Experimental investigation on channel characteristics in tunnel environment for Time Reversal Ultra Wide Band techniques

Authors


Abstract

[1] The objective of this paper is to investigate the potential advantages of the Time Reversal (TR) technique applied to Impulse Radio Ultra Wide Band (UWB) signals for communications in tunnels. Indeed, in an environment with significant multipaths, it has already been outlined that this technique allows mitigating intersymbol interference and increases the peak power received at a target antenna. However, in a tunnel, as a result of the guiding effect of the structure, the spatial diversity degree decreases as the distance between the transmitter and receiver increases. An in-depth analysis is therefore needed, and we first thus present the main characteristics of the UWB channel deduced from measurements made in a long straight arched tunnel and for a frequency band extending from 2.8 to 5 GHz. In the time domain, waveforms of the impulse radio signal are obtained through an inverse Fourier transform of the measured frequency response and examples are given for different distances varying from 50 m to 500 m. Delay spread and peak-to-peak gain are then studied, depending on the communication range. The case for multiple antenna transmission is also considered.

1. Introduction

[2] In the transportation domain, and more specifically in underground subways, there is a growing demand to ensure a high and reliable bit rate for train to track or train to train communication. Increasing the channel capacity will allow, for example, for coping with the growing complexity of control-command systems.

[3] To achieve this goal, a first possibility which has already been investigated, is to use a multiple antenna transmission scheme, as in Multiple Input Multiple Output (MIMO) techniques. Such techniques are well recognized as an effective way to improve communication performance in a strong multipath configuration, as occurs in indoor or urban environments [Foschini and Gans, 1998; Paulraj et al., 2004]. However, the guiding structure of the tunnel may decrease the channel diversity. A number of papers were thus devoted to studying the narrow band channel characteristics as the spatial correlation [Molina-Garcia-Pardo et al., 2008a], in order to determine whether spatial multiplexing would yield a significant increase in the channel capacity [Valdesueiro et al., 2010]. In all these studies, the carrier transmitting frequency is limited to a few GHz to minimize path loss.

[4] Another possibility to improve the performance of the link in a tunnel environment could be by using an Ultra Wide Band (UWB) transmission. An additional advantage of this technique is that the location of a mobile can be established with good precision. A great number of papers have been published on UWB, covering numerous configurations, from indoor/in-home environments to factory halls [Win and Scholtz, 2002; Muqaibel et al., 2006; Molisch, 2009]. However, since the configuration of a tunnel is quite different from those previously considered, specific measurements are needed. For mine tunnels, the variation of path loss as a function of frequency from 2 GHz to 5 GHz is studied by Chehri et al. [2012], and a frequency domain autoregressive model was developed. Various communication links were also considered, including both line of sight (LOS) and non-LOS (NLOS) scenarios [Chehri and Fortier, 2006]. Last, for a road tunnel, the statistics for the electromagnetic field variation has been deduced from measurements made in an arched tunnel, which is the usual shape of road and railway tunnels [Molina-Garcia-Pardo et al., 2009].

[5] In the case of transmission in a rich scattering environment, Time Reversal (TR) signal processing, usually applied to acoustics [Fink et al., 2000], was recently extended to electromagnetic waves [Lerosey et al., 2004, 2005]. One of the main objectives is to focus the energy on the intended user while minimizing its interference to other users. It may be of great interest for multiuser communication and indoor environments containing multiple wireless communication nodes [Barton et al., 2007]. A specific application using TR to enhance data communication in ventilation ducts, thus in a guided structure, is reported by Henty [2006].

[6] The idea of combining UWB and TR to take benefit from the multipath propagation in indoor channels has been proposed [Naqvi et al., 2010; Pajusco and Pagani, 2009]. Another example of performances of TR UWB is given by Liu et al. [2008], based on typical IEEE UWB channel model parameters. A theoretical study of TR-UWB for train-to-wayside communication, and based on a software tool simulating the propagation in a rectangular tunnel, was presented by Saghir et al. [2009a], while modified-orthogonal waveforms for ensuring multiple access communications are discussed by Saghir et al. [2009b]. System architecture of a communication-based train control in tunnel is also presented in these papers emphasizing that both high resolution train location and a low probability of interception of the data to non-intentional receivers can be achieved. It must also be outlined that the guided structure of the tunnel leads to a small path loss which is thus not prohibitive for implementing UWB for medium range communication [Molina-Garcia-Pardo et al., 2009].

[7] Since, to our knowledge, there is a lack of experimental analysis of TR-UWB in tunnels for a wide communication range, measurements have been carried out in a frequency band extending from 2.8 to 5 GHz and for distances between the transmitter (Tx) and the receiver (Rx) varying from 50 m up to 500 m. Time domain characteristics of the received signal were deduced from measurements in the frequency domain through inverse Fourier transform. The objective of this measurement campaign was, on the one hand, to experimentally characterize UWB propagation in such environment and, on the other hand, to deduce some features of a TR link and information on the outcome of using TR impulse radio in tunnels, not necessarily fulfilling the assumption of a rich scattering environment. Indeed, the tunnel behaving as an oversized waveguide with lossy walls, the channel characteristics vary along the tunnel and one can expect that the spatial focusing gain and the temporal focusing gain will also be dependent on the distance Tx – Rx. This aspect will be studied by considering either a Single Input Single Output (SISO) or a Multiple Input Single Output (MISO) configuration.

[8] This paper is organized as follows: Section 2 briefly recalls the methodology of the UWB frequency domain measurement campaign carried out on a straight road tunnel in a frequency range extending from 2.8 to 5 GHz. Results of the mean path loss, small scale fading and delay spread are summarized in section 3. Typical waveforms of received pulses and correlation between signals received at different locations, are presented and analyzed in section 4. The concepts of SISO-TR and MISO-TR are briefly reviewed in section 5, the remaining part being devoted to the characterization and main features of the TR channel, such as delay spread and focusing gain. Section 6 summarizes the conclusions of this study.

2. Description of the Measurement Campaign

[9] Measurements took place in a straight arched tunnel, 3 km long, shown in Figure 1. Its transverse section was semicircular and the diameter of the cylindrical part was 8.6 m. The maximum height was 6.1 m at the center of the tunnel. The tunnel was nearly free of obstacles like road signs, lamps, cables, etc. Furthermore, the roughness of the walls was rather low, on the order of few cm.

Figure 1.

Straight road tunnel in which experiments were conducted.

[10] The tunnel was closed to traffic and consequently the channel can be considered as stationary during the experiments. The transmitting (Tx) and receiving (Rx) antennas were wideband conical antennas, their gain being nearly flat over the bandwidth of interest.

[11] Both Tx and Rx antennas were mounted on a rail, placed at 1 m above ground and allowing their displacement, controlled by a stepper motor, with a maximum distance of 33 cm. During this measurement campaign, these rails were positioned perpendicular to the tunnel axis. The spatial step in this transverse plane was 3 cm, corresponding to half a wavelength at 5 GHz. This leads, for each axial distance d between Tx and Rx and for each frequency, to a set of 144 values of the channel transfer function H. The axial step was chosen to be equal to 4 m when 50 m < d < 206 m, and to 6 m when 206 m < d < 498 m. The configuration of these wideband measurements is shown in Figure 2.

Figure 2.

Configuration of the wideband measurements.

[12] The channel sounder was based on a vector network analyzer (VNA). The Rx antenna was directly connected to one port of the VNA using a low attenuation coaxial cable and a 30 dB low-noise amplifier. To be able to take measurements up to 498 m, the signal of the Tx port of the VNA was converted into an optical signal which was sent through fiber optics. It was then converted back to radio-frequency and amplified, being the output power of 1 W. The frequency step is 1.37 MHz from 2.8 to 5 GHz. Further details concerning the experimental aspects of this study, e.g., the calibration of the measurement system, are given by Molina-Garcia-Pardo et al. [2009].

3. Mean Path Loss, Small Scale Fading, and Delay Spread

[13] In narrow band communication systems, path loss is frequency and distance dependent, while small scale fading is due to the constructive and destructive interference of all possible paths between Tx and Rx. For impulse radio UWB signals, the most important characteristics are related to the variation in the energy of the pulse and not of its individual spectral components. Figure 3 gives the value of the UWB measured path loss defined as the ratio of the Tx power to the received power at a distance d, this ratio being averaged over the whole frequency band (2.8–5 GHz) and over the 144 transverse positions of Tx and Rx. We clearly observe the guiding effect of the tunnel, the additional attenuation between 100 m and 500 m only being 4 dB. The variation of experimental values of path loss can be modeled by the d0.55 law, as shown in Figure 3.

Figure 3.

Mean path loss versus distance.

[14] To determine the characteristics of the small-scale fading, we consider a rectangular grid containing successive Rx positions [Garcia-Pardo et al., 2011]. The width of the grid, i.e., its dimension along the transverse axis, is equal to 33 cm and corresponds to the maximum displacement of the antenna in the transverse plane. Along the tunnel axis, we consider 3 successive distances as shown in Figure 4. Thus the length L of the grid is either 8 m or 12 m depending on whether the distance d between Tx and Rx is smaller or larger than 206 m, as explained in section 2. The standard deviation (std) of the path loss in the rectangular grid, normalized to its average value in this grid and thus expressed in %, was calculated for successive values of d varying between 50 m and 486 m and also by considering, for each value of d, the 12 possible positions of the Tx antenna in the transverse plane of the tunnel. It appears that std varies between 8% and 20%, depending on the axial distance between Tx and Rx. This means that there is almost no fading as a result of interference and this is the same conclusion as in the case of propagation in a typical in-building environment [Muqaibel et al., 2006; Molisch, 2009].

Figure 4.

Successive positions of Rx for calculating the standard deviation of the path loss. L = 8 m for d ≤ 200 m and L = 12 m for 206 m ≤ d ≤ 486 m.

[15] In the time domain, the channel impulse response (CIR) can be easily deduced from measurement results in the frequency domain by applying an inverse Fourier transform. In the time domain, an interesting parameter characterizing the channel properties is the RMS delay spread Ds defined as the normalized second-order moment of the CIR. For each axial distance d, the average delay spread is deduced from the CIR calculated for each of the 12 × 12, i.e., 144, channels associated with the possible positions of the antennas in the transverse plane. Numerical results show that Ds decreases from 5 ns at 50 m to 2–3 ns at a greater distance. This point will be treated in more detail in section 5 for examining the role of a TR technique on the reduction of Ds.

4. Time Dispersion and Spatial Correlation

[16] In this section, the change in the waveform of the pulse propagating in the tunnel is first presented. Then the correlation coefficient between signals received at different locations is calculated to get an idea of the correlation distance.

4.1. Transmitted and Received Waveform

[17] As previously outlined in section 2, the complex channel transfer function was measured in the frequency domain between 2.8 and 5 GHz. The equivalent transmitted pulse is represented in Figure 5a. It has been obtained by applying on the complex transfer function, measured in the frequency domain, a Hamming window and an inverse Fourier transform. The maximum amplitude of the pulse is normalized to 1 mV. The pseudo-carrier frequency corresponds to the center of the frequency band under analysis (3.9 GHz). Examples of the received signal waveform at a distance of 50 m, 200 m and 498 m are given in Figures 5b–5d. To avoid time shift due to the propagation delay, the origin of the time axis in this figure, and in the following figures, is quite arbitrary.

Figure 5.

Waveforms of (a) the transmitted pulse, and (b–d) of the received signals at different distances.

[18] At 50 m, we observe a first pulse, which includes the direct path, and which has a peak amplitude of 3 × 10−4 V. Then, there is a series of other delayed corresponding to multipath propagation. For a delay of 30 ns, the maximum amplitude of the pulse is 0.7 × 10−4 V, which is not still negligible, referred to the amplitude of the strongest pulse. At d = 200 m, the first received pulse has a width of about 2 ns and has nearly the same amplitude and shape as that obtained at 50 m, but the amplitudes of the delayed pulses are very small. This result can be explained from a theoretical modeling of the propagation in a straight tunnel, based on a ray theory [Molina-Garcia-Pardo et al., 2008b]. Due to the finite bandwidth (even if it is equal to 2.1 GHz), interferences between rays reflecting on the tunnel walls occur. The total signal can be arbitrary put in the sum of two contributions: on the one hand the direct path and rays reflecting on the walls with a grazing angle of incidence and, on the other hand, rays experiencing many reflections on the walls. It numerically appears from the theoretical model that, for a distance between the transmitter and the receiver on the order of 200 m, destructive interference occurs between rays of high order reflection, leading in the time domain to delayed pulses of small amplitude. This critical distance of 200 m in our case, of course depends on the tunnel geometry.

[19] For a distance equal to 498 m, the curve plotted in Figure 5d shows a high multipath density, but within a short time delay, of about 10 ns. Indeed at large distance, the main contribution to the signal is due to rays propagating nearly parallel to the tunnel axis [Molina-Garcia-Pardo et al., 2008b]. It is thus interesting to determine the correlation function between signals received at different locations to be able to interpret the results which would be obtained with TR techniques.

4.2. Transverse Correlation

[20] For an axial distance d and for a given position i of the Tx antenna, one can compute the correlation ρ(dij) in the transverse plane, between the signal received by Rx situated at j = 1, and the signal received at another position j (Figure 4). Since the spatial step is 3 cm, the correlation is thus calculated between two Rx antennas whose spacing is xj = 3j (cm), with j varying from 1 to 11.

[21] For each spacing xj, the correlation was averaged over the 12 positions i of the transmitter:

display math

[22] Results are presented in Figure 6 for three values of d: 102, 314 and 498 m. The slope of the decrease of the correlation coefficient is much greater at 102 m that at 498 m. If we consider a spacing of 12 cm, the correlation coefficient is 0.5 for a distance of 102 m, but is still equal to 0.7 and 0.9 for a distance of 314 m and 498 m, respectively. This result can be explained by the electromagnetic field distribution in the transverse plane. Indeed, as the transverse dimensions of the tunnel are much larger than the wavelength, the tunnel behaves as an oversized waveguide and supports the propagation of hybrid modes [Mahmoud, 2005]. However, high order modes suffer large attenuation when the distance d increases. Since the field distribution in a transverse plane is the sum of the individual contribution of the modes, one can expect to get a more coherent transverse field far away from the transmitter. The correlation coefficient is also related to the angular dispersion of the waves at the transmitter and receiver. It is thus interesting to mention that the power angular spectrum of the rays have been deduced from experimental results using antenna arrays both at the Tx and the Rx site, and by applying high resolution algorithms [Garcia-Pardo et al., 2011, 2012]. The variations in the angle of departure and arrival of the rays are quite similar. The angular spread decreases from 10° at 50 m from Tx to about 3° at 200 m and then remains nearly constant beyond this distance.

Figure 6.

Correlation in the transverse plane for different axial distances.

4.3. Axial Correlation

[23] Due to experimental constraints, the spacing between successive measurement points along the tunnel axis were Δd = 4 m or 6 m, depending on the distance d. This axial step Δd is thus not small enough to clearly point out the continuous decrease of the correlation coefficient versus the antenna spacing.

[24] However, it is interesting to point out the variation of the average correlation between points situated at d and d + Δd, when d varies from 50 m to 498 m. This average correlation is defined, as for the transverse correlation, by:

display math

where i denotes the position of a Tx antenna. The results plotted in Figure 7 show that in the first zone, i.e., when d varies from 50 m to 206 m and Δd = 4 m, the correlation coefficient varies from 0.4 to 0.9.

Figure 7.

Axial correlation coefficient versus distance d between 2 points, 4 m apart (if d < 204 m) or 6 m apart (if d > 204 m).

[25] The high value of the correlation coefficient around d = 200 m can be explained by a strong attenuation of the multipath components as previously outlined. In the second zone of measurement, i.e., when 250 m < d < 498 m and Δd = 6 m, the correlation increases from 0.7 to 0.8. The average increase of the correlation coefficient between 50 m and 500 m, can be explained, as in the case of the correlation in the transverse plane, by the decrease of the number of modes propagating at large distances from the transmitter.

5. Time-Reversal in Tunnel Environment

5.1. Principle of UWB Time Reversal

[26] Let us first consider the Single-Input Single-Output (SISO) configuration, with a single antenna being used at the Tx site and at the Rx site. The implementation of TR involves the previous estimation of the CIR. Let us assume a bidirectional and stationary channel where the transmitter and receiver are separated by a distance d0. Let us also assume that the CIR h(d0τ) has been estimated. This response can then be inverted and conjugated, h*(d0, − τ), and used as the pre-coding of the transmitted UWB pulse [Lerosey et al., 2004, 2005]. Note that in our case of Impulse Radio (IR) UWB, the CIR is real and the conjugate operation is not required. If the transmitted pulse is noted p(τ), the received signal at any distance d from the transmitter, yTR(dτ) can be expressed as follows:

display math

The equivalent CIR, using TR is thus given by:

display math

[27] Since in our study of propagation in tunnels, measurements were carried out in the frequency domain, (3) can also be written as:

display math

In this formula, P(f) is the frequency content of the transmitted pulse, and H(d0, f) and H(d, f) are the complex passband transfer functions for both positive and negative frequencies, deduced from the measurement results.

[28] In practical systems, rather than evaluating the intrinsic channel transfer function, the pre-coding signal used at the transmission site is the real channel impulse response h(d0, τ) convolved with the pulse p(τ) as a result of a previous demand from the transmitter to the receiver. Furthermore, to carry out a fair comparison of the received signals with or without TR, the transmission power must be the same in both cases. Taking these two aspects into account, the received signal can be put in the following final form:

display math

[29] To increase the gain when using TR, a possible solution which has already been investigated is to employ multiple antenna transmission schemes, such as MISO [Qiu et al., 2006; Kyritsi et al., 2004; Naqvi and El Zein, 2008]. If there are M antennas at the Tx site, the received signal is the coherent sum of all the TR signals at the target receiver and can be expressed as:

display math

where Hj (d0, f) is the passband transfer function between the transmitter j and the target receiver.

[30] In order to point out the benefits of using TR techniques in tunnels, examples will first be given for three different distances d between Tx and Rx: around 50 m and 500 m corresponding to the maximum and minimum values of d in the experiments, and at around 200 m. This particular distance has been chosen since in this zone the delay spread reaches its minimum value, equal to 1.3 ns.

5.2. Spatial Focusing of SISO-TR

[31] One of the advantages of TR, pointed out in the literature, is that the signal can only be optimally received by the target receiver associated with the CIR used in the pre-coding technique. In order to outline this spatial focusing, we first consider the case of an optimal pre-coding, i.e., when the CIR h(d0τ) has been estimated at the location of the receiving point (d = d0). The signal obtained in this case with SISO-TR and at a distance d = 50 m is plotted in Figure 8a. Let us now assume that the receiver moves to d = 54 m and then to d = 58 m but by keeping the CIR at 50 m for pre-coding. Since the axial correlation coefficient is equal to 0.4 between two points 4 m apart (Figure 7), the focusing effect of the TR no longer appears.

Figure 8.

Received signal with TR: (a) d = 50 m, (b) d = 54 m but using the CIR at 50 m, and (c) d = 58 m but using the CIR at 50 m.

5.3. Temporal Focusing: Comparison Between SISO-TR and MISO-TR

[32] Before extracting some TR characteristics from all measurement results, it is interesting to present typical waveforms of the received signal. It is presumed in this section that the pre-coding is optimum, i.e., it uses the channel estimation at the receiving point. This means that in (6) d = d0. As an example, Figure 9a indicates the waveform of the signal at 50 m with SISO TR. For this last configuration, TR is equivalent to a coherent summation of all paths, giving rise to an increase in the Rx power at τ = 0, and a decrease of the side lobes. All quantitative aspects will be considered in section 5.4.

Figure 9.

Waveform of the received signal at different distances with SISO TR and MISO TR.

[33] An illustration of the application of MISO TR is given in Figure 9b. Four Tx antennas have been considered in this case, the spacing between each antenna being 9 cm. This corresponds to the maximum possible spacing in our experiments. Consequently, only one Tx virtual array can be considered. Comparing Figures 9a and 9b shows for MISO TR, a gain factor of around 2 on the peak value of the strongest signal is observed. As already mentioned, this is due to the coherent addition of the peaks from each branch in the MISO TR response. It has been shown that the gain factor on the peak of the channel response with MISO TR is math formula higher than the peak average over all the M SISO cases [Zhou et al., 2006].

[34] Last, waveforms of the signal received at a distance of 200 m and 498 m are plotted in Figures 9c–9f. At 200 m, we have already mentioned in paragraph 4.1. that the delayed multipath components of the signal without TR are strongly attenuated, the pulse having duration of about 2 ns. Therefore, the benefit in terms of a reduction of the signal spread and in terms of gain brought about by TR is not significant, as can be shown by comparing Figures 5c and 9c. At 498 m, the received pulse without TR being slightly wider than at 200 m, the main interest of using SISO TR or MISO TR is to increase the peak value of the received pulse.

[35] Curves presented in Figure 9 clearly show that the improvement which could be expected on the temporal focusing by using TR, is dependent on the distance d between the transmitter and the receiver inside the tunnel. The next paragraph is thus devoted to the variation of the focusing characteristics versus this distance.

5.4. Decrease of the Delay Spread and Peak-to-Peak Gain With SISO-TR and MISO-TR

[36] Various figures of merit are proposed in the literature to evaluate the main features of TR. The first possible metric is the average RMS delay spread (Ds) describing the temporal compression of the signal. The three curves in Figure 10 have been plotted for the following configurations: SISO without TR, SISO TR and MISO TR. For MISO, the number M of transmitting elements is, as previously, equal to 4.

Figure 10.

Average RMS delay spread: SISO without TR, SISO TR, and MISO TR.

[37] For each distance d, Ds was averaged over the 12 positions of the Rx antenna in the transverse plane and over the 12 positions of the Tx antenna in the SISO case, and over the 12 positions of the Rx antenna in the MISO case.

[38] At a distance of 50 m, Ds is on the order of 5 ns, and reduces to 3.5 ns with SISO TR. A noticeable improvement is obtained for MISO TR, with Ds decreasing to 1 ns. However, the significance of using TR becomes small at large distances, since the average delay spread for the 3 configurations is quite similar. Indeed in this case, the transmitting bandwidth is not sufficiently important to profit from the multipath propagation, the delay spread without TR being only 2 ns. To clearly indicate the reduction of Ds by using SISO TR and MISO TR, the reduction factors of delay spread, noted RSISO_TR and RMISO_TR respectively and expressed in percentages, have been computed from the following expressions:

display math
display math

[39] In (8) and (9), DS (d, i, j), DS-TR (d, i, j) and DS-MISOTR (d, i, j) are the RMS delay spreads, without TR, with SISO-TR and MISO TR respectively, and calculated at an axial distance d. The indices i and j characterize the location of Tx and Rx in the transverse plane respectively (Figure 4).

[40] The curves in Figure 11 correspond to the Cumulative Distribution Function (CDF) of RSISO_TR and RMISO_TR. Two zones have been considered: One close to Tx (50 m < d < 100 m), and the other far away from Tx (400 m < d < 500 m). For a probability of 0.5, the reduction of Ds with SISO TR is only 15% in the near zone and 5% in the far zone. Furthermore, there is even a small probability that Ds slightly increases, corresponding to a negative value of the delay spread reduction. This occurs in a zone of the tunnel where the number of multipath components is small, such as when d = 200 m, as shown in Figure 10. This absence of reduction of Ds with TR alone is due to the autocorrelation operation which nearly doubled the duration of the impulse response. With MISO TR and for a probability of 0.5, the delay spread reduction is 75% in the near zone but decreases to 20% at large distances from the transmitter.

Figure 11.

CDF of RSISO_TR and RMISO_TR for short range (d < 100 m) and for long range (400 m < d < 500 m) communication.

[41] For a simple receiver picking up the peak energy of the impulse response, another interesting metric is the focusing gain, also called the peak to peak gain, noted Gp2p and defined as the ratio of the strongest tap power received with TR or without TR [Naqvi and El Zein, 2008; Pajusco and Pagani, 2009]. It is thus given by:

display math

where yTR (d0, τ) and y(d0, τ) denotes the received signal amplitude using TR and not using TR, respectively. The curves in Figure 12 represent the variation of Gp2p versus distance, for TR and for 4 × 1 MISO TR, respectively. We note that the gain with SISO TR is between 2 and 6 dB, except in the zone situated at 200 m from the transmitter where the gain becomes negligible, as already outlined. When using MISO TR, Gp2p is 6 dB better than for SISO TR, since all the energies from different elements coherently add up.

Figure 12.

Peak to peak gain for SISO TR and MISO TR configurations.

6. Conclusion

[42] The novelty in this paper, dealing with TR-UWB, lies mainly in the nature of the environment studied and which consists of a tunnel. Indeed, the channel characteristics are quite different than in indoor environment because the guiding structure leads to a low mean average path loss and a correlation between received signals which strongly depends on the distance between the transmitter and the receiver. We have seen that, in the 2.8–5 GHz band, the average attenuation between 50 m and 500 m is of about 4 dB. At a distance less than 100 m from the transmitter, the signals received at different locations in the transverse plane of the tunnel are rapidly uncorrelated, the correlation coefficient being equal to 0.4 if the receiving points are 9 cm apart. However, the correlation increases at large distances of the transmitter due to the attenuation of high order propagating modes, which leads to a decrease in the number of modes and thus of the diversity.

[43] The performance of TR technique applied to impulse radio UWB channels has been analyzed both for SISO and MISO configurations. As already outlined in previous papers published on this subject, the potential advantages of TR-UWB are, for example, spatial focusing reducing the interferences caused by multiusers and high resolution in mobile locations. These properties could be interesting for communication-based train control systems. In a tunnel configuration, it has been shown that SISO TR does not appreciably reduce the delay spread. In contrast, when the distance between the transmitter and the receiver does not exceed 250 m, the delay spread with MISO TR is reduced from a few ns without TR to 1 ns.

[44] The peak to peak power gain with SISO TR is 3 dB on average, except in a zone of the tunnel where the number of multipath components becomes small, this zone being situated at about 200 m from the transmitter in our tunnel configuration. If 4 antennas are used on the transmitting site, the peak to peak gain increases by a factor of 2 compared to SISO TR, as it would be expected from previous works on MISO TR, and reaches 10 dB.

[45] Despite the guiding effect of the tunnel, leading to a propagation of the waves nearly along the tunnel axis, i.e., to rays reflecting on the tunnel walls with a grazing angle of incidence, MISO TR can be an interesting solution to improve the performance of the link.

Acknowledgments

[46] This work was supported by the Ministerio de Educación y Ciencia, Spain (TEC2010-20841-C04-03), and the Fundación Séneca of Murcia, Spain (08818/PI/08, 14809/EFPI/10 and 06640/FPI/07), by the European FEDER funds, the Region Nord Pas de Calais and the French Ministry of Research, as part of the International Campus on Safety and Intermodality in Transportation Systems (CISIT) project (France).

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