Frequency Assignment for IEEE Wireless Networks

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1 Frequecy Assgmet for IEEE 8 Wreless Networks K K Leug Bell Labs, Lucet Techologes Murray Hll, NJ 7974 k@bell-labscom Byoug-Jo J Km AT&T Labs Research Mddletow, NJ 7748 macsbug@researchattcom Abstract The IEEE 8 stadard specfes both rado ad MAC protocol desg We observe that ts CSMA protocol helps avod much of co-chael terferece by sharg rado resources tme at the potetal expese of degraded etwork performace Due to the couplg betwee the physcal ad MAC layers, covetoal frequecy allocato methods for typcal cellular etworks caot be appled drectly to the 8 etworks I ths paper, by focusg o teractos amog access pots, we formulate the chael assgmet problem for the 8 etwork, cosderg the traffc load at the MAC layer, ad prove that the problem s NP-complete I lght of computatoal complexty, a heurstc algorthm s proposed ad aalyzed The algorthm s the appled to two cellular settgs wth kow optmal assgmets for verfcato For oe of the settgs, the proposed techque geerates the optmal chael assgmet As for the secod case of a large etwork, although oly a suboptmal soluto s obtaed by the algorthm, t s show to be excellet Thus, as the 8 etworks are wdely deployed, the proposed method ca serve as a valuable tool for frequecy plag of etworks wth o-uform coverage ad load I INTRODUCTION To meet the growg demad for wreless data servces, may compaes have started deployg the IEEE 8b wreless local-area-etworks (WLAN) [I99, VAM99] places such as arports, hotels, coffee shops, etc The 8 techology s partcularly attractve due to ts maturty ad low cost The 8 capablty has bee cluded as stadard equpmet may laptop computers ad had-held devces The b WLAN supports data rates up to Mbps, far exceedg that of the thrd geerato (G) wreless etworks such as EDGE [SAE98] ad W-CDMA etworks [HT] The 8b (ad future 8g [I]) etworks operate the ulcesed ISM bad at 4 GHz Despte the relatvely abudat spectrum (e, 75 MHz) at the ISM bad, as the etworks are deployed wdely, they start to teract wth each others, thus causg etwork performace to degrade Oe way to avod such degradato s to effcetly assg the avalable frequeces the etworks Ths s the subject of ths paper Let us frst expla why the frequecy assgmet for the 8 etwork s dfferet from that for the tradtoal wreless etworks I typcal cellular etworks cludg the GSM [R96] ad EDGE etwork [SAE98], two separate rado chaels, amely the traffc ad cotrol chaels, are used to carry user data ad cotrol traffc, respectvely Typcally, termals access the cotrol chaels to sed cotrol formato va some coteto mechasm After a base stato (BS) successfully receves the formato, the termal s assged wth a specfc traffc chael for trasmttg ts data Exstg frequecy assgmet methods [KN96] were devsed maly for such traffc chaels The key dea there s to keep terferece to a acceptable level I practcal etworks, there s o coordato amog BSs the assgmet of traffc chaels to termals dfferet cells O the other had, all user data ad cotrol formato ( both drectos betwee termals ad APs) are carred o the same physcal chael the 8 etwork Rather, the access to the chael by multple trasmtters s coordated by the MAC protocol - Carrer Sesg Multple Access (CSMA) wth collso avodace That s, a trasmtter may start ts trasmsso oly f the chael s curretly sesed dle Thus, eve f two closely located APs are allocated wth the same chael or overlappg chaels, much terferece ca be avoded by the CSMA protocol I a sese, the MAC protocol provdes a dstrbuted mechasm to coordate the chael access For ths reaso, the 8 APs stll operate properly, whch show the robustess of the desg, at the expese of creased delay (due to backoff whe chael busy) ad degraded etwork throughput Cosequetly, exstg frequecy allocato methods that do ot cosder the combed effect of physcal chael ad MAC protocol are ot applcable to the 8 etworks So, we propose ad aalyze a ew frequecy allocato techque ths paper The orgazato of the rest of ths paper s as follows I Secto II, we formulate the frequecy allocato problem, ad prove t to be NP-complete Thus, we propose ad aalyze a heurstc algorthm Secto III, ad valdate ts performace Secto IV Fally, our cocluso s Secto V II FORMULATION OF CHANNEL ASSIGNMENT The IEEE 8 [I97, I99, I] MAC protocol supports the depedet basc servce set (BSS), whch has o coecto to wred etworks (e, ad-hoc etwork), as well as a frastructure BSS, whch cludes a access pot (AP) coectg to a wred etwork The latter s smlar to cellular etworks wth base statos replaced by AP s We cosder oly the frastructure BSS ths paper The 8 MAC supports the Pot Coordato Fucto (PCF) ad the Dstrbuted Coordato Fucto (DCF) [I97, OP99] The PCF provdes coteto-free access, whle the DCF uses the //$7 IEEE 4

2 CSMA/CA for coteto based access The two modes ca be used alterately tme The DCF s most commo commercal 8 products So, we focus o the chael assgmet problem for the DCF mode here I North Amerca, the ISM bad at 4 GHz s dvded to chaels for the 8 etwork [OP99] where adjacet chaels may partally overlap wth each other Amog these chaels, there are completely, o-overlappg oes, separated by 5 MHz at ther ceter frequeces Although all chaels are avalable for allocato 8 etworks, expermetal results reveal that partal overlappg chaels ca cause eough terferece [M] Thus, we cosder the assgmet of o-overlappg chaels here, although our approach ca be exteded to cosder allocato of overlappg chaels wth approprate weghtg factors As a frst approach, let us focus o the trasmsso by the APs the 8b etwork Such a focus s approprate for typcal offce ad Iteret applcatos, because the badwdth cosumpto for dowlk (e, from AP to termal) flueces applcato performace tha that for uplk (e, from termal to AP) Let the etwork have M APs, dexed from to M By the CSMA protocol, a AP wth traffc ready to trasmt, frst determes f the assged chael s busy or dle That s, f the AP detects that the receved power wth the chael s greater tha α mw (typcally about 76 dbm or lower [I97]), the chael s declared to be busy Otherwse, t s dle Clearly, the chael busy status ca be due to a sgle trasmttg AP or a group of multple APs trasmttg smultaeously For effcet frequecy assgmet, let us classfy the terferers for each AP Specfcally, for each AP, let C () deote a set of terferg APs where trasmsso by ay oe AP the set ca cause eough terferece for AP to detect chael busy The APs the set C () are called class- terferers for AP Lkewse, let C () be a set of pars of two terferg APs where trasmsso by ay par of APs the set ca cause AP to sese chael busy APs C () are called class- terferers I geeral, to determe the terferer sets C () ad C () for each AP requres measuremets or estmates of sgal path loss betwee each par of APs the etwork Let p j ad h j deote the trasmsso power at AP j ad the sgal path loss from AP j to AP If AP j belogs to C (), t requres h j p j α () Smlarly, f AP par m ad belog to C (), we have Besdes a receved power threshold, the 8 stadard also allows a commoly mplemeted opto of determg chael busy by detectg a vald 8 sgal (carrersese), whch s ofte possble a same chael aroud -95 dbm wth lttle other chael mparmets Wthout loss of geeralty, we cosder the method by a receved power threshold ths paper, sce the carrer-sese ca be traslated to a equvalet power level wth mor smplfyg assumptos h m p m + h p () Note that the trasmsso power () ad () are assumed to be fxed ths paper ad chael assgmet wth dyamc power cotrol s a topc for future study α Smlarly, we ca defe class- or eve hgher classes of terferers However, due to the coteto ature of the CSMA protocol, the traffc load o each chael (e, the probablty of trasmsso at a gve AP) caot be too hgh Thus, the probablty of havg class- terferers, whch requre smultaeous trasmsso at all terferg APs that could ot hear each other, s much smaller relatve to that of the class- ad terferers For smplcty, we oly cosder class- ad terferers here Let us defe addtoal otato Let ρ be the offered traffc load for AP terms of chael utlzato wthout terferece from ay source There are totally N (ooverlappg) chaels, dexed by to N, avalable for allocato As poted out above, N= for the 8b etwork Wthout loss of geeralty, we assume that each AP s assged wth oe ad oly oe chael Further, we deote j = f AP s assged wth chael j ad otherwse Sce the CSMA protocol prohbts APs from trasmttg whe the chael s sesed busy, we defe the effectve chael utlzato U as the fracto of tme at whch the chael ca be sesed busy or s used for trasmsso by AP That s, N U ρ + k [ ρ j jk k = j C () () + ρ m ρ mk k ] ( m, ) C () Ths defto ca be terpreted as follows The frst term o the rght had sde s the offered load assocated wth AP The frst summato term sde the brackets represets the total traffc load of all class- terferg APs that are assged wth the same chael as AP Ths s so because accordg to the CSMA protocol ad the detecto threshold α use, AP seses chael busy whe ay oe of ts class- terferers trasmts o the same chael Smlarly, the last summato term represets the effectve chael utlzato due to class- terferers f they use the same chael Our objectve fucto for the chael assgmet s to mmze the utlzato at the most stressed bottleeck AP: { U, U, U } Mmze Max, M (4) over the assgmet dcator { j } The optmal assgmet s feasble f ts objectve fucto value s less tha That s so because to mata chael stablty, we requre U < (5) for all AP = to M I fact, the RHS of (5) ca be a value less tha to accout for CSMA overhead ad stablty marg Theorem The optmzato problem wth the objectve fucto (4) s NP-complete //$7 IEEE 4

3 Proof Cosder the multprocessor schedulg problem A5 [GJ79, p8] wth m processors ad T tasks Each task requres l() tme uts to process The optmal schedulg s to assg tasks to processors such that the maxmum total processg tme o all processors s mmzed Our proof s to reduce the schedulg problem, whch s NP-complete, to the frequecy assgmet problem as follows Each processor the schedulg problem s treated as a rado frequecy the assgmet problem So, N=m Each task s represeted by a AP (thus M=T) ad each processg tme l() becomes the traffc load ρ for the correspodg AP To complete the reducto, all APs are treated as class- terferers to each other Defe that V k s the total traffc load assocated wth all APs assged wth frequecy k for each k= to N Clearly, mmzg the maxmum total processg tme o all processors s detcal to mmzg {V k } for all k= to N Note that V k = U f k = for each k ad Further, U =U j f k = k for some frequecy k= to N because all APs ad j are class- terferers to each other Thus, the proof s completed by observg that maxmzg {V k, k= to N} s detcal to maxmzg {U k, k= to M} (4) I lght of NP-completeess, t s ulkely that a effcet method exsts for the optmal chael assgmet Thus, we propose a heurstc method ad study ts effectveess below III A HEURISTIC METHOD FOR CHANNEL ASSIGNMENT We propose a heurstc algorthm that attempts to mmze the effectve chael utlzato for the bottleeck AP (4) The ew algorthm makes use of the followg kow parameters: offered traffc load ρ ad ts terferer sets C () ad C () for each AP We outle the algorthm as follows: Geerate a radom, tal chael assgmet for the etwork, whch s treated as the best assgmet obtaed so far Let the maxmum effectve chael utlzato for the assgmet be deoted by V (e, V=max{U }) Based o the best assgmet, detfy the AP (say ) wth the hghest effectve chael utlzato I case of te, oe such AP s chose radomly as the bottleeck For the bottleeck AP, detfy ts curret assged chael, say k For each avalable chael from to N wth k ad each co-chael AP (say j) C () (e, those APs the set that have bee assged wth chael m), temporarly modfy the chael assgmet by reassgg oly AP j wth chael Based o (), recompute the maxmum effectve chael utlzato, deoted by W j, for the ew assgmet After completg such testg for all such ad j, let W be the mmum amog all the W j s 4 Compare W wth V ad perform the followg: a If W<V, the replace V by W ad record the assocated ew assgmet as the ew best soluto (e, to falze the chael chage for oe AP that mmzes the objectve fucto the most a greedy step) Cotue wth Step b If W=V, the wth a pre-specfed probablty δ, replace V by W ad record the ew assgmet as the best soluto Cotue wth Step c If W>V, a local optmum has bee reached (e, the best assgmet obtaed so far s the local suboptmal soluto) Cotue wth Step 5 5 Repeat Steps to 4 wth a umber of radom, tal assgmets The fal soluto s chose to be the best, accordg to (4), amog the local suboptmal assgmets 6 Test f costrats (5) for all APs are satsfed for the fal assgmet If so, the fal assgmet s feasble Otherwse, t s cosdered that o feasble soluto exsts for the etwork uder cosderato Clearly, ths algorthm does ot explctly cosder the costrats (5) However, focusg o (4) by the algorthm s approprate sce mmzg the maxmum U automatcally ehaces the chace of satsfyg costrats (5) for all APs Now, let us cosder a property of the proposed algorthm Theorem Wth >δ> Step 4, the heurstc algorthm does ot have fte loopg Proof Sce the umber of APs M ad avalable chaels N are fte, Steps ad ca be completed a fte amout of tme The oly possblty that the algorthm has a fte loop s that Steps to 4 are executed repeatedly wthout stop Assume that such loopg ca happe ad the V value after the m-th executo (terato) of Step 4 be deoted by V m To proceed, let δ= Step 4b for a momet To form the fte loopg, we must have V >V > >V m wth m Wth both M ad N beg fte, there are oly a fte umber of all possble chael assgmets Sce each ew assgmet falzed by Step 4a has a uque maxmum effectve chael utlzato, t s thus mpossble that m goes to fty That s, Step 4c must be reached after a fte amout of processg Let us assume that fte loopg s possble wth >δ> Based o the above argumet, we ow must have V > >V =V + > >V j =V j+ > V m wth m for some ad j Sce the argumet above has already ruled out the possblty of havg subsequeces of V s of fte legth betwee two = sg o ths lst, t must cota a fte umber of = sg Sce each = sg correspods to a executo of Step 4b wth probablty δ, the probablty of executg ths step for a fte umber of tme s thus zero Hece, the fte loopg caot exst We remark that based o the proof, the algorthm ca exclude Step 4b ad treat the case of W=V as reachg a local optmum as part of Step 4c, wthout causg ay fte loopg However, our umercal experece reveals that Step 4b helps explore varous assgmets for ehaced results, especally whe there are multple bottleeck APs for the chael assgmet uder cosderato Sce heurstcs s volved the proposed algorthm, achevg the optmal soluto s ot guarateed Now, let us quatfy the qualty of the suboptmal soluto geerated by the algorthm Toward ths goal, we observe that Step bascally tests out varous chael assgmets to detfy a better soluto As the algorthm s executed for a gve tal, radom assgmet, let Y, Y, Y,, Y m deote the (radom) sequece of the maxmum effectve chael utlzato //$7 IEEE 44

4 assocated wth the chael assgmets uder testg We deote that Y s the quatty for the tal, radom assgmet Based o the Y sequece, we costruct aother sequece,,,, as follows We start wth =Y ad set = For each j=,,, m, compare Y j wth If >Y j, the we set =+ ad =Y j Otherwse, repeat Step for the ext j value I essece, the sequece s s costructed by examg Y j oe by oe We start wth =Y ad Y j s added as the last elemet the sequece oly f Y j s less tha Y for all <j (or equvaletly, Y j s less tha, the last elemet the curret sequece) Clearly, the sequece s mootoc strctly decreasg Physcally, s represet the sequece of the maxmum effectve chael utlzato for a mproved assgmet falzed by Step 4a or 4b that yelds a maxmum utlzato lower tha ay assgmets examed by the algorthm so far the search process Recall that the algorthm s repeated for a gve umber (say K) of tal radom assgmets For each tal assgmet, we ca obta oe such sequece s as dscussed above Note that the sequeces assocated wth dfferet tal assgmets have dfferet legths ad are mutually depedet of each other (although elemets the same sequece are depedet) Furthermore, whe the algorthm evetually stops, assume that t has ecoutered a total of mproved assgmets (e, mproved over those examed earler ad derved from the same tal assgmet), whch s the sum of legths of the sequeces s mus K Oe ca vew that the maxmum effectve chael utlzato for all possble assgmets for the gve etwork has a probablty dstrbuto Let T be the maxmum utlzato for the top--fracto of assgmets (eg, the top percetle assgmets) Hece, for a radom assgmet wth ts maxmum utlzato, we have P [ T ] = (7) Let Q be the probablty that the fal suboptmal soluto by the algorthm falls wth the top--fracto of assgmets Theorem If the algorthm have ecoutered a total of mproved assgmets at the completo of ts executo, the + Q > ( ) (8) Proof Frst cosder the case of ecouterg mproved assgmets for oe tal, radom assgmet By defto, Q = P[ m T ] = P[m ] (9) The evet of (m >T ) the above s detcal to havg o >T, >T,, ad >T Gve that s are a strctly decreasg (radom) sequece, we have P[ ] () < P[ > T > T > T ] Where s a radom varable depedetly draw from the same dstrbuto for for = to Oe ca obta () by replacg o the left had sde by o the rght sde for oe at a tme Sce the varables are depedet, P[ + > T > T ] = { P[ ]} () Usg the defto (7), substtutg () to () ad the puttg to (9) yelds (8) The case wth multple tal radom assgmets s prove by explotg the property that the sequeces s assocated wth dfferet tal assgmets are mutually depedet IV METHOD VALIDATION For valdato, we apply the proposed algorthm to two cellular layouts for whch the optmal assgmet s kow Specfcally, the settgs correspod to a etwork wth 7 ad 7 cells Fg ad, respectvely A cell s dvded to sectors, each of whch s represeted by a clover-leaf hexago ad served by a access pot (AP) at the ceter of the cell (a dot the fgures) Each AP atea has a beamwdth of 6 o ad pots toward a approprate drecto to serve the assocated sector Thus, there are ad APs Fg ad, wth APs each cell co-located at the cell ceter The atea ga has a parabolc shape; that s, a db drop relatve to the frot drecto occurs at the half badwdth agle Atea ga the frot drecto s about 5 db Ay Fg Assgmet for Network wth 7 Cells ad APs drecto beyod a threshold agle clockwse or atclockwse drecto suffers a gve, fxed atteuato relatve to the ga at the frot drecto, whch s called the frot-toback (FTB) rato The FTB s set to be 5 db Recall that oly the AP-to-AP teracto s cosdered our curret formulato The rado lk betwee ay par of APs s characterzed by a path-loss model wth a expoetal of 5 Cell radus s Km ad the path loss at m from the cell ceter s -7 db Trasmt power for each AP atea s dbm (or W) To esure that the optmal assgmet s kow, shadowg ad fast fadg are ot cosdered ad all APs have detcal amout of offered traffc I addto, the chael-busy detecto threshold α s set to be 5e- µw (or - 86 dbm) As poted out earler, there are o-overlappg chaels avalable for assgmet the 4 GHz ISM bad Based o the parameter settgs for both 7 ad 7-cell etworks, the optmal assgmet s the tradtoal frequecy //$7 IEEE 45

5 reuse of [L89] That s, o adjacet sectors use the same chael Whe the proposed algorthm was appled to the etwork wth 7 cells ad APs, the algorthm was able to geerate the optmal chael assgmet, based o 5 tal radom assgmets The optmal assgmet wth chaels to assged to varous sectors (APs) s show Fgure As for the etwork wth 7 cells ad APs, the proposed algorthm was ot able to yeld the optmal assgmet The suboptmal soluto obtaed from the algorthm usg, tal radom assgmets s preseted Fgure The chaels are represeted red, blue ad gree color As show the fgure, most of the sectors (APs) use a chael dfferet from those adjacet sectors I the worst case, at most two adjacet sectors share the same chael I the search process, the algorthm ecoutered ad falzed a total of 55,6 mproved assgmets Based o the aalyss Secto III, wth a probablty hgher tha 994%, the suboptmal soluto Fgure falls wth the top th percetle, whch s qute acceptable I ths case, the algorthm took 9 mutes to ru o a SUN Sparc workstato A exhaustve search must exame the order of 5 assgmets Clearly, the advatage of ths algorthm s evdet whe appled to a large WLAN layout wth o-uform traffc loads over the etwork ad other costrats where a good frequecy assgmet, let aloe a optmal oe, s ot as obvous as the examples used here for verfcato purposes Fg Assgmet for Network wth 7 Cells ad APs V CONCLUSION We observe that the CSMA protocol use 8 helps avod much of co-chael terferece at the possble expese of degraded etwork throughput Due to the couplg betwee the physcal ad MAC layers, covetoal frequecy allocato methods, typcally for traffc chaels o cellular etworks, caot be appled drectly to the 8 etworks I ths paper, by focusg o teractos amog access pots (APs), we formulate the chael assgmet problem for the 8 etwork, whch s the prove to be NPcomplete I lght of computatoal complexty, a heurstc algorthm s proposed ad aalyzed Specfcally, the algorthm was show to be loop-free A metrc to assess the qualty of the soluto geerated by the algorthm s proposed ad prove For valdato, the algorthm was appled to two cellular settgs wth kow optmal assgmets For oe of the settgs, the proposed algorthm was able to geerate the optmal chael assgmet As for the secod case of a large etwork, although oly a suboptmal soluto was obtaed by the algorthm, ts qualty has bee show to be excellet Therefore, as the 8 etworks are wdely deployed, the proposed algorthm ca serve as a valuable tool for frequecy plag of WLAN etworks I terms of future work, we are extedg the proposed approach to cosder o-uform trasmsso power by the APs, uplk traffc, ad adaptve chael assgmet to meet the tme fluctuato of traffc load at varous APs VI ACKNOWLEDGMENTS We thak Bruce McNar for sharg hs results wth us ad for hs dscusso Thaks are also due to Leoard Cm, Paul Hery ad ora Kostc for ther dscusso VII REFERENCES [GJ79] MR Garey ad DS Johso, Computer ad Itractablty: A gude to the Theory of NP- Completeess, WH Freema ad Compay, Sa Fracsco, 979 [HT] H Holma ad A Toskala (Ed), WCDMA for UMTS, Joh Wley & Sos, New York, [I97] IEEE 8, Wreless LAN Medum Access Cotrol (MAC) ad Physcal Layer (PHY) Specfcato, 997 [I99] IEEE 8b, Part : Wreless LAN Medum Access Cotrol (MAC) ad Physcal Layer (PHY) Specfcato: Hgh-Speed Physcal Layer Exteso the 4 GHz Bad, 999 [I] IEEE 8g, Wreless LAN Medum Access Cotrol (MAC) ad Physcal Layer (PHY) Specfcatos: Hgher Speed Physcal Layer (PHY) Exteso to IEEE 8b, [KN94] I Katzela ad M Naghseh, Chael assgmet schemes for cellular moble telecommucato systems: a comprehesve survey, IEEE Persoal Commu, Vol:, Jue 996, pp - [L89] WCY Lee, Moble Cellular Telecommucatos Systems, McGraw-Hll, New York, 989 [M] B McNar, prvate commucatos, [OP99] B O Hara ad A Petrck, IEEE 8 Hadbook, IEEE Press, New York, 999 [R96] T S Rappaport, Wreless Commucatos: Prcples ad Practce, New York: IEEE Press ad Pretce Hall, 996 [SAE98] P Schramm, et al, Rado Iterferece Performace of EDGE, a Proposal for Ehaced Data Rates Exstg Dgtal Cellular Systems, Proc of IEEE VTC, Ottawa, Caada, May 998, pp [VAM99] R va Nee, et al, New Hgh-Rate Wreless LAN Stadard, IEEE Commu Mag, Dec 999, pp //$7 IEEE 46

K-Map 1. In contrast, Karnaugh map (K-map) method provides a straightforward procedure for simplifying Boolean functions.

K-Map 1. In contrast, Karnaugh map (K-map) method provides a straightforward procedure for simplifying Boolean functions. K-Map Lesso Objectves: Eve though Boolea expressos ca be smplfed by algebrac mapulato, such a approach lacks clear regular rules for each succeedg step ad t s dffcult to determe whether the smplest expresso