Abstract. Introduction. Statistical Approach for Analyzing Cell Phone Handoff Behavior. Volume 3, Issue 1, 2009

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1 Volum 3, Issu 1, 29 Statistical Approach for Analyzing Cll Phon Handoff Bhavior Shalini Saxna, Florida Atlantic Univrsity, Boca Raton, FL, Sad A. Rajput, Farquhar Collg of Arts & Scincs, NSU, Fort Laudrdal, FL, Abhijit S. Pandya, Florida Atlantic Univrsity, Boca Raton, FL, Minsoo Suk, School of Information & Communications, Sungkyunkwan Univrsity, Suwon, Kora, Abstract A handoff bhavior valuation mthod is proposd that uss ral data collctd from actual drivs to valuat th prformanc. This data is aggrgatd to prform statistical analysis. A chi-squar statistical tst is thn prsntd to valuat th prformanc of spcific cll phon modl by comparing th bhavior of a tst modl against a wll-stablishd bhavior profil. This tchniqu can also b usd to compar prformanc of st of modls in on rgion to prformanc of sam st in othr rgion, and to dtrmin th ffct of dirctionality on th cll phons. Introduction Sinc th invntion of wirlss communications [1], innovations hav continuously pushd th limit of capacity of wirlss systms. First, frquncy division multiplxing was usd to transmit and rciv multipl signals simultanously. Thn Tim division multiplxing was usd to furthr xpand th capacity of communications. [2]. Evr incrasing nd for wirlss call traffic on limitd lctromagntic spctrum or frquncy band ld to th dvlopmnt of th cllular radio ntworks [3]. It incrass th numbr of simultanous convrsations possibl (calld usr capacity) in a givn mobil radio tlphon systm by frquncy rus [3]. In cllular ntworks, numrous lowr-powr transcivrs, ach with shortr covrag, ar stratgically dployd to covr a larg gographic ara. Frquncy rus factor xprsss th rat at which a givn frquncy can b usd in a givn ntwork. Svral low powr transcivrs ar part of a bas station that srvics a cll. Th bas station also contains a control unit that manags continuity of individual phon calls. Multipl frquncy bands ar assignd to ach cll, so th bas station is capabl of communicating with cll phons in that cll on any of thos frquncis. In a givn cllular architctur, th numbr of frquncy bands assignd to a cll dpnds on th traffic xpctd in that cll. Adjoining clls ar assignd diffrnt group of frquncis to avoid intrfrnc and crosstalk. Howvr, clls that ar sufficintly far apart can rus th sam frquncis sinc radio signals strngth diminishs with distanc [3]. To achiv this, frquncis ar usually bundld into colors. Thus, th problm of frquncy allocation maps to th map-coloring problm [4,5]. In a ral cllular ntwork, at any givn instanc, a numbr of mobil units ar moving in a cll, and thy activly communicat with th bas station. Svral channl assignmnt stratgis ar discussd in th convntional rsarch publications for instanc, [6] discusss an aggrssiv channl allocation schm to rduc call loss du to faild hand ovr rqusts and call blocking in a multipl call hand-off contxt. Each bas station is connctd to a mobil switching cntr, which srvs multipl bas stations. Th mobil switching cntr routs th calls dpnding on th location of th mobil unit, assigns voic channl to ach call, prforms handoffs, and monitors th call for billing information [3]. In this papr this mchanism will b calld mobil call managmnt. Whn a mobil unit movs from covrag ara of on bas station to anothr it is said to hav crossd th cll boundaris. Th mobil unit must switch th traffic channl assignd to th old bas station to th nw bas station as it crosss ovr its cll boundary. This procss is calld handoff and is prformd ubiquitously. Th Rcivd Signal Strngth Indicator (RSSI) gts wakr as th mobil unit movs away from th bas station. Whn a nighboring sit is strongr than th srving/currnt cll, th mobil unit rqusts a handovr to anothr sit [3]. Aftr th handovr, th RSSI typically ss significant improvmnt. Cll dragging may occur whn a cll phon movs a considrabl distanc into th nighboring cll ara without making a handoff, rsulting in an incrasd lvl of systm intrfrnc [7]. Cll dragging may lad to incrasd numbr of call drops. In ordr to masur th rat of call drops [8]has dvlopd a mthod of procssing information about droppd calls in a cllular ntwork by using mobil station locations and information about locations whr calls ar droppd. A handoff schm that utilizs two adaptiv algorithms in combination; on using a rlativ thrshold and th othr an absolut thrshold, has bn proposd in [7]. This schm aims at minimizing cll dragging. Othr works [9 and 1] hav proposd modls to configur cllular ntworks basd on subscribr mobility btwn clls. In

2 [11] Magnusson, and Olofsson hav proposd an algorithm to dynamically dtrmin nighboring cll lists i.. handovr candidats and thir associatd broadcast control channls for ach cll in th systm. Bansal t.al [12] propos using knowldg of th cll trrain, th mobil trajctory, and th vhicular movmnts in a cllular ntwork to prdict handoff rats. In [13] a systm has bn dvlopd to monitor cllular tlphon systm that collct call prformanc information lik signal strngth and call vnts. This Cllular Communications Driv Tst Systm nabls mapping of th call information basd on GPS information collctd. Anothr nhancmnt in th fild of driv tst was prformd in [14] for providing signal quality masurmnts in driv tst systms for wirlss ntworks. This rsarch dos not try to valuat or compar th prformanc of various handoff algorithms; instad it valuats th prformanc of various phons modls. Littl has bn publishd to-dat that provids mthods of analyzing th ral world prformanc phons from th usr s prspctiv. This work dvlops a comprhnsiv statistical tst that masurs th dgr to which any cll phon modl is implmnting th handoff dsign and it valuats th phon s prformanc indpndnt of th handoff algorithm implmntd. Th focus of this valuation is on th bhavior of th phon irrspctiv of what handoff algorithm th srvic is using. In sction 2 provids th profils of dsirabl and undsirabl mobility bhaviors. In sction 3 discusss th proposd stratgy in how th data is collctd, and aggrgatd. In this sction also provids a stochastic modl and how th data is usd to calculat th statistical chi-squar tst on obtaind data. Sction 4 prsnts th rsults and show modls that mad poor mobility dcisions can b succssfully distinguishd with this approach. To protct th propritary information, gnric nams for proposd modls ar usd, vn though th data was collctd using actual phon cll modls. Mobility bhavior A normal dcision consists of a handovr to th nw towr that provids th unit with highr RSSI (strongr signal) as a cll phon movs from a wakr towr sit to its nighborhood. This dcision procss is illustratd in Figur 1. Position 1 in Figur 1 dpicts th bhavior of th cll phon whil it is moving from on cll to anothr cll. At position 1 it is within th covrag rgion of Bas station A that has assignd Color Cod X. It is moving towards Bas station B that uss Color Cod Y. At position 2 it movs away from A it gos in th ovrlapping rgion btwn th two bas stations. In this rgion th RSSI from two stations ar clos in valus. To avoid xcssiv handoffs in this rgion th cll phons ar dsignd to rtain connction with th prvious towr till th signal from towr B is at last 6dB strongr. Figur 1 Mobility Bhavior of phon Whn th cll phon movs to position 3, th phon has movd closr to bas station B and is closr to th bas station B than th bas station A. Th phon at this point is xpctd to prform a handoff to cll sit B with th nw frquncy. Whn th phon (position 4) crosss th rang of bas station A, a normal phon switchs th mobil communication with th bas station B and prforms a handoff such that it now uss color cod Y of cll sit B. Th bas station A hands ovr th communication channl it allocatd to communicat with th mobil to bas station B so that it can stablish th sam communication with th cll phon. Undr ths conditions if th phon fails to handoff, it is said to mak a poor mobility dcision. Th poor mobility dcision in this cas would b to continu to us bas station A whil Bas station B s RSSI is highr than 6dB. This is calld cll

3 dragging whr a cll phon movs a considrabl distanc into th nighboring cll ara B without making a handoff. This abnormal bhavior of cll dragging mostly lads to poor audio quality during th call. It can also caus th call to b droppd. Thr ar othr ways in which th phon can bhav abnormally. For instanc, th phon can switch to nw towr prmaturly, or it can switch back and forth btwn th two stations multipl tims. Ral world is much mor asymmtrical than what is dpictd in Figur 1. Signals from multipl towrs might not ovrlap and th signal may not dcay in a nonincrasing fashion du to gographical and physical conditions. Poor mobility dcisions ar mad du to varity of rasons that may or may not dpnd on th quality of th phon. Howvr, an ill-dsignd phon will xhibit poor mobility dcisions mor frquntly than normal units. Modl and Stratgy In th approach prsntd in this papr, first a baslin modl is slctd that has a spcific modl which is gnrally known to bhav wll in th fild. Th unit blonging to a spcific cll phon modl to b tstd (calld tst modl) is thn compard to th baslin modl. Data Acquisition To collct ral data for this analysis, th baslin modls and/or th tst modls ar mountd on a tst vhicl and ar connctd to th masurmnt quipmnt that is dsignd to gathr and analyz diagnostic data provid by th tst modls through spcial intrfacs. Th vhicl is drivn ovr a gographic closd loop rout (calld driv-loop, driv tst loop or simply driv tst). Figur 2 Googl Map for a sampl Driv Tst Loop Figur 2 is an xampl of a sampl driv tst as sn on Googl Map. For ach driv th diagnostic data is rcordd in th tst logs. Hnc, this data rprsnts a liv phon call in a ral world condition. Such driv tsts produc approximatly on rcord vry scond. Each rcord includs latitud, longitud, color cod and RSSI data capturd at that instanc whil th phon is in th call. Color cods ar usd to distinguish carrir signal from its co-channl intrfrnc. A color cod st consists of diffrnt intgral numbrs. Each numbr is allocatd to on of th frquncy sts that ar gographically narby to ach othr [15]. Th comparison btwn tst modl and baslin modl is mad by comparing th data in ths tst logs. To mak ths tsts mor maningful data is analyzd sparatly for clockwis and countr-clockwis dirction in th driv tst loop. Similar tchniqus can also idntify rgions of covrag or ach towr basd on RSSI data and dtrmin significant dviation of a cll phon s RSSI from nighboring cll phons.

4 Data Aggrgation Proposd analysis is basd on th color cod and GPS location. Using th GPS data th driv tst rout is dividd into 5m x 5m squars and color cod information is aggrgatd. In a squar, numbr of rcords collctd is rankd basd on a masur that is basd on statistical tchniqus. Th choic of 5m x 5m squars smd to provid most consistnt rsults for proposd analysis. Figur 3 shows a diagrammatic rprsntation of th 5m x 5m grid that is usd to divid th driv tst rout. In th arly phas smallr grid siz of 3m x 3m was trid and thn largr grid siz of 1m x 1m was usd. Smallr grids did not hav nough data in unit aras to provid significant sampl sizs, whil in th biggr grids data rsolution rducd. On obsrvation whil analyzing smallr grids was that thr ar mor valid grid points to us for comparison. Du to th motion of th car and th on-scond dlay btwn sampls associatd with moving at 6mph it was not fasibl to choos squars smallr than 3m. Figur 3 Grid drawn ovr th Driv tst Loop Not: Grid is not drawn to scal Th aggrgatd data is thn usd to idntify poor mobility dcisions that ar mad by th cll phon. Bas Unit Path Tst Unit 1 Path Tst Unit 2 Path Color cod b Color cod 5 Color cod Figur 4 Color Cods obsrvd for thr driv tsts To aggrgat th data for a cll th numbr of sam color cod sampls for th sam typ of cll phon in th squar was countd. This numbr is dividd by th total numbr of obsrvations in that squar to obtain th frquncy of that color.

5 Whn th color cod is tratd as a random variabl, this color frquncy distribution stimats th distribution of this random variabl. Th undrlying sampl spac for a givn squar for this random variabl will hav all th color cods. Figur 4 shows a sampl squar in th gographic grid with thr drivs and th colors of th obsrvations. Th paths of th driv vhicl ar indicatd by dashd curvs whil th colord symbols indicat th color obsrvations during thos drivs. In this papr, diffrnt symbols hav bn usd for ach color. f f 5 b (a) Color cod 5 b (b) Color cod f f 5 b (c) Color cod 5 b (d) Color cod Figur 5 Frquncy distribution for bas modl (a), tst modl 1 (b), tst modl 2 (c) and aggrgatd frquncy distribution for all thr modls (d). Th rsulting probability distributions ar shown in Figur 5(a) for bas modl, (b) for tst modl 1, and Figur 5(c) for tst modl 2. To obtain a mor accurat distribution, on can also aggrgat data from multipl tst drivs that blong to th sam cll phon modl as illustratd by th distribution shown in Figur 5 (d). Stochastic Modl Th basic unit of this stochastic procss is th squar in th grid ovr which th obsrvations ar mad. Th basic xprimnt consists of two tst drivs through this squar, on for th tst modl and th othr for th bas modl. Th color cod distribution has alrady bn discussd. That corrsponds to a color cod random variabl for a givn cll phon is usd to dnot this random variabl with c i,j,t, whr (i,j) corrspond to th longitud and latitud coordinats of th squar in th grid and t corrsponds to th tst ID of th particular driv. Th phon unit can also b tratd as a random variabl as wll and rprsnt it by p i,j,t In proposd modl, this random variabl has two valus bas modl and tst modl. Th two random variabls c i,j,t, and p i,j,t form a joint probability spac for a givn cll. Bcaus thr ar 16 color cods in on cllular modl and two phons, thr ar 32 possibl outcoms. For instanc (bas, rd) is an outcom that indicats that th bas modl is connctd through th rd frquncy. Th probability of this outcom is givn by th rlativ frquncy distribution obsrvd for that color cod and th cll phon. Thus, this joint probability spac can b organizd as a contingncy tabl. Tabl 1 is an xampl of a 2 x 16 contingncy tabl for th two phons (baslin and tst) and 16 color cods. Th column total and row total ar marginal totals. Tabl 1 A 2 x 16 Contingncy tabl for Color cods and phons Color Cod a b c d f Total Modl Tst Total Th objctiv of th tst was to dtrmin if th slction of cll phon affcts th color cod distribution. If th two cll phons bhav in a similar fashion, th color cod distribution should b unaffctd whn th cll phons ar switchd. That

6 would imply that th color random variabl is indpndnt of cll phon random variabl. Howvr, if thy hav diffrnt color cod distribution for that givn squar thn th cll phons bhav diffrntly, th two random variabls ar dpndnt. Hnc, this problm can b stup as a statistical Indpndnc hypothsis tst problm, whr th Null Hypothsis bing that th random variabl color is indpndnt of cll phon. H : Color cod distribution is indpndnt of cll phon slction (i.. c i j, t pi, j, t, Χ ) H a: Th variabls ar dpndnt To stablish this indpndnc, th approach is to calculat th Chi-Squar tst statistic for ach squar and rjcting all th squars in which th null hypothsis is not rjctd using th p-valu tst. Only th squars in which th null hypothsis is succssfully rjctd ar kpt. Ths ar th squars whr changing th two cll phons providd diffrnt color cod distributions. Th nxt sction compars th hand-off bhavior of cll phons in a squar using on tst driv for th bas modl and on tst driv for th tst modl. Th hand-off bhavior of cll phons using th aggrgatd data from multipl tst-drivs for th bas modl is compard and modl in slctd squars of th aformntiond grid is tstd. Rsults This sction also compars th handoff bhavior using on tst driv for th bas modl and on tst driv for th tst modl. To improv th accuracy of rsults data aggrgatd from multipl drivs is compard so that th numbr of sampls in a singl squar is highr. Rsults from thr squars that wr studid ar prsntd. Th first comparison for th singl tst driv and multipl tst drivs is conductd on a squar with th latitud and longitud coordinats as 176 and 415 rspctivly. 6 5 Bas Modl Tst 1 Frquncy Color Cod Figur 6 Tst modl 1 compard with th bas modl using data from a singl tst driv, Chi-Squar = , dgr of frdom = 1 and p-valu =.7 Figur 6 shows data from whn a singl driv tst data of bas modl is compard with th tst data of a singl driv of out tst modl 1. In this data, thr ar two obsrvd frquncis of colors 6 and in this squar so th contingncy tabl will b of siz 2 x 2). Th Chi-squar valu for this comparison is and dgr of frdom (DoF) is 1. At significanc lvl.1 using th p-valu.698 it is infrrd that th handoff bhavior for Tst 1 is significantly diffrnt from bas modl and rquirs furthr inspction.

7 Similarly, w compar bas modl with tst modl 2. Again w s th sam two colors 6 and but diffrnt frquncis as shown in Figur 7. At significanc lvl.1 using th p-valu it is infrrd that th handoff bhavior for Tst 1 is significantly similar to th bas modl and should b a good cll phon modl Bas Modl Tst 2 Frquncy Color Cod Figur 7 Tst modl 2 compard with th bas modl using data from a singl tst driv, Chi-squar = 3.18 dgrs of frdom = 1 and p-valu =.8235 For th sam squar multipl tst-drivs can b compard for bas modl to multipl tst-drivs of tst modl 1, tst modl 2 and a phon moving in opposit dirction. First comparison was bas modl to tst modl 1 (Figur 8). At significanc lvl.1 th handoff bhavior for Tst 1 is dtrmind to b significantly diffrnt from bas modl and rquirs furthr inspction. Frquncy Bas Modl Tst 1 6 Color Cod Figur 8 Tst modl 1 compard with th bas modl using data aggrgatd from multipl tst drivs. Chi-squar = 16.31, dgr of frdom = 1 and p-valu = 6.23x1-5 Th comparison of multipl tst-drivs for th bas modl and Tst modl 2 is dscribd in Figur 9. Using th p-valu it can clarly b infrrd that tst modl 2 bhavs similar to th bas modl and this cll phon modl should b a good phon. A comparison was also conductd to analyz th affct of dirctionality on handovrs in th sam squar. Figur 1 shows th color cod distribution for two phons moving in opposit dirctions. At a significanc lvl.1 it can b infrrd that this tst modl moving in dirction has a handovr bhavior that is notably diffrnt from th bas modl moving in dirction 1.

8 Frquncy Bas Modl Tst 2 6 Color Cod Figur 9 Tst modl 2 compard with th bas modl using data aggrgatd from multipl tst drivs. Chi-squar=.248 Dgr of frdom=1 and p-valu =.6184 Frquncy Dirction 1 Dirction 6 Color Cod Figur 1 Comparison of sam modl drivn in diffrnt dirctions using aggrgatd data from multipl drivs. Chi-squar=1.283, dgr of frdom =1 and p-valu =.1343 Ths rsults vidntly show that Chi-Squar Statistical Tst is vry powrful in comparing th handovr bhaviors for not only on tst driv to anothr singl tst driv but also aggrgatd data of multipl tst-drivs. Th comparison of a singl tst driv and aggrgatd data for th sam tst modl yildd sam rsults. Th ffcts of dirctionality on handovrs can also b xamind using Chi-squar Statistical Tst. Tabl 2 shows a summary of th comparisons conductd on squar (415,176). Anothr Chi-Squar Statistical Tst was conductd on a squar with th latitud and longitud coordinats as 11 and 443 rspctivly. Th aggrgatd data was compard for th sam multipl tst drivs that wr studid in abov squar (415, 176) in this squar as wll.

9 Frquncy Bas Modl Tst 1 3 Color Cod 8 Figur 11 Tst modl 1 compard with th bas modl using data aggrgatd from multipl tst drivs. Chi-squar = Dgr of frdom = 1 and p-valu = 8.2x1-13 W first compard bas modl to tst modl 1(Figur 11). At significanc lvl.1 it was stablishd that th handoff bhavior for Tst 1 is significantly diffrnt from bas modl. Frquncy Bas Modl Tst Color Cod Figur 12 Tst modl 2 compard with th bas modl using data aggrgatd from multipl tst drivs. Chi-squar = 4.45 Dgr of frdom = 1 and p-valu = Th comparison of multipl tst drivs for th bas modl and Tst modl 2 as dscribd in Figur 12 shows that Tst modl 2 bhavs similar to bas modl. Th p-valu of can b usd to infr that tst modl 2 should b a good phon.

10 18 16 Dirction 1 Dirction 14 Frquncy Color Cods 8 Figur 13 Comparison of sam modl drivn in diffrnt dirctions using aggrgatd data from multipl drivs. Chi-squar= Dgr of frdom =1 and p-valu = x 1-13 Figur 13 shows th color cod distribution for two phons moving in opposit dirctions. At a significanc lvl.1 it is obvious that this tst modl moving in dirction has a handovr bhavior that is notably diffrnt from th bas modl moving in dirction 1. Tabl 2 shows a summary of th comparisons conductd on squar (443,11) is consistnt with th rsults from squar (415,176). Th rsults for th third comparison of th aggrgatd data from th sam multipl tst drivs on a squar with coordinats (449, 69) is no prsntd. In this squar mor than 2 color cods wr obsrvd Bas Modl Tst 1 Frquncy Color Cod 7 c Figur 14 Tst modl 1 compard with th bas modl using data aggrgatd from multipl tst drivs. Chi-squar = Dgr of frdom=4 and p-valu=.2857 At a significanc lvl of.1with th p-valu of.2857 it can b concludd that tst modl 1 bhavd diffrnt from th baslin. Figur 14 shows th color cod distribution for th two cll phons.

11 1 8 Tst 2 Bas Modl Frquncy Color Cod 8 Figur 15 Tst modl 2 compard with th bas modl using data aggrgatd from multipl tst drivs. Chi-squar = Dgr of frdom =2 and p-valu =.1373 Th comparison of baslin to tst modl 2 conforms to th rsults prsntd arlir in this papr as wll. Figur 15 dscribs th color cod distribution for this comparison. Using th p-valu.1373 it can b infrrd that both phons bhav similarly as obsrvd in othr squars Dirction 1 Dirction Frquncy Color Cod 8 Figur 16 Comparison of sam modl drivn in diffrnt dirctions using aggrgatd data from multipl drivs. Chi-squar= Dgr of frdom = 2 and p-valu = x 1-9 Th comparison for dirctionality for two phons moving in opposit dirctions also yildd rsults as found in th othr squars. Figur 16 dscribs this comparison. At significanc lvl.1 th p-valu of x 1-9 it can b clarly dtrmind that th two phons bhav notably diffrnt. Th comparison of two phon modls moving in opposit dirctions yildd significant rsults. Th rsults as dscribd in Figur 1, Figur 13 and Figur 16 clarly indicat that vn though th sam phon modls ar usd for th driv tst

12 but th phons bhav significantly diffrnt. This is an xpctd bhavior as th handoff bhavior ovr a givn cll for phons moving in opposit dirctions should b markdly diffrntly. Th rsults ar summarizd in th Tabl 2. On all 3 squars, it is obvious that th bhavior of tst modl 1 is significantly diffrnt from th bas modl. Thrfor, it is suspctd, and upon furthr invstigation was found dfctiv. Crtainly, th tst modl 2 is clarly accptabl. Th Chi-Squar Statistical tst is also vry fficint in showing th diffrnc in bhavior of th sam modl moving in opposit dirctions. Finally, from th rsults in Tabl 2 it is clar that th rsults on th thr squars ar consistnt. Tabl 2 Summary of Chi-Squar Valu for Aggrgatd Driv Tst Data c(lon,lat) Chi-Squar DoF p-valu Conclusion c(415,176) Tst Modl E-5 diffrnt Tst Modl similar Dirction diffrnt c(443,11) c(449,69) Tst Modl E-13 diffrnt Tst Modl similar Dirction E-13 diffrnt Tst Modl diffrnt Tst Modl similar Dirction E-9 diffrnt Givn th bas modl that has an accptd bhavior; Chi-Squar Statistical Tst bcoms an fficint mthodology in comparing two phons. Th rsults prsntd in this sction clarly show that it is asy to undrstand whn th tst modl is a good or bad modl in rfrnc to th bas modl. Th bhavior of th phons can also b invstigatd basd on dirctionality. Conclusion With th incrasing numbr of subscribrs for th cllular srvic th handoff bhavior of phons is an important factor to achiv high quality of srvic in a cll phon systm. This papr providd a practical approach that was dsignd to idntify phon modls that frquntly xhibit prmatur, dlayd or xcdingly snsitiv handoff dcisions also known as poor mobility dcisions. In litratur till-dat rsarch has focusd mostly on improving or valuating handovr algorithms using data collctd undr pristin laboratory conditions. Unlik ths convntional this papr valuats diagnostic data that was collctd from cllular phons during th fild tst undr ral world conditions, whil trating th cll phon as a black-box. A phon that maks good mobility dcisions undr laboratory conditions may not bhav as xpctd undr ral world conditions. Thrfor for this xprimntal stup, w trat th tst mobil unit as a black box to obtain rliabl rsults. Th tsts hav shown th viability of chi-squar statistical tst as an ffctiv mchanism that dtrmins th hand-off bhavior of cll phons. By mans of contingncy tabls this work compars th obsrvd frquncis of color cods in a small gographic rgion for th tst modl and th bas modl. Th Chi-squar is calculatd using ths contingncy tabls and by mans of indpndnc hypothsis tsting th handoff bhavior of th two phons is compard. P-valu that is calculatd using chi-squar is usd as a thrshold to accpt or rjct th indpndnc hypothsis. This tst is usd to compar handoff bhavior in crtain gographical rgions. In this papr w prsntd th rsults of handovr comparisons of th aggrgatd driv tst data from th sam st of multipl tst drivs on diffrnt rstrictd gographical locations. Th consistnt rsults on ths tsts show th fficincy of proposd statistical approach. Th rsults also show that this statistical masur is vry ffctiv in studying th handoff bhaviors of phons that ar moving in diffrnt dirctions. In conclusion, it has bn shown that this statistical approach is highly ffctiv in studying th handoff bhaviors of cll phons to dtrmin th diffrnc in thir handovr bhaviors, if any.

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