Performance Analysis of Time-of-Arrival Mobile Positioning in Wireless Cellular CDMA Networks

Transcription

1 Performance Analyss of Tme-of-Arrval Moble Postonng n Wreless Cellular CDMA Networks X Performance Analyss of Tme-of-Arrval Moble Postonng n Wreless Cellular CDMA Networks M. A.Landols, A. H. Muqabel, A. S. Al-Ahmar, H.-R. Khan and R. A. Al-Nmnm EE Department, Kng Fahd Unversty of Petroleum & Mnerals KFUPM, P.O. Box 1413, Dhahran 3161, Saud Araba 1. Introducton Recently, wreless moble communcaton systems have experenced a tremendous growth and became an ntegral part of people s daly lfe worldwde. Ths global predomnance of wreless communcatons has been ever more pronounced wth the success of new generatons of wreless communcaton standards that support a rch set of value-added features n addton to basc phone servces. Among these features s the possblty to offer radolocaton servces whereby the moble system (MS) poston s determned by combnng relevant nformaton (such as sgnal tme of arrval or angle of arrval) from dfferent base statons (BSs) havng rado lnks wth the ntended moble. Ths postonng capablty can support many servces rangng from medcal emergency help, securty and law enforcement, on-the-road assstance, locaton-dependent commercal advertsement, etc. As such, moble radolocaton has been mandated by several of the recently ntroduced wreless standards, and s beng wdely deployed by cellular network operators worldwde (Rappaport et al., 1996). Wth the deployment of the 3 rd generaton wreless cellular standards such as the Unversal Moble Telecommuncaton System (UMTS) (Dahlman et al., 000), the use of wdeband code dvson multple access (CDMA) sgnals s posed to offer hghly accurate postonng capabltes wth tme-of-arrval (TOA) nformaton owng to the fne tmng resoluton of the hgh chp rate wdeband spread-spectrum waveforms used. There are however some mparments such as mult-path fadng, mult-user nterference and nose, that can affect the performance of moble postonng schemes. In partcular, because of the need to use sgnal detecton at several base statons n moble postonng, the problem of near-far nterference at remote base statons (whereby a far-away moble weak sgnal can be overwhelmed by strong sgnals from close-n mobles) can consttute a major lmtng factor. In CDMA networks, ths s further exacerbated by power control (Vterb, 1995). Indeed, power control loops operate n such a way to mantan the receved power from dfferent users at the same level at ther respectve servng base staton. However, at other non-servng base statons (not actvely nvolved n a call wth the ntended moble), the moble receved power level can be extremely low, thereby gvng rse to a problem of sgnal hearablty, whch, n turn,

2 438 Trends n Telecommuncatons Technologes wll affect the accuracy of the moble postonng algorthms (Gosh & Love, 1998). A thorough analyss of these dfferent aspects under realstc channel modelng and network traffc loadng condtons s therefore necessary n order to obtan an accurate assessment of the achevable postonng performance. In ths work, we study the accuracy of moble radolocaton under near-far nterference, and show that t can vary consderably dependng on the moble lnk qualty wth the base statons nvolved n poston determnaton. We frst present a detaled performance analyss of moble TOA estmaton n broadband CDMA wreless cellular networks at the dfferent base statons surroundng the moble termnal. In most prevous works, the proposed radolocaton algorthms have smplstcally assumed that the tme-of-arrval measurements are Gaussan-dstrbuted, wth a fxed known varance that s commonly set rrespectve of the actual RF channel and nterference condtons or other system parameters. Moreover, the same TOA varance s typcally assgned for all base statons nvolved n postonng, whch s an naccurate and overly optmstc assumpton, as our results wll show. Instead, our approach s the use of complete statstcs for the moble tmng estmaton errors, derved by takng nto account realstc system parameters at the dfferent base statons of nterest. Snce precse TOA estmaton n CDMA recevers s typcally mplemented by delay-locked loop (DLL) trackng systems (Vterb, 1995), a detaled study of the DLL TOA trackng s ntroduced under fadng and mult-user nterference condtons assumng a cellular model wth multple ters of base statons, and t s shown that the DLL trackng performance can vary wdely dependng on the level of multple-access nterference and RF propagaton condtons of the lnks between the moble and base statons. Usng the TOA data collected at the base statons nvolved n moble postonng, a numercally-effcent, quas-optmum algorthm, based on Approxmate Maxmum Lkelhood (AML) estmaton (Chan et al., 006), s presented, and a generalzaton of ths algorthm s also derved under the realstc assumpton of un-equal TOA estmaton errors at the dfferent base statons. Based on our analyss, the mpact of moble lnk condton and ts relatve poston wth respect to the base statons nvolved n ts postonng s fully quantfed for a number of scenaros dependng on the near-far nterference envronment and the level of Soft Handoff (SHO) connectvty of the moble wth the base statons. Our results show that postonng accuracy s greatly mproved when the moble staton s n -way, and partcularly n 3-way SHO (.e., wth two and three base statons, respectvely), compared to sngle connectvty wth only the home servng base staton. The rest of the chapter s organzed as follows. Frst, n Secton, we present an overvew of radolocaton technques, focusng n partcular on network-based approaches wth TOA processng sutable for cellular systems. The system modelng and analyss of near-far nterference n CDMA networks s presented n Secton 3, followed by a detaled analyss of the performance of delay-locked loops for tme-of-arrval trackng n Secton 4. Then, n Secton 5, the approxmate maxmum lkelhood postonng algorthm s presented, and varous llustratve examples and numercal results are dscussed n Secton 6, followed by summary and fnal conclusons n Secton 7.

3 Performance Analyss of Tme-of-Arrval Moble Postonng n Wreless Cellular CDMA Networks 439. Wreless Network-Based Moble Radolocaton.1 Overvew The concept of wreless radolocaton refers to the determnaton of the geographc poston nformaton of a moble user n terms of ts geographc coordnates wth respect to a reference pont. Wreless locaton s also commonly referred to as moble postonng, radolocaton, or localzaton. Poston locaton technques can be classfed nto two man categores: handset-based and network-based. A well known example of handset-based radolocaton s the Global Postonng System (GPS) and other smlar systems (Kaplan, 1996). The other category conssts of network-based technques that utlze the exstng wreless cellular networks to obtan locaton nformaton (Sayed, et al., 005). In ths work, we manly focus on the network-based approach whch ntegrates seamlessly wth the wdely deployed moble cellular nfrastructures throughout the world. The basc archtecture of such systems s llustrated n Fgure 1. Fg. 1. Network-based wreless moble radolocaton The network-based postonng schemes rely on data collected by several base statons surroundng the moble staton of nterest, and can be based on the moble s sgnal strength (SS), angle of arrval (AOA), tme of arrvals (TOA) or tme dfference of arrval (TDOA) measurements. Usng these measurements, specfc geometrc and/or statstcal sgnal processng algorthms are used to determne the moble locaton. Hybrd methods nvolvng more than one of type of measurements can also be used (Sayed, et al., 005). In general, locatng a moble n two-dmensons requres a mnmum of three sets of measurements from correspondng base statons, although for AOA methods, two base statons are

4 440 Trends n Telecommuncatons Technologes suffcent. However, n the presence of nosy measurements, statstcal sgnal processng algorthms usng data collected from multple base statons are preferred n order to resolve the ambgutes arsng from multple crossngs of the lnes of poston, and to mprove the postonng accuracy.. Tme-of-Arrval Moble Radolocaton TOA-based technques offer several advantages compared to the other methods, ncludng low cost and ease of use. The TOA data s readly avalable from tmng synchronzaton mechansms at the dfferent base statons, wthout requrng complex hardware as wth the Angle-of-Arrval methods. In partcular, wth the wdespread deployment of the latest 3G CDMA-based wreless cellular networks, the spread-spectrum sgnalng waveforms offer hgh tme resoluton and good robustness vs-à-vs the rado channel mparments (fadng, shadowng, and near-far nterference), and are therefore well-suted to ad n achevng the requred accuracy n poston locaton servces. In the TOA-based moble radolocaton approach, the dstance between an MS and a BS s measured by fndng the one-way propagaton delay under drect lne-of-sght (LOS) propagaton condtons. The TOA measurements at the dfferent base statons are therefore drectly proportonal to the moble-base dstance separaton. The nvolved base statons are assumed to have a common tmng reference, wth a known moble transmsson tme. Geometrcally, the moble poston wll trace a crcle centered at the base statons. By usng three base statons to resolve ambgutes, the moble poston s gven by the ntersecton of these crcles as llustrated n Fgure. It should be ponted out that, n the presence of nosy TOA data due to nterference and synchronzaton errors, the three crcles may not ntersect at a sngle pont. Therefore, the geometrc approach wll not produce a sngle ntersecton pont, and statstcal technques are typcally adopted to process the nosy data, as wll be further dscussed subsequently when we ntroduce the AML algorthm. Fg.. TOA radolocaton based on ntersecton of base staton centered crcles

5 Performance Analyss of Tme-of-Arrval Moble Postonng n Wreless Cellular CDMA Networks Near-Far Interference Analyss 3.1 Sgnal and System Models Consder a cellular CDMA network employng sgnalng schemes wth quaternary phaseshft keyng (QPSK) modulaton and complex spreadng (conformng to 3G/UTMS standards (Dahlman et al., 000). At the transmtter, the complex baseband sgnal for a gven moble user s gven by s ( t ) s h ( t mt ) (1) m m c where {s m } are the complex spreadng chp symbols, and T c the chp duraton. The nformaton data bts are omtted here for smplcty as ths wll be applcable for a pure plot sgnal that can be used for postonng purposes. The mpulse response h(t) of the pulse-shapng flter s assumed to be a root-rased cosne flter wth roll-off factor %, as recommended n the UMTS standard. As wll be seen next, the Fourer transform H(f) of the flter mpulse response h(t) wll have a major mpact on the other-user nterference n cellular CDMA networks. For wreless fadng channels, the receved sgnal at the output of the rado frequency (RF) recever flter s wrtten as M j fct r( t) P Re s t ( t) a ( t) e n( t ) () 1 where P s the receved sgnal power, M s the number of resolvable multpath sgnals, wth a and denotng the -th path complex Gaussan tap factor (wth a Raylegh-fadng magntude) and ts propagaton delay, respectvely, and f c s the carrer frequency. The nose sgnal n(t) models the total nose-plus-nterference terms and s assumed to be zero-mean Gaussan random process. For the dfferent resolvable multpath sgnal epochs, we manly focus on the frst arrvng sgnal whch wll be tracked to estmate ts TOA. The combned multple-access nterference (MAI) terms from both same-cell and other-cell users can be modeled as beng Gaussan dstrbuted, whch s a vald assumpton for a large number of users. In ths case, t can be shown that the total composte power spectral densty (PSD), I 0, that captures the effect of both thermal nose and MAI terms (assumed to be statstcally ndependent) s gven by (Vterb, 1995) o 4 o I 4 0 N0 H( f ) df H( f ) df N0 H( f ) df T T c c (3) where N o s due to the thermal nose component and the factor represents both same-cell and other-cell MAI terms. The functon H(f) denotes the Fourer transfer of the chp shapng flter mpulse response h(t). The MAI PSD term s typcally the domnant factor n CDMA systems, and wll depend on network loadng, fracton of nter-cell to ntra-cell MAI, channel pathloss and shadowng models. For typcal system parameters of nterest, t s

6 44 Trends n Telecommuncatons Technologes found that the o MAI factor s approxmately 1.6(K u -1), where K u s the number of users per cell (Vterb, 1995). 3. Near-Far Interference and Soft Handoff Impact We consder a cellular network wth a central cell and two ters of surroundng cells as llustrated n Fgure 3, where mobles are assumed to be unformly dstrbuted across the coverage area. BS8 BS19 BS9 BS18 BS BS10 BS7 d d 3 BS3 BS17 d 1 BS1 BS11 BS6 BS4 BS16 BS5 BS1 BS15 BS13 BS14 Fg. 3. Cellular network model, wth center cell and two ters of nterferng cells. The moble receved power at a gven base staton, BS, s multpled by an attenuaton factor,, that reflects dstance path loss, p(d), and log-normal shadowng factor,, accordng to (Vterb, 1995): BS /10 ( d, ) p( d )10 (4) BS BS BS The path-loss factor s assumed to follow the model: p( d) 10 n log 10 d (5)

7 Performance Analyss of Tme-of-Arrval Moble Postonng n Wreless Cellular CDMA Networks 443 where n s the path loss exponent and d the moble s relatve poston wth respect to the base staton. For a gven moble locaton, shadowng vs-à-vs the dfferent base statons s typcally assumed to be partally correlated, log-normally-dstrbuted, and gven by (Vterb, 1995): a b (6) BS c where c and denote the common and ndependent terms, respectvely, and a +b =1. Wth closed-loop CDMA power control, a gven moble wll have the same receved power at ts home (servng) base staton compared wth other ntra-cell mobles. On the other hand, at the neghborng base statons, the moble wll be receved at much lower power due to the so-called near-far problem (whch cannot be mtgated due to the lack of nter-cell power control). However, when the moble s n soft-handoff wth other neghborng base statons, ts receved power s relatvely close to that at the home cell, and ths greatly mprove radolocaton accuracy, as wll be dscussed next. Snce TOA estmaton accuracy depends on the tmng synchronzaton mechansm, whch s n turn affected by the receved nterference levels at the dfferent base statons, the near-far nterference at the non-servng base statons wll have a major mpact on the fnal moble postonng accuracy. To llustrate ths pont, we consder a system where the moble s served by the center base staton BS 1 and s rado-located usng TOA data from three or more base statons BS 1, BS,, BS 7 (sorted n a descendng order from BS 1 that receves the hghest average receved power). The near-far nterference mpact can be convenently assessed by defnng the rato of ts average receved power at BS compared to BS 1 (for whch the power wll be normalzed to 1, and used as a reference value). We then defne the followng: P P 1 (7) where P s the receved power at BS and. A wde fluctuaton n the factors s expected dependng on the moble poston relatve to the base statons of nterest. It should be noted that, due to power control, all mobles wll be receved at equal power ( =1) at ther respectve home servng base statons, but much lower values of are expected at far-away base statons (because of the near-far problem). Ths however wll depend on the relatve poston of the moble wth respect to the other base statons (.e., ts proxmty to the cell border). Soft Handoff (SHO) s one of the salent features of CDMA cellular systems whch allow the moble to be smultaneously connected to more than one servng base staton. In fact, the possblty of SHO calls enables a stronger sgnal recepton at multple base statons, and ths wll n turn mprove postonng accuracy. To further nvestgate ths pont, we consder dfferent scenaros denoted by Cases 1,, and 3, respectvely. Case 1 refers to a moble n close proxmty (wthn half the cell radus, R) of ts servng BS 1, wth a sgnal at least 10dB above that at the other nearest two base statons. Case represents a two-way soft handover scenaro, wth the moble power at BS wthn 3dB from that at BS 1. Fnally, Case 3 corresponds to a 3-way soft handover stuaton where

8 444 Trends n Telecommuncatons Technologes the moble sgnal at both BS and BS 3 s wthn 3dB compared to BS 1. The numbers chosen here merely serve to llustrate the varablty n receved sgnal power (and ts subsequent mpact on TOA estmaton accuracy), but do not attempt to model the specfc thresholds and soft handover mechansms used n CDMA standards. Table 1 and Table gve the dfferent factors for the three cases of nterest, and for dfferent values for the pathloss and shadowng models, where a typcal 50% correlaton factor s assumed (a=b). For the numercal results, we assumed typcal parameters for the rado propagaton channel model. A two-segment pathloss model wth breakpont at dstance d o =00m and exponents n= and 4, respectvely, was used, wth a load of 0 users per cell, and a cell radus of Km. The relatve powerfactors gven n Table 1 and Table clearly show that large varatons occur across the base statons dependng on the moble soft handoff condtons and ts proxmty to one or more base staton, and ths wll mpact the accuracy of sgnal estmaton at the dfferent base statons as wll be dscussed next. β 1 β β 3 β 4 β 5 β 6 β 7 Case 1 (moble close to home BS) Case (moble n two-way SHO) Case 3 (moble n three-way SHO) Table 1. Relatve receved power factors for varous moble soft-handoff lnk condtons. Shadowng s.t.d 8dB. β 1 β β 3 β 4 β 5 β 6 β 7 Case 1 (moble close to home BS) Case (moble n two-way SHO) Case 3 (moble n three-way SHO) Table. Relatve receved power factors for varous moble soft-handoff lnk condtons. Shadowng s.t.d 1dB. 4. Sgnal Tme-of-Arrval Estmaton 4.1. Delay-Locked Loop Tme Trackng Tmng synchronzaton for CDMA sgnals s typcally mplemented n two steps consstng of an ntal coarse tmng acquston (wthn an uncertanty range on the order of one-chp nterval), followed by fne tme trackng acheved by a delay-locked loop (DLL) mechansm (Vterb, 1995). In ths work, we assume that the ntal tmng acquston has been acheved, and focus on the more accurate DLL trackng as the man sgnal tmng estmaton mechansm. For each base staton nvolved n moble postonng, a DLL devce contnuously attempts to brng the local code tmng estmate n perfect algnment wth the

9 Performance Analyss of Tme-of-Arrval Moble Postonng n Wreless Cellular CDMA Networks 445 ncomng moble sgnal. However, ths tmng estmaton wll be subject to error due to nose, fadng and multple-access nterference. In the followng, we consder TOA estmaton based on a non-coherent DLL (NC-DLL) scheme. In practce, the NC-DLL s preferred over a coherent structure because of ts nsenstvty to carrer phase error and data modulaton. Fgure 4 depcts a block dagram showng the dfferent processng stages of a NC-DLL code trackng loop. Because QPSK spreadng s used, the NC-DLL employs both I & Q branches where the I & Q receved sgnals, after down converson and chp matched flterng, are fed to two early & late branches whch correlate the spread-spectrum waveforms wth advanced and delayed code sequence replcas. The outputs obtaned at the I & Q channels of the early & late branches can be obtaned as (Vterb, 1995) Y AN PT R ( )cos (8) I C Y AN PT R ( )cos (9) Q C where A s the fadng sgnal envelope modeled as a Raylegh random varable, and θ s ts unform phase. s the early & late tmng offset (typcally set to T c /), P s the sgnal power, and N s the number of accumulated chps. The functon R() s a correlaton functon gven by the convoluton of the mpulse responses of the pulse-shapng flter and ts matched flter (Vterb, 1995): R( ) h( ) h( ) H( f ) cos( fc ) df (10) The DLL I & Q correlator outputs are combned as shown n Fgure 4, and a resultng dscrmnator metrc Z s low-pass fltered to form an error sgnal used to drve a numercally-controlled oscllator (NCO) that controls the code tmng adjustment. The DLL dscrmnator output can be obtaned as (Vterb, 1995): Z AS ( ) (11) where s the power reducton factor reflectng the mpact of DLL operaton at dfferent base statons (compared to the man servng base staton, as dscussed prevously). The term represents the combned Gaussan nose term wth varance I 0. The functon S() s known as the normalzed DLL S-curve, and s gven by S( ) R ( ) R ( ) (1) where s the normalzed tmng error gven by wth denotng the correct TOA and ˆ the estmated one. ( ˆ )/ T c (13)

10 446 Trends n Telecommuncatons Technologes A common fgure of mert for assessng the DLL performance s based on the trackng jtter varance. For addtve whte Gaussan (AWGN) channels, a smple upper-bound approxmaton for the trackng jtter varance, vald for lnearzed frst-order DLL models, s derved n (Vterb, 1995) as I 4NE I N E o c o c (14) where E c s the receved chp energy, s the slope of the S-curve at the orgn, and I 0 s the varance of the thermal nose & MAI terms. However, there s no smple equvalent result for the case of frequency-selectve multpath fadng channels consdered n ths work, and the above approxmaton s only vald for hgh moble receved Sgnal-to-Nose Rato (SNR) condtons, whch s not necessarly the case at the remote base statons (other than the home servng one), as dscussed prevously. In ths work, we resort to a more accurate performance analyss vald for all SNR condtons and based on the computaton of the full statstcs (probablty densty functon) of the DLL trackng loop, as dscussed next. Fg. 4. DLL system used for CDMA sgnal tmng synchronzaton and TOA estmaton 4.. DLL Trackng Error Statstcs For the purpose of analyzng the mpact of TOA estmaton error on moble postonng accuracy, we need to obtan accurate statstcs for the TOA measurements at each of the base statons nvolved n trackng the gven moble TOA. Hypothetcal dstrbutons (Gaussan models) are commonly assumed for the TOA tmng estmaton error. The same varance s

11 Performance Analyss of Tme-of-Arrval Moble Postonng n Wreless Cellular CDMA Networks 447 usually assgned to the TOA error at all base statons nvolved n moble postonng, and ths varance s sometmes set rather arbtrarly. In ths work, we use results based on a more rgorous analyss wth full dervaton of the TOA error probablty densty functon (PDF). The results are obtaned followng the approach presented n (Su & Yen, 1997) and extended to quadrature-spread CDMA sgnals n (Khan, 009). Assumng a dscrete-tme model, the analyss s based on a dscrete-tme Markov model for the resdual DLL error, accordng to the followng equaton: k k1 K NCO Ak 1S( k1 ) k1 (15) where K NCO s the NCO gan, and k s the addtve Gaussan nose term. It can be seen that the resdual trackng error follows a dscrete-tme Markov process for whch the frst order probablty dstrbuton can be obtaned usng the Kolmogorov-Chapman equaton (Su & Yen, 1997): pk( ) fk1 x pk1 x 0 dx (16) where 0 s the ntal tmng error, p k-1 (x 0 ) s the PDF of x gven 0, and f k-1 ( x) s the transton pdf of k gven x. Through detaled analyss, one can calculate the exact expressons f k-1 ( x) under assumpton of a Raylegh fadng channel. Usng numercal ntegraton, t s then possble to terate the Kolmogorov-Chapman equaton to get the PDF of the TOA estmaton error. The lengthy detals of ths dervaton are not ncluded here, but can be found n (Khan, 009). The procedure outlned above can be done for dfferent scenaros reflectng moble TOA estmaton at a gven base staton of nterest. For our purpose, we analyze the performance of TOA DLL trackng at the dfferent base statons for each one of the three cases descrbed n Secton 3. The results are shown n Fgures 5 through 7, where t s clearly seen that the TOA resdual error behavor can vary wdely dependng on the moble poston vs-à-vs the trackng base staton. For example, n Fgure 5 whch corresponds to a moble very close to ts home servng base staton, the resdual error at the home base staton s well-confned and nearly Gaussan-dstrbuted (wth a standard devaton found to be on the order of 0.15T c ), whereas for the other two base statons, the tmng errors reman nearly unformlydstrbuted wth a standard devaton of 0.9T c (whch shows that the DLL loops at those base statons are not effectvely trackng the moble sgnal TOA). On the other hand, n Fgure 6 and Fgure 7 correspondng to -way and 3-way SHO, respectvely, the moble tme trackng performance at BS and BS3 s markedly better, wth dstrbutons approachng that of the home BS1. It s to be noted that the number of users per cell (assumed the same for all cells, for smplcty) can also have a major mpact on the tmng estmaton accuracy, regardless of the moble poston scenaro (.e., for all dfferent cases dscussed prevously). Indeed, as shown n Fgure 8, when the number of users ncreases, the trackng error PDFs are more wde-spread, and have an ncreasng error s.t.d (gven wth a normalzaton factor of 1/T c ).

12 448 Trends n Telecommuncatons Technologes Fg. 5. Moble TOA Trackng error PDF at BS1, BS, BS3 for Case 1 (MS wthout handoff) Fg. 6. Moble TOA trackng error PDF at BS1, BS, BS3 for Case (MS n -way soft handoff)

13 Performance Analyss of Tme-of-Arrval Moble Postonng n Wreless Cellular CDMA Networks 449 Fg. 7. Moble TOA tme trackng error PDF at BS1, BS, BS3 for Case 3 (MS n 3-way soft handoff) Trackng Error Dstrbuton as Functon of Number of Users n a Cell 10 users, std= users, std= users, std= PDF normalzed trackng error Fg. 8. Illustraton of the mpact of the number of users on the TOA trackng error probablty densty functon.

14 450 Trends n Telecommuncatons Technologes 5. TOA Processng for Moble Postonng 5.1. Approxmate Maxmum Lkelhood Algorthm In tme-of-arrval radolocaton technques, the dstance s calculated as the propagaton tme multpled by the speed of lght c. Lne-of-sght (LOS) propagaton s assumed, whereby the moble sgnal travels on a drect path at the constant speed of lght n free space. It s further assumed that the base statons are synchronzed and the moble transmsson tme s known (set to zero for smplcty). The TOA measurements, produced at each base staton, are therefore drectly proportonal to the moble-base dstance separaton. Geometrcally, crcles centered at the base statons can be drawn wth the calculated dstance as the radus. Wth the help of three base statons, the moble locaton can be found geometrcally as the ntersecton of the correspondng crcles. However, n the presence of nose and nterference, the three crcles may not ntersect at a sngle pont. Therefore, the geometrc approach s not sutable, and several other statstcal technques have been proposed (Caffrey, 1999), (Sayed et al., 005) to process the nosy data. Many of these are based on teratve algorthms usng least-squares or gradent search mnmzaton. On the other hand, snce the postonng equatons nvolved are typcally nonlnear, some tradtonal approaches based on lnearzaton followed by a gradent search were proposed (Nezgoda & Ho, 1994). However, these approaches suffer from senstvty to ntalzaton errors and convergence problems. More recently, some researchers ntroduced new closedform lnear technques (Caffrey & Stuber, 000), (Chan & Ho, 1994), but the drawback of these methods s that optmum locaton estmates can only be found at hgh SNR values, whch may not always be the case n practce. Another nterestng soluton was proposed by (Chan et al., 006) and shown to have nearoptmum performance, wth the added advantage of reduced complexty. Ther method uses an Approxmate Maxmum Lkelhood (AML) algorthm, whch we adopt n ths study. In the followng, we gve a general overvew of the AML algorthm processng steps, and ntroduce a modfcaton talored towards the case of unequal TOA varances at the dfferent base statons, and relevant to moble radolocaton under near-far nterference condtons (whch s the focus of ths work), as wll be outlned subsequently. Based on the assumed cellular geometry, the true dstances between the BSs and MS are gven by R x x y y =1,,,N BS (17) where N BS s the number of nvolved BSs. The measured dstances, l, s gven by where ε s the DLL tmng error. In matrx form, ths s wrtten as Dvdng by c to get the measured TOA vector T, we obtan l R =1,,,N BS (18) l = R +ε (19)

15 Performance Analyss of Tme-of-Arrval Moble Postonng n Wreless Cellular CDMA Networks 451 R c ε T c T 0 + e (0) where and t R R1 R N R( Θ) (1) t e e e... () 1 N s the vector of addtve measurement nose, and T 0 s the vector of true TOAs. The orgnal AML algorthm proposed by (Chan et al., 006) assumes that all BSs have an equal error varance. Hence, the elements of e are assumed to be ndependent, zero-mean Gaussan random varables wth covarance matrx t Q E ee I (3) The AML algorthm can be generalzed to account for dfferent values of the error varance at dfferent BSs. If the varance of the error can be estmated at each BS, one can use ths nformaton to mprove the localzaton performance by gvng more trust to BSs wth lower error varance. In ths case the elements of e are assumed to be ndependent, zero mean Gaussan random varables wth covarance matrx: t dag 1 N Q E ee (4) The condtonal probablty densty functon (PDF) of T gven Θ s gven by where N BS 1 J f ( T Θ) ( ) (det Q ) exp (5) 1 t 1 0 e1 N R( Θ) 1 R( Θ) BS T Q T N c c 1 0 N e N J e e (6) The ML estmate of the MS poston (x, y) s the Θ that mnmzes J (Trees, 1968). Mnmzng J s done by settng ts gradent wth respect to Θ to zero. Consderng frst the dervatve wth respect to the poston varable x, we have

16 45 Trends n Telecommuncatons Technologes NBS NBS J 1 e 1 e e x x x 1 1 (7) By expressng the tmng error n terms of the dfference between the true TOA and measured one, ths gves Utlzng Equaton (17), we may wrte e R 1 R T x x c c x x x x x R 1 x R R Substtutng the result n Equaton (8) yelds e 1 x x x c R Substtutng n Equaton (7), we get NBS J 1 1 x x e x c R 1 NBS 1 c R l x x 1 R (8) (9) (30) (31) The above steps startng wth Equaton (7) can be repeated for J/ y n a straghtforward manner. Fnally, by settng the gradent of J wth respect to Θ to zero, we get the two ML equatons N BS 1 1 R l x x 1 N BS R R l y y R (3) The above equatons can be expressed n matrx notaton as where g x gy x g s K l hx hx y h s K l (33) s x y (34)

17 Performance Analyss of Tme-of-Arrval Moble Postonng n Wreless Cellular CDMA Networks 453 K x y (35) x x g R R l y y h R R l (36) (37) In a more compact form, Equaton (34) can be re-wrtten as AΘ = b (38) wth the matrx A and vector b beng functons of Θ. A suboptmal soluton based on a lnear model (Chan & Ho, 1994) can be used as a frst ntal estmate of Θ, whch wll n turn gve startng values of A and b. Then, solvng Equaton (33) produces a new value of Θ to update A and b, and subsequently Θ. Ths teratve procedure frst gves an approxmate maxmum lkelhood (AML) estmator, whch can then be terated a number of tmes to obtan a fnal soluton. The fnal soluton takes the Θ that gves the smallest J n Equaton (6). Ths ensures that the AML wll not dverge. In fact, smulaton results presented n (Chan et al., 006) show that the AML can nearly acheve the Cramer Rao lower bound (CRLB) wth a small number of teratons (typcally on the order of fve updates are found to be suffcent). It should be noted that, for the specal case of equal measurement varance assumpton (as n the orgnal AML), the common term drops from Equaton (3). However, wth the modfed AML n Equaton (33), the quanttes g and h wll be dfferent for dfferent BSs, and ths s found to yeld some mprovement n performance as wll be dscussed next. 5.. Postonng Accuracy wth the Modfed AML Algorthm To llustrate the mpact of the modfed AML that takes nto account the unequal error varances, we consder an example of three BSs wth dfferent measurement error statstcs for mobles located n three dfferent regons, as descrbed n the dfferent cases of Secton 3. Fgure 9 shows the geometry of the layout used for ths purpose, where dstances are shown n meters. The dense scatter ponts represents a total of 10 5 nosy moble locatons generated accordng to the TOA statstcs for the dfferent cases of nterest whch are referred to as MS1, MS, MS3, correspondng to mobles classfed n Secton 3 as Case 1,, and 3, respectvely. For each moble locaton, the AML and modfed AML algorthms are executed to obtan the estmated moble coordnates, and by comparng wth the known moble poston, the resultng postonng error can be computed. The dfferent parameters for the rado channel and relatve receved power factors used are based on the results gven n Table 1 of Secton 3.

18 454 Trends n Telecommuncatons Technologes Fg. 9. Layout of the moble localzaton geometry used to test the accuracy of the AML algorthm. Varous aspects of moble postonng performance are llustrated n Fgure 10 based on the cumulatve dstrbuton functon (CDF) of the radolocaton error. Frst, t can be seen that the modfed AML whch takes nto account the dfferences n TOA nose statstcs at the varous base statons (as proposed n ths work) outperforms, albet slghtly, the conventonal AML whch assumes equal TOA nose varance at all base statons. Ths s more pronounced for mobles categorzed as MS1 (.e., whch are n close proxmty to ther home base statons). The other major observaton from Fgure 10 s that a large dfference n radolocaton accuracy s present dependng on the moble relatve poston wth respect to the base statons. It s clearly seen that MS and partcularly MS3 mobles, correspondng to mobles n -way and 3-way soft handoff, respectvely, acheve much better performance as opposed to MS1. Ths s due to the poor TOA accuracy at BS and BS3 for the latter case, owng to the overwhelmng near-far nterference experenced by the moble at the remote bases statons, as dscussed n Secton 4. As an example, the probablty of the resdual postonng error beng less than 0m s almost one for MS3 mobles, whle t s on the order of 70% for MS, and only 50% for MS1 type mobles. Smlar observatons also hold for other dstances. Therefore, as hghlghted throughout ths study, the accuracy of moble postonng s best when the moble s n close proxmty to a border cell regon where soft handoff connectvty s establshed wth one or two more cells nvolved n ts postonng n addton to ts home servng cell.

19 Performance Analyss of Tme-of-Arrval Moble Postonng n Wreless Cellular CDMA Networks 455 Fg. 10. Illustraton of moble postonng accuracy wth the Approxmate Maxmum Lkelhood Algorthm. 6. Concluson Ths study dealt wth the performance analyss of tme-of-arrval (TOA) technques for moble postonng n CDMA wreless cellular networks. Snce several base statons are typcally needed for moble radolocaton, the problem of weak sgnal hearablty at remote base statons s a major challenge, and a detaled analyss of ths ssue was presented by takng nto account the near-far nterference usually present n CDMA cellular networks. TOA-based postonng methods are well-suted for wde deployment of radolocaton servces snce the synchronzaton crcuts that can extract tmng nformaton are readly avalable at the base statons recevng the moble sgnal. For CDMA sgnals, the delaylocked loop (DLL) s commonly used as a TOA estmaton devce, and a detaled analyss of DLL-based TOA trackng was presented takng nto account the cellular network layout, cell loadng and other-user nterference, as well as RF channel shadowng and pathloss that affect receved sgnal strength at the dfferent base statons. In partcular, t was shown that the TOA trackng error statstcs can vary consderably dependng on the moble lnk condtons wth respect to the base statons nvolved n ts postonng, and soft handoff (SHO) lnks wth two or three base statons for mobles close to border-cell regons were found to mprove the precson of moble TOA trackng. Usng TOA nformaton, a moble radolocaton postonng algorthm based on a computatonally-effcent, near-optmum approxmate maxmum lkelhood (AML) processng was presented, and a generalzaton to the case of unequal tmng error varances at the dfferent base statons was also derved. Numercal results were presented to quantfy

20 456 Trends n Telecommuncatons Technologes the achevable postonng accuracy of the AML algorthms, and t was also shown that SHO rado lnks wth two or partcularly three base statons have a clear mpact on the precson of moble radolocaton. Fnally, t should be noted that the problem of non-lne-of-sght (NLOS) propagaton, whch consttutes another major challenge to moble postonng accuracy, was not ncluded n ths study, and would be addressed n future work. Acknowledgment Ths work was gratefully supported by Kng Abdulazz Cty for Scence & Technology and Kng Fahd Unversty of Petroleum & Mnerals, Saud Araba. 7. References Caffrey, J. J. (1999). Wreless Locaton n CDMA Cellular Rado Systems. Kluwer Academc Publshers. Caffrey, J. J. & Stuber, G. L. (000). Effects of multple access nterference on the noncoherent delay lock loop. IEEE Transactons on Communcatons, Vol. 48, (December 000) Chan, Y-T.; Hang, H. & Chng, P-C. (006). Exact and approxmate maxmum lkelhood localzaton algorthms. IEEE Transactons on Vehcular Technology, vol. 55, No. 1, (January 006) Chan, Y. T. & Ho, K. C. (1994). A smple and effcent estmator for hyperbolc locaton. IEEE Transactons on Sgnal Processng, Vol. 4, No. 8, (August 1994) Chan, Y. T.; Yau, C. H. & Chng P. C. (006). Exact and approxmate maxmum lkelhood localzaton algorthms. IEEE Transactons on Vehcular Technology, Vol. 55, No. 1, (January 006) Dahlman, E.; Gudmundson, B.; Nlsson, M. & Skold, A. (000). UMTS/IMT-000 based on wdeband CDMA. IEEE Communcatons Magazne, (September 000) Gosh, A. & Love, R. (1998). Moble staton locaton n a DS-CDMA system, Proceedngs of IEEE VTC, Vol. 1, pp Kaplan, E. (1996). Understandng GPS: Prncples and Applcatons. Norwood, MA: Artech House. Khan, H. R. (009). DLL Code Trackng for CDMA Sgnals under Fadng and Multple Access Interference, M.S. Thess, Kng Fahd Unversty of Petroleum & Mnerals, February 009. Nezgoda, G. H. & Ho, K. C. (1994). Geolocaton by combned range dfference and range rate measurements, Proceedngs of Internatonal Conference Acoustcs, Speech, Sgnal Process (ICASSP 94), Adelade, Australa, Vol., 1994, pp Rappaport, T.; Reed, J. & Worner, B. (1996). Poston locaton usng wreless communcatons on hghways of the future. IEEE Communcatons Magazne, (October 1996) Sayed, A. H.; Targhat, A. & Khajehnour, N. (005). Network-Based Wreless Locaton. IEEE Sgnal Processng Magazne, (July 005) Su, S. L. & Yen, N. Y. (1997). Performance of dgtal code trackng loops for drect-sequence spread-spectrum sgnals n moble rado channels. IEEE Transactons on Communcatons, Vol. 45, (May 1997) Trees, H. L. V. (1968). Detecton, Estmaton, and Modulaton Theory: Part 1, Wley, New York. Vterb, A. J. (1995). CDMA: Prncples of Spread Spectrum Communcaton, Addson-Wesley.

21 Trends n Telecommuncatons Technologes Edted by Chrstos J Bouras ISBN Hard cover, 768 pages Publsher InTech Publshed onlne 01, March, 010 Publshed n prnt edton March, 010 The man focus of the book s the advances n telecommuncatons modelng, polcy, and technology. In partcular, several chapters of the book deal wth low-level network layers and present ssues n optcal communcaton technology and optcal networks, ncludng the deployment of optcal hardware devces and the desgn of optcal network archtecture. Wreless networkng s also covered, wth a focus on WF and WMAX technologes. The book also contans chapters that deal wth transport ssues, and namely protocols and polces for effcent and guaranteed transmsson characterstcs whle transferrng demandng data applcatons such as vdeo. Fnally, the book ncludes chapters that focus on the delvery of applcatons through common telecommuncaton channels such as the earth atmosphere. Ths book s useful for researchers workng n the telecommuncatons feld, n order to read a compact gatherng of some of the latest efforts n related areas. It s also useful for educators that wsh to get an up-to-date glmpse of telecommuncatons research and present t n an easly understandable and concse way. It s fnally sutable for the engneers and other nterested people that would beneft from an overvew of deas, experments, algorthms and technques that are presented throughout the book. How to reference In order to correctly reference ths scholarly work, feel free to copy and paste the followng: M. A.Landols, A. H. Muqabel, A. S. Al-Ahmar, H.-R. Khan and R. A. Al-Nmnm (010). Performance Analyss of Tme-of-Arrval Moble Postonng n Wreless Cellular CDMA Networks, Trends n Telecommuncatons Technologes, Chrstos J Bouras (Ed.), ISBN: , InTech, Avalable from: InTech Europe Unversty Campus STeP R Slavka Krautzeka 83/A Rjeka, Croata Phone: +385 (51) Fax: +385 (51) InTech Chna Unt 405, Offce Block, Hotel Equatoral Shangha No.65, Yan An Road (West), Shangha, 00040, Chna Phone: Fax: