# Propagation in Tunnels: Experimental Investigations and Channel Modeling in a Wide Frequency Band for MIMO Applications

- J.-M. Molina-Garcia-Pardo
^{1}Email author, - M. Lienard
^{2}and - P. Degauque
^{2}

**2009**:560571

https://doi.org/10.1155/2009/560571

© J.-M. Molina-Garcia-Pardo 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

## 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 (GMS-R) 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 out-of-zone 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 cross-section 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 EM-6116) 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.

*d*, both the Tx and Rx antennas were moved in the transverse plane on a distance of 33 cm, with a spatial step of 3 cm, corresponding to half a wavelength at 5 GHz. A transfer matrix is thus obtained, the configuration of the measurements being schematically described in Figrue 3. Fine spatial sampling was chosen for measurements in the transverse plane because, as recalled in the introduction, antenna arrays for MIMO applications have to be put in this plane to minimize correlation between array elements.

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 large-scale 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 EM-6116) |

Transmitter power | 20 dBm |

Dynamic range | >100 dB |

Position in the transverse plane | 12 positions every 3 cm ( |

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.

*d*, for the various transverse positions of the antennas. Furthermore, one can also average over few frequencies, considering a frequency bandwidth smaller than the channel coherence bandwidth. In this example, the coherence bandwidth being on the order of 10 MHz, was averaged over 7 frequencies around

*f*, the frequency step being 1.37 MHz, and over the 144 successive combinations of the transverse positions of the Tx and Rx antennas. The average value is also plotted in Figure 4.

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 ultra-wideband 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 non-LOS, 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*, high-order 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.

## 4. Field Distribution in the Transverse Plane

### 4.1. Field Distribution Function

*d*, the possible combinations of the Tx and Rx antennas, and 7 close frequencies, within a 10 MHz band, as earlier explained. This has been done for various frequency bands between 2.8 and 5 GHz. We have compared the measured data to those given by a Rayleigh, Weibull, Rician, Nakagami and Lognormal distribution, and then using the Kolmogorov-Smirnov [20] test to decide what distribution best fits the experimental results. A Rice distribution appears to be the optimum one, whatever the frequency. The mathematical expression of its probability density function (PDF) is given by

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

*K*at a distance

*d*and a frequency

*f*, from the following expression:

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.

*K*factor is below −15 dB, which means that the received power strongly varies in the transverse plan, nearly following a Rayleigh distribution. However,

*K*increases with distance and reaches 0 dB or more beyond 400 m, the constant part of the distribution becoming equal to or greater than the random part.

This increase of *K* is due to the fact that the contribution of high-order 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.

*K*over groups of 7 frequencies and over 144 successive combinations of the transverse positions of the transverse positions of the Tx and Rx antennas, an empirical expression of the average

*K*factor in terms of frequency and distance can be found. It is given by

*K*is given by .

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

*ν*and can be calculated. Note that mean value of the field would be determined by the large-scale fading, and fast variations around the mean value by the Rice distribution. Therefore, can be computed using (8) and (12):

*ν*is immediately deduced from (12). As an example, curves (a) and (b) in Figure 8 compare the PDFs deduced from the measurements to those assuming a Rice distribution, for m and GHz, and m and GHz, respectively. We see the rather good agreement between measurements and the empirical formulation; the confidence level of the Smirnoff-Kolmogorov test remaining below 0.05.

## 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.

*d*, and for each frequency

*f*, the amplitude of the complex correlation function was deduced from the channel matrix, whose elements are associated to the successive positions of the Tx and Rx antennas in the transverse plane. Let

*s*be the spacing between two receiving points. Figure 9 shows, for GHz, the variation of versus the axial distanceand for different values of

*s*: 3, 9, 21, and 33 cm.

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 high-order 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.

*A*slightly increases with frequency, as it occurred in the case of the longitudinal correlation (Section 4). Again, using all measured frequencies, an empirical formula giving the position of the "breakpoint_trans" point is given by

*B*, one can calculate the mean value (

*s*, zone

*B*,

*f*) by averaging over the axial distance

*d*. The results are the curves plotted in Figure 10, versus frequency and for different values of

*s*: 3, 9, 21, and 33 cm.

*s*, zone

*B*,

*f*) is nearly frequency independent and that an empirical formula fitting the experimental results can be obtained:

*A*assumes an average linear variation with distance. The adequate formula in this zone is

## 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 cross-section, 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.

**H**, the following steps can be followed:

- (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)
- (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.

**H**can be computed as [22]

where
is the
identity matrix,
is the transpose conjugate operation and SNR is the signal-to-noise 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 low-loss guiding structure. Along the investigated transverse axis of the tunnel, over 33 cm long, the small-scale fading follows a Ricean distribution. However, for distances between the transmitting and receiving antennas up to 200 m, the*K* 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 Nord-Pas de Calais, and the French ministry of research, in the frame of the CISIT project.

## Authors’ Affiliations

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