Modified 2D Finite-Difference Time-Domain Based Tunnel Path Loss Prediction for Wireless Sensor Network Applications

Transcription

1 214 JOURNAL OF COMMUNICATIONS, VOL. 4, NO. 4, MAY 2009 Modified 2D Finite-Difference Time-Domain Baed Tunnel Path Lo Prediction for Wirele Senor Network Application Yan Wu Computer Laboratory, Univerity of Cambridge, Cambridge, United Kingdom Min Lin and Ian J. Waell Computer Laboratory, Univerity of Cambridge, Cambridge, United Kingdom {ml406, Abtract 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 for the tunnel environment i required. For mot of the exiting propagation meaurement that have been 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-towall meaurement at 868MHz and 2.45GHz in curved arched-haped tunnel are preented along with prediction made uing a newly propoed Modified 2D Finite-Difference Time-Domain (FDTD) method. Since mot currently available wirele enor node have a communication range le than about 0m, we will focu on path lo meaurement and modelling up to a maximum range of everal hundred metre. 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. Index Term tunnel path lo, FDTD, large cale computing, field meaurement I. INTRODUCTION Having knowledge of the Path Lo (PL) veru ditance characteritic for a particular civil infratructure cenario avoid having to go back and repeat propagation tet if wirele node with different characteritic are deployed in the future. Therefore the determination of appropriate PL model enable effective Wirele Senor Network (WSN) planning and deployment, for example in our cae, to monitor and ae deformation in tunnel. The increae of path lo with ditance generally varie between 20 db per decade for free pace condition and may exceed 50 db per decade for a non-line of ight Manucript received December 1, 2008; revied March 6, 2009; accepted March 23, (NLOS) urban ituation with very high building denitie [1]. For modelling radio propagation in tunnel, a common approach i to treat them a a large cale waveguide. In [2], Zhang 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. In addition, the Modal Theory of electromagnetic (EM) propagation in rectangular or circular tunnel applied in [3] provide a reaonably accurate prediction of the periodic behaviour of the PL oberved for antenna eparation over a range of everal kilometer. However, near ditance PL accuracy i poor and cloe to wall antenna deployment i not amenable to prediction uing thi technique. To try and addre thee problem, a Ray Tracing technique ha been employed in [4] to perform tunnel PL prediction, but unfortunately it doe not provide the flexibility to cope with the variability of tunnel environment and alo exhibit poor accuracy in ome ituation. The Finite-Difference Time-Domain (FDTD) method propoed by Yee [5] ha been erving the EM modelling community for more than 40 year. Although a huge amount of effort ha been dedicated to improving thi method, the conventional FDTD i till renowned for it tability and for being traight forward to implement. Thee iue are of fundamental importance for the largecale EM imulation required in our ituation. Even o, the truth i that it i almot impoible to perform a full 3D tunnel imulation uing the conventional FDTD method ince the computational cot i overwhelming to any regular peronal computer (PC). In thi paper, we are going to preent our field meaurement for antenna mounted on the ide wall of the tunnel and then propoe the Modified 2D FDTD tunnel technique for generating PL prediction. The paper i organied a follow. The meaurement equipment, procedure and the geometry of the initial tunnel invetigated are introduced in Section II. Meaurement reult and analyi follow in Section III, including a further three tunnel field meaurement cenario. In Section IV, the Modified 2D FDTD model i preented

2 JOURNAL OF COMMUNICATIONS, VOL. 4, NO. 4, MAY along with imulation reult and comparion with meaured reult. Finally, Section V draw our concluion. mall circle repreent the poition of the centre tranmitter and the ide tranmitter antenna. II. FIELD MEASUREMENT SETUP Our primary meaurement are conducted at 868MHz and 2.45GHz within the Aldwych diued underground railway tunnel in London, which i 3.8m in diameter and 3.2m from the track bed to the crown. Fig. 1 give a cro-ectional view of the tunnel. The ide mounted tranmitter wa poitioned cloe to the tunnel wall at the height of 2m (Y), 0.02m (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,Z0). The receiver poition i repreented a R(x,Y,z), where x i the relative ditance of antenna to wall eparation; z i the ditance along the tunnel from the reference ditance Z0. For reference and comparion purpoe, we alo ued a tranmit antenna mounted at a height of 2m at the centre line of the tunnel. 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 m 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 [6]. Fig. 2 illutrate the 2D plan view of the tunnel while on the right hand ide, two Figure 1. Aldwych Cro-Sectional View and Tranmitter Poition. For each frequency, we carried out ix et of meaurement in the Aldwych tunnel, which are decribed in Table 1. The meaurement technique ued for each et of meaurement i alo indicated in the table. 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 m 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 0 ample are recorded. By uing thi technique, the fading due to the trong multipath characteritic 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 Figure 2. Aldwych 2D Geometry Plan and Tranmitter Poition. Table 1: Six Set of Meaurement Set Tx Rx Meaurement i Centre to Centre (C-C): both tranmitter and receiver are deployed at equal ditance (noted a Xc) to both ide wall ( X Y Z ) c,, 0 ( X, Y, z) c LR & HR ii Side to Centre (S-C) ( X Y Z ) ( X, Y, z),, 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) ( X Y Z ),, 0 ( X, Y, z) iii LR iv Side to Same Side 11cm (S-SS 11cm): receiver i 11cm away from Wall S ( X Y Z ),, 0 ( X, Y, z) iv HR v Side to Oppoite Side 2cm (S-OS 2cm): receiver i 2cm away from the wall oppoite to Wall S ( X Y Z ),, 0 ( X, Y, z) v LR vi Side to Oppoite Side 11cm (S-OS 11cm): receiver i 11cm away from the wall oppoite to Wall S ( X Y Z ),, 0 ( X, Y, z) vi HR

3 216 JOURNAL OF COMMUNICATIONS, VOL. 4, NO. 4, MAY 2009 tunnel while the received ignal trength i recorded at a rate of one ample per wavelength. Thi method provide u with detailed PL information againt ditance. In contrat to the LR method the meaurement reult till exhibit ignal fading a a function of ditance. It i not poible to take meaurement at 2cm from the tunnel ide with any accuracy owing to flange that protrude by about cm 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. III. FIELD MEASUREMENTS RESULTS AND ANALYSIS The PL i defined differently in variou context. To avoid confuion, here we define our PL in db a: PL = P + G + G P + P, (1) ( db) Tx( dbm) Tx( db) Rx( db) Rx( dbm) cable_ lo( db) where P i the tranmit power; Tx P i the receive Rx power; P _ i the coaxial cable lo, which add -1.5 cable lo db at 868MHz and -2.0 db at 2.45GHz; G and Tx G are Rx the tranmit and receive antenna gain repectively (both are 2 dbi). From the LR meaurement preented in Fig. 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. During previou tunnel PL tudie, emphai i often placed on the effect of key factor, uch a operating frequency, tunnel material, hape and coure. From our finding it i clear that antenna poition i important, particularly in the WSN context. In the following ection, we will illutrate the effect owing to each factor. A. Antenna Poition It can be een from Fig. 3 that the PL woren with ide mounted antenna, pecifically in the order C-C, Side Cae (i.e., S-C, S-SS and S-OS). In other word, more tranmit power i needed uing ide mounted antenna to achieve the ame coverage a for the C-C cae. 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 Fig. 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 receive antenna give a wore overall performance. Note that for clarity, we only plotted one fifteenth of the ample collected from thee HR meaurement. We alo added offet to the plot of +60dB, +30dB, 0dB and -30dB in Fig. 4(a), (b), (c) and (d) repectively in order to conerve pace. The detailed invetigation in term of antenna radiation pattern due to cloe to wall antenna pacing have been preented in [7]. In practical deployment, wirele enor are often attached to wall with an antenna to wall pacing of le than cm. In which cae, it i important to conider the ignificant PL performance degradation owing to the antenna poition. In [8], the practical iue encountered during variou WSN field intallation are decribed in detail. Figure 3. Aldwych PL Performance Comparion at Different Antenna Poition: Top Plot - 868MHz; Bottom Plot GHz. 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. To confirm our concluion, we have conducted further imilar meaurement in three different ection of the Bond Street underground railway tunnel in London hown in Fig. 5. Specifically we have: Bond T1 which i a traight 180m-long concrete tunnel from Ring no to 2280; Bond T2 which i a curved 120m-long cat iron

4 JOURNAL OF COMMUNICATIONS, VOL. 4, NO. 4, MAY Bond T3 Bond T2 Figure 5. Bond Street Underground Railway. Bond T1 tunnel from Ring no to 1983 and Bond T3 which i a curved 8m-long concrete tunnel from Ring no to Both Bond T2 and Bond T3 have the ame radiu of curvature and both loe Line of Sight (LOS) at a ditance of approximately 45m. All of the three tunnel ection have an internal diameter of about 3.8m. Due to the contraint on working hour in operational London underground tunnel, we only carried out HR meaurement in the Bond Street tunnel. For clarity, we have only preented the C-C and S-OS HR reult in Fig. 6, 7, 8 and 9 correponding with Aldwych, Bond T1, Bond T2 and Bond T3 repectively. In term of antenna poition, it can be een that each ub-figure upport our previou propoition that at either frequency, regardle of the wall material and the coure, the C-C cae alway ha a better PL than doe the S-OS cae. Note that all the S-OS cae in the variou tunnel give imilar reult to their correponding S-SS cae (not hown to conerve pace). Figure GHz PL HR Meaurement in Two Straight Tunnel with Different Material: (a). Aldwych Cat Iron C-C v. S-OS, where it firt 130m i traight; (b). Bond T1 Concrete C-C v. S-OS. Figure GHz PL HR Meaurement in Two Curved Tunnel with Different Material: (a). Bond T2 Cat Iron C-C v. S-OS; (b). Bond T3 Concrete C-C v. S-OS. Figure MHz PL HR Meaurement in Two Straight Tunnel with Different Material: (a). Aldwych Cat Iron C-C v. S-OS, where it firt 130m i traight; (b). Bond T1 Concrete C-C v. S-OS. Figure MHz PL HR Meaurement in Two Curved Tunnel with Different Material: (a). Bond T2 Cat Iron C-C v. S-OS; (b). Bond T3 Concrete C-C v. S-OS. B. Tunnel Material and Coure In term of the wall material of a tunnel, we oberved from our meaurement that operating at a frequency of 868MHz, cat iron give a noticeably better PL performance than doe concrete, while at an operating frequency of 2.45GHz, the PL performance are very imilar in both material. Fig. illutrate the urface of the cat iron and concrete ection. It can be een that at either operating frequency, the cat iron tunnel meaurement exhibit far more fat fading than do thoe in the concrete tunnel, owing to the urface roughne caued by the flange between each cat iron egment. In addition, the cat iron material itelf give low lo reflection at cloe ditance, which again give rie to deeper fading. In term of the coure of a tunnel, it i een not to have a large impact on the PL performance at cloe range, although we note that traight tunnel yield lightly better

5 218 JOURNAL OF COMMUNICATIONS, VOL. 4, NO. 4, MAY 2009 reult than do the curved one, epecially for non-los condition. In Fig. 11, we have preented a erie of PL comparion between 868MHz and 2.45GHz for the C-C cae. We alo added the offet of 0dB, -40dB, -80dB and -120dB for Fig. 11(a), (b), (c) and (d) repectively in order to conerve pace. It can be een that in general 868MHz give a better PL performance than doe 2.45GHz in the C-C cae. Aldwych Figure. Cat Iron Lining (Left) and Concrete Lining (Right). Within thi paper, we only conider arched croection tunnel, however we would expect that the croectional hape of a tunnel will affect the tructural fading within the PL reult but may till yield a imilar mean PL performance. Some dicuion concerning the effect of cro-ection hape are preented in [4, 9]. C. Operating Frequency In [], it i hown that at higher operating frequencie, lower ignal attenuation i.e., better PL performance can be achieved at long ditance (i.e., everal kilometer) in a tunnel. However, baed on our reult at the communication range of interet to u (i.e., everal hundred metre at mot), we will how that the previou concluion doe not apply. We dicovered that we can decribe the general trend for cloe range communication baed on invetigation of the C-C cae and the Side Cae. a. C-C Cae In Fig. 3, it can be oberved that the C-C cae operating at 868MHz give a better PL performance than at 2.45GHz for antenna eparation up to 180m. We alo noticed that a the antenna eparation approache 180m that the PL at 868MHz tend to woren at a fater rate than i evident at 2.45GHz. Conequently beyond thi ditance, it may be expected the PL at thee two frequencie will reach the point of equality and then at even greater ditance, 2.45GHz will have a better mean PL performance than doe 868MHz. To be more pecific, we would expect better PL performance for a lower operating frequency at cloe range (i.e., everal hundred metre) and wore PL performance at longer ditance (i.e., everal kilometer). So for the communication range likely to be experienced in a WSN deployment, operating at 868MHz will give a better PL performance than at 2.45GHz for the C-C cae. Thi i probably owing to the fact that diffraction loe will be greater at 2.45GHz owing to the maller wave length involved, i.e., 12cm compared with 35cm. Thi alo mean that we would expect le fat fading to be evident on the meaurement reult at 868MHz compared with thoe at 2.45GHz, and indeed thi i what we oberve. On the other hand, for general wirele communication over longer range, we would recommend higher operating frequencie, e.g., 2.45GHz for the reaon decribed previouly. Bond T1 Bond T2 Bond T3 Figure MHz v. 2.45GHz C-C Cae Comparion: (from top down): a. Aldwych Tunnel; b. Bond T1; c. Bond T2; d. Bond T3. We alo note a ignificant difference between the environment for the Aldwych meaurement and that for the other, pecifically the preence of a railway train approximately 120m behind the tranmit antenna. To identify the effect of potential ignal reflection from the train, we moved the train o that after the firt and econd move it wa 54.5m and 14.5m repectively behind our tranmit antenna, yielding the reult hown in Fig m 54.5m 14.5m Figure MHz v. 2.45GHz C-C Cae when the Train i 120m, 54.5m (-40dB Offet) and 14.5m (-80dB Offet) away from the Tranmit Antenna. It can be een in Fig. 12, that when the eparation between the train and the tranmitter decreae the PL gap between the 868MHz and 2.45GHz meaurement increae. In fact, the PL performance at 868MHz and 2.45GHz both improve, but the improvement at 868MHz i more ignificant than that at 2.45GHz. Thi i probably becaue 2.45GHz ha a wavelength of approximately

6 JOURNAL OF COMMUNICATIONS, VOL. 4, NO. 4, MAY cm compared with 35cm at 868MHz, which render the front of the train a better reflector in the latter cae. Conequently the reflection at 2.45GHz will be more cattered and more power will penetrate the gap between the train and the tunnel wall, i.e., le power will be reflected back at 2.45GHz from the front of the train. We would anticipate imilar effect due to the train for the correponding ide antenna cae. b. Side Antenna Cae Unlike the C-C cae where a ignificant difference exit between 868MHz and 2.45GHz PL performance for all tunnel at cloe antenna eparation, in the ide cae, the PL performance remain imilar at both operating frequencie for all tunnel except Aldwych. Fig. 13 and Fig. 14 how comparion for the SSS cae and for the SOS cae in Aldwych, Bond T1, T2 and T3 tunnel. 868MHz and 2.45GHz. Conequently it may be reaonable to aume that when the tunnel paage i completely clear (a with all the tunnel meaurement except for Aldwych), the difference between 868MHz and 2.45GHz for SSS and SOS cae will be ignificantly reduced. 14.5m 120m 120m Aldwych Bond T1 14.5m Figure MHz v. 2.45GHz SSS and SOS Cae when the Train i 120m and 14.5m (with -40dB Offet) away from the Tranmit Antenna. Bond T2 Bond T3 Figure MHz v. 2.45GHz SSS Cae Comparion: (from top down): a. Aldwych (0dB Offet); b. Bond T1 (-40dB Offet); c. Bond T2 (-80dB Offet); d. Bond T3 (-120dB Offet). Aldwych Bond T1 Bond T2 Bond T3 Figure MHz v. 2.45GHz SOS Cae Comparion: (from top down): a. Aldwych (0dB Offet); b. Bond T1 (-40dB Offet); c. Bond T2 (-80dB Offet); d. Bond T3 (-120dB Offet). Fig. 15 further invetigate the Aldwych ide antenna reult in term of the ditance of the tationary train behind the tranmit antenna. Once again, greater difference are evident between the PL performance at IV. MODIFIED 2D FDTD TUNNEL MODEL By directly olving Maxwell equation in the time domain, the FDTD method fully account for the effect of reflection, refraction and diffraction. The medium contitutive relation i incorporated into the exact olution of Maxwell formulation. The advantage of the FDTD method are it accuracy and that it provide a complete olution for the ignal coverage information throughout a defined problem pace. Therefore it i well uited to the tudy of the Electromagnetic propagation 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. Indeed, for the axial ditance of interet in our tunnel propagation cenario, the problem pace involved exceed that of even the mot ophiticated computing machine when implementing FDTD method [11]. Conequently, the problem ha become to ee how we can 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. There are two condition needed to convert a 3D FDTD into a 2D problem [12]: The property of the incident wave (ignal ource) and the property of the modeled tructure. To make the tranformation from 3D into 2D realitic, we will have to handle thee two iue eparately.

7 220 JOURNAL OF COMMUNICATIONS, VOL. 4, NO. 4, MAY 2009 A. Signal Source Converion and the Correction Factor Previouly in [13], we have conidered free pace and plane earth model, which both atify Taflove' tructural decription for the 3D to 2D converion. We note that in a 3D environment, the wave from a point ource pread out in a pherical manner. In contrat, we oberve that in a plane, propagation occur in a circular manner. The actual relationhip between a 3D ource and a 2D ource in the FDTD technique ha been revealed in term of Correction Factor (CF), i.e., CF db = log R + log ( f ) 23., (2) ( ) ( ) 2123 where R i the ditance between the tranmitter and the receiver in m and f i the ignal frequency in MHz. By ubtracting the unique CF pecified in (2) from the conventional 2D FDTD imulation reult, we are able to achieve a cloe match between 2D FDTD imulation reult and thoe expected in full 3D free pace and plane earth model. The CF can be conveniently determined becaue both the free pace path lo model in (3) and plane earth path lo model in (4) have well-etablihed analytical olution a decribed in [14]: PL db = log R / log ( f ) 32., (3) ( ) 20 ( ) h h PL( ) = log λ t r db 1+ ρ exp jk, (4) 4πR R where ρ i the reflection coefficient for the reflected ray; k i the free pace wave number 2π/λ. For example, ρ in the TE model i expreed a: (inψ ρte = (inψ + 2 ( ε r jx) co ψ ), (5) 2 ( ε jx) co ψ ) r where x =18 9δ/f; ε r i relative permittivity of the ground; δ i conductivity of the ground; ψ i the angle between the incident wave and the ground urface. B. Structural Converion and 2D FDTD Tunnel Model Baed on current undertanding, it i known that antenna poition, tranmit frequency, tunnel diameter, building material and coure are the main factor which affect radio propagation PL performance in a tunnel. Therefore our converted model ha to at leat take thee factor into conideration a our converion guideline. Here we take the Aldwych tunnel a an example to illutrate the 2D FDTD model contruction. The 2D tunnel tructure ued in the FDTD imulation i that hown in the plan of the Aldwych tunnel given in Fig. 2. Fig. 16 illutrate the layout of the model in our imulation, where the TE(Ez,Hx,Hy) mode in the conventional 2D FDTD method i ued to match our meaurement etup, pecifically the tranmit and receive antenna are parallel to the tunnel wall and perpendicular to the track. In thi model, all the parameter are preerved, i.e., tunnel diameter, wall material, flange (if the wall i made of cat iron egment), tunnel coure and the antenna poition relative to the wall. Similarly, we have alo created FDTD model for Bond T1, Bond T2 and Bond T3 tunnel. Figure 16. Modified 2D FDTD Aldwych Tunnel Structure. To maintain the imulation accuracy, our unit cell ize i defined to be equal to one twentieth of the correponding frequency wavelength, i.e., 1.73cm at 868MHz and 0.61cm at 2.45GHz. In term of the phyical contant at each unit cell, cat iron lining i repreented a (ε r = 1.0, µ r = 1.0, σ = 20 3 ), (ε r = 7.0, µ r = 1.0, σ = 0.015) for concrete lining and (ε r = 1.0, µ r = 1.0, σ = 0) for air. The 2D FDTD implementation i mainly baed on [15]. To enure that our imulation i cloe to teady tate before our field ampling begin, we et the number of time tep to be 8 time larger than the time tep needed for the FDTD to cover the entire length of the tunnel. C. Tunnel CF Hy Hx Ez So far we have hown how to tranform a 3D into a 2D point ource for free pace and flat earth model, and have alo propoed how a 3D tunnel tructure can be repreented in a 2D FDTD imulation. However, neither PL analytical formulation nor proven imulation model are available for u to determine the tunnel CF a we did previouly for the free pace and plane earth cenario, particularly for cloe to wall antenna ituation. In order to find a uitable CF for thi cenario, we have utilied the field meaurement preented previouly in thi paper. Having reult from four different tunnel with a total of 38 et of field meaurement, we have conducted invetigation to determine the appropriate CF. We will aume that the CF for our Modified 2D FDTD tunnel model for each meaurement cae ha the ame general form that applied previouly, i.e., CF( db ) = a log ( R) + b log( f ) + c, (6) where a, b, and c are the unknown variable, which we have een for the free pace and plane earth model are: a =, b = and c = Each variable of (a, b, c) i aumed to lie between 0 and 0. The Mean Square Error (MSE) between the meaurement reult and the corrected imulation reult are calculated accordingly with variou (a,b,c) combination. We now have 38 3D matrice of the overall MSE for the 38 cae. By earching for the (a,b,c) combination which yield the 1500 lowet variance (out of the one million poible combination) in each matrix, we reveal the range of interet for (a,b,c) and the correponding range of variance value a hown in Table 2. We have lited only 24 et from our analyi in order to conerve pace. From Table 2, we realie that there are common value for (a,b,c) among all the cae, i.e., 18 a 20; 4 b 29; 3 c 95, which indicate that we may be able to produce a unique CF for the general Modified 2D FDTD tunnel model.

8 JOURNAL OF COMMUNICATIONS, VOL. 4, NO. 4, MAY TABLE 2: RANGE OF (A,B,C) YIELDING THE LOWEST CORRESPONDING VARIANCES IN EACH CASE Aldwych 868MHz: (a,b,c,variance) - CC [18, 20]; [3, 35]; [-1, -95]; [7.72, 7.73] - SSS [14, 20]; [3, 38]; [-1, -0]; [8.81, 8.87] - SOS [18, 25]; [1, 37]; [-1, -0]; [8.35,8.47] 2.45GHz: (a,b,c,variance) - CC [14, 20]; [2, 33]; [-1, -0]; [7.61, 7.70] - SSS [18, 31]; [1, 33]; [-1, -0]; [9.41, 9.77] - SOS [18, 37]; [1, 33]; [-1, -0]; [8.75, 9.77] Bond T1 868MHz: (a,b,c,variance) - CC [18, 20]; [3, 36]; [-3, -0]; [7.86, 7.87] - SSS [9, 20]; [1, 39]; [-1, -0]; [7.83, 8.11] - SOS [18, 20]; [1, 34]; [-3, 0]; [8.50, 8.51] 2.45GHz: (a,b,c,variance) - CC [11, 20]; [1, 32]; [-1, -0]; [7.34, 7.56] - SSS [18, 23]; [1, 29]; [-1, -0]; [8.46, 8.54] - SOS [18, 24]; [1, 30]; [-1, -0]; [7.60, 7.71] Bond T2 868MHz: (a,b,c,variance) - CC [9, 20]; [1, 39]; [-1, -0]; [7.08, 7.35] - SSS [9, 20]; [3, 42]; [-1, -0]; [7.66, 7.94] - SOS [18, 26]; [1, 37]; [-1, -0]; [7.57, 7.72] 2.45GHz: (a,b,c,variance) - CC [1, 20]; [1, 39]; [-1, -0]; [7.30, 8.28] - SSS [15, 20]; [2, 32]; [-1, -0]; [9.05, 9.] - SOS [18, 20]; [4, 33]; [-3, -0]; [8.12, 8.13] Bond T3 868MHz: (a,b,c,variance) - CC [7, 20]; [1, 39]; [-1, -0]; [6.57, 7.02] - SSS [7, 20]; [1, 40]; [-1, -0]; [6.23, 6.71] - SOS [9, 20]; [1, 39]; [-1, -0]; [6.92, 7.15] 2.45GHz: (a,b,c,variance) - CC [18, 20]; [1, 29]; [-2, -97]; [7.09, 7.] - SSS [3, 20]; [1, 37]; [-1, -0]; [7.59, 8.24] - SOS [5, 20]; [1, 37]; [-1, -0]; [6.97, 7.50] By adding together all the 38 3D variance matrice of variance value, we now produce a ingle variance matrix for the entire tunnel model. The trend of the urface, which i defined by variable c and containing the minimum variance in the matrix i hown in Fig. 17. The ide view of Fig. 17 illutrate a moothly curved plane with only a ingle turning point when it reache the line of minima. Looking into the line of minima with repect to variable a and b independently a hown in Fig. 18, the problem of determining (a,b,c) i alway determinitic, and there i only one et of (a,b,c) that yield the bet fit CF for our 2D FDTD tunnel model. To achieve better numerical accuracy for (a,b,c), we further refine the range containing the line of minima. Conequently the optimal et of (a,b,c) for the minimum overall variance i obtained and o the CF can be expreed a: CF db =.4log R + 4log ( f ) 8.. (7) ( ) 18 ( ) 0 During our initial work when only the Aldwych meaurement data wa available, we took the ame approach that we have jut decribed in thi ection. The reulting CF formula for the 2D FDTD tunnel model wa expreed a: CF db = log R + 8log ( f ), (8) ( ) 20 ( ) 19 which alo lie around the line of minima previouly hown in Fig. 17 and Fig. 18. Figure 17. Overall Variance for Tunnel Model 3D View, for c = D. Evaluation Point of Minimum Line of Minima Point of Minimum Figure 18. Obervation from Variable a and b. The Modified 2D FDTD tunnel PL prediction are obtained by ubtracting the CF from the original 2D FDTD imulation data. A cloe correpondence between the meaurement reult and our imulation reult can be een in Fig. 19 for the Aldwych example, which how that the newly propoed CF for tunnel i appropriate for correcting conventional 2D FDTD reult o that they repreent meaurement conducted in a full 3D environment. The FDTD imulation ha a very high reolution compared with the meaurement, i.e., of the order of 4 ample in the imulation, 2 ~ 3 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 38 cenario conducted are hown in the 2nd column in Table 3. 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 3rd 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 0 ample both to the imulation and to the meaurement

9 222 JOURNAL OF COMMUNICATIONS, VOL. 4, NO. 4, MAY 2009 data. A a reult, the rm error i further reduced a hown in the 4th column of Table 3. TABLE 3: COMPARISONS OF RMS ERROR (DB) FOR THE MODIFIED 2D FDTD TUNNEL MODEL CF of (a, b, c) Initial Set (20, 8, -19) Final Set (18.4, 4, -8) Firt Comparion Second Comparion Third Comparion There are everal iue that we want to addre in term of the rm error. Concerning the imulation, the total number of time tep for the FDTD iteration may not be large enough to cover the multipath effect at the far end of the tunnel, therefore we may expect larger error to occur toward the far end. In term of the way that we contruct our FDTD model, we are effectively dealing with a 2D environment rather than 3D, which mean the tructural fading caued by the tunnel, will not be fully repreented in the modified model and may affect the ditribution of the fat fading data. Future work will invetigate the fading tatitic from the imulation data to ee how it compare with that obtained from the meaurement. The imulation reult reinforce our concluion concerning the effect of each of the factor, i.e., antenna poition, operating frequency, tunnel material and coure, which were drawn in Section III.A, III.B and III.C. A part of our future work, we plan to viit more tunnel having different dimenion in order to further validate our propoed Modified 2D FDTD tunnel model. Note that our 2D FDTD imulation were performed on a 3.46GHz, 8GB RAM, Dell Preciion PWS 380 computer. The current imulation time for 868MHz invetigation i approximately 15 hour, riing to 90 hour for 2.45GHz, which can be further reduced by about 70% with the ue of our Segmented FDTD method propoed in [16]. V. CONCLUSIONS For WSN application, we have hown that the PL woren with ide mounted antenna. The mean PL alo become wore at hort antenna eparation when the operating frequency i increaed, which i particularly relevant when implementing WSN that uually have hort expected communication range. Although material and coure are alo important element to conider in tunnel radio propagation for WSN, i.e., the hort range ituation, they have a le ignificant impact than do antenna poition and operating frequency. Baed on our extenive meaurement reult, we have been able to develop our Modified 2D FDTD tunnel model, which can be employed to predict the PL performance at hort range (i.e., everal hundred metre) and for antenna that are poitioned cloe to the tunnel Figure 19: Aldwych 868MHz and 2.45GHz Evaluation (from top down in each ubfigure): a. C-C (+90dB Offet); b. S-C (+60dB Offet); c S-OS 11cm (+30dB Offet); d. S-OS 2cm (0dB Offet); e. S-SS 11cm (-30dB Offet); f. S-SS 2cm (-60dB Offet).

10 JOURNAL OF COMMUNICATIONS, VOL. 4, NO. 4, MAY wall. The propoed modelling technique ha been hown to have a reaonable accuracy, particularly for etimating the overall mean PL. ACKNOWLEDGMENT The author would like to acknowledge the financial upport of the Engineering and Phyical Science Reearch Council (EPSRC) titled Smart Infratructure: Wirele Senor Network Sytem for Condition Aement and monitoring of Infratructure under Grant EP/D076870/1. The work decribed in thi paper i an extenion of that originally preented in [17]. REFERENCES [1] 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 , Sep [2] Y.P. Zhang, Novel Model for Propagation Lo Prediction in Tunnel, IEEE, Tran. Veh. Technol., vol. 52, No. 5, pp , Sep [3] J. M. Molina-García-Pardo, A. Nar, M. Liénard and P. Degauque, On the Poibility of Interpreting Field Variation and Polarization in Arched Tunnel Uing a Model for Propagation in Rectangular or Circular Tunnel, IEEE Tran. Antenna Propag., vol. 56, No. 4, pp , Apr [4] Dirk Didacalou, Jürgen Maurer and Werner Wiebeck, Subway Tunnel Guided Electromagnetic Wave Propagation at Mobile Communication Frequencie, IEEE Tran. Antenna Propag., vol. 49, No. 11, pp , Nov [5] K.S. Yee, Numerical Solution of Initial Boundary Value Problem involving Maxwell Equation in Iotropic Media, IEEE Tran. Antenna Propag., vol. 14, No. 3, pp , May [6] M. Lin, Y. Wu, I.J. Waell, Wirele Senor Network: Water Ditribution Monitoring Sytem, the IEEE Radio & Wirele Sympoium, Jan [7] Y. Wu, M. Lin, and I.J. Waell, Invetigation of Cloeto-Wall Wirele Senor Deployment uing 2D Finite- Difference Time-Domain Modelling, the International Conference on Wirele Communication in Underground and Confined Area, Aug [8] Neil A. Hoult, Yan Wu, Ian Waell, etc., Challenge in Wirele Senor Network Intallation: Radio Wave Propagation, the International Conference on Structural Health Monitoring of Intelligent Infratructure (To Appear), Jul [9] T.-S. Wang, C.-F. Yang, Simulation and Meaurement of Wave Propagation in Curved Road, Tunnel for Signal from GSM Bae Station, IEEE Tran. Antenna Propag., vol. 54, No. 9, pp 2577~2584, [] Dougla O. Reudink, Propertie of Mobile Radio Propagation Above 400MHz, IEEE Tran. Veh. Technol., vol. VT-23, No. 4, pp , Nov [11] Donald G. Dudley, Martine Lienarcf, Samir F. Mahmoucf and Pierre Degauque, Wirele Propagation in Tunnel, IEEE Antenna Propag. Magazine, vol. 49, No.2, pp , Apr [12] Allen Taflove and Suan C. Hagne, Third Edition, Computational Electrodynamic the Finite-Difference Time-Domain Method, [13] Y. Wu, M. Lin, I. J. Waell, Path Lo Etimation in 3D Environment uing a Modified 2D Finite-Difference Time-Domain Technique, the IET 7 th International Conference on Computation in Electromagnetic, CEM 2008, pp , Apr [14] Simon R. Saunder, Antenna and Propagation for Wirele Communication Sytem, [15] Denni M. Sullivan, Electromagnetic Simulation uing the FDTD Method, IEEE Pre, Jul [16] Yan Wu, Ian Waell, Introduction to the Segmented Finite-Difference Time-Domain Method, the Biennial IEEE Conference on Electromagnetic Field Computation, May [17] Y. Wu, M. Lin, and I.J. Waell, Modified 2D Finite- Difference Time-Domain Technique for Tunnel Path Lo Prediction, the 2nd International Conference on Wirele Communication in Underground and Confined Area, Aug. 2008, Val-d or, Canada. Yan Wu wa awarded the BEng degree in Computer Sytem Engineering from the Univerity of Warwick in June From September 2003 to Augut 2004, he held an indutrial placement within the Storage Sytem Diviion in IBM Hurley. He ha been a PhD candidate at the Digital Technology Group, Computer Laboratory, Univerity of Cambridge ince October 1, Hi reearch project i on "Smart Infratructure: Wirele enor network ytem for condition aement and monitoring of infratructure" ponored by the Engineering and Phyical Science Reearch Council (EPSRC). Hi main reearch focu i on EM baed Propagation Modelling. Min Lin obtained hi BEng in Electrical and Electronic Engineering at Univerity of Edinburgh in He ha been a PhD candidate in Digital Technology Group, Computer Laboratory, Univerity of Cambridge ince October From October 2004 to March 2006, he i working on MIMO channel modelling for Fixed Wirele Broadband Acce, collaborating with Cambridge Broadband Laboratory. He i now working on channel modelling for wirele enor network project, Peronalied Information from Prioritied Environmental Sening (PIPES), funded by Department of Trading Indutry (DTI) and BT. Ian J. Waell joined the Univerity of Cambridge Computer Laboratory a a Senior Lecturer in January Prior to thi appointment, he wa with the Univerity of Cambridge, Department of Engineering for approximately ix and a half year. He received the PhD degree from the Univerity of Southampton in 1990 and the BSc., BEng. (Honour) Degree (Firt Cla) from the Univerity of Loughborough in He ha in exce of 15 year experience in the imulation and deign of radio communication ytem gained via a number of poition in indutry and higher education. He ha publihed more than 130 paper concerning wirele communication ytem ince joining the Univerity of Cambridge in May Hi reearch interet include broadband Fixed Wirele Acce (FWA) network, wirele enor network, radio propagation, coding and communication ignal proceing. He i a Member of the Intitution of Engineering and Technology (IET).