MODIFIED 2D FINITE-DIFFERENCE TIME-DOMAIN TECHNIQUE FOR TUNNEL PATH LOSS PREDICTION. Y. Wu, M. Lin and I.J. Wassell

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1 2 nd International Conference on Wirele Communication in Underground and Confined Area Augut 25-27, 2008 Val-d Or - Québec - Canada MODIFIED 2D FINITE-DIFFERENCE TIME-DOMAIN TECHNIQUE FOR TUNNEL PATH LOSS PREDICTION Y. Wu, M. Lin and I.J. Waell Computer Laboratory, Univerity of Cambridge, Cambridge, CB3 0FD, United Kingdom ABSTRACT To effectively deploy wirele enor network (WSN) for monitoring and aeing the condition of tunnel, a Propagation Path Lo (PL) Model, which decribe the power lo veru ditance between the tranmitter and the receiver in a pecific environment, i required. For mot of the exiting propagation meaurement conducted in tunnel, the antenna have been poitioned along the central axi of a tunnel. However thi i not repreentative of mot infratructure monitoring application where the wirele enor node will be mounted on the wall of the tunnel. In thi paper, the reult obtained from conducting cloe-to-wall meaurement at 868MHz and 2.45GHz in a curved arched-haped tunnel are preented along with prediction made uing a newly propoed Modified 2D Finite-Difference Time-Domain (FDTD) method. During our meaurement, the antenna are alway maintained at a height of 2m. However the antenna ditance to the tunnel wall i varied. By having the PL model a a guideline, we are able to determine the critical parameter for wirele communication in a tunnel, uch a maximum communication ditance, tranmit power and receiver enitivity. 1. INTRODUCTION Having knowledge of the Path Lo (PL) veru ditance characteritic for the infratructure cenario being conidered, enable u to predict the likely maximum communication range between wirele enor node for any particular wirele enor parameter, pecifically the receiver enitivity and tranmit power. Thi avoid having to go and repeat propagation tet if node with different characteritic are deployed in the future. In addition the PL model can be ued to perform etimate of the ignal power to interference power ratio. The determination of appropriate PL model enable effective WSN deployment, for example, to monitor and ae deformation in tunnel. The increae of path lo with ditance varie generally between 20 db per decade for free pace condition and may exceed 50 db per decade for NLOS imulation with very high building denitie [2]. In [3], Zhang further concluded that there are two propagation region in a tunnel. The initial region exhibit path loe imilar to that een in free pace followed by a region where the path lo get wore more gradually ince they act like overized wave guide. By directly olving Maxwell equation in the time domain, the Finite-Difference Time-Domain (FDTD) method [1] fully account for the effect of reflection, refraction and diffraction in a model. The medium contitutive relation i incorporated into the exact olution of Maxwell formulation. The advantage of the FDTD method are it accuracy and providing a complete olution for the ignal coverage information throughout a defined problem pace. Therefore it i well uited to the tudie of the Electromagnetic propagation characteritic in a complex environment. Note that the FDTD require memory to tore the baic unit element of the model and alo demand iteration in time in order to update the field along the propagation direction. In other word, exceively large computational power in term of CPU execution time and memory uage are often needed for conventional FDTD approache to large-cale problem. In thi paper, we are going to preent our field meaurement for ide mounted antenna and then propoe the Modified 2D FDTD tunnel model for the PL prediction. The paper i organied a follow. The meaurement equipment, procedure and the geometry of the invetigated tunnel are introduced in Section 2. Meaurement reult and analyi follow in Section 3, while in Section 4, the Modified 2D FDTD model i preented along with imulation reult and comparion with meaured reult. Finally, Section 5 draw our concluion. 2. FIELD MEASUREMENT SETUP Our meaurement are conducted at 868MHz and 2.45GHz within the Aldwych underground railway tunnel in London, which i 3.6m in diameter and 3.2m from the track bed to the crown. Figure 1 give a cro-ectional view of the tunnel. The ide mounted tranmitter wa poitioned cloe the tunnel wall at the height of 2m( Y ),

2 2 nd International Conference on Wirele Communication in Underground and Confined Area Augut 25-27, 2008 Val-d Or - Québec - Canada 0.05m( X ) away from the wall and oriented vertically to the tunnel bae. The ue of a vertical antenna i to limit intruion into the tunnel. Here we repreent the ide located tranmitter poition a T( X, Y, Z 0). The receiver poition i repreented a R ( x, Y, z ), where z i the ditance along the tunnel from reference point Z 0. For reference and comparion purpoe, we alo ued a 2m tranmit antenna mounted at the centre line of the tunnel. Figure 1: Aldwych Cro-Sectional View and Tranmitter Poition At the receiver, the ignal power i meaured uing a portable pectrum analyzer (SA) (Anritu MS2721A) which i connected to a dipole antenna via a 10m lowlo coaxial cable. At the tranmitter, AtlanTech ANS (800~1200MHz) and AtlanTech ANS (2000~3000MHz) battery powered ignal generator are ued. In addition, a Mini-Circuit power amplifier (PA) i ued to increae the tranmit power and a dipole antenna having an appropriate centre frequency i connected directly to the PA. The accuracy of thi meaurement etup ha been validated in our plane earth meaurement performed in [4]. Figure 2 illutrate the 2D plan view of the tunnel while on the right hand ide, two mall circle repreent the poition of the center tranmitter and the ide tranmitter antenna. Two different meaurement technique are applied a will now be decribed: a. A Low Reolution (LR) Technique, where meaurement are conducted at interval of 2m, 5m and 10m depending upon the tranmitter to receiver eparation and the operating frequency. At each meaurement poition, the tranmitter i moved randomly within a 1 quare meter area while 100 ample are recorded. By uing thi technique, the fading due to multipath can be averaged out allowing the mean path lo to be etimated. b. A High Reolution (HR) Technique, in which, the receiver i moved lowly and continuouly along the tunnel while the received ignal trength i recorded uing a ampling interval of 0.5. Thi method provide u with detailed PL information againt ditance. In contrat to the LR method the meaurement reult till exhibit ignal fading. It i Figure 2: Aldwych 2D Geometry Plan and Tranmitter Poition Set Meaurement i Centre to Centre (C-C): both tranmitter and receiver are deployed at equal ditance (noted a Xc) to both ide wall c,, 0 c LR & HR ii Side to Centre (S-C),, 0 c LR & HR iii Side to Same Side 2cm (S-SS 2cm): receiver i 2cm away from the wall with tranmitter mounted (noted a Wall S),, 0 iii LR iv Side to Same Side 11cm (S-SS 11cm): receiver i 11cm away from Wall S,, 0 iv HR v Side to Oppoite Side 2cm (S-OS 2cm): receiver i 2cm away from the wall oppoite to Wall S,, 0 v LR vi Side to Oppoite Side 11cm (S-OS 11cm): receiver i 11cm away from the wall oppoite to Wall S,, 0 vi HR Table 1: Six Set of Meaurement

3 2 nd International Conference on Wirele Communication in Underground and Confined Area Augut 25-27, 2008 Val-d Or - Québec - Canada not poible to take meaurement at 2cm from the tunnel ide with any accuracy owing to flange that protrude by about 10cm and other obtruction on the tunnel wall. Conequently, to obtain accurate reult at cloer pacing e.g., 1~2cm, the LR technique i more uitable. For each frequency, we carried out ix et of meaurement, which are decribed in Table 1. Appropriate meaurement technique are applied in each et of meaurement. 3. FIELD MEASUREMENTS RESULTS AND ANALYSIS The PL i defined differently in variou context. To avoid confuion, here we define our PL model in db a: PL = P + G + G P + P, (1) ( db) ( dbm) ( db) ( db) ( dbm) cable_ lo( db) where P i the tranmit power; P i the receive power; P _ i the coaxial cable lo, which add cable lo 1.5dB lo at 868MHz and 2.0 db lo at 2.45GHz; G and G are the tranmit and receive antenna gain repectively (both are 2 db). From the LR meaurement preented in Figure 3, in general, it can be een that the PL increae more rapidly in the near region than in the far region of the tunnel. The PL woren with ide mounted antenna, pecifically in the order C-C, S-C, S-SS, S-OS. In another word, more tranmit power i needed uing ide mounted antenna to achieve the ame coverage a for the C-C cae. In term of the tranmit frequencie, 868MHz ha a better performance than 2.45GHz. Thi i owing to the fact that diffraction loe will be greater at 2.45GHz due to the maller wave length, i.e., 12cm compared with 35cm. Comparion between the LR and the HR technique for the C-C cenario at 868MHz and 2.45GHz have hown cloe agreement. A can been een in Table 1, the S-SS and the S-OS cenario have been invetigated for receive antenna to wall pacing of 2cm and 11cm. From the meaurement reult hown in Figure 4, it can be een that in general the 11cm pacing perform better than doe the 2cm pacing. In other word, the cloe-to-wall cenario at the receive antenna give a wore overall performance. Note that for clarity, we only plotted one fifteenth of the ample collected from the HR meaurement. We alo added the offet of +60dB, +30dB, 0dB and -30dB for Figure 4(a), (b), (c) and (d) repectively in order to conerve pace. The detailed cloe-to-wall invetigation will be preented in [5]. (a) (b) Figure 3: PL Performance Comparion at Different Antenna Poition: a. 868MHz; b. 2.45GHz Figure 4: 2cm v. 11cm Cloe-To-Wall Antenna Poition Comparion (from top down): a. (S-OS-2cm) v. (S-OS-11cm) at 868MHz; b. (S-SS-2cm) v. (S-SS-11cm) at 868MHz; c. (S- OS-2cm) v. (S-OS-11cm) at 2.45GHz; d. (S-SS-2cm) v. (S- SS-11cm) at 2.45GHz

4 2 nd International Conference on Wirele Communication in Underground and Confined Area Augut 25-27, 2008 Val-d Or - Québec - Canada 4. MODIFIED 2D FDTD TUNNEL MODEL The conventional FDTD method propoed by Yee [1] ha been erving the EM modeling community for more than 40 year. Although a huge amount of effort ha been dedicated to improve thi method, the conventional FDTD i table and it i traight forward to implement. Thee iue are of fundamental importance for the largecale EM imulation required in our ituation. The truth i that it i almot impoible to implement a full 3D tunnel model uing the conventional FDTD method a the computational cot i overwhelming to any regular computer. Conequently, the problem ha become how can we convert a 3D tunnel model into a realitic 2D FDTD imulation, i.e., removing the computational burden while at the ame time preerving the factor that hape the radio propagation characteritic. Thi ha lead to our propoing the Modified 2D FDTD Method. Baed on the current undertanding, it i known that tranmit frequency, antenna poition, tunnel diameter, building material and coure are the main factor which affect radio propagation in a tunnel. The 2D tunnel tructure ued in the FDTD imulation i that hown in the plan of the Aldwych tunnel given in Figure 1. Figure 5 illutrate the layout of the model in our imulation, E, H, H mode in the conventional where the TM ( ) z x y 2D FDTD method i ued according to our meaurement etup. Figure 5: Modified 2D FDTD Tunnel Structure. The unit cell ize are 1.73cm at 868MHz and 0.61cm at 2.45GHz in order to maintain accuracy. The Cat Iron 3 lining i repreented a ( ε r = 1.0, µ r = 1.0, σ = ). Previouly we have hown that by applying the correction factor (CF) in Eqn. (2), we are able to achieve a cloe match between 2D FDTD imulation reult and thoe due to a full 3D free pace model or plane earth Figure 6: 868MHz (from top down): a. C-C (+90dB Offet); b. S-C (+60dB Offet); c S-OS 2cm (+30dB Offet); d. S-OS 11cm (0dB Offet); e. S-SS 2cm (-30dB Offet); f. S-SS 11cm (-60dB Offet). Figure 7: 2.45GHz (from top down): a. C-C (+90dB Offet); b. S-C (+60dB Offet); c S-OS 2cm (+30dB Offet); d. S-OS 11cm (0dB Offet); e. S-SS 2cm (-30dB Offet); f. S-SS 11cm (-60dB Offet).

5 2 nd International Conference on Wirele Communication in Underground and Confined Area Augut 25-27, 2008 Val-d Or - Québec - Canada mode [6]. CF db = log R + 10log ( f ) 23., (2) ( ) 10 10( ) where R i the ditance between the tranmitter and the receiver in m and f i the ignal frequency in MHz. We aume that the CF for the Modified 2D FDTD tunnel model i alo of the ame form, i.e., CF( db ) = a log10 ( R) + blog10 ( f ) + c, (3) where a, b, and c are the unknown variable. By comparing the difference between the initial imulation reult from the conventional 2D TM FDTD method and the meaurement data in the C-C cenario at both 868MHz and 2.45GHz, the following CF i determined: CF db = log R + 8log ( f ) 19.. (4) ( ) 20 10( ) The Modified 2D FDTD tunnel PL prediction are obtained by uing the CF to modify the 2D FDTD imulation data. A cloe correpondence between the meaurement reult and our imulation reult can be een in Figure 6 and Figure 7, which demontrate that the newly propoed CF i acceptable for correcting conventional 2D FDTD reult to repreent meaurement conducted in a full 3D environment. The imulation ha a very high reolution compared 4 with the meaurement, i.e., of the order of 10 ample in 2 3 the imulation, 10 ~ 10 in the HR meaurement and much le in the LR meaurement. The average Root mean quare (rm) error between the imulation and meaurement reult for all 6 cenario at each frequency are hown in the 2 nd column in Table 2. By applying a window filter, the imulation reult are reduced to the ame reolution a the meaurement. Thi econd comparion how a much reduced rm error a hown in the 3 rd column. In reality, we are intereted in quantifying the prediction error for the mean path lo. Conequently to remove the fading effect, we applied window filter with an averaging window ize up to 100 ample both to the imulation and to the meaurement data. A a reult, the rm error i further reduced a hown in the 4 th column of Table 2. 1 t 2 nd 3 rd 868MHz GHz Table 2: Comparion of RMS Error (db) for the Modified 2D FDTD Tunnel Model There are everal iue that we want to addre in term of the rm error. From the imulation apect, the total number of time tep for the FDTD iteration i not large enough to cover the multipath effect at the far end, therefore we may expect larger error occurring toward the far end. Alo we are effectively dealing with a 2D environment rather than 3D, thu due to the lack of one dimenion, we may expect reduced fading than in the full 3D radio propagation environment. Our 2D FDTD imulation wa performed on a 3.46GHz, 8GB RAM, Dell Preciion PWS 380 computer. The current imulation time for 868MHz i approximately 15 hour and 90 hour for 2.45GHz, which can be later reduced by 70% after uing the Segmented FDTD method a propoed in [7]. 5. CONCLUSIONS Within a pecific tunnel environment, the PL woren with ide mounted antenna, thi applie both to the receiver and tranmitter end. The PL alo become wore when the tranmit frequency i increaed. The Modified 2D FDTD Tunnel Model ha hown reaonable accuracy, epecially for the overall mean PL value. A part of our future work, we are targeting different contruction material, e.g. concrete, different diameter, e.g., 5m, and different tunnel coure when the tranmitter i deployed on the ide wall. Since there are baically two et of information involved in the FDTD imulation, i.e., field trength and phae, it hould alo be poible to invetigate ignal angle of arrival in a tunnel environment. 6. REFERENCES [1] K.S. Yee, Numerical Solution of Initial Boundary Value Problem involving Maxwell Equation in Iotropic Media, IEEE Tran. Antenna Propagat., vol. 14, No. 3, pp , May [2] D.J. Cichon, and T. Kurner, COST Telecommunication COST Action 231 Digital Mobile Radio Toward Future Generation Sytem Final Report, Chapter 4, Propagation Prediction Model, COST 231 TD(95), pp , Sept [3] Y.P. Zhang, Novel Model for Propagation Lo Prediction in Tunnel, IEEE, Tran. Vehicular Technol., vol. 52, No. 5, pp , Sept [4] M. Lin, Y. Wu, I.J. Waell, Wirele Senor Network: Water Ditribution Monitoring Sytem. 7th IEEE Radio & Wirele Sympoium, Jan [5] Y. Wu, M. Lin, and I.J. Waell, Invetigation of Cloe-to- Wall Wirele Senor Deployment uing 2D Finite- Difference Time-Domain Modelling, 2 nd International Conference on Wirele Communication in Underground and Confined Area (To Appear), Aug [6] Y. Wu, M. Lin, I.J. Waell, Path Lo Etimation in 3D Environment uing a Modified 2D Finite-Difference Time-Domain Technique, 7th International Conference on Computation in Electromagnetic, Apr [7] Yan Wu, Ian Waell, Introduction to the Segmented Finite-Difference Time-Domain Method. 13th Biennial IEEE Conference on Electromagnetic Field Computation (CEFC 2008), May 2008.

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