 Research Article
 Open Access
Propagation in Tunnels: Experimental Investigations and Channel Modeling in a Wide Frequency Band for MIMO Applications
 J.M. MolinaGarciaPardo^{1}Email author,
 M. Lienard^{2} and
 P. Degauque^{2}
https://doi.org/10.1155/2009/560571
© J.M. MolinaGarciaPardo et al. 2009
 Received: 25 July 2008
 Accepted: 10 February 2009
 Published: 23 March 2009
Abstract
The analysis of the electromagnetic field statistics in an arched tunnel is presented. The investigation is based on experimental data obtained during extensive measurement campaigns in a frequency band extending from 2.8 GHz up to 5 GHz and for a range varying between 50 m and 500 m. Simple channel models that can be used for simulating MIMO links are also proposed.
Keywords
 Transverse Plane
 Path Loss
 Multiple Input Multiple Output
 Axial Distance
 Multiple Input Multiple Output
1. Introduction
Narrowband wireless communications in confined environments, such as tunnels, have been widely studied for years, and a lot of experimental results have been presented in the literature in environmental categories ranging from mine galleries and underground old quarries to road and railway tunnels [1–4].
However, in most cases, measurements dealt with channel characterization for few discrete frequencies, often around 900 MHz and 1800 MHz. For example, in [5, 6] Zhang et al. report statistical narrowband and wideband measurement results. In [7], results on planning of the Global System for Mobile Communication for Railway (GMSR) are presented. In [8], simulations and measurements are also described in the same GSM frequency band. In [9], the prediction of received power in the outofzone of a dedicated short range communications (DSRC) system operating inside a typical arched highway tunnel is discussed, and in this case the channel impulse response was measured with a sounder at 5.2 GHz whose bandwidth is on the order of 100 MHz. Recently, in [10], measurement campaigns have been performed in underground mines in the 2–5 GHz band but the results cannot be extrapolated to road and railway tunnels since the topology is quite different. In a mine gallery, roughness is very important, the typical width is 3 m, the geometry of the crosssection is not well defined and lastly, there are often many changes in the tunnel direction.
Furthermore, to increase the channel capacity in tunnels, space diversity both at the mobile and at the fixed base station can be introduced. However, good performances of multiple input multiple output (MIMO) techniques can be obtained under the condition of a small correlation between paths relating each transmitting and receiving antennas. This decorrelation is usually ensured by the multiple reflections on randomly distributed obstacles, giving often rise to a wide spread in the direction of arrival of the rays. On the contrary, a tunnel plays the role of an oversized waveguide and decorrelation can be due to the superposition of the numerous hybrid modes supported by the structure [11]. Experimental results at 900 MHz for a MIMO configuration, are described in [12]. This paper shows that the antenna arrays must be put in the transverse plane of the tunnel to minimize the coupling between elements.
The objective of this work is thus to extend the previous approaches by investigating the statistics of the electric field distribution in the 2.8–5 GHz frequency range in a tunnel environment for MIMO applications. Empirical formulas based on the experimental results are also proposed.
We proceed in two steps: (1) determination of the mean path loss and of the statistical distribution of the average field which can be received by the various antennas of an MIMO system. This first approach can thus be used to determine the average power related to the H matrix of an MIMO link, (2) field distribution and correlation in a transverse plane.
The paper is distributed as follows. Section 2 explains the experiments in detail and more specifically the environment and methodology of the measurements that has been followed. Section 3 investigates path loss and axial correlation while, in Section 4, field statistics in the transverse plane are analyzed. Section 5 deals with the transverse spatial correlation and Section 6 presents the principle of modeling the MIMO channel and gives an example of application. Finally, Section 7 summarizes the contributions of the present work and gives conclusions.
2. Environment, Measurement Equipment, and Methodology
2.1. Description of the Environment
2.2. Measurement Equipment
The wideband biconical antennas (Electrometrics EM6116) used in this experiment have nearly a flat gain, between 2 and 10 GHz. Indeed, the frequency response of the two antennas has been measured in an anechoic chamber, and the variation of the antenna gain was found to be less than 2 dB in our frequency range. Nevertheless, we have subtracted the antenna effect in the measurements, as it will be explained in Section 3.
It must also be emphasized that, in general, the radiation pattern of wideband antennas is also frequency dependent. This is not a critical point in our case since, in a tunnel, only waves impinging the tunnel walls with a grazing angle of incidence contribute to the total received power significantly. This means that, whatever the frequency, the angular spread of the received rays remains much smaller than the 3 dB beam width of the main antenna lobe in the E plane, equal to about 80°, the antenna being nearly omnidirectional in the H plane.
Since the channel transfer function may also strongly depend on the position of the antennas in the transverse plane of the tunnel, both Tx and Rx antennas were mounted on rails. The position mechanical systems are remote controlled, optic fibres connecting the step by step motors to the control unit.
2.3. Methodology
The channel frequency response has been measured for 1601 frequency points, equally spaced between 2.8 and 5 GHz, leading to a frequency step of 1.37 MHz.
Due to the limited time available for such an experiment and to operational constraints, it was not possible to extensively repeat such measurements for very small steps along the tunnel axis. In the experiments described in this paper, the axial step was chosen equal to 4 m when 50 m <d < 202 m and to 6 m when 202 m <d < 500 m. This is not critical because we are interested, in the axial direction, by the mean path loss and by the largescale fluctuation of the average power received in the transverse plane. At each Tx and Rx position, 5 successive recordings of field variation versus frequency are stored and averaged.
Equipment characteristics and measurement parameters.
Frequency band  2.8–5 GHz 

Number of frequency points  1601 
Antenna  Biconical antenna (Electrometrics EM6116) 
Transmitter power  20 dBm 
Dynamic range  >100 dB 
Position in the transverse plane  12 positions every 3 cm (λ/2 at 5 GHz) 
Positions along the longitudinal axis  From 50 m to 202 m every 4 m 
From 202 m to 500 m every 6 m  
Number of acquisitions at each position  5 
3. Path Loss and Correlation Along the Longitudinal Axis
3.1. Path Loss
The path loss is deduced from the measurement of the scattering parameter. However, as briefly mentioned in the previous section, it can be more interesting to subtract the effects of the variation of the antenna characteristics with frequency by introducing a correction factor . We have thus made preliminary measurements by putting the two biconical antennas, 1 m apart, in an anechoic room. Let be the scattering parameter measured in this configuration. The correction factor is thus given by , where means the average of x over the frequency band.
To deduce from these curves a simple theoretical model of the mean path loss , these curves must be smoothed again by introducing a running mean over the axial distance. To get a very simple approximate analytical expression of , it is assumed that is the product of two functions, one depending on f and one depending on d [14].
The constant and the path loss exponents have been determined by minimizing the mean square error between the measurements and the model. The following values were found: dB, , and . The corresponding curves for 3 and 5 GHz have also been plotted in Figure 5. It must be outlined that all these values were deduced from measurements between 50 and 500 m and consequently, they are valid only in this range of axial distance.
It can be interesting to compare this value of to those already published in the literature and corresponding to attenuation factors measured for ultrawideband systems in indoor environments. However, in this case, the range is much smaller, typically below 50 m. In line of sight (LOS) conditions, values from 1.3 to 1.7 were reported by [16, 17], while for nonLOS, may reach 2 to 4 as mentioned in [18, 19]. The small value that we have obtained comes from the guiding effect of the tunnel.
3.2. Axial Correlation
One can expect that the variation of the average received power between one transverse plane and another will depend on the distance d, highorder propagating modes suffering important attenuation at large distances. To study this point, we have calculated, for a given frequency, the amplitude of the complex correlation coefficient between the transfer matrix elements measured at a distance d and the matrix elements measured at the distance , d varying between 50 m and 500 m. Let us recall that the step is equal 4 m while 50 m <d < 202 m and 6 m when 202 m <d < 500 m.
the standard deviation being also equal to 0.06.
4. Field Distribution in the Transverse Plane
4.1. Field Distribution Function
being a Laguerre polynomial.
Before explaining how the two parameters of the Rice distribution have been found, let us recall that, in the mobile communication area, a Rice distribution usually characterizes the field distribution in line of sight (LOS) conditions and in presence of a multipath propagation. Usually a K factor is introduced and defined as the ratio of signal power in dominant component, corresponding to the power of the direct ray, over the scattered, reflected power. One can follow the same approach by defining a K factor in a given receiving zone which is, in our case, defined by the segment 33 cm long in the transverse plane of the tunnel, along which measurements were carried out.
4.2. Ricean Factor
It must be clearly outlined that, in a tunnel, the K factor cannot be easily interpreted. Indeed, there is no contribution of random components to the received power, the position of the 4 reflecting walls being invariant. K could be related to richness in terms of propagation modes having a significant power in the receiving transverse plane, a high number of modes giving rise to a high fluctuating field. However, quantifying the relationship between K and mode richness is not easy since the field fluctuation depends not only on the amplitude of the modes but also on their relative phase velocity. In a tunnel, one can conclude that K just gives an indication on the relative range of variation of the received power in a given zone.
This increase of K is due to the fact that the contribution of highorder modes becomes less important leading to less fluctuation of the transverse field. The same interpretation based on the modes can be made to interpret the influence of frequency on the K values. The variation of K is of course related to the variation of the correlation coefficient along the tunnel axis, as described in the previous section.
Parameters to be introduced in (10) for modeling the variation of the K factor.




 

Values  −79  6.73  3.6  −0.37  4.9 
The curves labelled "model" in Figure 7 have been obtained by applying (10) and the above values for the parameters.
4.3. Determination of the Ricean Parameters and Modeling of the Field Variation in the Transverse Plane
5. Transverse Spatial Correlation
The knowledge of the spatial correlation in the transverse plane is of special interest for MIMO systems. It is assumed, for simplicity, that the correlations at the transmitter and at the receiver are separable [21]. Furthermore, since the Rx and Tx antenna arrays are situated in the same transverse zone of the tunnel, one can expect that the correlation statistics are the same for the Tx site and for the Rx site and thus, in the following, they are not differentiated.
is of course a decreasing function of the antenna spacing. Furthermore, for a given spacing, the correlation in the transverse plane increases when the axial distance increases, at least until the end of a zone, named A in Figure 9, occurring at a point called "breakpoint trans." This remark is connected to the comments made in Section 4 concerning the axial correlation, where we have outlined that, when the axial distance increases, the highorder modes are more and more attenuated, leading to a less fluctuating electromagnetic field. Beyond the "breakpoint trans" (zone B in Figure 9), keeps an average high value, even if local decreases are observed. The local decreases can be explained by the field pattern in the transverse plane of the tunnel. Indeed, this pattern does not present translation symmetry since it results from the combining of many modes, both in amplitude and in phase.
6. Full Model
The previous sections have proposed empirical formulas, based on experimental results, to model the path loss and the field fluctuation and correlation in a transverse plane. These formulas can be applied to randomly generate the transfer matrices H of an MIMO link in a straight tunnel having an arched crosssection, which is the shape of most road and railway tunnels. The transmitting and receiving arrays are supposed to be linear arrays, whose axes are horizontal and situated in the transverse plane of the tunnel, this configuration being quite usual. An approach based on the Kronecker model [21] was chosen for its simplicity.
 (1)
define the system parameters, such as frequency, distance between the transmitter and the receiver, number of array elements at the transmitter and at the receiver, element spacing and number of snapshots, corresponding to the number of realizations to be simulated;
 (2)
determine a value for the path loss using (3);
 (3)
compute a K factor from (11). We recall that in (3) and in (11), the value given by the model is the sum of two terms: a deterministic one plus a random variable whose standard deviation is known;
 (4)
knowing K and , the elements of a matrix, having the same size as H, are randomly chosen in a normalized Ricean distribution;
 (5)
as mentioned in Section 4, it was assumed that the correlations between either the transmitting elements or the receiving elements follow the same distribution. The terms of the correlation matrices at the transmitting and receiving sites, and , are thus deduced from (19).
To give an example of application of this formula, let us consider a MIMO system at 4 GHz, an array element spacing of 0.8 (6 cm at 4 GHz) and a distance d between the transmitter and the receiver of 250 m.
where is the identity matrix, is the transpose conjugate operation and SNR is the signaltonoise ratio at the receiver. The channel capacity C was calculated by assuming a fixed SNR equal to 10 dB. A constant SNR was chosen because we want to emphasize the influence of correlation and field distribution in the transverse plane. To compute the capacity assuming a fixed transmitting power, the contribution of the path loss must be added, which is straightforward.
7. Conclusion
The statistics of the electromagnetic field variation in a tunnel has been deduced from measurements made in an arched tunnel, which is the usual shape of road and railway tunnels, and in a frequency range extending from 2.8 to 5 GHz. Both the methodology of the experiments and the analysis were aimed at predicting the performance of an MIMO link in a wide frequency band.
It was shown, by subtracting the antenna effect, that the path loss is not strongly dependent on frequency and that the attenuation constant keeps small values, the tunnel behaving as a lowloss guiding structure. Along the investigated transverse axis of the tunnel, over 33 cm long, the smallscale fading follows a Ricean distribution. However, for distances between the transmitting and receiving antennas up to 200 m, theK factor is below −15 dB, meaning that the field is nearly Rayleigh distributed. It also appeared that K is an increasing function of distance, reaching 0 dB at about 400 m.
Empirical formulas to model the main propagation characteristics were proposed and applied to generate transfer matrices of an MIMO link.
Declarations
Acknowledgments
This work has been supported by the European FEDER funds, the Region NordPas de Calais, and the French ministry of research, in the frame of the CISIT project.
Authors’ Affiliations
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