MIMO Capacity in a Pedestrian Passageway Tunnel Excited by an Outside Antenna

MIMO Capacity in a Pedestrian Passageway Tunnel Excited by an Outside Antenna J. M. MOLINA-GARCIA-PARDO*, M. LIENARD**, P. DEGAUQUE**, L. JUAN-LLACER* * Dept. Techno. Info. and Commun. Universidad Politecnica de Cartagena SPAIN Josemaria.molina@upct.es **Dept IEMN/TELICE Université de Lille FRANCE Pierre.Degauque@univ-lille1.fr Abstract: - Numerous papers have already been published on the improvement of the channel capacity which can be obtained by using Multiple Input Multiple Output techniques. Various environments have been studied as indoor and urban environment. Since there is also a need to cover tunnels, recent works deal with the characterization of the channel transfer matrix in order to predict the performance of the link in such a configuration. However it was always assumed that both the transmitting antenna and the receiving antenna are situated inside the tunnel. Since, for short tunnels, an additional fixed antenna inside the tunnel is not always necessary, the objective of this paper is to examine the case of a mobile entering and moving inside a tunnel excited by an outside antenna. Since the capacity depends both on the path loss and on the correlation between array elements, a parametric study shows the influence of the offset angle characterizing the direction of the fixed antenna array referred to the tunnel axis. Results are based on experiments carried out in a pedestrian tunnel and at a frequency of 2.45 GHz. Key-Words: - MIMO, tunnel, capacity, angular spread, correlation. 1 Introduction In third generation systems, data transmission at high data rates might be guaranteed in different radio propagation environments as rural, suburban, urban, in-buildings but also in tunnels [1]-[5]. To improve the performances of the link, Multiple- Input Multiple-Output (MIMO) technology can be used, and numerous papers have been published on MIMO channel characterization, mainly in indoor and urban environment. Concerning MIMO in tunnels, theoretical and experimental approaches have been carried out in railway or subway tunnels [6], [7] and in road tunnel [8]. In order to simplify the theoretical approach, the propagation model is often based on the assumption of straight rectangular tunnels. In this simplified approach, a ray theory or a modal theory can be used to predict and interpret the MIMO channel capacity [9]. However, to our knowledge, in all previous MIMO studies, the transmitting (Tx) array and the receiving (Rx) array are always supposed to be situated inside the tunnel. The objective of this paper is thus to consider the case of a base station (BS) outside the tunnel and a mobile station (MS) entering the tunnel. This configuration may occur in case of short tunnels, an additional BS inside the tunnel being not necessarily needed. For this configuration, one can expect that the capacity will strongly depend on the relative position of the BS, referred to the tunnel axis, and on the location of the MS inside the tunnel. A measurement campaign has thus been carried out in a pedestrian passageway tunnel and for a carrier frequency of 2.45 GHz. All measurements of channel transfer functions were made in the frequency domain and based on linear virtual arrays. Results on channel characteristics and capacity, assuming a narrow band transmission, are presented. This work thus extends to MIMO, previous experiments made in the same tunnel for characterizing a SISO (Single Input Single Output) link [10]. The paper is organized as follows: Section II presents the tunnel geometry and the experimental set up. Section III deals with the characteristics of the propagation channel depending on the location of the fixed outside array, and expressed in terms of path loss, Ricean K-factor and correlation between antennas. Results on the channel capacity are given ISBN: 978-1-61804-018-3 132

in Section IV, the case of a constant Signal to Noise Ratio (SNR) or of a constant transmitting power being successively envisaged. Finally, section V summarizes the contributions of the present work and gives conclusions. 2 Description of the Experiments The geometrical configuration of the experiments and the methodology which has been followed to extract the channel characteristics are presented. 2.1 Geometrical configuration A top view of the environment where the measurements where performed is depicted in Fig. 1 [10]. The tunnel is 2.8 m high and 23 m long. Its width in the entrance plane is 2.5 m but all along the tunnel, the width is 4.2 m. Three positions of the transmitter (,, ), at a distance R = 20m from the tunnel entrance have been selected. If the middle of the entrance is chosen as the origin, the direction of a transmitter is referred to its angle ϕ with respect to the tunnel axis, as shown in Fig. 1. is situated along the tunnel axis (ϕ 1 = 0 ) while the angles ϕ 2 and ϕ 3 for and are equal to15º and 30º, respectively. Garden Parking d ϕ 3 = 30º Rx20 ϕ 2 = 15º Rx1 Fig. 1. Geometrical configuration of the tunnel. From the first location situated in the entrance plane, the receiver is moving along a maximum distance d of 20 m, from Rx1 to Rx20, with a spatial step of 1 m. 2.2 Methodology of the channel sounding A MIMO (4,4) link, with thus 4 Tx antennas and 4 Rx antennas (or array elements), were studied. These 8 identical antennas (Cisco AIR-ANT2506) are omnidirectional in the horizontal plane and have a gain of 5 dbi. They were situated at a height of 1.8 m and the spacing between each array element may vary from 6 cm up to 24 cm. Measurements of the channel transfer function were made with a 5-port vector network analyzer (VNA) in a frequency band extending from 2.4 to 2.5 GHz, the number of equally spaced frequency points being 1601. One port of the VNA is used as a transmitter and 4 other ports are connected to the Rx antennas, as shown in Fig. 2. A switch allowed successively selecting one of the 4 Tx antennas. The receiving array in the tunnel was orientated in such a way that its broadside direction was aligned to the tunnel longitudinal axis. Similarly, the broadside direction of the Tx array was oriented towards the tunnel entrance, whatever the offset angle ϕ (Fig. 1). VNA G LAN 50 m R Fig. 2 Experimental set-up. Tx Switch GPIB laptop A 30 db low noise amplifier being inserted at the output port of the VNA (Fig. 2), the Tx power was 0 dbm. Whatever the location of the antennas, the signal to noise ratio remains larger than 20 db in the entire frequency band. 3 Characteristics of the Propagation Channel The received power inside the tunnel will strongly depends on the offset angle of the Tx array [4] and will have of course a strong impact on the capacity of the MIMO channel. The other important parameter is the channel diversity which can be first characterized in terms of the variability of the channel, i.e., of its Rician K-factor defined as the ratio of signal power in dominant component over the (local-mean) scattered power. Correlation between array elements playing also a leading part on MIMO performances, we will successively present in this section results on these different parameters and based on experimental results. 3.1 Path loss The average path loss for a given position of the Tx array and of the Rx array was calculated by averaging the received power over the 16 possible combinations Tx/Rx and over the 1601 frequency points. When Tx is situated along the tunnel axis (position ), curve in Fig. 3 shows that the attenuation increases from 10 db from the entrance to the exit of the tunnel. For an offset angle of 15 G ISBN: 978-1-61804-018-3 133

or of 30, we observe an additional attenuation at the end of the tunnel of 3 db and 6 db, respectively. One can mention that for very long tunnel, the slope of the path loss at large distance would tend to the same value equal to the low attenuated EH11 mode propagating in the tunnel [4] 80 K-Factor (db) 10 5 0 75-5 Path Loss (db) 70 65 60 Fig. 3. Measured path loss when Rx moves inside the tunnel. 3.2 K-Factor measure The Ricean K-factor is defined as the ratio of the fixed to variable power components and is thus an interesting parameter for interpreting MIMO results. This parameter can be estimated from the measured transfer function H(d, f, i, j) between the Tx antenna i and the Rx antenna j, by using the moment-method proposed in [11]. Its average value K(d) at a distance d inside the tunnel is given by: 1 γ ( d) Kd ( ) = (1) 1 1 γ ( d) where 2 2 γ ( d) = V[( Hd (, fij,, ) ]/( E[( Hd (, fij,, ) ]) 2 V[.] denotes variance and E[.] the expectation operation. Averaging and variance operation were made over the 16 combinations of Tx and Rx (i and j varying from 1 to 4) and over the 1601 frequency points. At 1 m inside the tunnel, K is between 5 and 7 db since the direct path always plays a dominant role. When d = 3 m, K decreases to 2 db for ϕ = 15 and to -2 db for ϕ = 30. This can be easily explained by the geometry of the problem since beyond 2 m, Rx is in NLOS conditions. For these offset angles, we also note that K then keeps the same average value, on the order of 4 db. -10 Figure 4: Measured K-Factor inside the tunnel. 3.3 Correlation Correlation properties of MIMO matrices have a strong impact on the capacity of a multiantenna system [12]. Let i and j be the ith column and the jth row of the channel transfer matrix H. The normalized complex correlation coefficient between the Rx antennas i and j can be measured as the complex correlation coefficient between the columns of H [20]: i i j j E ( h < h > )( h < h > ) * i, j ρrx = (2) i i 2 j j 2 E h < h > E h < h > where E[.] is the expected value calculated on all four receiving antennas, * indicates complex conjugate and <.> the mean operation. The definition of the normalized complex correlation coefficient between the transmitting antenna elements is quite similar. One can then define an average correlation coefficient between all Rx antennas as: ave i, j ρrx = E ρrx (3) Curves in Fig. 5 represent the variation of this average correlation between the Rx antennas, when Tx is situated either on the tunnel axis () or makes an offset angle of 30 (). When Tx is situated along the tunnel axis, the correlation remains very high, greater than 0.95, even at large distance from Tx. Indeed, the direct path plays a leading role, as we previously observed by examining the variation of the K-factor. If the contribution of the multiple reflected paths is dominant, as in the case for location, the correlation strongly decreases to 0.7-0.8 beyond few meters from the tunnel entrance and does not strongly vary for an antenna spacing of λ or λ/2. ISBN: 978-1-61804-018-3 134

Correlation 1.0 0.9 0.8 0.7 - λ/2 - λ - λ/2 - λ Fig. 5. Correlation at the receiver for 2 positions of Tx and for 2 different antenna spacing. 4 Capacity It is well known, that for a narrow band MIMO system with M transmitting antenna elements and N receiving antenna elements, the maximum theoretical capacity for a uniform distributed transmitted power and with a signal to noise ratio equal to ρ can be expressed as [13], [14]: ρ H C = log2 det IN + HH M (4) where I N is the identity matrix of size (N,N). The upper script H means the complex conjugate and H is the Frobenius normalized MIMO transfer matrix. Let us first consider the case of a constant SNR, supposed to be equal to 25 db. Since in this case, only correlation plays a role on the capacity C, we see in Fig. 6 that for, C varies between 14 and 16 bit/s/hz, whatever the distance d, as it can be expected from the variation of the correlation factor plotted in Fig. 5. Capacity (bit/s/hz) 26 24 22 20 18 16 14 12 Fig. 6. Capacity versus distance assuming a constant SNR of 25 db and for an antenna spacing of λ/2. This capacity remains better than for the SIMO (Single Input Multiple Output) case and than for the SISO (Single Input Single Output) case, equal to 10.3 and 8.3 bits/s/hz, respectively. When the offset angle of Tx increases, the correlation is decreasing, leading to a highest capacity which reaches 22 and 25 bit/s/hz at the end of the tunnel, for and, respectively. A more realistic case corresponds to a constant transmitted power. For simulating this configuration, it was assumed that the SNR at the end of the tunnel, i.e. at location Rx20, is 10 db. Capcity (bit/s/hz) 18 16 14 12 10 8 Fig. 7. Capacity versus distance assuming a constant transmitting power. Curves were normalized by assuming a SNR of 10 db at the end of the tunnel, i.e. at location Rx20. If the BS is placed along the tunnel axis (), the capacity is continuously decreasing when the mobile moves from 5 m to 20 m. Indeed, on one hand the correlation between antennas remains very high, as shown in Fig. 5, and on the other hand, path loss increases of 10 db between the entrance and the end of the tunnel (Fig. 3). For an offset angle of 30 of the BS, we first observe in Fig. 7 a strong decrease of the capacity along the first 8 m. Despite the fact that the correlation between antennas decreases from 0.95 to 0.7, the increase in path loss plays a dominant role. Beyond 8m, the capacity does not vary appreciably, both path loss and correlation being almost constant. We also note that beyond 15m, the channel capacity is better with than with. 5 Conclusion In this paper, the problem of illuminating a tunnel far from its entrance was treated. The MIMO channel was investigated in a small tunnel, by means of measurements using a sounder based on a multiport network analyzer. The channel response ISBN: 978-1-61804-018-3 135

for a 4x4 MIMO system has been measured between 2.4 and 2.5 GHz. It results that correlation between antennas strongly depends on the location of the outside base station, referred to the tunnel axis. Indeed, this correlation remains larger than 0.9 whatever the position of Rx inside the tunnel when the transmitter is located on the direction of the tunnel axis. However, the correlation strongly decreases for offset positions of the transmitter. A trade off thus appears between correlation and path loss and has a strong impact on channel capacity. For such short and narrow tunnels, if Tx presents an offset angle of 30, the MIMO capacity at the end of the tunnel, 20 m long, and with a SNR of 10 db, is still equal to 10 bits/s/hz compared to 3.5 bits/s/hz and 5.4 bits/s/hz which would be obtained for the SIMO and SISO cases, respectively. References: [1] M. Lienard and P. Degauque, Propagation in Wide Tunnels at 2 GHz: A Statistical Analysis, IEEE Trans. on Vehicular Techno., vol. 47, no. 4, 1998, pp. 1322 1328. [2] T.-S. Wang and C.-F. Yang, Simulations and Measurements of Wave Propagations in Curved Road Tunnels for Signals From GSM Base Stations, IEEE Trans. on Antennas and Propag., vol. 54, no. 9, 2006, pp. 2577-2584. [3] Y. P. Zhang and Y. Hwang, Characterization of UHF Radio Propagation Channels in Tunnel Environments for Microcellular and Personal Communications, IEEE Trans on Vehicul. Techno., vol. 47, no. 1, 1998, pp. 283 296. [4] P. Mariage, M. Lienard and P. Degauque, Theoretical and Experimental Approach of the Propagation of High Frequency Waves in Road Tunnels, IEEE Trans. on Antennas and Propag., vol. 42, no. 1, pp. 75-81, January 1994. [5] G. Siy Ching, M. Ghoraishi, M. Landmann, N. Lertsirisopon, Jun-ichi Takada, T. Imai, I. Sameda, and H. Sakamoto, Wideband Polarimetric Directional Propagation Channel Analysis Inside an Arched Tunnel, IEEE Trans. on Antennas and Propag., vol. 57, no. 3, 2009, pp. 760 767. [6] M. Liénard, P. Degauque, J. Baudet and D. Dégardin, Investigation on MIMO channels in subway tunnels, IEEE J. on Selected Areas in Commun., vol. 21, no. 3, 2003, pp. 332-339. [7] J. A. Valdesueiro, B. Izquierdo, and J. Romeu, On 2x2 MIMO Observable Capacity in Subway Tunnels at X-Band: An Experimental Approach, IEEE Antennas and Wireless Propag. Letters, vol. 9, 2010, pp. 1099-1102. [8] D. G. Dudley, M. Lienard, S. F. Mahmoud and P. Degauque, Wireless propagation in tunnels, IEEE Antennas Propag. Mag., vol. 49, n 2, 2007, pp. 11 26. [9] J. M. Molina-Garcia-Pardo, M. Lienard, P. Degauque, D. G. Dudley and L. Juan Llacer, Interpretation of MIMO Channel Characteristics in Rectangular Tunnels From Modal Theory, IEEE Trans. on Vehicular Techno., vol. 57, n 3, 2008, pp. 1974-1979. [10] J.M. Molina-Garcia-Pardo, J.V. Rodríguez and L. Juan-Llacer, Wide-band measurements and characterization at 2.1 GHz while entering in a small tunnel, IEEE Trans. on Vehicular Techno., vol. 53, 2004, pp. 1794-1799. [11] A. Abdi, C. Tepedelenlioglu, M. Kaveh, and G. B. Giannakis, On the estimation of the k- parameter for rice fading distribution, IEEE Commun. Lett., vol. 5, no. 3, 2001, pp. 92 94. [12] D. S. Shiu, G. J. Foschini, M. J. Gans and J. M. Kahn, Fading Correlation and its Effects on the Capacity of Multielement antenna Systems, IEEE Trans. on Commun., vol. 48, no. 3, 2000, pp. 673-650. [13] G. J. Foschini and M. J. Gans, On limits of wireless communications in a fading environment when using multiple antennas, Wireless Personal Commun., vol. 6, no. 3, 1998, pp. 311-335. [14] I. E. Telatar, Capacity of Multi-Antenna Gaussian Channel, European Trans. on Telecom., vol. 10, 1995, pp. 585-595. ISBN: 978-1-61804-018-3 136