Estimated antenna gains at 0.1 m separation for different bandwidths.

## 1. Introduction

The subject of this chapter is to investigate the effect of bandwidth on a short range indoor UWB channel performance. This research is based on a measurement campaign performed on a wooden desk surface placed in an office room at our faculty building. A vector network analyzer (VNA) is used to sweep the 1 GHz, 2 GHz, 5 GHz and 7.5 GHz bandwidths centered at 6.85 GHz, obtaining the frequency response of the channel. Using the VNA time domain capability the channel impulse response is obtained. This is equivalent to sounding the channel with frequency chirp pulses equal in duration to the inverse of the frequency bandwidth. In other words, a narrower bandwidth results in a wider pulse in time domain.

Although the measurements are performed in same environment for all bandwidths, it is expected that an UWB channel itself would not be equally perceived by different pulse widths. A wider system bandwidth results in shorter pulses, which in turn account for finer temporal and spatial resolution. In this way more multipath components can be resolved as the pulses overlap in a lesser extent.

The fundamental differences between an UWB channel and a narrowband channel arise from the frequency selectivity of the propagation process (Molisch, 2005). As the UWB signal has a wide frequency spectrum which may extend to several gigahertz, the frequency dependence of diffraction/reflection coefficients and dielectric constants can be significant (Di Benedetto et al., 2006). A number of papers report on the effect of carrier frequency on channel parameters. One such investigation (Cassioli et al., 2004) finds a strong dependence between the path loss model exponent and the carrier frequency, yet states that there is no correlation with the bandwidth. (Ghassemzadeh et al., 2005) presented an extensive measurement campaign at two different bandwidths (1.25 GHz and 6 GHz) centered at 5 GHz, reporting mostly minor differences in parameter values between the two bandwidths. Another paper (Choi et al., 2009) models the path loss exponent variation as a function of frequency. A research project (Chang & Tarng, 2007) investigates the effects of bandwidth on observable multipath clustering and Δ-*K* model parameters for an indoor UWB wireless channel with signal bandwidths of 0.5, 1 and 2 GHz. However, to authors’ knowledge, so far there have been no attempts to investigate the effects of bandwidth on estimating the path loss, shadowing, mean excess delay and RMS delay spread in short range UWB scenarios, which are the key parameters for assessing the link budget, signal-to-noise ratio and intersymbol interference of the system.

The next section of the chapter explains the measurement procedure and equipment and describes the measurement environment. The subsequent sections present the path loss, shadowing, mean excess delay and RMS delay spread parameter values estimated from the measured power delay profiles, respectively. The obtained results are discussed in the seventh section. The chapter is concluded in the eighth section, briefly summarizing all the key findings of this research.

## 2. Experimental setup

The measurement campaign took place on an empty desk in one of the offices at our faculty building. The surface of the desk is cleared to ensure the line of sight (LOS) between the transmitter and the receiver. The desk used in measurements is made of wood, chipboard and MDF. Inner walls that separate offices and laboratories are mainly made of plasterboard constructed with a thin wire grid composition, while the external wall and floors are made of reinforced concrete. The floor is entirely covered with wooden parquetry. The doors are made of plywood, while the office furniture is made of various wooden materials and glass. In the vicinity of the desk on which the measurements are conducted is another desk with the measurement equipment and two cabinets in the bottom left corner of the office, as shown on the office plan on Fig. 1. This additional furniture in the office is introduced as an intentional scattering system to approximate a real-life scenario.

A 1.6 m x 0.7 m grid with 0.1 m spacing is drawn on a sheet of paper (Fig. 2) which is fixed on a surface of a plain office desk. This forms a matrix of 17 x 8 measurement points across the desktop. The transmitting antenna (presented by a red disk in Fig. 2) is placed on the top of the 9^{th} column in a fixed position. The receiving antenna (presented by a blue disk in Fig. 2) is moved along the remaining 135 points for each measurement. Both antennas are erected on styrofoam blocks at the same height of 4.5 cm with their azimuth planes being parallel to the desk surface (Θ = 0°).

### 2.1. Measurement setup

The measurement setup is presented on Fig. 3. The transmitting antenna (Tx) is connected to the port 1 of the HP 8720A vector network analyzer (VNA) by a semi-rigid coaxial cable. The receiving antenna (Rx) is connected to the port 2 of the VNA by a flexible coaxial cable. The attenuation of the cables is compensated by the calibration procedure. The measured data from the VNA is transferred by the HP interface bus (HP-IB) to the data acquisition PC (PC-DAQ), where the data is stored for further processing.

#### 2.1.1. Vector network analyzer

A vector network analyzer (VNA) is used to measure the system’s forward complex transmission coefficients *S* _{21}(*f* _{i }) at 801 discrete evenly spaced frequencies within a given frequency span. In this way the band-limited transfer function of the system *H* is obtained:

where *H* _{meas }is the measured transfer function and *W* is the selected transformation window of the VNA.

Using an inverse Fourier transform ℑ^{-1}, the measurement results can be observed in the time delay domain, presenting the power delay profile (PDP) which gives the time distribution of the received signal power from a transmitted pulse:

The measured data acquired from the VNA thus presents the frequency averaged power delay profiles.

The excess delay *t* is obtained by subtracting the time of arrival *τ* _{0} of the first multipath component of the power delay profile from the time delay *τ* relative to the time instant of transmitting the pulse:

By activating the VNA’s averaging function, the last 16 measurements are averaged to reduce the temporal variations in the system. This results in a time averaged power delay profile:

where *N* =16.

Prior to each measurement the VNA is calibrated using a specific calibration standard. The measured data is acquired via HP-IB interface to a PC for further analysis and correction. Before the parameter extraction procedure each measured PDP is corrected with respect to the predefined threshold, which was set to 5 dB above the noise level for all measured points. This correction sets all the delay bins with energies below this threshold to zero-energy bins.

#### 2.1.2. Antennas

A pair of omnidirectional UWB antennas used in this measurement campaign was built according to the design proposed in (Taniguchi et al., 2006). To verify the omnidirectionality of the built antennas, their radiation patterns were measured in a TESEQ 750 GTEM cell at different frequencies generated by a HP 8340A synthesized sweeper. This method is based on measuring the power received by antenna under test (AUT) which is placed inside the cell. The received power was measured using a Rohde&Schwarz NRP-Z21 universal power sensor. Electric field in the vicinity of the AUT is measured by an isotropic electric field probe HI-4455 positioned next to the AUT. The antenna gain *G* in dBi is calculated using the following expression (Živković & Šarolić, 2010):

where *f* is the signal frequency in Hz, *P* _{rec }is the power received by AUT expressed in dBm, and *E* _{i }is the incident electric field in dBV/m. The radiation patterns measured at 4 GHz, 7 GHz and 10 GHz are presented on Fig. 4.

In addition, the VNA was used to measure the VSWR throughout the widest frequency bandwidth of 7.5 GHz, centered at 6.85 GHz. A full port calibration was performed before each measurement. The results, presented on Fig. 5, show that the VSWR is less than 2.5 throughout the entire frequency span.

Finally, the power delay profiles for different bandwidths were measured at a reference distance *d* _{0} (= 0.1 m) at 0°, 45°, 90°, 135° and 180° in azimuth plane, while keeping both antennas at same height *h* (= 4.5 cm). Averaging the measured results and calculating the path loss from the power delay profile (Section 3) the total path loss at 0.1 m was estimated:

where *PL* _{FS }is the free space path loss, *G* _{r }and *G* _{t }are receiving and transmitting antenna gains, respectively, all expressed in dB.

Applying the Friis equation with *f* _{c }(= 6.85 GHz) as the center frequency, *c* (= 3*10^{8} m/s) as the velocity of light and *d* _{0} (= 0.1 m) as a referent antenna separation, the free space path loss is obtained:

Under the assumption that antenna gains are equal (*G* _{r }= *G* _{t }= *G* _{a }) we estimate the antenna gain within a given bandwidth:

The results are shown in Table 1.

Bandwidth | 1 GHz | 2 GHz | 5 GHz | 7.5 GHz |

Antenna gain | -0.475 dB | -0.54 dB | -0.035dB | 0.26 dB |

The measurement results show that the antenna gain may be approximated to 0 dBi, implying a ±1 dB tolerance.

#### 2.1.3. System resolution and dynamic range

After a preliminary observation of the power delay profiles on various measurement points at different bandwidths, it is noticed that the noise threshold is constant (slightly below -90 dB). Besides that, as the power in the profile decays with delay, there are no observable multipath components above the noise threshold approximately 60 ns after the time instant of transmitting the pulse for each bandwidth. According to this fact the display window from 0 ns to 80 ns is chosen for all considered bandwidths and measurement points. Since this window is sampled at 801 points, the display resolution for all measurements is 0.1 ns.

The temporal resolution of the measurement system is equal to the inverse of the bandwidth and has a value greater than the display resolution. Otherwise, the display window would exceed the maximum observable delay (Hovinen et al., 2002).

Once the VNA was calibrated, the pulse shape was observed it the time delay domain for each different bandwidth (Fig. 6). All pulses have a different peak value at *τ* = 0, which is caused by normalizing the measurement results to the total energy of the pulse.

The VNA provides a windowing feature which is needed because of the abrupt transitions at the start and stop frequencies of the measured frequency span. The band limiting of a frequency domain response causes overshoot and ringing in a time domain response. This limits the usefulness of the time domain measurement in terms of the sidelobes and a pulse wider than the system resolution. The window used in the presented measurements is the normal window, which has a sidelobe level 44 dB below the pulse peak value and extends the pulse width to value of 3.84 times the system resolution for a bandpass mode (Hewlett-Packard Company, 1989). This has a direct consequence in spreading the pulse spatially, so that the spatial resolution of the system is degraded and the system can no longer resolve the multipath components with the precision expected from the system resolution. Another consequence is that when observing the delays in relation to the time instant of the peak of the transmitted pulse, one can observe a certain amount of energy received in negative delay times. To eliminate this, several power delay profiles where the total energy was not captured are removed from the final set of measured data. Hence, the minimum measurement distance is half of the spatial width of the pulse at a given bandwidth.

Furthermore, the RMS delay spread is estimated for each pulse, as this value is to be subtracted from the measured RMS delay spread of each power delay profile (Section 6). The results are presented in Table 2.

Bandwidth | 1 GHz | 2 GHz | 5 GHz | 7.5 GHz |

System resolution | 1 ns | 0.5 ns | 0.2 ns | 0.133 ns |

Display resolution | 0.1 ns | 0.1 ns | 0.1 ns | 0.1 ns |

Pulse width | 3.84 ns | 1.92 ns | 0.768 ns | 0.512 ns |

Spatial width | 1.152 m | 0.576 m | 0.23 m | 0.154 m |

Estimated pulse power | 1.66 dB | 1.66 dB | 1.66 dB | 1.66 dB |

Pulse RMS delay spread | 567 ps | 283.4 ps | 113.4 ps | 75.6 ps |

Fig. 7 shows a detail of normalized power profiles for different bandwidths. All the profiles are measured at 0.78 m antenna separation. It is evident that the measurement system with a narrow bandwidth cannot resolve as much multipath components as the same measurement system with wider bandwidth.

## 3. Path loss

The total path loss is defined as attenuation in the energy of pulse while propagating from the transmitting antenna to the receiving antenna. This can be expressed as a ratio of total energy of the transmitted pulse vs. total energy of the received power delay profile:

The path loss model (Ghassemzadeh at al., 2003) defines the path loss exponent *n* which characterizes the log-distance dependence and equals 2 for the free space propagation:

where *d* is the separation between the transmitter and the receiver, *PL*(*d* _{0}) is the path loss at the reference distance *d* _{0}, and *S* denotes the shadowing term (Section 4).

The total energy received at the Rx antenna is estimated by summing the energy in the entire corrected power delay profile. By subtracting the measured total path loss at a reference distance from this value, we estimate the relative path loss:

where *PL*(*d*) presents the path loss estimated from the power delay profile measured at distance *d*, and *PL*(*d* _{0}) is the measured total path loss at a reference distance, which is selected as *d* _{0} = 0.1 m (see Table 1).

The relative path loss values estimated from the measured power delay profiles are presented on Fig. 8 at different system bandwidths as a function of antenna separation in a logarithmic scale. In this manner the linear regression lines can be fitted into the measurement data using the least square method. The calculated free space path loss line (7) is added for comparison. Note that the correlation coefficient increases while the path loss exponent slightly decreases with increasing bandwidth.

The path loss exponent values estimated in this measurement campaign are comparable to the values found in literature up to date.

A indoor LOS measurement campaign which took place inside an anechoic chamber on a 1.2 m x 0.8 m rectangular aluminum conductive plate simulating a heavy-duty office desk (Suzuki & Kobayashi, 2005) found a path loss exponent value of *n* = 1.6 using a vertically polarized transmission. This value is lower than the free space path loss exponent (*n* =2) and the authors attribute this discrepancy to the effects of the diffracted waves from the finite plate edges. The frequency of the UWB signal spanned from 3.1 GHz to 10.6 GHz.

Short range indoor LOS measurements have also been performed in a 6 GHz to 8 GHz frequency band, with a transmitter-receiver distance ranging from 1 m to 5 m (Bose, 2006). A path loss analysis yields a path loss exponent of *n* = 1.85.

A 3.6 GHz – 6 GHz measurements in 1 m – 11 m range (Cassioli & Durantini, 2004) report a path loss exponent of *n* = 1.916 for indoor LOS scenarios.

An UWB indoor LOS channel measurement campaign was evaluated in (Cassioli et al, 2001), finding a path loss exponent of *n* = 2.4.

An extensive research based on analysis of over 300000 power delay profiles measured in 4.375 GHz – 5.625 GHz in various indoor LOS scenarios presented in (Ghassemzadeh et al., 2002) finds the average path loss exponent to have a value of *n* = 1.7.

Although the frequency dependence analysis of the channel parameters investigated in (Cassioli et al., 2004) resulted in a wide range of path loss exponent values between 0.6 and 2.2 for indoor LOS scenarios, there is no marked dependence on the system bandwidth.

## 4. Shadowing

The shadowing term *S* denotes a zero-mean Gaussian random variable with standard deviation *σ*, which is estimated from the experimental data:

The shadowing term captures the path loss deviations from its median value.

Fig. 9 presents a comparison of empirical cumulative distribution functions (CDF) of the estimated shadowing term *S* and theoretical lognormal CDFs with respective standard deviations for different bandwidths, shown in Table 3. For comparison, a far-right column showing the calculated parameter values in free space at central frequency of 6.85 GHz (7) is added.

In a 3.6 GHz – 6 GHz indoor LOS measurements (Cassioli & Durantini, 2004) shadowing is modeled as lognormal, with standard deviation of 1.42 dB for indoor LOS scenarios.

System BW | 1 GHz | 2 GHz | 5 GHz | 7.5 GHz | Free space (7) |

PL _{0} | 30.12 dB | 30.24 dB | 29.23 dB | 28.63 dB | 29.16 dB |

n | 2.28 | 2.24 | 2.2 | 2.05 | 2 |

σ | 1.87 dB | 1.67 dB | 1.57 dB | 1.39 dB | 0 dB |

An UWB indoor LOS channel measurement campaign was evaluated in (Cassioli et al, 2001), finding standard deviation of shadowing term of 5.9 dB.

An extensive research based on analysis of over 300000 power delay profiles measured in 4.375 GHz – 5.625 GHz for indoor LOS scenarios presented in (Ghassemzadeh et al., 2002) reports on the standard deviation of the shadowing term of 1.6 dB.

## 5. Mean excess delay

Mean excess delay is commonly used to describe the time dispersion characteristics of a transmission channel. It is defined as the first moment of the power delay profile:

The scatter plot of the mean excess delay values, estimated according to (13) from the measured power delay profiles, is presented on Fig. 10 in dependence on the antenna separation for different bandwidths.

Fig. 11 presents a scatter plot of the estimated mean excess delay in function of the estimated total path loss for different bandwidths. We find a significant correlation between these two parameters, which is slightly increasing with the bandwidth.

## 6. RMS delay spread

RMS delay spread is another parameter that characterizes the time dispersion of the channel. It is defined as a square root of the second central moment of the power delay profile:

As omitting the subtraction of the RMS delay spread of the calibrated pulse would yield overestimated results (Varela & Sánchez, 2001), in order to estimate the RMS delay spread it is necessary to subtract the RMS delay spread of the calibrated pulse from the RMS delay spread of each measured PDPs (Saleh & Valenzuela, 1987):

where *τ* _{RMSmeas }is the RMS delay spread estimaed from the measured power delay profile (14) and *t* _{RMSpulse }is the estimated RMS delay spread value of the calibrated pulse at a given bandwidth (Table 2). The results show a certain dependence on the antenna separation, where the correlation coefficient rises as the bandwidth increases (Fig. 12).

Fig. 13 presents a comparison of empirical cumulative distribution functions (CDF) of the estimated RMS delay spread values and theoretical normal CDFs with respective standard deviations for different bandwidths, shown in Table 4. Note that the mean value of the estimated RMS delay spread values decreases with increasing bandwidth.

System BW | 1 GHz | 2 GHz | 5 GHz | 7.5 GHz |

Mean | 5.93 ns | 4.85 ns | 3.85 ns | 3.9 ns |

Std. dev. | 1.37 ns | 1.37 ns | 1.25 ns | 1.36 ns |

An extensive research based on analysis of over 300000 power delay profiles measured in 4.375 GHz – 5.625 GHz presented in (Ghassemzadeh et al., 2002) reports on normally distributed mean excess delay and RMS delay spread with mean value of 4.7 ns and standard deviation of 2.3 ns for indoor LOS scenarios. This increase is explained to be largely due to paths with longer delays having larger path loss values associated with them.

Fig. 14 presents a scatter plot of estimated RMS delay spread in dependence of the total path loss. It is evident that these two parameters are strongly correlated.

A scatter plot of estimated RMS delay spread in function of the estimated mean excess delay is presented on Fig. 15. A strong correlation is observed for all bandwidths.

## 7. Discussion

The research presented in this chapter showed a certain dependence of the estimation of channel parameters on the system bandwidth.

First, the estimated path loss exponent slightly decreases with increasing the system bandwidth. An explanation can be found in the frequency selective propagation mechanisms, since different frequency components experience different impact of diffraction, reflection and transmission, where the coefficients that define these processes are dependent on the frequency of the transmitted signal. The estimated path loss exponent is slightly higher than the free space path loss exponent (between 2.05 and 2.28 for different bandwidths). Considering that the path loss exponent estimates for UWB indoor scenarios found in the literature are regularly below 2, the additional loss in the presented measurement campaign might be explained by the influence of the used desk, made of wood, chipboard and MDF.

Second, the estimated standard deviation of the shadowing term evidently decreases with increasing the system bandwidth, which in turn causes the increase in correlation between the estimated total path loss and antenna separation. This can also be explained as a direct consequence of the frequency selective propagation mechanisms. At larger bandwidths, more frequency components will be immune to reflections and diffraction, so that the received signal will be more consistent.

Third, the estimated RMS delay spread decreases with increasing the system bandwidth, because the system with wider spectrum is able to resolve more multipath components.

It is shown that estimated correlations between the various channel parameters investigated in this research are greater as the system bandwidth increases. This is obviously another consequence of better temporal resolution in due to shorter pulses at wider bandwidths.

## 8. Conclusion

The main scope of this chapter was to explore the validity of well established empirical methods used for UWB channel modeling and to propose the estimated values of the model parameters for a specific propagation environment.

An indoor UWB measurement campaign presented in this chapter was performed on an empty surface of a desk placed in a typical office room. The channel impulse responses were measured on the surface of the desk at different system bandwidths using a VNA method. The channel parameter values were estimated from the measurement results for each different bandwidth. The estimated values are comparable with the ones found in literature.

Analyzing the estimated values we have found that the estimations of the channel parameters show a certain dependence on the system bandwidth. The estimated path loss exponent values, standard deviations of the shadowing term, RMS delay spread mean values and mean excess delay values are all decreasing with increasing bandwidth for this indoor LOS scenario.

The analysis of correlation between the estimated values showed that the correlation coefficients tend to be higher at wider bandwidths.

## Acknowledgments

The authors wish to thank Prof. A. Šarolić and Mr. Z. Živković for use of their GTEM cell and assistance in measuring the antennas’ radiation patterns.