model [40]. The scatterer placement and properties are bound to the geometry of the considered scenario. The parameters for the stochastic part of the model are derived from measurements. As only few additional scattering contributions per surface are added, the increase in computational effort is very little. The placement of scatterers ensures that part of the contributions are resolvable for the UWB system. Some preliminary results of this model were previously presented in

To get an impression of the sources of dense multipath components, the spatial behavior of

(b) Simulation environment

the channel a stationary office scenario (scenario A), shown in Fig. 7, is analyzed.

**Figure 7.** Schematic diagram of the measurement (left) and simulation scenario (right, view from

The measurement setup used consists of a vector network analyzer, low noise amplifier and of a set of step motor controlled positioners. The frequency range sampled by the analyzer is 2.5 - 12.5 GHz. For the measurements in scenario A, the motor controlled turntable is used to rotate the strongly directive antenna array described in [2] around its *z*-axis. This antenna is used as a receiver (Rx) and placed approximately in the middle of the room. The transmitter (Tx) is equipped with a UWB omnidirectional monocone antenna and placed at 5 positions

In the same scenario, ray tracing simulations, as shown in Fig. 7 (right), with up to 5 reflections and up to 3 diffractions have been performed. At this point, no scattering is considered in the simulations. The transmission has not been considered here, earlier radar measurements in comparable rooms, [23], showed that no significant paths are to be expected from their side of the walls. On the other hand, objects inside the wooden cabinets may cause significant dense contributions. The patterns of the antennas used in the measurements have been measured in an anechoic chamber for the considered frequency band, and are considered

In Fig. 8 the measured and simulated power delay profiles (PDP) are depicted for the transmitter position 1, see Fig. 7 (left). For each rotation angle indicated on the *x*-axis, the

outside through the windows) for the DOA analysis of dense multipath components.

[23], [24] and [25].

scenario

marked in Fig. 7 (left).

in the simulations.

(a) Schematic diagram of the measurement

To achieve the clustering effect, additional contributions are generated by placing point scatterers around the reflection points calculated by the ray tracing model, see Fig. 10. These scatterers represent small structures on the surface, which have not been considered in the

**Figure 9.** Averaged angle-dependent power delay profiles for the transmitter position Tx1.

scenario data so far, as well as interactions with inhomogeneities inside the objects and with objects behind the walls. The delay time of the additional multi-path contributions due to the scattering points is approximately equal to the delay time of the reflected path. Their scattering coefficients are adjusted so that the resulting amplitudes of these multi-path components are slightly below the amplitude of the reflected path.

**Figure 10.** Modeling approach for single reflections.

The number of scatterers *n* = 1... *N* is a model parameter and is assumed to be constant for all clusters. The scatterers are distributed uniformly on the objects' surface within a radius *r* around the reflection point. The scatterers whose position is outside the considered area are discarded.

In order to keep the model as general as possible, each scatterer is characterized by the complex full polarimetric scattering matrix **S**. The field scattered from the n-th scatterer **E**<sup>s</sup> is described in the frequency domain by:

$$\underline{\mathbf{E}}^{\rm s} = \frac{\boldsymbol{\varepsilon}^{-jk\_0d}}{d} \cdot \underline{\mathbf{S}} \cdot \underline{\mathbf{E}}^{\rm i} \tag{1}$$

factor Γ is calculated at the position of the scatterer using the material parameters of the corresponding surface. Depending on the polarization of the impinging wave, the reflection coefficient either for parallel or vertical case is used. Thus, in the case of single reflection paths and assuming vertical polarization, the resulting field at the receiver consists of the reflection

> *e*−*jk*0*dn dn*

Due to the single scattering approach, the model covers only the part of the power delay profile with relatively short excess delay times. For the reliable simulation of delay spreads longer multiple reflected propagation paths have to be considered. The intuitive approach would be to place additional scatterers around the higher order reflections points and to use the impinging reflected wave as an excitation, see Fig. 11. This would then have to be incorporated into the reflection path search algorithm of the ray tracing approach, which would require much computational effort. To keep the excess simulation time of the hybrid part of the model as short as possible, the multiple scattering processes are replaced here with "virtual" single bounce scatterers. These scatterers are placed at the point of the multiple reflections. Their scattering factors contain an additional term *e*−*jk*0*δ*, where *δ* corresponds to the path length between the point of the first interaction and the considered higher order interaction. This term adds *δ*/*c*<sup>0</sup> to the delay corresponding to the distance between the

(a) 1st order reflection (b) 2nd order reflection - simplified approach

Thus, the delay time similar to the delay of a propagation path containing one or more reflections can be realized. However, the amplitude of such a path decreases proportionally to *δ* · *d*geom whereas the amplitude of a path containing the reflection would experience a slower decay. To counterbalance this effect, an additional term *p* · *δ* is included in the scattering coefficients of the higher order scatterers resulting in the following expression for all scatterers:

*S* = (*a* + *p* · *δ*) · Γ · *e*

this case *δ* = 0. Thus, the resulting model is characterized by 4 parameters:

For the scatterers placed around single reflection, this expression reduces to *S* = *a* · Γ since in

*N* ∑ *n*=1 v,tot given by:

Cooperative Localization and Object Recognition in Autonomous UWB Sensor Networks 191

v,*<sup>n</sup>* (2)

<sup>−</sup>*jk*0*<sup>δ</sup>* (3)

· *<sup>a</sup>*Γv,*<sup>n</sup>* · *<sup>E</sup>*<sup>i</sup>

contribution and of the sum of scattered contributions *E*<sup>s</sup>

transmitter and the scatterer *d*geom.

**Figure 11.** Modeling approach for multiple reflections


*E*s v,tot =

where **E**<sup>i</sup> is the incident field, *k*<sup>0</sup> is the wave number, and *d* is the distance between the scatterer and the observation point.

In this subsection, only the vertical co-polarized element *S*vv is considered. The parameterization of other scattering matrix components can be done in the same way. As the frequency band used is very wide, at least some of the contributions can be resolved by the system. Therefore, the scattering contributions in the model are coherently summed at the receiver.

To obtain the amplitudes of scattered contributions in the same order of magnitude as the amplitudes of the reflected path, their scattering factors are related to the reflection coefficient Γ by a proportionality factor *a*, which is derived from the measurements as well. The reflection factor Γ is calculated at the position of the scatterer using the material parameters of the corresponding surface. Depending on the polarization of the impinging wave, the reflection coefficient either for parallel or vertical case is used. Thus, in the case of single reflection paths and assuming vertical polarization, the resulting field at the receiver consists of the reflection contribution and of the sum of scattered contributions *E*<sup>s</sup> v,tot given by:

$$\underline{E}\_{\rm v,tot}^{\rm s} = \sum\_{n=1}^{N} \frac{e^{-jk\_0 d\_n}}{d\_n} \cdot a \underline{\Gamma}\_{\rm v,n} \cdot \underline{E}\_{\rm v,n}^{\rm i} \tag{2}$$

Due to the single scattering approach, the model covers only the part of the power delay profile with relatively short excess delay times. For the reliable simulation of delay spreads longer multiple reflected propagation paths have to be considered. The intuitive approach would be to place additional scatterers around the higher order reflections points and to use the impinging reflected wave as an excitation, see Fig. 11. This would then have to be incorporated into the reflection path search algorithm of the ray tracing approach, which would require much computational effort. To keep the excess simulation time of the hybrid part of the model as short as possible, the multiple scattering processes are replaced here with "virtual" single bounce scatterers. These scatterers are placed at the point of the multiple reflections. Their scattering factors contain an additional term *e*−*jk*0*δ*, where *δ* corresponds to the path length between the point of the first interaction and the considered higher order interaction. This term adds *δ*/*c*<sup>0</sup> to the delay corresponding to the distance between the transmitter and the scatterer *d*geom.

**Figure 11.** Modeling approach for multiple reflections

Thus, the delay time similar to the delay of a propagation path containing one or more reflections can be realized. However, the amplitude of such a path decreases proportionally to *δ* · *d*geom whereas the amplitude of a path containing the reflection would experience a slower decay. To counterbalance this effect, an additional term *p* · *δ* is included in the scattering coefficients of the higher order scatterers resulting in the following expression for all scatterers:

$$
\underline{S} = (\mathfrak{a} + \mathfrak{p} \cdot \delta) \cdot \underline{\Gamma} \cdot e^{-j\mathbf{k}\_0 \delta} \tag{3}
$$

For the scatterers placed around single reflection, this expression reduces to *S* = *a* · Γ since in this case *δ* = 0. Thus, the resulting model is characterized by 4 parameters:


12 Will-be-set-by-IN-TECH

(a) Tx1 – PDP averaged over the angle (b) Tx1 – PDP averaged over the delay time

scenario data so far, as well as interactions with inhomogeneities inside the objects and with objects behind the walls. The delay time of the additional multi-path contributions due to the scattering points is approximately equal to the delay time of the reflected path. Their scattering coefficients are adjusted so that the resulting amplitudes of these multi-path

The number of scatterers *n* = 1... *N* is a model parameter and is assumed to be constant for all clusters. The scatterers are distributed uniformly on the objects' surface within a radius *r* around the reflection point. The scatterers whose position is outside the considered area are

In order to keep the model as general as possible, each scatterer is characterized by the complex full polarimetric scattering matrix **S**. The field scattered from the n-th scatterer **E**<sup>s</sup>

where **E**<sup>i</sup> is the incident field, *k*<sup>0</sup> is the wave number, and *d* is the distance between the scatterer

In this subsection, only the vertical co-polarized element *S*vv is considered. The parameterization of other scattering matrix components can be done in the same way. As the frequency band used is very wide, at least some of the contributions can be resolved by the system. Therefore, the scattering contributions in the model are coherently summed at the

To obtain the amplitudes of scattered contributions in the same order of magnitude as the amplitudes of the reflected path, their scattering factors are related to the reflection coefficient Γ by a proportionality factor *a*, which is derived from the measurements as well. The reflection

*<sup>d</sup>* · **<sup>S</sup>** · **<sup>E</sup>**<sup>i</sup> (1)

**<sup>E</sup>**<sup>s</sup> <sup>=</sup> *<sup>e</sup>*−*jk*0*<sup>d</sup>*

**Figure 9.** Averaged angle-dependent power delay profiles for the transmitter position Tx1.

components are slightly below the amplitude of the reflected path.

**Figure 10.** Modeling approach for single reflections.

is described in the frequency domain by:

and the observation point.

discarded.

receiver.


These parameters are estimated from the measurements. The derivation approach is described in the following Sections.

single position in the middle of the Rx and Tx array of an office scenario. The measured delay

Cooperative Localization and Object Recognition in Autonomous UWB Sensor Networks 193

The curves show that depending on the chosen model parameter (*a* and *p* have the strongest influence here) the inclusion of reflections of up to 3rd order influences the delay spread. The same has been observed in other scenarios and for the path loss. Thus, in the following the

To test the parameterized model, it is compared with measurements with respect to path loss, delay spread, azimuth spread, power delay profiles and azimuth spectra at the receiver [25]. For the estimation of the power delay profiles and azimuth spectra, the first Tx position and a rectangular track along the edges of the positioning table at Rx is considered. Each edge of the rectangular track is placed 9 cm (3 Rx positions) away from the edge of the positioning table. The estimation of azimuth angle is done using the sensor-CLEAN algorithm [8] using 4×4 elements with a spacing of 6 cm, with the midpoint at each comparison-track point. In contrast to the measurement the simulations can provide also the angle of arrival of individual paths. However, due to the enormous amount of data obtained if the properties of each individual path are recorded, it is more convenient to apply the estimation also to the simulation data. In this case, only the coherent sum of all paths for a particular Tx/Rx position has to be recorded. The placement of the comparison points and of the arrays used for calculating the angles of

**Figure 13.** Placement of the comparison points and of the arrays used for the calculation of AoA at the

The "array X" configuration is used for positions along the shorter edge, whereas the "array Y" configuration is used for positions along the longer edge of the rectangular positioner. The

**Figure 12.** Influence of the considered reflection order on the delay spread in scenario 2.

scatterers will be placed around the reflection points of up to the 3rd order.

spread for this point is 3.8 ns.

**3.3. Model performance**

rectangular positioner.

arrival (AoA) at the receiver is shown in Fig. 13 .
