# Characterization and modeling of temporal variations on an ultrawideband radio link

Patrice Pajusco, Pascal Pagani

► To cite this version:

Patrice Pajusco, Pascal Pagani. Characterization and modeling of temporal variations on an ultra-wideband radio link. IEEE Transactions on Antennas and Propagation, 2006, 54 (11-1), pp.3198 - 3206. 10.1109/TAP.2006.883961. hal-02316321

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# Characterization and Modeling of Temporal Variations on a Ultra-Wideband Radio Link

Pascal Pagani and Patrice Pajusco

France Telecom, Research and Development Division, RESA / NET

6 avenue des usines – BP 382 – 90007 Belfort Cedex – France

email : { pascal.pagani ; patrice.pajusco } @francetelecom.com

## Abstract

In order to develop efficient Ultra-Wideband (UWB) systems for high rate wireless links, an accurate knowledge of the propagation mechanisms is necessary. Anticipated usage scenarios in office or residential environments predict a significant impact of mobile persons on the UWB radio link. However, the issue of temporal variations in the UWB propagation channel has only scarcely been investigated so far. This paper presents a comprehensive study of the time variance of UWB channels. A real-time measurement campaign involving moving scatterers was performed in the 4 GHz - 5 GHz band. The analysis of measured data, regarding the shadowing effect and fast signal fluctuations, provides a detailed description of the phenomena involved in a time varying UWB channel. As a result, a complete model is described for the temporal variations observed on the main propagation paths in a fixed UWB link. By considering a set of independent propagation echoes followed by clusters of dense multipath, the modeling procedure is then extended for the generation of realistic UWB Channel Impulse Responses in a dynamic environment.
# 1. Introduction

Ultra-wideband (UWB) radio is a promising technology for short-range, high-rate wireless links, and has received enthusiastic attention from researchers and industrials for the last few years. For the purpose of simulation and design of future UWB-based communication systems, a precise knowledge of the UWB propagation channel characteristics is necessary. Thus, much effort has recently been expended on the design of UWB channel models ([1], [2], [3]). Significant research work has been carried out in this field by the IEEE 802.15.3a task group by providing a set of standard channel models, for the evaluation of UWB physical layer proposals [4].

Considering the anticipated usage scenarios for the UWB wireless technology [5], the corresponding radio channel seems most likely to undergo considerable variation over time. For portable devices like Personal Digital Assistants, spatial fluctuations are expected, as the transmitter, emitter, or both, may be displaced while in operation. On another hand, in many applications like office or residential WLANs, mobile people and pieces of furniture might act as moving scatterers in a fixed radio link, and hence generate temporal fluctuations.

For the development of efficient UWB communication systems, these time variations need to be properly taken into account, and a suitable channel model is necessary for the design of the system parameters. As an example, parameters related to temporal fading, such as the system symbol rate or the fading margin, need to be optimized in accordance with realistic channel realizations. A time varying channel model may furthermore be used in link level simulations for the assessment of the system robustness. However, while substantial modeling work has been achieved concerning the UWB channel under static conditions, the issue of time variance in UWB links has scarcely been addressed, due to the lack of suitable experimental data. A model including spatial fluctuations based on static measurements is proposed in [2], while theoretical investigations of the effect of moving scatterers are reported in [6] and [7].
In this paper, we propose an original model for the time variance of UWB channels. Using an innovative real-time channel sounder, we designed a propagation experiment to collect data in presence of moving scatterers, in the frequency range extending from 4 GHz to 5 GHz. The analysis of the measurement results provides insights of the propagation mechanisms involved in time varying UWB channels. The paper is organized as follows: Section 2 recalls the issues linked to the measurement of dynamic UWB channels, and presents our real-time sounding equipment. After the description of our measurement experiment (Section 3), Section 4 develops the characterization of the UWB channel temporal variations, through the study of both large-scale and small-scale fading, along with spectral analysis. Finally, Section 5 describes a complete model for the time variance due to mobile scatterers in a UWB propagation channel.

## 2. Real-time UWB Channel Sounding

The experimental observation of time variations in a UWB radio link necessitates the deployment of adequate equipment capable of sounding dynamic channels. Traditional Vector Network Analyzers are not suitable for such experiments, in consequence of the duration of the measurement process, lasting for several seconds. For real-time channel sounding, a first solution consists in emitting actual UWB pulses, while recording the channel impulse response (CIR) using a Digital Sampling Oscilloscope [8]. This technique, however, presents a low dynamic range, and the control on the transmitted waveform is limited. Another solution is the development of channel sounders based on the pulse compression technique, with ultra-wide bandwidth. For this purpose, pseudo-noise sequences with the required bandwidth are generated at the emitter, and the CIR is recovered at the receiver using some correlation method. The design of a 2 GHz bandwidth channel sounder is presented in [9], while the feasibility of real-time measurements in the 0.8 GHz – 5 GHz band in a Multiple Input, Multiple Output configuration has been demonstrated in [10]. The method enables measurements with a high
dynamic range, but presents some degree of complexity at the implementation stage. Hence, this
method has not been used so far to investigate the UWB radio channel under temporal
disturbances due to, e.g., moving people.

For our real-time experiment, an intermediate technique has been developed. Using a wideband
channel sounder, we measured several adjacent partial bands of 250 MHz each to scan the
desired ultra-wide bandwidth extending from 4 GHz to 5 GHz. We showed that the main issues,
i.e. dynamic switching of the partial bands, synchronization, and calibration, were conveniently
handled by applying minor changes to a Single Input, Multiple Output sounder. This principle
exploiting the duality between multiple input measurements and multi-band measurements, as
well as the full validation of the system were presented in [11].

3. Propagation Experiment

<figure><img src="image_2.png" /><figcaption>Fig 1. Experimental setup. F : forward movement, B : backward movement</figcaption></figure>

In order to evaluate the time variance observed in the UWB radio channel, a propagation
experiment was conducted in the premises of the laboratory France Telecom Division R&D, as
presented in Fig. 1.
**3.1. Measurement setup**

Our real-time UWB channel sounder was used to record consecutive samples of the CIR with a
repetition time set to 10 ms, hence measurements of Doppler shifts up to 50 Hz were achievable.
The scanned bandwidth extended from 4 GHz to 5 GHz, with a 2 MHz step. The Transmitter
(Tx) and Receiver (Rx) antennas were CMA 118/A UWB monocones presenting an
omnidirectional, relatively constant gain over the selected bandwidth. While the Rx antenna was
fixed at a height of 2.40 m, the Tx antenna was mounted on a trolley at a height of 1.35m.

**3.2. Experiment scenario**

All measurements took place near a bend of the building main hallway. In order to assess the
temporal variations of the UWB channel, the Tx antenna was located in the middle of the
hallway at a distance of 11 m from the Rx antenna. Measurement were taken over the fixed
radio link while groups of people were walking towards the end of the hallway and coming
back, occasionally obstructing the Line-Of-Sight (LOS) path and other main paths of the CIR.
The number of moving people in a group varied between 1 and 12. This situation could be
experienced by the user of a WLAN standing in a crowd of people. The overall measurement
process corresponds to a collection of 27 records of the time varying UWB channel containing
about 3000 CIRs each.

**4. Analysis of the UWB channel temporal variations**

A typical CIR collected during the experiment is represented in Fig. 2, where the excess delay
has been converted in excess path (m) for an easier interpretation. After the direct path (a),
whose length corresponds to the Tx-Rx distance (11 m), one can distinguish two main paths of
lengths 18 m and 42 m respectively. The first one (b) corresponds to a reflection on the wall
situated behind the one supporting the Rx antenna. The double transmission through the wall
supporting the Rx antenna explains the observed attenuation. The second path (c) is due to a
reflection on the wall opposite to the Rx antenna.

<figure><img src="image_3.png" /><figcaption>Fig 2. Typical channel impulse response (LOS)</figcaption></figure>

A first observation of the effect of people on the CIR is given in Fig. 3, where the time-varying
CIR is depicted in the case of 12 people walking back and forth through the radio link.
Successive measurements are represented from left to right, while the vertical axis represents the
excess delay converted in excess path (m). The influence of moving people on the CIR appears
clearly on this graph. The main paths (a) and (b) are regularly obstructed by moving people,
during both forward (t = 15 s to 27 s) and backward (t = 63 s to 74 s) displacements along the
hallway. At other values of the excess path, one can observe strong signal fluctuations, with
respect to the stationary part of the diagram. The shape in "V" formed by the fading parts of the
diagram is due to the hallway particular configuration : paths with larger delays correspond to
reflections or diffractions occurring farther in the hallway. They are thus still affected when
people reach the end of the hallway. This graph shows that the radio channel is not globally
stationary.
<figure><img src="image_4.png" /><figcaption>Fig 3. Time varying CIR in the case of 12 moving people</figcaption></figure>

4.1. Large-scale fading

As a first step in the analysis, we observed the large-scale fading generated by human beings in the vicinity of the radio link. For this purpose, we studied the slow temporal evolution of the mean power received in the LOS path in presence of people. When considering spatially varying radio signals, the estimate of the slow fading component is obtained by locally averaging the received power over a route of 20 to 40 wavelengths [12]. Similarly, in our experiment involving a time varying radio channel, fast fading fluctuations were eliminated by averaging the received power using a sliding window of duration *T* = 1.28 s. Over this period, the maximum elongation of a signal path scattered by a person moving at a speed *v* = 1 m.s⁻¹ is 2.v.T ≈ 38 λ. Other techniques, such as low-pass filtering the LOS signal, lead to similar smoothing results.

Figure 4 represents an example of large-scale fading pattern for one person moving across the LOS path. Different stages of the process are distinguishable. In the first regime (1), the person is sufficiently far away from the LOS path, and thus induces no effect on the received signal. In the second regime (2), the person is approaching the main path, possibly creating an additive,
scattered echo, or blocking an existing echo that previously caused destructive interference. As a result, one may occasionally observe a signal disturbance corresponding to an increase of up to 1 dB in the mean received power. In the third regime (3), the person acts as an obstruction of the main path, significantly decreasing the received power. In general, the progress of 1 person through the LOS path yields an attenuation of the mean power of about 8 dB, the shadowing effect lasting for about 4 s. In the fourth regime (4), the person once again acts as a scatterer, possibly disturbing the mean received power. Eventually, in the fifth regime (5), the person leaves the region corresponding to the LOS path delay bin, and does not affect the received signal anymore.

<figure><img src="image_5.png" /><figcaption>Fig 4. Example of large-scale fading pattern for the LOS component, 1 person</figcaption></figure>

Figure 5 present the aggregate effect of several persons passing through the main signal path. The obstruction duration increases with the number of persons, up to about 15 s for a group of 12 people. In this case, the maximum attenuation of the mean power is about 15 dB. This increase of the power attenuation with the number of persons could be expected: as several persons obstruct the main path simultaneously, the transmitted signal undergoes more severe attenuation. One clearly notices that the shadowing pattern obtained for groups of people is
composed of superimposed individual contributions. However, the particular effect of each person is not always distinguishable, as for example in the case involving 4 persons.

<figure><img src="image_6.png" /><figcaption>Fig 5. Typical large-scale fading patterns for the LOS component</figcaption></figure>

No significant change in the large-scale fading pattern was observed when reducing the analyzed bandwidth. As real-time UWB sounders are not available for bandwidths of several GHz, the experimental analysis for larger bandwidth is not yet possible. Nevertheless, one may expect a decrease in the individual shadowing duration with increasing bandwidth, linked to the shrinking of the region around the main path where scattered echoes fall within the main path delay bin.

## 4.2. Small-scale fading

In addition to the large-scale fading generated by moving people, small-scale fading is observed while people are walking in the vicinity of the radio link. As depicted in Fig. 6, the signal received at delays corresponding to the main paths of the CIR may be thought of as a vector summation of several multipath components, as would be the case in a typical situation exhibiting Rician fading. We will distinguish between the dominant component, accounting for
the signal normally received in a static environment, and the random component, which represents the summation of all waves scattered by moving people.

<figure><img src="image_7.png" /><figcaption>Fig 6. Vector decomposition of the received signal</figcaption></figure>

In order to analyze the small-scale fading due to temporal fluctuations, all conditions encountered in the case of spatial fluctuations (i.e. the case of moving antennas) are not met, and some specific issues need to be taken into account. First, the dominant component represents a fixed path, but is occasionally obstructed by passing persons. As such, this component presents time varying amplitude but rather stable phase. Consequently, spectral analyses may not be performed on the total received signal, as the dominant component would generate a DC bias. This effect does not appear in traditional analysis of spatially varying channels, as all components of the CIR may be considered as rotating phasors. Second, the random component represents fast fluctuations due to the presence of moving scatterers. As such, this component encompasses all incoming waves scattered by one or several mobile persons. In a stationary situation, fast fluctuations are generally normalized by simply scaling with respect to the mean received power. Considering the non-stationarity of the dominant component, such a normalizing procedure is proscribed, as the value of the received power at a given instant *t* would directly impact the fast fluctuations amplitude. To properly analyze the small-scale fading
observed in our experiment, we first isolated the random component, and subsequently
considered the distribution of the amplitude in the total received power. In order to separate the
random component, the dominant component was vectorially subtracted from the received
signal. Its amplitude was computed using a sliding window of duration 1.28 s on both real and
imaginary parts of the signal, and its constant phase was extracted from the measurement
periods corresponding to a static environment.

<figure><img src="image_8.png" /><figcaption>Fig 7. Fluctuations of the random component, LOS path (12 persons)</figcaption></figure>

Figure 7 represents both magnitude and phase fluctuations of the random component extracted
from the signal received via the main path, when obstructed by 12 moving people. The
corresponding collected signal is the one depicted in Fig. 5 (right hand side). Interestingly, the
magnitude of the small-scale fading presents a high degree of regularity, compared to the non-
stationary large-scale fading pattern. One may observe that the time separation between a peak
and a null is about 0.5 s, indicating a channel coherence time in the order of 0.1 s. Such a
coherence time is greater by one order of magnitude than coherence times generally observed in
spatially varying channels. This may be explained by the fixed position of the antennas, as channel variations are generated by moving scatterers only. As will be shown in section 5.2, the Doppler effect generated in this case is much less severe with respect to a configuration involving mobile terminals.

Both visual inspection of the temporal fading CDF and a Kolmogorov-Smirnov testing procedure revealed that in almost all measurement records, the fading amplitude distribution of the random component could be closely fitted to a Rayleigh distribution, independently of the number of moving people. Considering the total signal received at delays corresponding to the main paths of the CIR, composed of a Rayleigh random component and a dominant component of greater amplitude, the resulting signal hence follows a Ricean distribution. The Ricean *K* parameter is defined as the power ratio between the deterministic component and the random fluctuations. As the deterministic component presents a slowly time varying amplitude, the *K* parameter varies over time accordingly, depending on the obstruction of the main path. One may notice in this example that the mean signal power of the random component is about 12 dB below the unobstructed signal level. Depending on the attenuation level of the deterministic signal, the *K* parameter varies from about 12 dB down to less than -20 dB, where the total received signal follows a Rayleigh distribution. These results were observed on other measurement records, with maximum values of *K* varying between 8 and 13 dB. In cases where only 1 or 2 persons were crossing the radio link, the minimum value of *K* was about 5 dB, but the rapid obstruction did not allow for a significant collection of data.

In a previously published experiment involving moving people in a fixed UWB link [13], we observed that the Weibull distribution was a good fit to the variations of the signal envelope. Constructing a Ricean-like variable *r* from a random component with power $2\sigma^2$ and a deterministic component with amplitude *A* determined by its density function $p_A(A)$, the overall PDF may be computed as:
$$ (1) \qquad p_r(r) = \int_0^\infty \frac{r}{\sigma^2} e^{-\frac{r^2+A^2}{2\sigma^2}} \times I_0\left(\frac{rA}{\sigma^2}\right) \times p_A(A) \times dA, $$

where we recognize the Ricean distribution in the left-hand part of the integral. Numerical investigations showed that the main effect of the amplitude variations in the deterministic component was an increase in the weight of the distribution tail. Heavy-tailed distributions, like the Weibull distribution, may hence sensibly appear in experimental results.

Finally, the phase of the random component depicted in Fig. 7 presents a rather unstable behavior while people are interfering with the main path of the CIR, with distinct periods of linear progress. However, one may note rapid and significant phase shifts at instants corresponding to fading nulls (indicated by arrows on the figure), due to the quickly decreasing power.

### 4.3. Spectral analysis

Temporal variations of the signal received via the main paths of the CIR have been studied in the frequency domain. Figure 8 depicts the average Power Spectral Density (PSD) of the random component for the signal corresponding to the LOS path. Measurements involving 1 to 12 moving persons are taken into account, and we distinguished the collected records according to the direction of the movement. The general shape of the PSD is triangular, with an average Doppler shift centered around 0 Hz. The spectrum width was computed in terms of Doppler spread $f_{RMS}$, as defined in equation (2), where $S(f)$ represents the PSD for the Doppler shift $f$, and $f_a$ represents the average Doppler shift.

$$ (2) \qquad f_a = \frac{\int_{-\infty}^{\infty} f \cdot S(f) \cdot df}{\int_{-\infty}^{\infty} S(f) \cdot df}, \qquad f_{RMS} = \left[ \frac{\int_{-\infty}^{\infty} [f - f_a]^2 \cdot S(f) \cdot df}{\int_{-\infty}^{\infty} S(f) \cdot df} \right]^{\frac{1}{2}} $$
In this calculation, Doppler shifts where $S(f)$ was 25 dB or more below the PSD maximum level were eliminated to mitigate the effect of noise. The computed Doppler spread varied between 0.6 and 3.3 Hz with no marked influence of the number of moving persons. Similar 0 Hz-centered, triangular shapes of the PSD are reported from CW measurements of the channel temporal variations performed at frequencies around 1 GHz in [14] and [15].

<figure><img src="image_9.png" /><figcaption>Fig 8. Average PSD of the random component for forward and backward motions, LOS path</figcaption></figure>

As depicted in Fig. 8, some asymmetry has been observed between measurements performed during forward and backward movements. Table 1 presents the average distribution of power between positive and negative Doppler shifts when groups of people are walking forward and backward through the LOS path. Over all data records collected when people were crossing the link in the forward direction, two thirds of the power corresponding to temporal fluctuations is located in the negative part of the PSD. When people are walking in the backward direction, the situation is inverted. This trend is still observed when considering each number of moving persons individually.
<table><caption>Table 1. Power distribution between negative and positive Doppler shifts</caption><thead><tr><th rowspan="2"># moving persons</th><th colspan="3">Forward direction</th><th colspan="3">Backward direction</th></tr><tr><th># meas.</th><th>Neg. Doppler shifts</th><th>Pos. Doppler shifts</th><th># meas.</th><th>Neg. Doppler shifts</th><th>Pos. Doppler shifts</th></tr></thead><tbody><tr><td>1</td><td>3</td><td>71 %</td><td>29 %</td><td>2</td><td>27 %</td><td>73 %</td></tr><tr><td>2</td><td>2</td><td>65 %</td><td>35 %</td><td>2</td><td>41 %</td><td>59 %</td></tr><tr><td>4</td><td>3</td><td>70 %</td><td>30 %</td><td>3</td><td>34 %</td><td>66 %</td></tr><tr><td>6</td><td>1</td><td>40 %</td><td>60 %</td><td>1</td><td>29 %</td><td>71 %</td></tr><tr><td>8</td><td>1</td><td>92 %</td><td>8 %</td><td>1</td><td>26 %</td><td>74 %</td></tr><tr><td>10</td><td>2</td><td>63 %</td><td>37 %</td><td>2</td><td>42 %</td><td>58 %</td></tr><tr><td>12</td><td>2</td><td>58 %</td><td>42 %</td><td>2</td><td>31 %</td><td>69 %</td></tr><tr><td>All</td><td>14</td><td>66 %</td><td>34 %</td><td>13</td><td>34 %</td><td>66 %</td></tr></tbody></table>

## 5. Modeling approach

In order to model the temporal fluctuations observed on the main paths of the CIR in presence of moving people, we will distinguish between the effects observed on the dominant component and the random component of the total received signal. The dominant component is mainly affected by obstructing people and is thus responsible for the large-scale fading observed on the global signal. The random component results from the summation of incoming waves scattered by moving people and generates small-scale fluctuations. The two components are finally added and global parameters, such as the distribution of the signal amplitude, should be computed from to total received signal. Note that a single person may act as an obstruction and as a scatterer simultaneously. These two effects will however be considered separately in the development of the model.
## 5.1. Dominant component

As observed in our measurements, individual contributions are clearly distinguishable in the large-scale fading pattern generated by a group of people. The modeling approach will thus consist in producing large-scale fading templates corresponding to the effect of 1 person, and then summing time-shifted templates according to the instants where people are passing through the signal path. Time shifts may be randomly chosen, or computed according to the location of people in, e.g., a ray tracing simulation.

When represented in a logarithmic scale, the large-scale fading pattern caused by 1 moving person presents a Gaussian-like shape, as depicted in Fig. 4. Accordingly, two functions based on the Gaussian curve are proposed to model the individual large-scale fading pattern affecting the received power in dB.

$$ (3) \qquad \begin{aligned} g_1(t) &= -A_s \cdot \exp\left(-2 \cdot \left(t - t_0\right) \cdot \frac{2}{T_s}\right) \\ g_2(t) &= -A_s \cdot \left(1 - \left(t - t_0\right) \cdot \frac{2}{T_s}\right)^2 \cdot \exp\left(-u \cdot \left(t - t_0\right) \cdot \frac{2}{T_s}\right) \end{aligned} $$

In (3), $A_s$ represents the maximal shadowing attenuation in dB, $T_s$ represents the shadowing duration in seconds, and $t_0$ represents the shadowing instant. Compared to $g_1(t)$, the small positive disturbances observed in the measurements at the margins of the large-scale fading pattern are taken into account in $g_2(t)$, by appropriately setting parameter $u$. Recommended values are in the range from 5 dB to 10 dB for $A_s$, in the range from 3 s to 5 s for $T_s$, and about 1 for $u$.

Note that these values are calibrated from our experiment involving a bandwidth of 1 GHz. In particular, the value of $T_s$ should theoretically decrease for greater bandwidths, as suggested in section 4.1. Other parameters could be added to this first model as other experiments will be conducted, as for instance the angle of incidence of the person entering the main path.
## 5.2. Random component

Regarding the small-scale fading generated by the additional random component, we will first investigate further the physical phenomena at play in order to explain the observed spectral characteristics. The final model will then take account of the small-scale variations in a statistical way, by generating a complex random process with appropriate amplitude distribution and PSD.

<figure><img src="image_10.png" /><figcaption>Fig 9. Uniformly distributed scatterers model : (a) antennas below body height, (b) Rx antenna above body height</figcaption></figure>

A physical interpretation of the observed characteristics for the temporal fading is proposed as depicted in Fig. 9. A group of persons walking in the vicinity of the LOS path may be considered as a set of uniformly distributed scatterers. We first consider the simple case where both Tx and Rx antennas are situated below the average body height (a). One should note that we are interested in the signal arriving in a single delay bin only; hence the considered scatterers are located in a 3D ellipsoid with foci Tx and Rx. The allowed excess delay corresponds to the size of a delay bin, which is 1 ns for a bandwidth of 1 GHz. It may be argued
that moving persons act not only as point scatterers but also as obstructions within the ellipsoid. However, in the present case, all waves scattered within the ellipsoid undergo a similar attenuation due to obstructing persons, and thus the assumption of uniform effect for all scatterers holds. Using classical computation of Doppler spectrum [16], the Doppler shift $f$ generated by an elementary scatterer $S$ evolving as depicted in Fig. 9 with a speed $v$ may be computed as :

$$ (4) \qquad f = -f_0 \frac{v}{c} \cdot (\cos(\alpha) + \cos(\beta)) $$

where $\alpha$ and $\beta$ are given on Fig. 9, $c$ is the speed of light, and $f_0$ is the central frequency of the transmitted signal. Note that Fig. 9 presents a 2D view of the configuration for clarity, but equation (4) holds for the 3D case, provided that the angles $\alpha$ and $\beta$ are suitably measured with respect to the displacement of the scatterer $S$. Some observations are worth mentioning at this point. Firstly, this model makes clear that all moving scatterers generate Doppler shifts as the scattered wave elongates, except scatterers evolving along the Tx-Rx path, where no path elongation is present. Secondly, as scatterers progress between the Tx and Rx locations, an increase in the Tx-S path corresponds to a decrease in the S-Rx path, and vice versa. Hence, the global elongation of the Tx-S-Rx path is quite low with respect to path variations observed in a situation involving moving terminals. As a result, temporal channel fluctuations generate less Doppler shifts, and accordingly lead to a higher channel coherence time, when compared to spatial fluctuations.

The global PSD $S(f)$ may be determined by integrating the Doppler shifts generated by all scatterers uniformly distributed within the ellipsoid. A close form for $S(f)$ is not directly available. Instead, we computed an estimate of $S(f)$ using a Monte Carlo procedure, and setting the parameters $f_0 = 4.5$ GHz, and $v = 1$ m.s$^{-1}$. The result depicted in Fig. 10 (thin dotted line)
shows that a uniform distribution of scatterers within the ellipsoid leads to a triangularly shaped
PSD, as observed in our experiment.

<figure><img src="image_11.png" /><figcaption>Fig 10. Estimated PSD of the random component with models (a) and (b)</figcaption></figure>

If we now consider a case where the Rx antenna is elevated above body height as in Fig. 9 (b),
the possible location of scatterers is limited to a height of about 1.80 m. In this situation,
scatterers may still be assumed to be uniformly located within this delimited area, but the
obstruction of scattered waves is not homogeneous anymore. More precisely, the signal
scattered near the Tx antenna undergoes less attenuation, since part of the Tx-S-Rx path benefits
from LOS propagation. In the Monte Carlo estimation of S(f), we used different attenuation
factors to account for the possible obstruction of scattered paths. The results are depicted in Fig.
10 (bold lines). As in our experiment, one may observe an asymmetry in the PSD, which is
linked to the forward or backward direction of the scatterers. Thus, the PSD asymmetry seems to
be mostly linked to the variable shadowing of the scattered paths.

More experimental measurements are needed to build on these first observations. An example
implication of this model would be that the Doppler spread should depend on the signal
bandwidth, since it dictates the ellipsoid dimensions. Due to the limited width of the hallway
where the experiment took place, this effect could not be observed when reducing the processed
bandwidth on our measurement data. Real time measurements of UWB channels with bandwidths of several GHz are not yet available. However, the physical interpretation described above may lead to theoretical conclusions on the effect of an increased bandwidth. As the frequency bandwidth of the signal increases, the ellipsoid dimensions will shrink, and thus less scatters will interfere in the main path delay bin. From equation (4), it is clear that waves scattered nearer from the main path generate lower Doppler shifts. Hence an increased bandwidth would lead to a reduced Doppler spread. As a consequence, the effect of the random component would decrease, leading to a more deterministic situation.

As a first approach, a 0 Hz-centered, triangular shape of the PSD may be assumed in the modeling process. We recommend using the Laplacian PSD, which may be formulated as :

$$ (5) \qquad S(f) = \frac{\sigma_0^2}{\sqrt{2} \cdot f_{\text{RMS}}} \cdot \exp\left(-\frac{\sqrt{2}}{f_{\text{RMS}}} \cdot |f|\right), $$

where $\sigma_0^2$ represents the signal power, and $f_{\text{RMS}}$ is the Doppler spread. As more experimental data will become available, this first model could be refined, particularly in order to take the potential asymmetry of the distribution into account. In accordance with our measurement results, typical values of $f_{\text{RMS}}$ should be in the range from 1 Hz to 3 Hz.

### 5.3. Time variance model

This section presents a global model for the effect of moving people crossing a UWB link. A simulation of the time variance observed on the signal received at one of the main paths of a CIR may be generated by completing the following steps.

1) Generate $N_p$ large-scale fading templates $\{s_k(t)\}_{k=1...N_p}$ corresponding to the individual effects of $N_p$ moving persons, using one of the functions given in equation (3) and the parameter settings suggested thereafter.
2) Select $N_p$ time shifts $\{t_k\}_{k=1...N_p}$ corresponding to the passing instants of the $N_p$ moving persons. These time shifts can be randomly generated or deterministically computed according to the situation geometry.

3) Compute the dominant component amplitude variations $d(t)$ in linear scale according to equation (6).

$$ (6) \qquad d(t) = \prod_{k=1}^{N_p} 10^{s_k(t-t_k)/20} $$

4) Generate complex random fluctuations $r(t)$ following a Rayleigh amplitude distribution and having a Laplacian PSD. The Doppler spread $f_{RMS}$ should be in the range from 1 Hz to 3 Hz (see Section 5.2). The mean power of the random component should be 8 dB to 13 dB below the power level of the non-obstructed deterministic component (see Section 4.2).

5) Compute the complex time variations $a(t)$ of the received signal by vectorially adding the deterministic and random components, i.e. $a(t) = d(t) + r(t)$. In particular, if the considered CIR path undergoes a power attenuation $A_0$ when not obstructed, the amplitude variations of the received signal are expressed in a logarithmic power scale as :

$$ (7) \qquad A(t) = A_0 - 20 \cdot \log_{10}(|d(t)| + r(t)) $$

One critical point in this model could be the generation of a random component with arbitrary amplitude distribution and arbitrary PSD. In practice, as the targeted Rayleigh distribution may be generated from a complex Gaussian process, a range of implementation methods are available to fulfill both amplitude and spectral requirements. A thorough discussion on this topic is proposed in [17]. We used the Method of Exact Doppler Spread developed therein, with some minor modifications to adapt the original algorithm to the Laplacian PSD (see Appendix).
<figure><img src="image_12.png" /><figcaption>Fig 11. Simulated large-scale fading patterns for the LOS component</figcaption></figure>

Examples of simulated fading patterns corresponding to 1, 4 and 12 persons are given in Fig. 11.
In this simulation, the Doppler spread $f_{RMS}$ was set to 1.2 Hz, and the power of the random
component was set 13 dB below the power of the non-obstructed deterministic component. One
can observe a close similarity between the simulated (Fig. 11) and the measured (Fig. 5) time
variations in the received signal. As parts of the simulated signal (e.g. the passing instants of
mobile persons, or the variations of the random component) are generated from random
processes, simulations and measurement are not expected to be identical. However, the large-
scale fading pattern assigned to the dominant component produces realistic slow fading
variations of the total received power. Furthermore, the design procedure of the model ensures
that the fluctuations of the random component present a Rayleigh amplitude distribution and the
selected Doppler spread. Hence, the proposed model could be used to account for the effect of
moving scatterers on a fixed UWB radio link in a rather realistic way.

**5.4. Model extension**

The algorithm presented above describes how to model the effect of moving persons on the
signal received from the main paths in the CIR. A simple extension of this model may be
applied in order to obtain a set of complete time varying CIRs. The first step is to generate a CIR corresponding to a static environment. This can be done using a statistical procedure such as, e.g., one of the channel models developed by the IEEE 802.15.3a task group [4]. Alternatively, the static CIR may be deterministically generated using a ray tracing approach. For all delays corresponding to the main paths of the CIR, the abovementioned algorithm is then applied to simulate the effect of moving persons. In the case of a statistical CIR, the passing instants computed for each delay should be randomly generated. If the CIR results from a ray-tracing approach, the passing instants may be computed according to the trajectory of each person in the environment geometry. Finally, the remaining delays of the CIR correspond to clusters of dense multipath. As we already observed from preliminary experiments involving moving persons [13], the temporal fluctuations experienced at these delays should be modeled by simply applying a Rayleigh distribution to the signal amplitude.

A similar procedure is suggested in [7], but the theoretical concepts developed therein are based on the obstruction effect only. As a result of our measurement-based method, the time-varying CIRs produced by our extended model are expected to closely approach the time variance experienced in a real UWB system.

## 6. Conclusion

In a context of high-rate, office or residential WLAN application, UWB wireless systems are likely to undergo significant temporal variations due to the presence of mobile scatterers in the vicinity of the radio link. Nevertheless, most UWB propagation studies are based on static measurements and this topic has been scarcely addressed. In this paper, we presented a comprehensive characterization of the time variance induced by moving persons in a fixed UWB link. Based on a set of real-time measurements in the 4 GHz – 5 GHz band, the analysis
revealed the impact of the shadowing effect on the main paths of the CIR. Furthermore, we showed that moving people caused additional random fluctuations, whose amplitude could be fitted to a Rayleigh distribution, with spectral components following a Laplacian PSD. From these observations, a model has been proposed to account for the temporal variations experienced on the main paths of the CIR, and a set of measurement-based parameter was provided. Finally, an extension of this model was described for the generation of reliable time varying CIR for an UWB link in a dynamic environment. The implementation of this model for link level simulations should greatly improve the design of future UWB systems, by providing an accurate description of the propagation channel under realistic usage conditions.

7. References

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2. J. Kunisch and J. Pamp, "An Ultra-Wideband Space-Variant Multipath Indoor Radio Channel Model," in *Proc. IEEE Conf. on Ultra Wide Band Systems and Technologies*, Reston, VA, Nov. 2003, pp. 290-294.

3. S. S. Ghassemzadeh, R. Jana, C. W. Rice, et al., "Measurement and modeling of an ultra-wide bandwidth indoor channel," *IEEE Trans. Commun.*, vol. 52, no. 10, pp. 1786-1796, Oct. 2004.

4. J. Foerster, Ed., "Channel Modeling Sub-committee Report Final," IEEE P802.15 Working Group for WPANs, Tech. Rep. IEEE P802.15-02/490r1-SG3a, 2003.

5. D. Porcino and W. Hirt, "Ultra-wideband radio technology: potential and challenges ahead," *IEEE Commun. Magazine*, vol. 41, no. 7, pp. 66-74, July 2003.
6. S. V. Schell, "Analysis of Time Variance of a UWB Propagation Channel," IEEE P802.15 Working Group for WPANs, Tech. Rep. IEEE P802.15-02/452r0-SG3a, Nov. 2002.

7. A. F. Molisch, "Time variance for UWB wireless channels," IEEE P802.15 Working Group for WPANs, Tech. Rep. IEEE P802.15-02/461r1-SG3a, Nov. 2002.

8. M. Z. Win, R. A. Scholtz, and M. A. Barnes, "Ultra-Wide Bandwidth Signal Propagation for Indoor Wireless Communications," in *Proc. IEEE Int. Conf. on Commun.*, Montreal, June 1997, pp. 56-60.

9. T. Takeuchi and M. Tamura, "A Ultra-Wide Band Channel Sounder for Mobile Communication Systems," in *Proc. IEEE Int. Symp. on Personal, Indoor and Mobile Radio Commun.*, San Diego, CA, Sept. 2001, vol. 2, pp. 111-115.

10. R. Zetik, R. Thomä, and J. Sachs, "Ultra-Wideband Real-Time Channel Sounder Design and Application," presented at the COST 273 Workshop, Prague, Sept. 2003, Technical Document TD(03)201.

11. P. Pajusco and P. Pagani, "Extension of SIMO Wideband Channel Sounder for UWB Propagation Experiment", in *Proc. IEEE Conf. on Ultra Wideband Systems and Technologies*, Reston, VA, Nov. 2003, pp. 250-254.

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13. P. Pagani and P. Pajusco, "Experimental Assessment of the UWB Channel Variability in a Dynamic Environment," in *Proc. IEEE Int. Symp. on Personal, Indoor and Mobile Radio Commun.*, Barcelona, Sept. 2004, vol. 4, pp. 2973-2977.

14. H. Hashemi, M. McGuire, T. Vlasschaert, et al., "Measurements and modeling of temporal variations of the indoor radio propagation channel," *IEEE Trans. Vehicular Technol.*, vol. 43, no. 3, pp. 733-737, Aug. 1994.
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17. M. Pätzold, *Mobile Fading Channels*. Chichester: Wiley, 2002.

## 8. Appendix

The simulation of a random component with Rayleigh amplitude distribution and arbitrary PSD is based on the generation of a complex deterministic Gaussian process, defined as [17, Eq. (4.5)]:

$$ (8) \qquad \tilde{\mu}(t) = \tilde{\mu}_1(t) + j \cdot \tilde{\mu}_2(t), $$

where the real deterministic Gaussian processes $\tilde{\mu}_1(t)$ and $\tilde{\mu}_2(t)$ are given by [17, Eq. (4.4)]:

$$ (9) \qquad \tilde{\mu}_i(t) = \sum_{n=1}^{N_i} c_{i,n} \cos(2\pi f_{i,n} t + \theta_{i,n}), \quad i = 1, 2. $$

The parameters $c_{i,n}$, $f_{i,n}$, and $\theta_{i,n}$ are respectively called the Doppler coefficients, discrete Doppler frequencies and Doppler phases. The number of harmonic functions $N_i$ was fixed to 25 in our simulation.

For the computation of simulation parameters, the Method of Exact Doppler Spread is detailed for the Jakes PSD and the Gaussian PSD in [17, pp. 128-133]. In the selected method, the values of $c_{i,n}$ and $\theta_{i,n}$ hold for any type of PSD. For the computation of the discrete Doppler frequencies in the case of a Laplacian PSD, we adapted the approach used for the Gaussian PSD through minor modifications. More precisely, for values of $n$ lying between 1 and $N_i - 1$, the discrete
Doppler frequency $f_{i,n}$ is the solution of the following equation [17, Eq. (5.27), (5.28), and comments on p. 131] :

$$ (10) \qquad \frac{\sigma_0^2}{2} \left( 1 + \frac{2n-1}{2N_i} \right) = \int_{-\infty}^{f_{i,n}} S(f) df, $$

where $\sigma_0^2$ represents the signal power.

The value of $f_{i,Ni}$, selected so as to guarantee that the model Doppler spread equates the theoretical Doppler spread, is given by [17, Eq. (3.13b), (3.15b), and (5.76b)] :

$$ (11) \qquad f_{i,N_i} = \sqrt{N_i \cdot f_{RMS}^2 - \sum_{n=1}^{N_i-1} f_{i,n}^2}, $$

where $f_{RMS}$ is the Doppler spread.

Considering a Laplacian PSD as defined by equation (5), equation (10) yields to :

$$ (12) \qquad \frac{\sigma_0^2}{2} \left( 1 + \frac{2n-1}{2N_i} \right) = \sigma_0^2 \cdot \left( 1 - \frac{1}{2} \cdot \exp \left( -\frac{\sqrt{2}}{f_{RMS}} \cdot f_{i,n} \right) \right), \quad n = 1..N_i-1 $$

Hence :

$$ (13) \qquad f_{i,n} = -\frac{f_{RMS}}{\sqrt{2}} \cdot \ln \left( 1 - \frac{2n-1}{2N_i} \right), \quad n = 1..N_i-1. $$

Finally, $f_{i,Ni}$ is computed according to equation (11).