**3.2.1 Characteristics determined from a propagation model in a rectangular tunnel**

It has been previously outlined that, at a short distance from Tx, numerous modes or a large number of rays contribute to the total field. At a given distance of Tx, the number of active modes increases with the transverse dimensions of the tunnel, the attenuation of the *EHmn*  modes being a decreasing function of the width or of the height as shown in (4). If the tunnel width increases, interference between modes or rays will give a more rapidly fluctuating field with frequency, and thus a decrease in the coherence bandwidth *Be.* As an example, for

a frequency of 2.1 GHz in a tunnel 8 m high, Be decreases from 40 MHz to 15 MHz when the tunnel width increases from 5 m to 20 m. The channel impulse response (CIR) can be established from the channel transfer function calculated in the frequency domain by applying a Hamming window, for example, and an inverse Fourier transform. In Fig. 7, for a tunnel 13 m wide and 8 m high and a bandwidth of 700 MHz, the theoretical amplitude of the received signal in a delay-distance representation has been plotted, in reference to an arbitrary level and using a color scale in dB. At a given distance, the successive packets of pulses, associated with reflections on the walls, clearly appear. We also see that the excess delay is a decreasing function of distance .

Fig. 7. Theoretical channel impulse response in a wide rectangular tunnel.

At first glance, one could conclude that the excess delay is a decreasing function of distance. However, a more interesting parameter is the delay spread, *Ds,* defined as the second-order moment of the *CIR* (Molisch, 2005). It is calculated at each distance *d* by normalizing each CIR to its peak value. For a threshold level of -25 dB, *Ds* varies in this wide tunnel, between 5 and 28 ns, but the variation is randomly distributed when 50 m < *d* < 500 m. From the theoretical complex CIRs, the DOA/DOD of the rays can be calculated by using high resolution algorithms such as SAGE or MUSIC (Therrien, 1992). At a distance *d* of 50 m, the angular spectrum density determined from MUSIC is plotted in Fig. 8. It represents the diagram (delay, DOA), each point being weighted by the relative amplitude of the received signal, expressed in dB above an arbitrary level, and conveyed in a color scale. The DOA is referred to the tunnel axis.

At a distance of 50 m, the rays arriving at an angle greater than 50° are strongly attenuated . A parametric study shows that the angular spread is a rapidly decreasing function of the distance d. This can be easily explained by the fact that rays playing a dominant role at large distances, impinging the tunnel walls with a grazing angle of incidence.

#### **3.2.2 Characteristics determined from measurements in an arched tunnel**

Measurement campaigns in the 2.8-5 GHz band have been carried out in the arched tunnel described in 3.1.2. The channel sounder was based on a vector network analyser (VNA) and on two virtual linear arrays. More details on the measurement procedure can be found in

(Molina-Garcia-Pardo et al., 2009c, 2009d). The mean delay spreads are given in Table 3, calculated in 5 successive zones, from 100 m to 500 m from Tx. As shown in Table 3, the delay spread in this range of distance remains nearly constant, in the order of a few ns, whatever the distanced. This result is strongly related to the DOA/DOD of the rays. The variation in their angular spread As is plotted in Fig. 9. At 50 m, As is equal to about 12° and then decreases with distance (Garcia-Pardo et al., 2011) .

Fig. 8. Theoritical angular power spectrum of the DOA in the plane (delay, direction of arrival), in a wide tunnel and at 50 m from the transmitter .

Fig. 9. Angular spread of the DOA/DOD of the rays in a road tunnel (Garcia-Pardo et al., 2011).


Table 3. Mean delay spread in a semi arched road tunnel.

The fact that the delay spread remains constant can thus be explained by this decrease of *As*  leading to constant time intervals between successive rays. Other measurements carried out in curved tunnels or tunnels presenting a more complex structure are reported for example in (Wang & Yang, 2006; Siy et al., 2009).

### **4. MIMO communications in tunnels**

To improve the performances of the link, one of the most effective approaches recently developed is based on MIMO techniques (Foschini & Gans, 1998). Enhancement of spectral efficiency and/ or decrease of the bit error rate (BER) were clearly emphasized for indoor environments, but in this case the paths between the Tx and Rx array elements are not strongly correlated (Correia, 2006). In a tunnel, however, the DOA/DOD of the rays are not widely spread, and one can wonder whether the number of active modes produce both a sufficient spatial decorrelation and a distribution of the singular values of the **H** matrix so that space time coding will yield a significant increase in the channel capacity .

#### **4.1 Prediction of capacity from propagation models**

To compute the elements of the **H** matrix, ray theory can be applied by adding all complex amplitudes of the rays received at each Rx antenna, this process being repeated for all Tx antennas. However, the computational cost increases when the receiver is placed far from Tx since the number of reflections needed to reach convergence becomes very large. A more interesting approach is the modal theory (Kyritsi & Cox, 2002; Molina-Garcia-Pardo et al., 2008a). In an *MxN* MIMO system (M being the number of Tx antennas and *N* the number of Rx antennas), the *Nxl* received signal y is equal to:

$$
\vec{y} \equiv H\vec{x} + \vec{n} \tag{7}
$$

where x is the *Mxl* transmitted vector and ii is the *Nxl* additive white Gaussian noise vector. The transfer matrix **H** is fixed, i.e. deterministic, for any given configuration. The capacity for a given channel realization is given by (Telatar, 1995; Foschini & Gans, 1998):

$$\mathbf{C} = \log\_2\left(\det\left(I\_N + \frac{\text{SNR}}{M}\mathbf{H}\mathbf{H}^\dagger\right)\right) = \sum\_{i=1}^{\min\{N,M\}} \log\_2\left(1 + \text{SNR}\,\mathbb{A}\_i\right) \tag{8}$$

where *IN* is the *NxN* identity matrix, t represents the conjugate transpose operation, A; are the normalized eigenvalues of *HHt* and *SNR* is the signal-to-noise ratio at the receiver. Let *A~n* ( z) be the amplitude of the mode produced by the *jth* transmitting array element at the receiving axial location z. Each term h;j(z) of **H,** is the transfer function between the Tx element j and the Rx element *i.* This transfer function can be easily determined from (3):

$$h\_{\vec{\eta}}(z) = \sum\_{j=1}^{M} \sum\_{m} \sum\_{n} A\_{mn}^{j} \begin{pmatrix} z \ \end{pmatrix} e\_{mn} \langle \mathbf{x}\_{i}, y\_{i} \rangle \tag{9} = \sum\_{j=1}^{M} \sum\_{m} \sum\_{n} A\_{mn}^{j} \begin{pmatrix} 0 \end{pmatrix} e\_{mn} \langle \mathbf{x}\_{i}, y\_{i} \rangle \ e^{\tau \gamma\_{m} z} \tag{9}$$

In the above summation, the two terms *~n* ( z) and *emn (xi, Yi)* are functions of the position of the Tx element and of the Rx element of coordinates *(xi, Yi),* respectively. We note that if the two sets of modes excited by two transmitting elements h and h have the same relative weight, two columns of **H** become proportional. In this case, **H** is degenerated and spatial multiplexing using these elements is no longer possible. In (Molina-Garcia-Pardo et al., 2008a), two rectangular tunnels were considered, with transverse dimensions 8 **m x** 4.5 m (large tunnel) and 4 m x 4.5 m (small tunnel). One conclusion of this work is that the Tx antenna must be off-centered, so that a large number of modes are excited with nearly similar weights, contrary to the case of an excitation by a centered element. Numerical applications show that, at a distance of 600 m and for an excitation by an antenna offset of 1/ 4 of the tunnel width, there are five modes whose relative amplitudes, when referred to the most energetic mode, are greater than -7 dB, whereas for the centered source, there are only three modes. In the following, we thus consider off-centered source positions, in order to excite a large number of active modes. Another limiting factor in MIMO performance is the correlation between receiving array elements (Almers et al., 2003). As an example, assume that the transmitting array is situated at 1/4 of the tunnel width and at 50 cm from the ceiling. For the two previous tunnels, we calculate the average spacing /:u that produces a correlation coefficient p, between vertical electric fields at x and x+t:u, smaller or equal to 0.7. Results in Fig. 10 show that the correlation distance is an increasing function of the axial distance, due to the decrease in the number of active modes.

Fig. 10. Horizontal correlation distance (for p = 0.7) for two tunnels for a frequency of 900 MHz. Curve with successive points deals with the tunnel 8 m wide, the other curve corresponds to the tunnel 4.5 m wide, the dashed lines give the averaged values (Molina-Garcia-Pardo et al., 2008a).

One can also calculate the correlation Plih (z) between the electric fields received in a transverse plane, when the transmitting elements are ji and ji, successively. Mathematical expressions of this correlation function are given in (Molina-Garcia-Pardo et al., 2008a), these authors also introduce a correlation function between modes. An example is given in Fig. 11, where the variation of PJij <sup>2</sup>(z) for the large tunnel is plotted. We observe that, as expected, *PJijz* (z) increases with distance. It is strongly dependent on the spacing between the Tx elements, and especially when this spacing becomes equal or smaller than 2A.

Fig. 11. Average correlation between the electric fields produced by two transmitters in the large tunnel for different array element spacing (61, 4.A., 2A and 1) (Molina-Garcia-Pardo et al., 2008a).

Fig. 12. Capacity of a 4x4 MIMO system for a *SNR* of 10 dB in both tunnels (Molina-Garcia-Pardo et al., 2008a).

Finally, the theoretical ergodic capacity C, calculated for an *SNR* of 10 dB versus distance, is presented in Fig. 12 for the two tunnel widths. At short distances, important fluctuations in C are found in the large tunnel due to the great number of active modes. In the small tunnel, due to the reduction in the number of modes and of correlation effects, C is smaller. For the same reason, we observe that in both tunnels, C is a continuously decreasing function of distance. We have thus seen that the concept of spatial diversity usually used in MIMO must be replaced, in tunnels, by the concept of modal diversity, the problem being to optimize the antenna array to excite numerous modes and thus to guarantee a low correlation between the multipath channels.

To conclude this section, it is interesting to have a measure of the multipath richness of the tunnel, and thus of the capacity, independent of the number of array elements. Therefore, we define a reference scenario corresponding to a uniform excitation of the tunnel and to a recovery of all modes in the Rx plane. This can be theoretically achieved by putting, in the whole transverse plane of the tunnel, a two-dimensional (2D) equal-space antenna array with inter-element spacing smaller that Ji,/2 (Loyka, 2005). In such a reference scenario, even if unrealistic from a practical point of view, each eigenvalue Ai corresponds to the power *Pmn* of a mode *EHmn* in the receiving plane (Molina-Garcia-Pardo et al., 2009a, 2009b). In this case, the capacity *crefsce* in this scenario is given by:

$$\mathbf{C}^{ref\,\mathrm{sc}} = \lim\_{k \to \infty} \left[ \sum\_{i=1}^{k} \log\_2 \left( \mathbf{1} + \text{SNR} \,\Lambda\_i^{ref\,\mathrm{sc}} \right) \right] \text{ with } \quad \Lambda\_i^{ref\,\mathrm{sc}} = \frac{\exp \left( 2 \left( a\_{11} - a\_{mn} \right) z \right)}{\sum\_{m,n} \exp \left( 2 \left( a\_{11} - a\_{mn} \right) z \right)} \tag{10}$$

cref•ce only depends on the *SNR* and on the attenuation constants *amn* of the modes and thus on the frequency and on the electrical and geometrical characteristics of the tunnel.

Fig. 13 shows the variation in *crefsce* versus the number *k* of eigenvalues of Hor of the modes taken into account, the thodes being sorted in decreasing power, for different frequencies between 450 and 3600 MHz. The distance between Tx and Rx is 500 m. At 450 MHz, only one mode mainly contributes to the capacity, and at 900 MHz the capacity still rapidly converges to its real value, since high order modes are strongly attenuated. At 1800 MHz, the summation must be made on at least 10 modes, since the attenuation constant in a smooth rectangular tunnel decreases with the square of frequency. At 3600 MHz, the attenuation of the first 30 modes is rather small and it appears that the curve nearly fits the curve "Rayleigh channel" plotted by introducing i.i.d. values as entries for the *H* matrix.

Finally, for this reference scenario and for a frequency of 900 MHz, Table 4 gives the number of modes needed to reach 90% of the asymptotic value of the capacity at different distances. It clearly shows the decreasing number of modes playing a leading part in the capacity when increasing the distance.


Table 4. Number of modes needed to reach 90% of the asymptotic value of the capacity at 900 MHz and for different distances.

Fig. 13. Capacity *crefsce* for the reference scenario versus the number *k* of eigenvalues or modes taken into a~count. The distance between Tx and Rx is 500 m, the tunnel being 5 m wide and 4 m high (Molina-Garcia-Pardo et al., 2009b).

To sum up this section, let us recall that the excitation of the modes plays a leading part in MIMO systems. It is thus interesting to excite the maximum number of modes, with nearly the same amplitude at the receiver plane. Optimum array configurations must thus be designed to obtain the maximum profit from MIMO systems. Furthermore, changes to the tunnel shape, such as narrowing or curves, will modify the weight of the modes and consequently the MIMO performance, as we will see in the next section.

#### **4.2 MIMO channel capacity determined from experimental data**

As stated before, many experiments have been conducted in mines and tunnels to extract both narrowband and wideband channel characteristics, but MIMO aspects were only recently considered. To illustrate both the interest of using MIMO in tunnels and the limitation of this technique, two scenarios are successively considered. First, the expected capacity will be determined from measurement campaigns in a subway tunnel whose geometry is rather complicated. Then we will consider the straight road arched tunnel discussed in 3.1.2, and whose photo is given in Fig. 4, to discuss the interest or not of using polarization diversity in conjunction with MIMO systems. Other studies, published in the literature, deal with pedestrian tunnels (Molina-Garcia-Pardo et al., 2003, 2004) where the position of the outside antenna is critical for the performance of the system. More recently, investigations into higher frequency bands have been carried out either for extracting double directional characteristics in road tunnels (Siy Ching et al., 2009), or for analyzing the performance of **MIMO** in the Barcelona Metro (Valdesuerio et al., 2010).

#### **4.2.1 MIMO capacity in a subway tunnel**

Measurements were made along the subway line, shown in Fig. 14, between two stations, Quai Lilas and Quai Haxo, 600 m apart (Lienard et al., 2003). The geometrical configuration

can be divided into two parts : Firstly, there is a two-track tunnel that exhibits a significant curve along 200 m, from Lilas (point A) to point B, and then the tunnel is straight from point B to point D (100 m apart) . Beyond this point and up to Haxo, the tunnel is narrow, becoming a one-track tunnel for the last 300 m (from D to C). The width of the one-track and of the two-track tunnel is 4 m and 8 **m,** respectively . The height of the tunnel is 4.5 m. Its cross-section is arched, but numerous cables and equipment are supported on the walls.

Fig. 14. Plan view of the tunnel. The distance between Quai Lilas and Quai Haxo is 600 **m.** 

For studying a 4x4 MIMO system, 4 horn antennas were located on the platform. On the train, due to operational constraints, the patch antennas had to be placed behind the windscreen. In order to minimize the correlation, these antennas were placed at each comer of the windscreen . The channel sounder was based on a correlation technique and at a center frequency of 900 MHz and a bandwidth of 35 MHz. Both theoretical and experimental approaches have shown that, within this bandwidth, the channel is flat. The complex channel impulse response can thus only be characterized by its complex peak value and the MIMO channel is described in terms of H complex transfer matrices. All details on these measurements can be found in (Lienard et al., 2003).

The orientation of the fixed linear array inside a tunnel is quite critical. Indeed, the correlation distance between array elements is minimized when the alignment of the array elements is perpendicular to the tunnel axis. This result can be easily explained from the interference between active modes giving a signal which fluctuates much more rapidly in the transverse plane than along the tunnel axis. From the measurement of the H matrices, the expected capacity C was calculated for any position of the train moving along the tunnel. If we consider the first 300 m, the fixed array being placed at Quai Lilas, the propagation occurs in the twotrack tunnel. Curves in Fig. 15 represent the variation in the cumulative distribution function of C using either a single antenna in transmission and in reception (SISO) or a simple diversity in reception (Single Input Multiple Output - SIMO) based on the maximum ratio combining technique or a 4x4 MIMO technique. These capacities can also be compared to those which would be obtained in a pure Rayleigh channel. In all cases, the signal to noise ratio (SNR) is constant, equal to 10 dB. An increase in capacity when using MIMO is clearly shown in Fig. 15.

Indeed, for a probability of 0.5, C is equal to 2, 5 and 9 bit/ s/Hz, for SISO, SIMO and MIMO, respectively. In a Rayleigh environment, C would be equal to 11 bit/ s/Hz.

Fig. 15. Cumulative distribution of the capacity in a two-way tunnel for different diversity schemes, for an *SNR* of 10 dB (Lienard et al., 2003).

When the mobile enters the one-track tunnel at point D, one can expect an important decrease in the capacity, even by keeping the same *SNR.* Indeed, as we have seen in 2.1, the high order modes will be strongly attenuated if the tunnel narrows, leading to a decrease in the number of active modes and thus to an increase in the correlation between elements of the mobile array. In Fig. 16, we see that the capacity, in the order of 9 bit/ s/Hz in the two-

Fig. 16. Capacity for a constant SNR of 10 dB. Transmission from the 2-track tunnel, reception first in the 2-track tunnel (0 - 300 m), and then in the 1-track tunnel (300m - 600m). (Lienard et al., 2006).

track tunnel, decreases to 5.5 bit/ s/Hz after the narrowing and thus reaches the capacity of a SIMO configuration. A more detailed explanation based on the correlation coefficients is given in (Lienard et al., 2006).

#### **4.2.2 MIMO capacity in a straight road tunnel and influence of polarization diversity**

Let us now consider the straight arched tunnel presented in 3.1.2 and a 4x4 MIMO configuration. In the experiments briefly described in this section, but detailed in (Molina-Garcia-Pardo et al., 2009c), the total length of each array is 18 cm. Different orientations of the elements, i.e. different polarizations, were considered:


In these 3 cases the inter-element spacing is thus equal to 6 cm. Another configuration, called "Dual", because Tx and Rx elements are dual-polarized, was also studied. In this case, the length of the array can be reduced from 18 cm to 6 cm. Channel matrix measurements were made in a frequency band extending from 2.8 to 5 GHz. Since the propagation characteristics do not vary appreciably in this band, average values of the capacity were determined from the experimental data, always assuming a narrow band transmission, i.e. a flat channel. The mean capacity C is plotted in Fig. 17 assuming a constant *SNR* of 15 dB, whatever the location of the mobile array. The worst configuration is W or llli, and is due to the decrease in the number of active modes at large distances, leading to an increase in the correlation between array elements, as previously explained. For VHVH, C does not appreciably vary with distance and remains in the order of 16 bit/ s/Hz. This better result comes from the low correlation between cross-polarized field components, the distance

Fig. 17. Mean MIMO capacity assuming a fixed *SNR* at the receiver of 15 dB (Molina-Garcia-Pardo et al., 2009c).

between co-polarized array elements also increasing from 6 cm to 12 cm. A similar result was obtained with the Dual configuration. As a comparison, the theoretical capacity of a 4x4 MIMO in a i.i.d. Rayleigh channel would be around 20 bit/s/Hz, while for a SISO link C would be 5 bit/ s/Hz, thus much smaller than for MIMO.

These results give some insight into the influence of the number of active modes and of the correlation between array elements on the capacity inside a tunnel. However, in practice, the Tx power is constant and not the *SNR.* Let us thus assume in a next step a fixed Tx power, its value being chosen such that at 500 m and for the VV configuration, an *SNR* of 15 dB is obtained. The capacities for the different array configurations and given in Fig. 18 do not differ very much from one another. This result can be explained by taking both the X-polar discrimination factor and attenuation of the modes into account. First we observe that VV gives slightly better results than HH, the attenuation of the modes corresponding to the vertical polarization being less significant. If we now compare HH and VHVH, we find that the two curves are superimposed. Indeed, we are faced with two phenomena. When using VHVH the spacing between co-polarized array elements is larger than for HH (or VV) and, consequently, the correlation between array elements is smaller. Unfortunately, the waves remain polarized even at large distances, as outlined in Table 3 of 3.1.2. This means that the signal received on a vertical Rx element comes only from the two vertical Tx elements and not from the horizontal Tx elements.

Fig. 18. Mean MIMO capacity assuming a fixed Tx Power (Molina-Garcia-Pardo et al., 2009c).

The total received power in the VHVH configuration is thus nearly half the total power in the HH ( or VV) case. It seems that, comparing VHVH and HH, the decrease in power is compensated for by the decrease in correlation, leading to the same capacity. A similar result has been obtained when calculating the capacity of the Dual array. In all cases, the capacity obtained with such MIMO configurations is much larger that the SISO capacity for vertical polarization, as also shown in this figure. In conclusion, changing the polarization of the successive elements of the antenna arrays, as for VHVH, does not result in an improvement in MIMO performance in an arched tunnel. The advantage of the Dual configuration is that it decreases the length of the array while keeping the same channel capacity.

#### **4.3 Performances of MIMO communications schemes**

In previous sections, propagation aspects and capacity have been studied, but the bit error rate (BER) is one of the most important system design criterion. The robustness of MIMO to cope with the high correlation between array elements strongly depends on the MIMO architecture. MIMO can be used in three ways: beamforming, spatial multiplexing and space-time coding. Beamforming is useful for increasing the *SNR* and reducing the interference, spatial multiplexing increases the throughput by transmitting the independent flow of data on each antenna, while space time codes decrease the BER. In the following, we will consider space time coding and spatial multiplexing and we will compare the robustness of two well-known architectures, namely Vertical Bell Laboratories Layered Space-Time - VBLAST - (Wolniansky et al., 1998) and Quasi-Orthogonal Space-Time Block Codes - QSTBC - (Tirkkonen et al., 2000; Mecklenbrauker et al., 2004; Tarokh, 1999), assuming a narrow band transmission, i.e. a flat channel. The symbol detection method is based on the Minimum Mean Squared Error (MMSE) algorithm.

The BER was determined from the measurement of the *H* matrices in the arched tunnel presented in 3.1.2. To be able to carry out a statistical approach, the BER was calculated for numerous Rx locations in the tunnel and for 51 frequencies equally spaced in a 70 MHz band around 3 GHz. In (Sanchis-Borras et al., 2010), two transmission zones were considered: One near Tx, between 50 m and 150 m, and one far from Tx, between 400 and 500 m. In the following, only the results far from Tx are presented. The statistics on the BER were calculated owing to a simulation tool of the MIMO link and by considering 100 000 transmitted symbols, leading to a minimum detectable BER of 10-5• The Tx power is assumed to be constant and was chosen such that a SNR of 10 dB is obtained at 500 m for the VV configuration. To make a fair comparison between MIMO and SISO, chosen as a reference scenario, the throughput and the transmitting power are kept constant in all cases. This means that the modulation schemes are chosen in such a way that the bit rate is the same for SISO and MIMO. In our examples, we have thus chosen a 16QAM scheme for SISO and QSTBC, and a BPSK for 4x4 VBLAST. The complementary cumulative distribution functions (ccdf) of the BER were calculated for the various transmission schemes, MIMO-VBLAST, MIMO-QSTBC and SISO, for two array configurations, VV and Dual. We have chosen these two kinds of array since, as shown in 4.2.2, they present the best performances of capacity under the assumption of constant transmitted power.

The results, presented in Fig. 19, show that there is no benefits from using VBLAST for the VV antenna configuration since the BER (curve 1) does not differ from the BER of a SISO link (curve 5). Despite the fact that the received power with co-polarized Tx and Rx arrays is maximized, the important correlation between the nearest antennas of the Tx/Rx arrays gives rise to a strong increase in the BER. Such a sensitivity of VBLAST to the correlation between antennas was already outlined in (Xin & Zaiping, 2004).

If VBLAST is used, but with dual-polarized antennas (Fig. 19, curve 2), the decrease in correlation allows for a better performance despite the fact that the average received power is smaller. We also note that QSTBC always gives better results than VBLAST. For this QSTBC scheme, contrary to what occurs for VBLAST, the BER is slightly better for VV polarization, i.e. for a higher received power, with QSTBC being much less sensitive to the correlation between antennas than VBLAST.

Fig. 19. Complementary cumulative distribution function of the BER far from the transmitter and for a fixed transmitting power (Sanchis-Borras et al., 2010).

As a comparison, we have also calculated the BER for a Rayleigh environment, assuming the same average *SNR* as for W in tunnel. Dual is not compared to Rayleigh because in tunnel the waves are strongly polarized leading to a non-uniform distribution of the *H* matrix elements, in contrast to the case of a pure Rayleigh distribution. It appears that results obtained with QSTBC in tunnels are close to those which would be obtained in a Rayleigh environment, even at great distances from Tx. In conclusion, for a communication link in tunnels, MIMO outperforms SISO not only in terms of mutual information but also in terms of BER, assuming of course the same transmitting power and the same throughput, and under the condition that the number of active modes in the receiving plane is sufficient. Due to the guided effect of the tunnel and the attenuation of high order propagating modes at a large distance from the transmitter, the correlation between array elements strongly increases with distance and the QSTBC transmission scheme is thus more appropriate.

#### **5. Concluding remarks**

From measurements carried out in a straight tunnel of arched cross-section, which is quite a usual shape, we have shown that experimental results can be interpreted by means of an equivalent rectangular tunnel. The relevance of using MIMO techniques in tunnels was then investigated by first studying the correlation between array elements and the properties of the MIMO channel transfer matrix. This has been done by introducing the concept of active modes existing in the receiving plane. Despite the fact that the waves are guided by the tunnel, leading to a small angular spread for the paths relating the transmitter and the receiver, it appears that MIMO improves the channel capacity owing to a so-called modal diversity. Results obtained in more complex environments were also presented, such as in subway tunnels. In terms of bit error rate with space-time coding, a transmission scheme robust against antenna correlation must be chosen.

#### **6. References**

