On the performance of packet-switched cellular networks for wireless data communications *

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1 Wrele Networ (995) 9^3 On the erformance of acet-wtched cellular networ for wrele data communcaton * Jean-Paul M.G. Lnnartz Deartment of EECS, Unverty of Calforna, Bereley, CA , USA, and Phl Reearch, Holtlaan 4, WY8, 5656 AA Endhoven, The Netherland Receved Setember 994 Abtract. Cellular frequency reue nown to be an effcent method to allow many wrele telehone ubcrber to hare the ame frequency band. However, for wrele data and mult-meda communcaton otmum cell layout dffer eentally from tycal oluton for telehone ytem. We argue that wrele rado ytem for burty meage traffc referably ue the entre bandwdth n each cell. Pacet queung delay are derved for a networ wth multath fadng channel, hadowng, ath lo and dcontnuouly tranmttng bae taton. Interference between cell can be reduced by arorately chedulng tranmon or by `atal collon reoluton'.. Introducton 3 Porton of th aer have been reented at the IEEE Internatonal Conference on Peronal Indoor Moble Rado Communcaton (PIMRC) of 993 n Yoohama and 994 n The Hague. Over the at everal year, wrele communcaton ha een an exlove growth n the number of ervce and tye of technologe that have become readly avalable. Sytem for cellular telehony, rado agng and cordle telehony have become commonlace and the demand for enhanced caacty growng. A the avalable rado ectrum lmted n bandwdth, networ oerator attemt to maxmze the number of crcut that can be uorted multaneouly by reung rado channel a denely a obly. It exected that n the near future, wrele data and mult-meda ervce wll alo become oular and that there wll be an ncreang need for ectrum-effcent rado networ to uort uch ervce. Drven by ectrum carcty, rado reource management for burty traffc radly becomng a major reearch toc. The roblem of managng nformaton and data flow n rado and wrele otcal networ aear to be gnfcantly dfferent from extng technque for wred or `guded' communcaton. Decade of reearch on harng communcaton reource among multle uer and ervce on wred networ ha led to a wde varety of technque for multlexng, wtchng and multle acce to communcaton reource uch a coaxal cable local area networ (LAN), e.g. [^4]. The common goal of thee cheme the dynamc agnment of bandwdth durng certan erod of tme. Many of thee multle-acce technque are alo ued n rado data networ. However, t oon aeared that the erformance of many random-acce cheme ubtantally dffer for guded (wred) and unguded (rado) channel, beng hghly deendent on the hycal charactertc of the channel. A revew n [5]. Meanwhle, the aect of atally reung carce rado ectrum reource have motly been addreed earately from allowng multle uer to hare the ame bandwdth-tme reource. Th for ntance llutrated by the fact that mot extng moble data networ ue a cellular frequency reue attern, and wthn each cell a random-acce cheme ued ndeendently of the traffc charactertc n other cell. Reult on how to dynamcally agn the ace-tme-bandwdth reource n rado channel however not yet well develoed. A crucal aect n the evaluaton and lannng of rado networ the comutaton of the effect of cochannel nterference n rado ln. The amount of nterference that can be tolerated determne the requred earaton dtance between co-channel cell and therefore alo the effcency of the networ. The ln erformance of cellular telehone networ wa frt tuded around 98 by Golng [6], French [7] and Cox [8]. Intal analye were lmted to outage robablte n contnuou wave (CW) voce communcaton, tang nto account ath lo and flat (frequency non-electve) Raylegh fadng. In the 98' the technque for comutng outage robablte wa refned te by te, ee e.g. [5^7], conderng among other thng hadowng [7], multle nterferng gnal cumulatng coherently [9] or, more realtcally, ncoherently [], the modulaton technque and error correcton method [8], and more recently the reence of a domnant lne-of-ght roagaton ath, a t occur n mcro-cellular networ [,3,8]. The tochatc occuaton of nearby co-channel cell accordng to the traffc law by Erlang wa ncluded n ome tude. Ä J.C. Baltzer AG, Scence Publher

2 ex 3 To future data or mult-meda ervce, queung and retranmon delay are far more mortant erformance meaure than outage robablty. Meage lot n a fade or due to nterference from other cell can mly be retranmtted, o outage robablte er e may not be an arorate crteron. Advanced method to fnd ln erformance, a develoed for cellular telehony, can tll be ued, but need to be extended to addre the ecfc Qualty of Servce requrement for data or mult-meda traffc. Th aer fnd the acet delay erformance n the downln,.e., from bae taton to termnal. We how that t otmum to ue the entre bandwdth n each cell. The correondng hgh nterference ower level from nearby tranmtter n adjacent cell requre a jont otmzaton and dynamc management of the atal frequency reue and the occuaton of ectrum wthn cell. The aer analye generc ytem, wthout mang ecfc aumton about the frequency band or roagaton envronment condered. The aumton of a contant channel tranfer functon durng the tranmon of a acet of data aear realtc for the arameter choen n mot modern VHF or UHF wrele networ. A econd aumton, conderng a flat tranfer functon over the tranmt bandwdth, reaonable a long a the ymbol tme longer than, ay, ten tme the rm delay read. In ytem wth large cell and hgh bt rate a n GSM, th aumton may not be atfed trctly, but the model ued here may be uffcently realtc for the uroe of the aer. If, n future moble mult-meda ytem, large cell are ued wth ymbol rate on the order of Megabt er econd, frequency electvty may requre ecal meaure to enure relable and effcent communcaton. The degn trade-off nvolvng both modulaton and multle acce tll ubject of current reearch for moble mult-meda alcaton. Th aer attemt to nvetgate ome of the acce ue and how how the extng model of cellular lannng for telehony may no longer be effcent. Intally th aer revew and further develo the technque for comutng and modellng ln erformance n cellular networ, whch ued later on a a tool to comute the networ erformance. Secton tart wth a tattcal decrton of the multath rado channel. Secton 3 how that Lalace Tranform facltate ome of the analye. Accurate numercal evaluaton can nonethele be lengthy, but ecton 4 rooe ere exanon that can be ued n comutatonally ntenve ta, uch a the lannng of ractcal net from toograhcal data bae. Secton 5 formulate a model for acet-wtched networ. The reult n ecton 6 combne ln erformance, a comuted n ecton 3 and 4, wth the model of ecton 5. Secton 7 rooe two new cheme that dynamcally combne frequency reue and nterference rotecton wth multle acce. Secton 8 conclude the aer.. Rado channel characterzaton A tycal rado channel exhbt multath receton, whch caue fadng. We addre narrowband ytem, that, we aume that the channel tranfer functon vrtually contant over the gnal bandwdth. Th correond to the aumton that Interymbol Interference doe not lay a major role n the erformance of the rado ln. A method to nclude the effect of channel deron on outage robablte wa rooed n [3]. The gnal amltude and hae receved from uer vare randomly wth antenna locaton and carrer frequency. Several tattcal model have been rooed to model the tochatc behavor of the gnal amltude and ower. Mot commonly acceted Rcan fadng, whch aume a domnant lne-of-ght comonent and a large et of reflected wave. The ntantaneou ower receved from the th uer, wth =, ha the robablty denty functon (df) f j ÿk K e ex ÿ K r 4K K ; I where the Rcan K-factor defned a the rato of the ower n the domnant comonent and the cattered (multath) ower, the total local-mean ower n the domnant and cattered wave, and I : denote the modfed Beel functon of the frt nd and order zero. In the ecal cae that the domnant comonent zero (K ), Raylegh fadng occur, wth an exonentally dtrbuted ower wth mean. Another exermentally verfed model for multath receton Naagam fadng [9,]. In th cae the ntantaneou ower ha the gamma df f j ÿ m m m mÿ ÿ m ; where ÿ m the gamma functon, wth ÿ m m! for nteger m. The arameter m called the `hae factor' of the dtrbuton. In the ecal cae that m, Raylegh fadng recovered, whle for larger m the fluctuaton of the gnal trength are le, comared to Raylegh fadng. For eae of analy, the Naagam model ometme ued to aroxmate the df of the ower of a Rcan fadng gnal []. Matchng the frt and econd moment of the Rcan and Naagam df gve m K K ; 3 K whch tend to m K = forlarge K. However ecton 4 how that n contrat to common belef, th aroxmaton le utable to model dee gnal fade of the wanted gnal. The Naagam model nonethele relevant a t model the receved gnal after m-branch dverty wth maxmum rato combnng. In a Raylegh-

3 ÿk n 3 fadng channel, th gnal become m-naagam [5,7]. A econd roagaton effect hadowng, reultng n a low varaton of the local-mean ower a the antenna move over dtance larger than a few meter. Meaurement ndcate that the receved local-mean ower converted nto logarthmc value, uch a db or neer, ha a normal dtrbuton. The local-mean ower n abolute unt (e.g. watt) thu ha the log- normal df f ex ÿ ln ; 4 where the logarthmc tandard devaton of the hadowng and the logarthmc area-mean ower of the -th uer. A tycal moble channel uffer from both hadowng and ether Rcan or Naagam fadng. The area-mean ower can be etmated from the dtance r between the th termnal and the bae taton. The mot mle ath lo model ued for analy of generc rado ytem r ; ÿ 5 where on the order of to 5. Harley [] uggeted ÿ ÿ r r 6 to mrove the accuracy for hort-range mcro-cellular roagaton, where r g a turnover dtance, often n the range m to 5 m. 3. Method for ln evaluaton In certan tuaton [5^7], t a uffcently good aroxmaton to aume that a meage receved uccefully f and only f the gnal-to-nterference-lunoe rato exceed a certan threhold z. Tycally z ontheorderofto(3todb).aumngcontant receved ower durng a acet tranmon tme, the robablty that the wanted gnal ower uffcently exceed the jont nterference lu noe ower t Pr > z t Z ÿ f t x r g Z zx f y dy dx ; 7 where we nert the arorate df of receved gnal ower a reented n ecton. The jont nterference gnal t the ncoherent um of multle ndvdual gnal. For ndeendent fadng, the df of the jont nterference ower the convoluton of the df of ndvdual nterference ower. In the ecal cae of a Raylegh-fadng wanted gnal, t df of gnal ower an exonental one. Hence, for robablte condtonal on the local-mean, the ntegral over y can be olved analytcally. An elegant mathematcal framewor ha been develoed by nterretng the reult a a Lalace tranform of the df of jont nterference ower. For a wanted gnal ubject to Raylegh fadng, th robablty can be exreed n the form [5,4,5,] Pr > z t j L f t ; z ; 8 where Lff ; g denote the one-ded Lalace tranform of the functon f at the ont. Wewllnowhowthat th aroach can be aled to a Rcan-fadng wanted gnal, ung the ere exanon I z X n ÿ n! 4 z for the modfed Beel functon I. Th gve Pr > z tj X Xn n K X n n n! K n n! Z zx e ÿ ÿk n ex ÿk ÿ zx K Xn! f t x dx Z ÿ x ÿx K 9 f t x dx : Ung the roerte of the lalace tranform, th can be wrtten a the ere Pr > z tj ÿkx e K Xn n n n!! d ÿ d L f t x ; ; For a Naagam-fadng wanted gnal, a mlar method ha been rooed by [6, 7]. Inertng the gamma df, one obtan Pr > z tj Xmÿ! n Xmÿ! n Z d ÿ L d x e ÿx f t x ; f t x dx : We conclude that n both cae, th robablty can be exreed n the generalzed form Pr > z tj X a ÿ! d d L f t; ; 3 where Table gve the arorate coeffcent a and argument. Table Coeffcent a and argument for ln ucce robablty. Channel fadng a Raylegh Rcan m-naagam a a for ;;... a a ÿ e Pÿ n K n! a for ;;...; mÿ a for m; m ;... z z K mz

4 " # ÿ! 3 Tycally, termnal wth burty traffc tranmt dcontnuouly, ay wth robablty Pr ON P on, tomnmze nterference to other uer. Tang th actvty factor nto account, the Lalace mage of the df of nterference ower become after ome traghtforward mathematcal manulaton [5], L f ; ÿpr ON ÿ Z ÿ ex ÿx dx ex x : 4 The Lalace tranform of the df of jont nterference ower, a needed n (3), the roduct of the Lalace tranform of ndvdual nterferng df, each of the form of (4). The effect of (man-made) noe can alo be modelled a a Lalace mage [3]. If the wanted gnal ubject to both multath fadng and hadowng, area-mean robablte are obtaned by averagng the above condtonal robablte over the lognormal local-mean ower of the wanted gnal (4). The robablty of ucceful tranmon, gven the area-mean ower, or equvalently, gven the roagaton dtance r, Q r Pr > z tjr Z Pr > z tj f d jr ; 5 where the robablty n the ntegrand of the form of (3). The outage robablty equal ÿ Q r. 4. Practcal exreon for outage robablty n telehone net The above method to fnd the robablty of a gnal outage can be gnfcantly fater than brute-force averagng over all df of multath fadng and hadowng, of the wanted and all nterferng gnal. In hexagonal networ, th may requre a 4 fold ntegraton. To the author' bet nowledge, no aer endeavor uch numercal evaluaton. Author ether ue aroxmate method, artcularly the one by Schwartz and Yeh [4], or, a ncreangly often erformed n recently ublhed wor, ue Lalace technque for Naagam or Raylegh channel, e.g. [4^7]. Nonethele the Lalace method can be tme-conumng and a fater method can be develoed for the lannng ractcal networ. The robablty of a gnal outage at large gnal-tonterference rato >> E t found from the behavor of the Lalace exreon at mall value for. Exandng the Lalace tranform nto a McLaurn ere gve L f t; ÿ Et! E ÿ: 6 t Fg.. Outage robablty veru the dtance between the bae taton and the moble termnal. r g :, C, z 4 (6 db) (a) K 4 MacLaurn (b) K 4, exact (c) K MacLaurn, (d) K, exact. Inertng th n exreon gve the outage robablty Pr out ÿpr > z tj z m! E m t m E t m m 7 for Naagam fadng wth nteger m. For Rcan fadng, we fnd Pr out e ÿk E t ÿ K e ÿk E t 3 E t 3 8 wth gven n Table. The reult are trngly dfferent for m larger than one. A the aroxmaton n (3) wa baed on the frt and econd moment, t lely to be mot accurate for value cloe to the mean. Outage robablte however hghly deend on the tal of the df for mall ower of the wanted gnal. We conclude that aroxmatng the df of a Rcan-fadng wanted gnal by a Naagam df hghly naccurate: Reult dffer even n frt-order. Th due to fact that Rcanfadng gnal exhbt relatvely dee fade wth a nonzero robablty denty for mall receved ower. Th n har contrat to vanhng robablty denty at zero ower for a Naagam-fadng gnal f m, 3,... Fg. comare exact reult for a Rcan fadng wanted gnal, wth a two-term McLaurn aroxmaton. For range of ractcal nteret,.e., outage robablte on the order of ÿ to ÿ3, the exanon aear accurate unle the lne of ght much tronger than the cattered ower, ay t utable for K < 4.

5 33 5. Queung delay for acet-wtched net The revou ecton dcued outage robablte n cellular ln. We now aly thee to the erformance of acet-wtched networ, uch a the one n Fg.. Each bae taton ha a acet queue for meage to be ent to moble termnal. Pacet have a unform length of L bt, arrve accordng to a Poon roce, and are detned for termnal unformly dtrbuted over the cell area. If a acet receved uccefully the termnal end an acnowledgement. If no acnowledgement receved, the bae taton reeat the acet untl ucceful receton occur. In a well functonng, table ytem, the ucceful throughut of meage over the rado ln mut be equal to the flow rate of meage nto the bae taton buffer (arrval rate). Whle n our model the arrval rate equal throughut, the attemted traffc on the rado channel may be much larger, due to retranmon. Th ecton comute the attemted traffc for a gven arrval rate. We ntally aume that all gnal exerence Raylegh fadng and hadow attenuaton, ndeendent of each other and ndeendent from one tranmon attemt to the next. The ath lo aumed contant durng all retranmon attemt. Interferng gnal arrve from bae taton n other cell. The area-mean ower of thee gnal taen from (5). In a hexagonal cell layout, the dtance between the center of two co-channel cell R 3C, where R the cell radu and C the cluter ze,.e., the number of dfferent frequence n ue. We aroxmate hexagonal cell of unty ze by crcular cell of radu R 3 3=4 :9 [5]. Th ecton derve acet queung delay n the bae taton. Snce the robablty of ucceful receton Q r decreae wth ncreang roagaton dtance r, the number of (re-) tranmon attemt, M, tattcally ncreae wth ncreang r. The ervce tme S er acet S MT L wth T L the duraton of a tme lot. The bt rate er Hz denoted a r,andthe total ytem bandwdth B N. So, T L L= B r T LC= B r N where B T denote the bandwdth er cell wth B T B N =C. The maxmum effectve throughut n uer bt er econd er bae taton er Hz r C E MŠ : 9 The robablty of ucceful receton of a data acet deend on the locaton of the termnal and on the actvty of nterferng bae taton. For dcontnuou tranmon, the robablty that an nterferng bae taton actve equal to the robablty that t queue nonemty. In a atally unform ytem, th robablty dentcal for all bae taton. The number of acet watng n the bae taton modelled a an M=G== queue. Servce tme condtonal on r are geometrc wth mean T L =Q r but the uncondtonal dtrbuton of ervce tme not a cloed-form exreon. We aroxmate the ervce tme of ucceve acet a..d. random varable. Th aumton, however, gnore the fact that the ervce tme of ucceve acet may be correlated. For ntance f one acet exerence heavy nterference from tranmon by anther bae taton, t more lely that the next acet wll alo ee an actve co-channel bae taton. Furthermore, two adjacent bae taton may contnue to attemt to tranmt to termnal at unfavorable locaton. We neglect th effect n the followng analy a a more detaled nvetgaton would requre u to comute delay n an nfnte feld of mutually nteractng queue. Th roblem notorouly hard to olve. But n ecton 7 we wll rooe an acce cheme that can reolve thee otental ntablty roblem. Moreover, aendx A evaluate the effect of correlated retranmon. The mean value of the ervce tme, exreed n number of lot and averaged over all locaton n the cell The econd moment E M E MŠ Š R R Z R Z R r dr Q r : ÿ Q r Q r r dr: The exected queung delay found from the Pollace- Khntchne exreon for M=G== queue, namely D LC E MŠ E M Š P on : B r N E MŠ ÿ P on 6. Reult Fg.. Cellular acet-wtched networ confguraton. Fg. 3 gve the exected number of requred tranmon attemt veru termnal locaton. That, t dect =Q r, rather than ÿ Q r a n mot other

6 34 Fg. 3. Exected number of requred tranmon attemt veru dtance for 6 db fat hadowng. Cluter ze C, (a) wth and (b) wthout AWG noe floor ( n :), and (c) wthout hadowng. Comaron wth (d) C 3 and (e) C!. aer, whch tudy outage robablte relevant to crcut wtchng. We addre a tycal modulaton technque wth recever threhold z 4 (6 db), UHF groundwave roagaton wth 4 and hadowng wth a read of 6 db :36). Servce tme n econd can be obtaned by multlyng reult n Fg. 3 by ( L= r N. B Fg. 4 gve the queung delay n the bae taton a a functon of the meage arrval rate er cell. It =r how that C otmum. The relatvely hgh bandwdth n each cell allow the bae taton to emty ther queue farly radly, whch reduced nterference to other cell. In contrat to the aumton n the above analy, hadow attenuaton can be hghly correlated for mall antenna dlacement. In uch cae hadow attenuaton lely to be almot dentcal durng all retranmon attemt. Moreover, at hgh traffc load the buy erod of each co-channel bae taton are lely to be much longer than the ervce tme exerenced by an ndvdual acet. For the lmtng cae of dentcal hadow attenuaton and dentcal nterference tuaton durng all retranmon attemt, E MŠ derved n Aendx A. Table 3 how that under heavy traffc, C doe not gve favorable erformance. Fg. 4. M=G== delay, normaled to lot duraton n networ wth C, veru normaled ectrum effcency for varou cluter ze. 6 db of fat hadowng. Recever threhold z 4 (6 db). UHF groundwave roagaton ( 4). For 3 db of low hadowng, C 3 found a an otmum cluter ze. For more evere hadowng, the networ become very ectrum-neffcent f one requre that the bae taton mut contnue to erform tranmon attemt to termnal n deely hadowed area. For 6 db of low hadowng, a cluter ze a large a C 9 would be requred. In ractce, th would be unaccetable and dynamc nterference rotecton may be needed. Alo we ee that for relatvely mall cluter ze, t more effcent to enure that each bae taton not fully loaded wth traffc,.e., P ON < for otmum throughut. Th contrat to the reult for ndeendent hadowng, where the throughut monotoncally ncreae wth P ON. 7. Satal rado reource management Accordng to the reult n the revou ecton, n hgh-caacty ectrum-effcent acet-wtched networ, adjacent bae taton referably comete for non-djont (.e., nterferng) ectrum reource. The Table 3 Maxmum achevable throughut wth low hadowng for varou cluter ze C. Recever threhold z 4 (6 db). UHF groundwave =r roagaton 4. Shadowng 3 and 6 db. Table Maxmum throughut S er bae taton for varou cluter ze C. C Shadowng: 3 db =r P ON 6 db =r P ON C =r Servce tme CE MŠ CE Mjr :9Š ^ ^

7 35 Fg. 5. Cellular acet data networ wth C under normal contguou frequency agnment (CFA) oeraton,.e., f no detructve collon occur. Any bae taton can tranmt n any tme lot, accetng the r of exceve nterference from cochannel tranmon n nearby cell. above comutaton howed that ectrum effcency otmal f the full ytem bandwdth can be ued n all cell. However, contnung nterference between tranmon from adjacent bae taton may everely affect the erformance of uch networ. Th ugget that effcent, coordnated reoluton of collon between acet retranmon n adjacent cell neceary to guarantee effcent erformance of wrele data and mult-meda networ. We now rooe two cheme that hel mtgatng the effect of contnued collon n acet-wtched rado data networ wth dene frequency reue:. Satal collon reoluton n the downln: All bae taton hare the ame tranmt channel, whch ha frame of three tme lot. The area covered by each bae taton are agned a equence number, or 3 accordng to a ma-colorng cheme whch enure that adjacent area alway have a dfferent number. In normal oeraton, a bae taton can tranmt n any tme lot regardle of t number (Fg. 5). If bae taton n adjacent area haen to tranmt multaneouly, mot gnal may nonethele `cature' ther ntended recever. Wth ome robablty however, nterference erae ome meage nvolved n th `collon'. In the latter cae, the bae taton wll retranmt the lot meage n the lot of the next frame wth the correondng number. Durng th retranmon, all adjacent bae taton are lenced to revent another collon (Fg. 6). Th coordnaton can be erformed by rotocol ung the fxed bacbone nfratructure, connectng all bae taton. A cheme that comletely avod multaneou tranmon n adjacent cell wa rooed n [7]. Bae aton tranmt accordng to a attern that choen n accordance wth the arrval rate n all cell.. Sace tme reervaton multle acce (STRMA) n the uln. Th cheme a atal extenon of the acet reervaton multle acce (PRMA) concet develoed at Wnlab, e.g. [5]. PRMA a framed acce cheme wth frame of a fxed number of lot. If a termnal ha a ere of acet or eech egment to tranmt, t comete for acce n any free lot. If t uccefully cature the bae taton, the termnal gan reervaton n the correondng lot of the next frame, untl t releae the reervaton. In PRMA, adjacent cell ue dfferent carrer frequence accordng to a cellular reue lan, but n STRMA they all ue the ame channel. We ynchronze bae taton and term- Fg. 6. Satal collon reoluton (SCR) n cellular acet data networ. Bae taton only tranmt n the tme lot wth the correondng equence number. Durng retranmon, all adjacent bae taton mut refran from tranmttng.

8 36 Fg. 7. Samle of three lot n Sace tme reervaton multle acce (STRMA) frame wth 6 termnal and cell. moble termnal, grey: nhbted lot to avod co-channel nterference, whte: free lot n whch acce cometton may tae lace,: lot reerved for tranmon. nal at lot level. Tme lot are common to all cell, and all cell ue the ame carrer frequence. However f a termnal gan a reervaton n one cell for certan tme lot, the bae taton of the frt ter of urroundng cell nhbt all other termnal to ue the ame tme lot. Hence reervaton occur not only n tme doman, a n PRMA, but alo n ace. Fg. 7 llutrate a oble reervaton amle for the cae of three lot er frame, wth actve termnal n cell A, B,...,E.Afxed frequency reue attern would not have been able to accomodate th artcular dtrbuton of actve uer. Intal mulaton by Van den Broe [8] at Delft Unverty of Technology revealed that for a unform dtrbuton of eech termnal, STRMA wth frame of lot outerform a PRMA wth ytem wth 7 lot er frame and a three cell reue attern. A ytem wth 5 erlang er cell wa addre, wth a eech actvty of.4 (4%) accordng to a Marovan on-off roce wth average duraton of eech burt of econd and average length of a ga of.35 econd. The eech clng robablty for PRMA wa about.5% and.% for STRMA, whle both ytem ue the ame ectrum bandwdth. Wth non-unform dtrbuton of uer, we exect a further erformance gan over PRMA. The STRMA ytem remaned effcent, alo at hgher meage traffc load. Synchronzaton of bae taton at tme lot level may requre ome mlementaton effort. All bae taton cloc could be laved to a (atellte) mater cloc, mlar to the concet ued for ynchronzaton of CDMA or DECT bae taton. Alternatvely, bae taton could fnd a common ynchronzaton by ltenng to each other tranmon. However, the elf-organzng roerte of `looely couled oclator' [6] are tll relatvely unexlored for wrele communcaton networ and ratcal realzaton are rare. 8. Concludng remar To the nowledge of the author, only few reult are avalable on (dynamc) frequency reue cheme for acet-wtched networ wth burty traffc. Th aer revealed that effcent moble acet data tranmon requre entrely dfferent ectrum reue than telehone net. To otmze ectrum effcency, uer caacty and networ erformance, reumably a new cla of acce cheme needed that dynamcally combne random acce wthn one cell wth rotecton agant nterferng gnal from other cell. Dynamc channel allocaton (DCA) nown to rovde a mean to hare bandwdth-tme-ace reource n a more dynamc and effcent way. However, DCA rmarly wor on a eon by eon ba, wherea burty teletraffc reumably bet uorted through acce cheme that agn rado reource on a acet by acet ba, or at leat on a burt by burt ba. Under certan aumton, contguou frequency agnment (CFA),.e., cluter ze C, can uort aroxmately.4 bt//hz/cell. Th aeared ubtantally more effcent than cellular frequency reue wth C 3, 4, 7,... CFA alo rovde the mallet acet delay at a gven atal acet throughut ntenty. Th ugget that, n order to enure mnmum delay at maxmum uer caacty, moble rado data networ hould be degned wth much dener frequency reue than tycally ued to enure an outage robablty on the order of ÿ or ÿ3. Th, however, reult n low gnal-to-nterference rato and large acet lo robablte, whch have to be addreed by arorate data-ln rotocol. In extreme cae, that tranmon to a artcular termnal alway ee the ame nterferng bae taton, o the number of requred tranmon attemt may become rohbtvely large for certan termnal. Th could have a detrmental effect on the entre networ erformance and t ha motvated u to tart develong new `atal' random acce rotocol. Performance analy toc of our current reearch. The reult of th aer have been derved from ln outage and ucce robablte comuted wth the ue of Lalace Tranform. Th technque wa recognzed revouly for Raylegh and Naagam fadng channel. We howed n th aer that the method can be generalzed further: t can alo be ued uccefully n Rcan-fadng channel. Of ractcal relevance alo the develoment of ere exanon that facltate ln evaluaton n cell lannng. Acnowledgement The author gratefully acnowledge frutful dcuon wth Rolando Deta and John Dav at Unverty of Calforna at Bereley and Caer van den Broe at Delft Unverty of Technology. The Calforna Deartment of Tranortaton (Caltran), Partner n Advanced Trant and Hghway (PATH) and Artouch Internatonal uorted our reearch reented n th aer.

9 37 Aendx A Number of tranmon attemt wth low hadowng In contrat to the aumton n the man body, we aume dentcal nterference tuaton durng all retranmon attemt of a artcular acet. The number of nterferng co-channel bae taton I treated a a bnomal random varable (I,,...,6)wth mean 6P ON, where I contant durng the ervce tme of an ndvdual acet. Gven the local-mean ower of the wanted and all actve nterferng gnal, the exected number of retranmon h E Mj ; f gi ; I YI z : 3 If the local-mean ower of gnal from nterferng bae taton are..d. log-normally dtrbuted, we fnd, after olvng the I-fold ntegraton, h E Mj ; f g I ; I YI z = e : 4 Rewrtng the roduct nto a um of I-term and ung the roerty that n a log-normal channel 3 ÿn E ÿn ex n we fnd the cloed-form exreon h E Mjf g I ; I XI I z n ;;... ; ex 5 ; 6 whch we average over the bnomal robablty ma functon of I. If the oton of the recevng moble unform wthn the cell, the exected number of (re-) tranmon er meage X 6 E MŠ Reference XI I 6!P I ON ÿ P ON 6ÿI 6 ÿ I! I ÿ!! ex R : z 3C ÿ= 7 [] L. Klenroc, Queung ytem, Vol. : Theory; Vol : Comuter alcaton (Wley, New Yor, 975, 976). [] D. Bertea and R. Gallager, Data Networ (Prentce-Hall, London, 987). [3] A.S. Tanenbaum, Comuter Networ (Prentce-Hall, London, 989). [4] J. Walrand, Communcaton Networ: A Frt Coure, Aen Aocate, Sere n Electrcal and Comuter Engneerng, Homewood, IL, 99. [5] J.P.M.G. Lnnartz, Narrowband Landmoble Rado Networ (Artech Houe, Norwood, MA, 993). [6] W. Golng, Protecton rato and economy of ectrum ue n land moble rado, IEE Proc. 7 (98) 74^78. [7] R.C. French, The effect of fadng and hadowng on co-channel reue n moble rado, IEEE Tran. Veh. Tech. VT-8 (979) 7^ 8. [8] D.C. Cox, Cochannel nterference conderaton n frequency reue mall-coverage-area rado ytem, IEEE Tran. Comm. COM-3 (98) 35^4. [9] K. Daou and H. Ohdate, Otmal channel reue n cellular land moble rado ytem, IEEE Tran. Veh. Tech. VT-3 (983) 7^4. [] R. Praad, A. Kegel and J.C. Arnba, Imroved aement of nterference lmt n cellular rado erformance, IEEE Tran. Veh. Tech. 4 (99) 4^49. [] R. Muammar and S.C. Guta, Cochannel nterference n hghcaacty moble rado ytem, IEEE Tran. Commun. 3 (98) 973^978. [] Y.-D. Yao and A.U.H. Sheh, Outage robablty analy for mcrocell moble rado ytem wth cochannel nterferer n Rcan/Raylegh fadng envronment, Electr. Lett. 6 (99) 864^866. [3] R. Praad and A. Kegel, Effect of Rcan faded and log-normal hadowed gnal on ectrum effcency n mcro-cellular rado, IEEE Tran. Veh. Tech. VT-4 (993) 74^ 85. [4] J.P.M.G. Lnnartz, Exact analy of the outage robablty n multle-uer moble rado, IEEE Tran. Commun. COM-4 (99) ^3. [5] K.W. Sowerby and A.G. Wlnon, Etmatng receton relablty n Cellular moble rado ytem, Proc. 4nd IEEE. Veh. Tech. Conf. Denver (99) 5^54. [6] M.-J. Ho, G.L. Stu«ber, Co-channel nterference of mcrocellular ytem on hadowed Naagam fadng channel, 43rd IEEE VTC 993, Seracucu, NJ (993) 568^57. [7] S. Chennaehu, A. Haan and J. Anderon, Caacty analy of a mxed mode low frequency hoed cellular ytem, Proc. IEEE 43rd Veh. Tech. Conf. (993) 54^543. [8] J.P.M.G. Lnnartz, A.J. 't Jong and R. Praad, Effect of codng n dgtal mcrocellular eronal communcaton ytem wth cochannel nterference, IEEE J. Select. Area Commun. JSAC- (993) 9^9. [9] M. Naagam, The m-dtrbuton ^ A general formula for the dtrbuton of rad fadng, Stattcal Method n Wave Proagaton, ed. W.C. Hoffman (Oxford/Pergamon, 96) 3^36. [] J. Grffth and J.P. McGeehan, Interrelatonh between ome tattcal dtrbuton ued n rado wave roagaton, IEE Proc. 9 (98) 4^47. [] H. Harley, Short dtance attenuaton meaurement at 9 MHz and.8 GHz ung low antenna heght for mcro-cell, IEEE J. Select. Area Commun. JSAC-7 (989) 5^. [] D. Verhult, M. Mouly and J. Szrgla, Slow frequency hong multle acce for dgtal cellular rado telehone, IEEE J. Select Area Commun. JSAC- (984) 563^574. [3] J.P.M.G. Lnnartz, Effect of delay read and noe on outage robablty n cellular networ, Int. J. Electr. Commun. (Archv fu«r Eletron und Uë bertragungtechn AEUë ) 48 (994) 4^8. [4] S.C. Schwartz and Y.S. Yeh, On the dtrbuton functon and moment of ower um wth log-normal comonent, Bell Syt. Tech. J. 6 (98) 44^46. [5] D. Goodman et al., Pacet reervaton multle acce for local wrele communcaton, IEEE Tran. Commun. 37 (989) 885^ 89. [6] S.H. Strogatz and I. Stewart, Couled ocllator and bologcal ynchronzaton, Sc. Amer. (Dec. 993) 68^75. [7] R. Ltjen, Conflct-free chedulng of broadcat n a lnear acet rado networ, M.Sc. The, Deartment of Econometrc, Tlburg Unverty, The Netherland (994). [8] C. van den Broe et al., A mulaton tudy of ace tme reervaton multle acce, ubmtted for conference reentaton (995).

10 38 Jean-PaulM.G.LnnartzwabornnHeerlen, The Netherland, n 96. He receved h Ir. (M.Sc. E.E.) degree n Electrcal Engneerng (Cum Laude) from Endhoven Unverty of Technology, The Netherland, n 986. Durng 987^988, he wored on frequency lannng and UHF roagaton wth the Phyc and Electronc Laboratory (F.E.L-T.N.O., The Hague) of the Netherland Organzaton for Aled Scentfc Reearch. From 988^99, he wa Atant Profeor at Delft Unverty of Technology, where he receved h Ph.D. (Cum Laude) on mult-uer moble rado net n December 99. Snce January 99, he wa an Atant Profeor n the Deartment of E.E.C.S. at the Unverty of Calforna at Bereley, USA. In 994, he returned to Delft Unverty of Technology n The Netherland, a an Aocate Profeor. Currently he wth Phl Natuurundg Laboratorum, Endhoven, The Netherland. H man reearch nteret are n (wrele) mult-meda communcaton, condtonal acce and nformaton ecurty, ntellgent vehcle hghway ytem, random acce to fadng channel, OFDM and CDMA. He receved the Dutch `Veder Prze' 99 for h reearch on tele-traffc aect n moble rado networ. In 993, he ublhed the boo ``Narrowband Land-Moble Rado Networ''. On the WWW, h URL : htt://dva.eec.bereley.edu/lnnartz. H e^mal addre : lnnartz@rl.hl.nl.