An Efficient and Low Complex Hyperbolic LocationScheme for Cellular Mobile Communications

Bo-Chieh Liu and Ken-Huang LinDepartment of Electrical Engineering

National Sun Yat-Sen UniversityKaohsiung, 80424, Taiwan

beliu(&pcsee.nsysu.edu.tw, khlin(&a nsysu.edu.tw

Abstract-In consequence of applications for the location of approach, for example, TDOA. In addition, the distancemobile subscriber (MS) of wireless services continue to expand, a difference can be estimated by using an approach which issimple and inexpensive method is needed by cellular mobile based on the difference between pairs of RSS measurements,communications for locating MS. Many location technologies i.e. the stationary signal-strength-difference (SSSD). This hastoday use different signal measurements which have their been analyzed in [6]. However, in order to obtain locationlimitation in accuracy and complexity. This paper proposes an estimation for all the above-mentioned methods, signaleffective estimation method for determining the MS location in a measurements from at least three base transceiver stationslow implementation complexity and promising accuracy. The (BTSs) are required.method is based on measuring a propagation delay, and then, thepseudo-distance-differences are available from the geometrical The aim of this paper is addressing the MS locationtransformations between multiple base transceiver stations estimated from the hyperbolic location technique, which can be(BTSs). Accordingly, the MS location can be estimated from the realized by measuring the signals from one BTS only. Signalhyperbolic location algorithm. Performing the field trial in a measurements in the proposed method are depended on thecommercial cellular mobile network, accuracy of the proposed propagation delay that is standard measurement reports in themethod shows promising results for the deployment of location- existing cellular mobile networks. In GSM/ UMTS/CDMAbased services. networks, the propagation delay is characterized by the time

cellular mobile communications; propagation delay;advance (TA), round-trip time (RTT), and round-trip delay

eyods- s RTD) respectively. Under availability and measurementconsideration, in our study, the system formulation of the fieldtrial is GSM cellular network. However, the proposed method

I. INTRODUCTION can be extended to UMTS and CDMA networks. In theLocation-based services (LBSs) offer personalized services literatures, several researches, mainly based on the TA

to the mobile subscriber (MS) based on their current location. parameters, have been reported and analyzed via computerWith location recognition, finding the nearest garage or ATM simulations and field trials in GSM network [7-11]. Referencecome within reach. People can locate their friends and receive a [7] is approached with hyperbolic location technique andvariety of LBSs such as mobile information, mobile reports the simulation results for location accuracy, whereas intransactions, and wireless advertising. The promise of new [8-11], circular location technique is applied and theLBSs is for a substantial part concentrated on location experimental results for location accuracy are presented. But, inestimation. Many location technologies today use different [8-10], no formulas for locating MS are provided. Furthermore,signal measurements such as angle of arrival (AOA), time in [7-10], signal measurements from at least three BTSs aredifference of arrival (TDOA), time of arrival (TOA) and required, whereas in [11], signal measurement from one BTS isreceived signal strength (RSS), which have their limitation in satisfactory. Reference [11] virtually uses one TA parameteraccuracy and complexity. Typically, wireless cellular operator measurement to construct the range of the estimated distanceneed to balance implementation complexity and required following the technical specifications; meanwhile, the two oraccuracy. Hence, there is a continuous demand for simple and more pseudo-distance range are constructed by usinginexpensive location technologies which offer sufficient geometrical transformations between home (i.e. serving) BTSaccuracy for most of the LBSs. and its neighbors. However, the contribution is different as

compared with the proposed method.Usually, one familiar technique for locating MS is based on

using the intersections of a set of hyperbolic curves [1-5]. By Contrary to [11], the basic idea of the method taken in thismeasuring the differences in the signals between pairs of paper is that we first regard the distances between the homesources, the distance differences could be obtained. Each of BTS and its neighbors as the pseudo-distances between the MSdistance differences determines a hyperbola, and the point at and the multiple pseudo-BTSs. Next, the information ofwhich these hyperbolas intersect is the MS location. Based on distance between the MS and the home BTS can be estimatedthe hyperbolic location technique, the distance difference as the propagation delay (TA parameter) is measured. Then, theestimated from the time-based measurements is a well-known differences between the estimated distance and the pseudo-

This work is partially supported by the Aim for Top University Plan ofNational Sun Yat-Sen University and Ministry of Education, Taiwan.

I1-4244-0574-2/06/$20.OO (0)2006 IEEE

distances are obtained, called the pseudo-distance-differences. scheme, each BTS sends every MS connected to a TAEventually, the MS location is estimated by means of the parameter to avoid overlapping of bursts at the BTS side.hyperbolic location algorithm. Since the proposed method Under GSM standard, TA parameter concerning a singletakes advantage of signaling information standardized in [12] communication is refreshed at the MS side every 480 ms. Inwith simple geometrical transformations, the impact on practice, TA parameter measurement is only available from thenetwork performance is kept at the minimum level and home BTS. Since TA parameter is integer numbers from 0 toreducing the complexity and requirements for hardware and 63, the information of distance between the home BTS and thesoftware changes. The proposed method is also much more MS is given byeffective than other solutions in cases when a mobile subscribercan only detect signals from a single BTS, which are R (rxTA) (2)encountered frequently in UMTS and CDMA networks due to 1 2the near-far effect.

where r= c xTb1108 m is the corresponding distance, c isThe paper is organized as follows. In Section II the the speed of light, and Tb = 48/13 =3.69,us is the bit duration.

proposed method is described. Section Im offers the hyperbolic In fact, according to technical specifications [13], Formula (2)location estimation. In Section LV, the results obtained from a can be formally expressed in the rangeseries of field trials are reported. We present a conclusion inSection V. [R1 -9,R1 +(] (3)

where the detection error due to noise and interference must beII. THE PROPOSED METHOD within z = r / 4 + K(r / 8) from which K varies from 0 to 1Consider a two-dimensional case, an MS is located at accounting for mobile speed and the quantization error does not

z = [x, y]T to be estimated, and the known coordinates of the exceed in magnitude r /4 = 277 m . The finite TA parameterithBTS is located at Z = [Xi, yf' for 1=1, 2 , N , where allows representing a ring circle with width around 554 m

where the MS is located. It is worth noting that the width ofN is the number of observed BTSs. Let RI = Z - z denotel ~~~ring circle depends on the accuracy of the measured TAthe distance from the MS to the home BTS, i.e. i = 1. Hence, parameter.the distance between the MS and the ith BTS is R = IlZi -Zll Generally speaking, TA is calculated on the first arrivedfor i = 2, 3. , N. Let R11 be the distance difference, between propagation path which has a significant reception power level,the home and ith BTSs, referenced to the MS where and not on the maximum received power level. Therefore, it is

assumed that TA represents the line-of-sight (LOS) signal.=,P=-, - RI = IlZi - zll - ||ZI -zll (1) However, due to terrain characteristics in a practical cellular

environment, the consideration of the non-LOS (NLOS) effectThe various quantities defined above are depicted in Fig. 1. is needed. For NLOS effects, it is known to be a major source

of error and systematically causes the MS to appear fartheraway from the BTS. As the reason, the range of the distancegiven by (3) requires to be adjusted so as to make it accurate.Without loss of generality, NLOS in the urban is larger thanthat in the suburban or rural. Consequently, TA parametermeasured in the urban will be inaccurate more than that

P 540i measured in the suburban or rural. For the purpose of keepinglow complexity, two parameters are required to compensate theNLOS effect in our study. One parameter is , called timingcoefficient, where its value fell in proportional to the measured

K"'"tt<i1, '>Xa,," _X.+gs.'' 'tj value of the TA parameter and varies from 0 to 1. The otherparameter is the bit period, x, where the value 1/2 is assumed;however, the validity of this assumption will be supported bynumerical experiments described in Section IV. Afterward, weemploy the value of D xx x (r / 2) to offset the maximumdistance of (3) in the dynamic state due to the value ,B varying

Figure 1. Geometric relation for the pseudo-distance-difference with TA parameter. The reason is that the distance error caused

As mentioned in Introduction, based on consideation of by the NLOS is always positive [13]. According to this

availability and measurement, the network formulation of the empirical approach, (3) can be rewritten as

field trial is GSM cellular network. In a GSM network, TA [R1min, R1 max] (4)parameter is a round-trip propagation delay measurement andis proportional to the distance between the MS and the BTS. where Ri min =R1 - p and R1 max =R1 + (p-(Jr)/4 .We noteBecause GSM is a TDMA system, in order to align the that (4) cannot be used as the measured TA parameter is zero,transmitted bursts with the TDMA frame defined in the access due to the zero value corresponding to no timing advance [14].

Next, we attempt to estimate the distance Rl . Ifwe need to MS can be solved by applying least square (LS) algorithmfind TA parameter from the ith BTS (excluding home BTS) to from the following conditions:the same MS, the forced handover must be performed from the 1) If RI = R, mi' then R11 - R11 mi for i = 2, 3, , Nhome BTS to another ones. The whole procedure certainly willdegrade call quality and reduce network performance. To avoid 2) If RI = RI max ' then RJ1= RJI max for i = 2, 3,, Nsuch obstacles, one simple method is based on geometricaltransformations to set the multiple pseudo-BTSs. As illustrated Therefore, we havein Fig. 1, we can calculate the distances from the home BTS toits neighbors, regarding as the pseudo-distances from the MS to z arg min(H - 2Gz)T (H - 2Gz)the multiple pseudo-BTSs. Based on this approach, we z 1respectively define the coordinates of the home BTS and its =-G H=-(GTG)-1GTHneighbors as (XI, Y4) and (Xi, 1) for i=2,3, ,N . The 2 2pseudo-distances from the MS to pseudo-BTSs can be The final location estimation is obtained by imposing theexpressed as known relation as RI= (XI-x)2 + (Yj - y)2 to the z estimated

R (X1 Xl)2 + (y _y§ by (11), because z and R( are independent being assumption.Then, the steepest descent method is applied to converge

It is worthwhile to note that the solution of the coordinates of toward the better location of MS. It is defined aspseudo-BTSs is not important in our work, inasmuch as we areonly interested in the solution of the pseudo-distance-difference; x /x (12)principally those are used instead of the real measured distance LY1k+l LYk L/Yi(X=Xk,y=Yk)difference. Eventually, the pseudo-distance-difference can beformulated in the range. That is where the relative error, X , is

R=i-R [Rii min, RI1, ma] (6) ( (( -x)2 +(Y' _y)2 _RI) (13)

where R11, max =R1 -R1 + p and R1 min1- -R1 -p+ (r)/4. which exists between the z and RI . Here, oc is the descent

rate parameter and the value 0.1 was applied in this study.III. HYPERBOLIC LOCATION ALGORITHM Ultimately, following the conditions, two possible solutions are

In this section, we state and solve the location estimation obtained, i.e., (xmin IYmin ) evaluated from the condition 1) andproblem as (6) is attained. As being analyzed in [6], wetransform R11 =R1 -RI into R =(R11 + RI)2 and all of the (xmax,' ma) evaluated from the condition 2). By averagingdistance differences can be determined completely from only those, an estimation yields close to the actual MS locationN -1 distance differences. It is (Xmas + i) =(max +Ymin ) (14)

X2 +y2 - 2Xx-2Yy +X2 +y2 =R72 +2RJlR? +R<2 (7) 2 2

Let 2~ \_A~X)2 { \)2 be evaluated by setting i IIt is worthwhile mentioning that, for TA = 0, we only obtain

RllX1-X) ~ -)2~ '-1 one solution from condition 2) due to RI = RI mn 0.and, subtracting it from (7), we have

Q-Q-R2_ R -IV.j-X -Y]F IV FIELD TRIAL RESULTSQYj To address the accuracy of the proposed method, we

performed the field trials in urban and suburban environmentswhere Q IX + }2 andQIXl + . Note that (8) is a from which a series of TA parameters were collected in GSM

set of linear equations with unknown MS location. The set of 1.8GHz network in Kaohsiung city. A laptop set inside a carN -1 equations can be written in matrix-vector form as was connected with GPS receiver and TEMS phone where both

devices mounted on the car. The true location collected by theH - 2Gz 0O (9) GPS receiver was recorded to compare with the estimated ones.

where For both environments, the total number of BTSs is 5 (5) in theurban (suburban) and each BTS has a 3-sectored cell. During

Q2 -2Q-R21 -2R21Rl X2-Xl Y2- Y the on-line phase, the MS is at random locations with stationary.The TEMS phone was linked with the GSM networks in

R2 dedicated mode, and signaling flows embedding the TAH = Q, - i- l2R1,R G = - lX ( 0) parameter measured from the home BTS which were recorded.

. . . ~~~~~~~~~Inthe urban (suburban) environment, we gather TA parameter

Q Q-R21 -2RNlR XN -X Y -Y at 41 (41) locations from 4 (3) home BTSs. At the same time,L QN - l - Nl-Nl Rlj L N N jthe pseudo-distance-difference was est:imated from the

anz[x~T *Fro (9,i*scerta tecodntsoh procedure described in Section II. We observe that, in most

cases, the measured values of the TA parameters in the urban operators providing LBSs to all customers with minimalwere either zero or one, whereas for the suburban environment, additional costs.the measured values of the TA parameters up to two weremeasured; however, over 9500 of the cases at least one were 750recorded. Measurement parameters are reported inUTable I. T 0 SUrban 3BTS

- Urban 4BTS650 0 Suburban 4BTS

-*-Urban 5BTSTABLE I. MEASUREMENT PARAMETERS IN THE FIELD TRIALS 600 A Suburban 5BTS

~550FIELD TRIAL ENVIRONMENT Measurement parameter 2 500

Urban Environment 450Cellular System GSM 1.8GHz network , 400Number of BTSs / Cells 5BTSs with 8 Cell numbers A .Number of Location 41 0Value ofTA 0 (22 locations) 300

1 (19 locations) 250

200Suburban Environment o 0.2 0.4 0.6 0.8 1Cellular System GSM 1.8GHz network Bit PeriodNumber of BTSs / Cells 5BTSs with 6 Cell numbersNumber of Location 41 Figure 2. Comparison of the mean error for different bit period parametersValue ofTA 0 (6 locations) when the number of BTSs is from 3 to 5

1(21 locations)2 (14 locations)

81 -U-- Urban 3BTS08 Suburban 3BTS0 Urban 4BTS

The collected measurement data is treated in off-line. To 0 Suburban 4BTS700-s- Urban 5BTSperform the statistical performance analysis, we present the L Suburban5BTSerror of the cumulative distribution function (CDF) at 67% as 66-.issued by U. S. Federal Communications Commission (FCC) 2

requirement. In addition, we also consider the values of the O 500 -

mean and root mean square (RMS) errors. The statistics of the 0

location error for different bit period parameters are plotted in 400 - o o EFig. 2-4 when the number ofBTSs is from 3 to 5. Fig. 2 shows ithe mean error. Fig. 3 shows the CDF error at 67%. Fig. 4 300shows the RMS error. From these figures, we can see that thelocation error may be reduced as bit period parameter increases. 200 IHowever, in four- and five-BTS cases, the good location 0.2 Bit Period 0.8 1

accuracy is almost taking place in 1/2 bit period among bothfield trial environments. Also, when the number of BTSs Figure 3. Comparison of CDF error at 67% for different bit periodincreases, the amount of information for locating MS also parameters when the number of BTSs is from 3 to 5increases. Therefore, comparable performance is observed.Upon 1/2 bit period accuracy, Fig. 5 graphs the CDF errorwhen the number of BTSs is from 3 to 5 and the numericalresults for the CDF error at 67%, mean and RMS errors are 600_.summarized in Table II. Outcomes have shown that, for five-BTS case in the urban, 9500 and 67% of MSs can be located 500within 350 m and 250 m, respectively. A A

2oV. CONCLUSION 3 ___

In this paper, an effective estimation method for locating .MS in a low implementation complexity and promising 200 * Urban 3BTSaccuracy is proposed. We validated the proposed method with * Suburban 3BTSaccuracy -~~~~~~~~~~~~~~~~~~~~~~~~~0- Urban 4BTSthe field trials collected in urban and suburban environments in 100 0 Suburban 4BTS

*- Urban 5BTSa commercial GSM cellular network. Field trial results A_ Suburban 5BTSdemonstrate that the proposed method is insensitive to the I 0.2 0.4 0.6 0.8 1suburban environment, but, it may good solution for urban Bit Periodenvironment. Although the proposed method does not satisfythe stringent requirements of the FCC mandate, it is suitable for Figure 4. Comparison of RMS error for different bit period parameters whenlocating legacy GSM phones and allows wireless cellular the number of BTSs is from 3 to 5

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