Frequency Assignment for Multi-Cell IEEE Wireless Networks

Transcription

1 Frequency Assgnment for Mult-Cell IEEE 8 Wreless Networks Kn K Leung Bell Labs, Lucent Technologes Murray Hll, NJ 7974 kn@bell-labscom Byoung-Jo J Km AT&T Labs Research Mddletown, NJ 7748 macsbug@researchattcom Abstract The IEEE 8 standard specfes both rado and MAC protocol desgn We observe that ts CSMA protocol helps avod much of co-channel nterference at the potental expense of degraded network throughput n a large mult-cell WLAN network Due to the couplng between the physcal and MAC layers, conventonal frequency plannng and allocaton methods for typcal cellular networks cannot be appled drectly to the 8 network In ths paper, by focusng on nteractons among access ponts based on ther traffc loads and rado propagaton, we formulate the channel assgnment for the 8 network as a - programmng problem, where one verson of the problem s shown to be NP-complete In lght of computatonal complexty, a heurstc algorthm s proposed and analyzed The algorthm s then appled to two cellular settngs wth known optmal assgnments For one of the settngs, the proposed technque generates the optmal channel assgnment As for the second case of a large network, although only a suboptmal soluton s obtaned by the algorthm, t s shown to be excellent Therefore, as the 8 networks are wdely deployed, the proposed method can serve as a valuable tool for frequency plannng of large-scale mult-cell WLAN networks I INTRODUCTION To meet the growng demand for wreless data servces, many companes have started deployng the IEEE 8b wreless local-area-networks (WLAN) [I99b, VAM99] n places such as arports, hotels, conventon centers, coffee shops, etc The 8b technology s partcularly attractve due to ts maturty and low cost The 8 capablty has been ncluded as standard equpment n many laptop computers and hand-held devces The WLAN supports data rates up to Mbps, albet over short ranges, far exceedng that to be offered by our thrd generaton (G) wreless networks such as EDGE [SAE98] and W-CDMA networks [HT] The 8 WLAN and G networks (or conventonal cellular wreless networks) have major dfferences n ther desgn at physcal and medum-access-control (MAC) layers to meet dfferent needs In general, the 8 desgn s much smpler than that of the G network Ths s so because the 8 standard was devsed to serve a confned area (eg, a lnk dstance of at most several hundred meters) wth statonary and slow-movng users, whle the G specfcatons were developed for ubqutous coverage, even for users travelng at a hgh speed As a result, the 8 network can support data rates hgher than those by the G networks In addton, the cost of 8 equpment s much lower than that for G equpment because of the smple and open desgn of the former networks, coupled wth competton among WLAN vendors In terms of operatons, the G spectrum (such as the PCS band at 9 GHz) s lcensed and very expensve As a result, every effort has been spent to optmze the spectral effcency, whle mantanng the qualty of servce n terms of coverage and data rate for a lmted spectrum allocaton In contrast, the 8b networks operate n the unlcensed ISM band at 4 GHz Snce the frequency band s free, there s apparently no pressng need to optmze the spectral effcency Rather, smplcty and thus achevng low cost for the equpment became more mportant Despte the relatvely abundant spectrum (e, a total of 75 MHz n the 4GHz Band) at the ISM band, as 8b networks are deployed wdely, they start to nterfere wth each others, thus causng network throughput to degrade One way to avod such degradaton s to effcently assgn the avalable frequences n the ISM band to varous access ponts (APs) n the networks Ths s the subject of ths paper To start, let us frst explan why the frequency plannng (or assgnment) for the 8b network s dfferent from that for the tradtonal cellular networks In typcal cellular wreless networks ncludng the GSM [R96] and EDGE network [SAE98], two separate rado channels, namely the traffc and control channels, are used to carry user data and control traffc, respectvely For example, termnals access the control channels to send control nformaton va some contenton mechansm After the nformaton s successfully receved and processed by a base staton (BS), the termnal s assgned wth a specfc traffc channel for transmttng ts data traffc Exstng frequency assgnment or rado-resource allocaton methods [KN96] were devsed manly for such traffc channels The key dea there s to avod mutual nterference among varous termnals or BSs usng the same frequency In practcal networks, there s no real-tme coordnaton among BSs n the assgnment of traffc channels to termnals n dfferent cells Thus, frequency assgnment or rado-resource allocaton s based on statstcal averages or worst cases, eg, 9 % chance of acceptable lnk qualty, across multple cochannel cells Ths work was done whle the author was wth AT&T Labs

2 On the other hand, there s no such dstncton between control and traffc channels n the 8b network Specfcally, all user data and control nformaton (n both drectons between termnals and APs) are carred on the same physcal channel Rather, the access to the channel by multple transmtters s coordnated by the MAC protocol, whch s the well-known, Carrer Sensng Multple Access (CSMA) protocol wth collson avodance feature That s, a transmtter can start ts transmsson only f t senses that the channel s currently dle As a result, even f two closely located APs are allocated wth the same frequency channel, much of the mutual nterference can stll be avoded by the CSMA protocol, and the avalable bandwdth are mplctly shared between the two cells, served by the two APs In a sense, the MAC protocol provdes an effectve, dstrbuted mechansm to coordnate the channel access among termnals and APs (or equvalently, BSs) In the worst case, both APs behave as f they share the same frequency Nevertheless, the 8 protocol stll works properly, whch demonstrates the robustness of ts desgn, at the expense of ncreased delay (due to backoff when sensng channel busy) and degraded network throughput Consequently, exstng frequency allocaton methods that do not consder the combned effect of physcal channel and MAC protocol are not drectly applcable to the 8 networks We propose and analyze a new frequency allocaton technque n ths paper The organzaton of the rest of ths paper s as follows We provde a bref descrpton of the rado and MAC protocol desgn for the 8 standard n Secton II In Secton III, we formulate the frequency allocaton as an nteger programmng problem, and show one of the formulatons to be NPcomplete Thus, we propose and analyze a heurstc algorthm n Secton IV, and valdate ts performance by examples n Secton V Fnally, our concluson s n Secton VI II IEEE 8 SPECIFICATION The orgnal IEEE 8 specfcaton [I97] allows three knds of physcal layer: drect sequence spread spectrum (DSSS), frequency hoppng spread spectrum (FHSS) and nfrared (IR) In partcular, the DSSS desgn supports data rates of and Mbps Subsequently, whle mantanng backward compatblty to the DSSS 8, the 8b [99b] was adopted to support data rates of 55 and Mbps, operatng n the 4 GHz ISM band As a result, the 8b network now can support,, 55 and Mbps, dependng on rado condtons Another extenson s 8a [I99a], whch uses a dfferent physcal layer known as orthogonal frequency dvson multplexng (OFDM) to support data rates rangng from 6 to 54 Mbps, operatng n the 55 GHz band (the U-NII band) It s mportant to note that t s the 8b networks that have been wdely used recently For ths reason, we focus on the 8b network here We also note that although data rates have been ncreased, the 8b network contnue to use the orgnal MAC protocol n the 8 specfcaton Furthermore, the MAC protocol supports the ndependent basc servce set (BSS), whch has no connecton to wred networks (e, an ad-hoc wreless network), as well as an nfrastructure BSS, whch ncludes an access pont (AP) connectng to a wred network The latter s smlar to cellular networks wth base statons replaced by AP s We consder only the nfrastructure BSS n ths paper We provde a bref descrpton of the 8 MAC protocol here [I97, OP99] The 8 specfcaton defnes fve tmng ntervals for the MAC protocol Two of them are consdered to be basc ones that are determned by the physcal layer: the short nterframe space (SIPS) and the slot tme The other three ntervals are defned based on the two basc ntervals: the prorty nterframe space (PIFS) and the dstrbuted nterframe space (DIFS), and the extended nterframe space (EIFS) The SIFS s the shortest nterval, followed by the slot tme The latter can be vewed as a tme unt for the MAC protocol operatons, although the 8 channel as a whole does not operate on a slotted-tme bass For 8b networks (e, wth a DSSS physcal layer), the SIFS and slot tme are and µs, respectvely The PIFS s equal to SIFS plus one slot tme, whle the DIFS s the SIFS plus two slot tmes The EIFS s much longer than the other four ntervals, and s used f a data frame s receved n error The 8 MAC supports the Pont Coordnaton Functon (PCF) and the Dstrbuted Coordnaton Functon (DCF) The PCF provdes contenton-free access, whle the DCF uses the carrer sense multple access wth collson avodance (CSMA/CA) mechansm for contenton based access The two modes are used alternately n tme However, to our knowledge, the PCF s not commonly mplemented and only the DCF s avalable n most commercal 8b products Thus, we present a bref overvew of the DCF protocol here The DCF works as follows A staton (ncludng the AP) wth a new packet ready for transmsson senses whether or not the channel s busy If the channel s detected dle for a DIFS nterval (e, 5 µs for 8b networks), the staton starts packet transmsson Otherwse, the staton contnues to montor the channel busy or dle status After fndng the channel dle for a DIFS nterval, the staton: a) starts to treat channel tme n unts of slot tme, b) generates a random backoff nterval n unts of slot tme, and c) contnues to montor whether the channel s busy or dle In the latter step, for each slot tme where the channel remans dle, the backoff nterval s decremented by one When the nterval value reaches zero, the staton starts packet transmsson Durng ths backoff perod, f the channel s sensed busy n a slot tme, the decrement of the backoff nterval stops (e, s frozen) and resumes only after the channel s detected dle contnuously for the DIFS nterval and the followng one slot tme Agan, packet transmsson s started when the backoff nterval reaches zero The backoff mechansm helps avod collson snce the channel has been detected to be busy recently Further, to avod channel capture, a staton must wat for a backoff nterval between two consecutve new packet transmssons, even f the channel s sensed dle n the DIFS nterval The 8 specfcaton requres a recever to send an ACK for each packet that s successfully receved

3 Furthermore, to smplfy the protocol header, an ACK contans no sequence number, and s used to acknowledge recept of the mmedately prevous packet sent That s, statons exchange data based on a stop-and-go protocol As shown n Fgure, the sendng staton s expected to receve the ACK wthn the µs SIFS nterval after the packet transmsson s completed If the ACK does not arrve at the sendng staton wthn a specfed ACK_tmeout perod, or t detects transmsson of a dfferent packet on the channel, the orgnal transmsson s consdered to have faled and s subject to retransmsson by the backoff mechansm In addton to the physcal channel sensng, the 8 MAC protocol mplements a network allocaton vector (NAV), whose value ndcates to each staton the amount of tme that remans before the channel wll become dle All packets contan a duraton feld and the NAV s updated accordng to the feld value n each decoded packet, regardless of the ntended recpent of the packet The NAV s thus referred to as a vrtual carrer sensng mechansm The MAC uses the combned physcal and vrtual sensng to avod collson The protocol descrbed above s called the two-way handshakng In addton, the MAC also contans a four-way protocol that requres the transmtter and recever exchange the Request-to-Send (RTS) and Clear-to-Send (CTS) messages before sendng actual data, as a means to resolve the so-called hdden termnal problem III FORMULATION OF CHANNEL ASSIGNMENT In North Amerca, the ISM band at 4 GHz s dvded nto channels for the 8 network [OP99] where adjacent channels partally overlap each other Nevertheless, among these channels, there are completely non-overlappng ones, separated by 5 MHz at ther center frequency In prncple, all channels are avalable for allocaton n a gven 8 network However, expermental results reveal that overlappng channels can cause enough nterference that t s not benefcal to assgn overlappng channels to APs [M] Therefore, we only consder the assgnment of nonoverlappng channels (Our approach can be extended to consder the allocaton of overlappng channels wth proper weghtng of the overlapped spectrum wth spreadng gans Ths wll be nvestgated n our future papers) As a frst approach, let us focus on the transmsson by the APs n the 8b network Such a focus s approprate for typcal offce envronment and Internet applcatons because the bandwdth consumpton for downlnk (e, from AP to termnal) s much hgher than that for uplnk (e, from termnal to AP) Let the network have M APs, ndexed from to M Accordng to the CSMA protocol, an AP wth traffc ready to be transmtted frst determnes f the assgned channel (frequency) s busy or dle More specfcally, f the AP detects that the receved power of co-channel nterference s equal or greater than α mw (whch corresponds to about -8 dbm n the 8b standard), the channel s consdered to be busy Otherwse, t s dle Clearly, t s possble that the channel busy status can be due to a sngle transmttng AP or a group of multple APs transmttng smultaneously For effcent frequency assgnment, let us classfy the nterferers for each AP Specfcally, for each AP, let C () denote a set of nterferng APs where transmsson by any one AP n the set can cause enough nterference for AP to detect channel busy The APs n the set C () s called class- nterferers for AP Lkewse, let C () be a set of pars of two nterferng APs where transmsson by any par of APs n the set can cause AP to sense channel busy APs n C () are called class- nterferers In general, determnng the nterferer sets C () and C () for each AP requres measurements or estmates of sgnal path loss between each par of APs n the network Let p j and h j denote the transmsson power at AP j and the sgnal path loss from APj to AP If AP j belongs to C (), t requres h j p j α () Smlarly, f AP par m and n belong to C (), we have h m p m + h n pn () Note that the transmsson power n () and () are assumed to be fxed n ths work and channel assgnment wth dynamc power control s a topc for future study α By a smlar way, we can defne class- or even hgher classes of nterferers However, due to the contenton nature of the CSMA protocol, the traffc load on each channel (e, the probablty of transmsson at a gven AP) cannot be too hgh Thus, the probablty of havng class- nterferers, whch requre smultaneous transmsson at all nterferng APs, s much smaller relatve to that of the class- and nterferers Hence, for smplcty, we only consder class- and nterferers here To proceed, let us defne addtonal notaton Let ρ be the offered traffc load for AP n terms of channel utlzaton wthout nterference from any source There are totally N (non-overlappng) channels, ndexed by to N, avalable for allocaton As ponted out above, N= for the 8b network Wth such a small N, we assume that each AP s assgned wth one and only one channel Further, we denote X j = f AP s assgned wth channel j and otherwse Snce the CSMA protocol prohbts APs from transmttng when a gven channel s sensed busy, we defne the effectve channel utlzaton U as the fracton of tme at whch the channel can be sensed busy or s used for transmsson by AP That s, N U ρ + X k [ ρ j X jk k = j C () () + ρ m ρ n X mk X nk ] ( m, n) C () Ths defnton can be nterpreted as follows The frst term on the rght hand sde s the offered load assocated wth AP

4 The frst summaton term nsde the brackets represents the total traffc load of all class- nterferng APs that are assgned wth the same channel as AP Ths s so because accordng to the CSMA protocol and the detecton threshold α n use, AP senses channel busy when any one of ts class- nterferers transmts on the same channel Smlarly, the last summaton term represents the effectve channel utlzaton due to class- nterferers f they use the same channel To mantan channel stablty (e, all traffc can be sent eventually), we requre U < (4) for all AP = to M Note that the rght hand sde of (4) can be replaced by a value less than to account for overhead of CSMA contenton We have two objectve functons for the channel assgnment A Mnmze the Effectve Utlzaton of Bottleneck AP { U, U, U } Mnmze Max, M (5) Over the assgnment ndcator {X j } subject to the constrants (4) for all = to M Clearly, the objectve functon n (5) s to assgn channels such that the effectve utlzaton of the most heavly loaded AP s mnmzed Ths results n more resources avalable for the most heavly loaded AP, gven offered loads B Mnmze Overall Interference Mnmze M = U (6) Over the assgnment ndcator {X j } subject to the constrants (4) for all = to M Note the sum of all U reflects the total effectve channel utlzaton Mnmzng the sum tends to mnmze the overall nterference n the network, whle mantanng stablty of each channel shared and detectable by multple neghborng APs Theorem The - nteger programmng problem wth the objectve functon (6) and constrants (4) for all APs to M s NP-complete Proof For a gven network settng, the offered load ρ and the nterferer sets C () and C () for each AP are known The programmng problem s non-lnear due to the cross-products of X j s n U, as defned n () Usng the technque n [C69], we can lnearze the problem by replacng X k X mk X nk by a new term Y kmn Smlarly, we replace X k X jk by a new term kj The resultant problem becomes a lnear nteger programmng, whch has been shown to be NP-complete [GJ79, p45] Despte our suspcon, we have not been able to prove that the optmzaton wth (5) as the objectve functon s NPcomplete or NP-hard Nevertheless, n lght of problem complexty, t s unlkely that an effcent algorthm exsts for the optmal channel assgnment For ths reason, we propose a heurstc algorthm and study ts effectveness as follows IV A HEURISTIC METHOD FOR CHANNEL ASSIGNMENT We propose an assgnment algorthm for the objectve functon n (5) subject to constrants (4) for all APs That s, the heurstc algorthm attempts to mnmze the effectve channel utlzaton for the bottleneck AP, although t can be extended to consder the objectve functon (6) The new algorthm makes use of the followng known parameters: offered traffc load ρ and ts nterferer sets C () and C () for each AP We outlne the algorthm as follows: Generate a random, ntal channel assgnment for the network, whch s treated as the best assgnment obtaned so far Let the maxmum effectve channel utlzaton for the assgnment be denoted by V (e, V=max{U }) Based on the random, ntal assgnment, dentfy the AP (say ) wth the hghest effectve channel utlzaton In case of te, one such AP s chosen randomly as the bottleneck Contnue wth Step For the bottleneck AP, dentfy ts current assgned channel, say k For each avalable channel n from to N wth n k and each co-channel AP (say j) n C () (e, those APs n the set that have been assgned wth channel m), temporarly modfy the channel assgnment by reassgnng only APj wth channel n Based on (), recompute the maxmum effectve channel utlzaton, denoted by W jn, for the new assgnment After completng such testng for all such n and j, let W be the mnmum among all the W jn s 4 Compare W wth V and perform the followng: a If W<V, then replace V by W and record the assocated new assgnment as the new best soluton (e, to fnalze the channel change for one AP that mnmzes the objectve functon the most a greedy step) Contnue wth Step b If W=V, then wth a pre-specfed probablty δ, replace V by W and record the new assgnment as the best soluton Contnue wth Step c If W>V, a local optmum has been reached (e, the best assgnment obtaned so far s the local suboptmal soluton) Contnue wth Step 5 5 Repeat Steps to 4 wth a number of random, ntal assgnments The fnal soluton s chosen to be the best, accordng to (5), among the local suboptmal assgnments 6 Test f constrants (4) for all APs are satsfed for the fnal assgnment If so, the fnal assgnment s feasble Otherwse, t s consdered that no feasble soluton exsts for the network under consderaton Clearly, ths algorthm does not explctly consder the constrants (4) However, focusng on (5) by the algorthm s approprate because mnmzng the maxmum U mplctly enhances the chance of satsfyng constrants (4) for all APs Now, let us consder the property of the proposed algorthm Theorem Wth >δ> n Step 4, the heurstc algorthm does not have nfnte loopng Proof Gven that the number of APs M and avalable channels N n the system are fnte, Steps and can be completed n a fnte amount of tme The only possblty that

5 the algorthm has an nfnte loop s that Steps to 4 are executed repeatedly wthout stop Let us assume that such loopng can happen and the V value after the m-th executon (teraton) of Step 4 be denoted by V m To proceed, let δ= n Step 4b for a moment In order to form the nfnte loopng, we must have V >V > >V m wth m Wth both M and N beng fnte, there are only a fnte number of all possble channel assgnments Snce each new assgnment fnalzed by Step 4a has a unque maxmum effectve channel utlzaton, t s thus mpossble that m goes to nfnty That s, Step 4c must be reached after a fnte amount of processng Let us assume that nfnte loopng s possble wth >δ> Based on the above argument, we now must have V > >V =V + > >V j =V j+ > V m wth m for some and j Snce the argument above has already ruled out the possblty of havng subsequences of V s of nfnte length between two = sgn on ths lst, t must contan an nfnte number of = sgn Snce each = sgn corresponds to an executon of Step 4b wth probablty δ, the probablty of executng ths step for an nfnte number of tme s thus zero Hence, the nfnte loopng cannot exst We remark that based on the proof, the algorthm can exclude Step 4b and treat the case of W=V as reachng a local optmum as part of Step 4c, wthout causng any nfnte loopng However, our numercal experence reveals that Step 4b helps explore varous assgnments for enhanced results, especally when there are multple bottleneck APs for the channel assgnment under consderaton Snce heurstcs s nvolved n the proposed algorthm, achevng the optmal soluton s not guaranteed Now, let us quantfy the qualty of the suboptmal soluton generated by the algorthm Toward ths goal, we observe that Step bascally tests out varous channel assgnments to dentfy a better soluton As the algorthm s executed for a gven ntal, random assgnment, let Y, Y, Y,, Y m denote the (random) sequence of the maxmum effectve channel utlzaton assocated wth the channel assgnments under testng We denote that Y s the quantty for the ntal, random assgnment Based on the Y sequence, we construct another sequence,,,, n as follows We start wth =Y and set = For each j=,,, m, compare Y j wth If >Y j, then we set =+ and =Y j Otherwse, repeat Step for the next j value In essence, the sequence s s constructed by examnng Y j one by one We start off wth =Y and Y j s added as the last element n the sequence only f Y j s less than Y for all <j (or equvalently, Y j s less than, the last element n the current sequence) Clearly, the sequence s monotonc strctly decreasng Physcally, s represent the sequence of the maxmum effectve channel utlzaton for an mproved assgnment fnalzed by Step 4a or 4b that yelds a maxmum utlzaton lower than any assgnments examned by the algorthm so far n the search process Recall that the algorthm s repeated for a gven number (say K) of ntal random assgnments For each ntal assgnment, we can obtan one such sequence s as dscussed above Note that the sequences assocated wth dfferent ntal assgnments have dfferent lengths and are mutually ndependent of each other (although elements n the same sequence are dependent) Furthermore, when the algorthm eventually stops, assume that t has encountered a total of n mproved assgnments (e, mproved over those examned earler and derved from the same ntal assgnment), whch s the sum of lengths of the sequences s mnus K One can vew that the maxmum effectve channel utlzaton for all possble assgnments for the gven network has a probablty dstrbuton Let T π be the maxmum utlzaton for the top-π-fracton of assgnments (eg, the top percentle assgnments) Hence, for a random assgnment wth ts maxmum utlzaton, we have P [ T π ] =π (7) Let Q π be the probablty that the fnal suboptmal soluton generated by the algorthm falls wthn the top-π-fracton of assgnments Theorem If the algorthm have encountered a total of n mproved assgnments at the completon of ts executon, then n + Qπ > ( π ) (8) Proof Let us frst focus on the case of encounterng n mproved assgnments for one ntal, random assgnment By defnton, we have Qπ = P[ mn Tπ ] = P[mn ] (9) The event of (mn >T π ) n the above s dentcal to havng o >T π, >T π,, and n >T π Gven that s are a strctly decreasng (random) sequence, we have P[ n ] () n < P[ ] Where s a random varable ndependently drawn from the same dstrbuton for for = to n One can obtan () by replacng on the left hand sde by on the rght sde for one at a tme Snce the varables are ndependent, P[ n n+ > T > Tπ ] = { P[ ]} π () Usng the defnton n (7), substtutng () nto () and then nputtng nto (9) yelds (8) The case wth multple ntal random assgnments s proved by explotng the property that the sequences s assocated wth dfferent ntal assgnments are mutually ndependent V METHOD VALIDATION To valdate the performance of the proposed algorthm, we appled t to two settngs of mult-cell network usng the 8 ar nterface for whch the optmal assgnment s

6 known Specfcally, the settngs correspond to a network wth 7 and 7 cells, as shown n Fgures and, respectvely A cell s dvded nto sectors, each of whch s represented by a clover-leaf hexagon n the fgures and served by an access pont (AP) at the center of the cell (a dot n the fgures) Each AP antenna has a bandwdth of 6 o and ponts toward an approprate drecton to serve the assocated sector Thus, there are and APs n Fgures and, respectvely, wth APs for each gven cell co-located at the cell center The antenna gan has a parabolc shape; that s, a db drop relatve to the front drecton occurs at the half bandwdth angle Any drecton beyond a threshold angle n clockwse or ant-clockwse drecton suffers a gven, fxed attenuaton relatve to the gan at the front drecton, whch s called the front-to-back (FTB) rato The FTB s set to be 5 db Recall that only the AP-to-AP nterference s consdered n our current formulaton The rado lnk between any par of APs n the network s characterzed by a path-loss model wth an exponental of 5 Cell radus s assumed to be Km and the path loss at m from the cell center s -7 db Transmsson power for each AP antenna s dbm (or W) All APs have dentcal amount of offered traffc (We note that the soluton generated by the proposed algorthm n ths case does not depend on the actual traffc load, but the feasblty of the fnal soluton does) In order to ensure that the optmal assgnment s known, shadowng and fast fadng are not consdered In addton, the channel-busy detecton threshold α s set to be 5e- µw (whch corresponds to -86 dbm) As ponted out earler, there are non-overlappng channels avalable n the ISM band for assgnment Based on our parameter settngs for both 7 and 7-cell networks, the optmal assgnment s the tradtonal frequency reuse of [L89] That s, no adjacent sectors use the same channel Fg Assgnment for Network wth 7 Cells and APs When the proposed algorthm was appled to the network wth 7 cells and APs, the algorthm was able to generate the optmal channel assgnment, based on 5 ntal random assgnments The optmal assgnment wth channels to assgned to varous sectors (APs) s shown n Fgure As for the network wth 7 cells and APs, the proposed algorthm was not able to yeld the obvous optmal assgnment of reuse of (Wthout consderng the boundary effect of the cell layout whch makes the nterference condtons non-unform) The suboptmal soluton obtaned from the algorthm usng, ntal random assgnments s presented n Fgure The channels are represented n red, blue and green color As shown n the fgure, most of the sectors (APs) use a channel dfferent from those n adjacent sectors In the worst case, at most two adjacent sectors share the same channel In the search process, the algorthm encountered and fnalzed a total of 55,6 mproved assgnments Based on the analyss n Secton IV, wth a probablty hgher than 994%, the suboptmal soluton n Fgure falls wthn the top th percentle, whch s qute acceptable In ths case, the algorthm ran for less than 9 mnutes on a SUN Sparc workstaton Fg Assgnment for Network wth 7 Cells and APs The above two examples have unform traffc load and unform propagaton envronments wth obvous solutons, and are only used to verfy the correctness of the proposed algorthm However, for any wreless network of consderable sze, the traffc load and the propagaton envronment are seldom unform usually wthout obvous channel assgnment solutons The proposed approach can easly produce a good channel assgnment solutons n such cases, albet suboptmal yet wth provable closeness to the optmal soluton Also, f the traffc load s slowly fluctuatng over tme, the proposed approach can be used to generate a seres of channel assgnment over tme to best accommodate the changng condtons VI CONCLUSION The IEEE 8 standard specfes both rado and MAC protocol desgn We observe that the CSMA protocol n use helps avod much of co-channel nterference at the possble expense of degraded network throughput Due to the couplng between the physcal and MAC layers, conventonal frequency plannng and allocaton methods, typcally for traffc channels on cellular networks, cannot be drectly appled to the 8 network

7 In ths paper, by focusng on nteracton among access ponts (APs), we have formulated the channel assgnment for the 8 network as an nteger programmng problem, where one verson of the problem has been shown to be NPcomplete In lght of computatonal complexty, a heurstc algorthm has been proposed and analyzed The algorthm was then appled to two cellular settngs wth known optmal assgnments For one of the settngs, the proposed algorthm was able to generate the optmal channel assgnment As for the second case of a large network, although only a suboptmal soluton was obtaned by the algorthm, t has been shown to be excellent Therefore, as the 8 networks are wdely deployed, the proposed algorthm can serve as a valuable tool for frequency plannng of such networks [R96] T S Rappaport, Wreless Communcatons: Prncples and Practce, New York: IEEE Press and Prentce Hall, 996 [SAE98] P Schramm, et al, Rado Interference Performance of EDGE, a Proposal for Enhanced Data Rates n Exstng Dgtal Cellular Systems, Proc of IEEE VTC, Ottawa, Canada, May 998, pp [VAM99] R van Nee, et al, New Hgh-Rate Wreless LAN Standard, IEEE Commun Mag, Dec 999, pp 8-88 In terms of future work, we are extendng the proposed approach to consder non-unform transmsson power by the APs, upstream traffc, overlappng channels and real-tme adaptve channel assgnment to meet the fluctuaton of traffc load at varous APs over tme VII ACKNOWLEDGMENTS We thank Bruce McNar for sharng hs results wth us and for hs dscusson Thanks are also due to Leonard Cmn, Paul Henry and oran Kostc for ther dscusson VIII REFERENCES [C69] WW Chu, Optmal Fle Allocaton n a Multple Computer System, IEEE Trans on Computers, C- 8, No, pp , Oct 969 [GJ79] MR Garey and DS Johnson, Computer and Intractablty: A gude to the Theory of NP- Completeness, WH Freeman and Company, San Francsco, 979 [HT] H Holma and A Toskala (Ed), WCDMA for UMTS, John Wley & Sons, New York, [I97] IEEE 8, Wreless LAN Medum Access Control (MAC) and Physcal Layer (PHY) Specfcaton, 997 [I99a] IEEE 8a, Part : Wreless LAN Medum Access Control (MAC) and Physcal Layer (PHY) Specfcaton: Hgh-Speed Physcal Layer Extenson n the 5 GHz Band, 999 [I99b] IEEE 8b, Part : Wreless LAN Medum Access Control (MAC) and Physcal Layer (PHY) Specfcaton: Hgh-Speed Physcal Layer Extenson n the 4 GHz Band, 999 [KN94] I Katzela and M Naghsneh, Channel assgnment schemes for cellular moble telecommuncaton systems: a comprehensve survey, IEEE Personal Commun, Vol:, June 996, pp - [L89] WCY Lee, Moble Cellular Telecommuncatons Systems, McGraw-Hll, New York, 989 [M] B McNar, prvate communcatons, [OP99] B O Hara and A Petrck, IEEE 8 Handbook, IEEE Press, New York, 999