Optimal Design of High Density WLANs

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1 Optmal Desgn of Hgh Densty 8. WLANs Vvek P. Mhatre Thomson Research Lab, Pars, France Konstantna Papagannak Intel Research Cambrdge, UK Abstract: The provsonng of hgh throughput performance nfrastructure wreless networks necesstates the deployment of a hgh densty of Access Ponts. Whle the latter mproves wreless lnk qualty to the clents, t can also ntroduce addtonal nterference unless the network s carefully planned and tuned. It has been shown that the reacton of CSMA/CA protocol to nterference s unnecessarly conservatve n hgh densty envronments. In ths work, we study the problem of nfrastructure wreless network desgn, and the nteracton between hgh densty and MAC parameter tunng. Through analyss and numercal results, we provde recommendatons on () optmum dmensonng of hgh densty networks, and () optmum tunng of ther MAC parameters. We demonstrate that 8.a networks are nherently nose-domnated, whle 8.g networks are nterference-domnated, thus requrng dfferent network desgn approaches. In sharp contrast to prevous work, we establsh that MAC parameter tunng has lmted beneft n properly planned 8.a networks. On the other hand, analytcal results on the optmal tunng of MAC parameters n nterference-domnated 8.g deployments show substantal throughput mprovements. Usng the nsght ganed through our analyss, we propose an algorthm for the optmal tunng of MAC parameters n unstructured hgh densty envronments. Opnet smulatons show that the proposed algorthm results n up to % mprovement n network throughput.. INTRODUCTION The wde acceptance of the IEEE 8. protocol for wreless access to the Internet has already led to hgh densty unstructured networks n urban areas, as well as hgh densty planned networks n enterprse envronments for etended coverage and hgher throughput support. Whle hgh densty s already present n certan areas, t s stll unclear how these networks need to be planned and tuned to optmally Ths work was done when the frst author was at Intel Research Cambrdge, UK. Permsson to make dgtal or hard copes of all or part of ths work for personal or classroom use s granted wthout fee provded that copes are not made or dstrbuted for proft or commercal advantage and that copes bear ths notce and the full ctaton on the frst page. To copy otherwse, to republsh, to post on servers or to redstrbute to lsts, requres pror specfc permsson and/or a fee. ACM CoNEXT Lsboa, Portugal. c ACM //...$5.. address the nterplay between ncreased nterference due to the closer promty of APs, and the gans of mproved lnk qualty to the clents []. In 8. MAC, each termnal (clent as well as AP) senses the wreless channel before attemptng a transmsson. In ths mechansm, termed physcal carrer sensng, f the receved power durng channel sensng s greater than a certan threshold (referred to as Clear Channel Assessment Threshold, or CCA threshold), then the termnal nfers that the wreless channel s currently busy, and therefore defers ts transmsson. By usng a small CCA threshold, the amount of nterference can be reduced by suppressng concurrent transmssons n the network, and thus the data rates can be mproved. However suppresson of concurrent transmssons also results n low network throughput due to reduced spatal reuse. Interestngly enough, the aforementoned problem only attracted the nterest of the research communty n the recent past [], [3], [4], [5]. In ths work, we study the problem of optmal desgn and tunng of hgh densty wreless networks to cover a partcular geographcal area at the mnmum cost (number of APs) whle offerng the best throughput performance to users. Interference s epected to play a key role n such networks. Unlke cellular networks, where nterference mtgaton s done through per-user power control, WLANs rely on the MAC protocol for a smlar task. Consequently, we ntroduce an analytcal framework that borrows desgn elements from cellular network desgn, but sgnfcantly epands to accurately ncorporate the MAC layer behavor. In contrast to prevous works [], [3], [4], [5], our framework takes nto account factors such as AP densty, avalable number of orthogonal channels, dfferent modulaton and codng schemes, and nose power. We demonstrate that all these factors have a sgnfcant mpact on the problem. Usng the aforementoned framework, we dentfy regmes under whch a WLAN s domnated by nose or nterference. Identfyng the operatng-regme s of prme mportance, because n a nose-domnated network, the carrer sensng parameter has almost no role to play. On the other hand, n an nterference-domnated network, the carrer sensng parameter has a pvotal role to play n determnng the network throughput. In ths contet, the key nsght that we provde s that typcal 8.g networks are nterference-domnated due to a shortage of orthogonal channels (3 orthogonal channels), whle typcal 8.a networks are nose-domnated due to the relatvely hgh number of orthogonal channels ( orthogonal channels). We also show that whle n hgh densty WLANs, hgh data rates could be possble between a

2 clent and ts AP due to close promty, t turns out that usng the hghest data rates may not be optmum from the overall network capacty perspectve. Our analytcal results are nstrumental n gudng us n the desgn of a CCA adaptaton algorthm that can be used by a wreless sender to mtgate the nterference t eperences n ts envronment. Our algorthm can work n arbtrary network topologes, n D as well as 3D envronments, rrespectve of the physcal layer employed, rrespectve of the effcency of the frequency selecton mechansm, and wthout makng any assumptons about the operatng regme of the network. Drven by actual channel measurements, our algorthm s capable of balancng throughput gans and the amount of nterference t accepts from the network. Usng Opnet smulatons t s further shown to lead to up to % throughput mprovement compared to today s default MAC settngs, whle outperformng a recently proposed counterpart algorthm, ECHOS [8], by up to 3%. The rest of the paper s organzed as follows. In Secton we descrbe the problems faced n hgh densty wreless networks, and lst the network desgn and MAC layer parameters determnng user throughput. The nterplay between network desgn and MAC layer tunng s studed analytcally n Secton 3. Relang the assumpton on fleblty n the deployment of the dense WLAN, we derve approprate formulatons for CCA adaptaton n Secton 4. Our analytcal fndngs are used to formulate a novel CCA adaptaton algorthm n Secton 5 that can work n arbtrary networks. Its performance s evaluated usng Opnet smulatons n Secton. We dscuss some of the related work n ths area n Secton 7, and conclude n Secton 8.. WLAN DESIGN AND CSMA/CA The prmary objectve of network operators deployng wreless networks s to provde geographcal coverage of a certan regon (such as an enterprse envronment, or a unversty campus) at the lowest network cost (AP densty), whle delverng the best possble performance to the end user. A sngle 8.a/g AP can typcally provde coverage up to a dstance of about m at a data rate of Mbps [3], []. However, n the presence of multple users and tmevaryng wreless condtons, the actual throughput on the cell boundary may be much lower than Mbps. Hence for mproved coverage and hgher throughput, t s necessary to deploy multple APs over the regon. In such hgh densty wreless networks (cell radus of to 5 m), nterference s epected to play a key role [, 3, 4, 5, 8].. The mpact of nterference When two nodes communcate wrelessly, the mamum rate at whch ths communcaton can be sustaned s determned by the Sgnal to Interference and Nose Rato (SINR) at the recever whch s gven by: SINR = S R S N + S I, () where S R s the power at whch the transmtted sgnal s receved at the recever, S N s the power of nose n the recever crcutry (eplaned n more detals n Secton.3), and S I s the total nterference power. The hgher the SINR, the hgher the data rate that can be sustaned. Gven that clents assocate wth ther closest AP, ncreased AP densty mples a reducton n the dstance between a clent and ts closest AP. Ths n turn mples that the sgnal strength receved by a clent from ts assocated AP (S R n equaton ()) can be ncreased, and ths results n an mprovement n the SINR as well as the data rate. For eample, although the communcaton range of 8.a s m, the rate t can support at that dstance s just Mbps []. If a user s wthn m of the AP, then a rate of up to 3 Mbps can be supported. Therefore hgh densty networks am at shrnkng the cell sze, so that hgher data rates can be supported on the cell boundary. However, note that the avalable number of orthogonal channels n 8. s lmted (3 n 8.g, and n 8.a []). As the AP densty ncreases, the dstance between cochannel APs decreases, and therefore the nterference n the network (S I n equaton ()) ncreases. When the nterference around a transmtter s sgnfcant, the 8. carrer sensng prevents the transmtter from accessng the medum so as not to corrupt the ongong communcaton. The Clear Channel Assessment (CCA) Threshold corresponds to that amount of S I that determnes whether a transmtter s allowed to access the medum or not. If the CCA threshold of 8. MAC s set to a small value, then concurrent transmssons on the same channel are suppressed, and n spte of havng a hgh densty of APs, not all the APs are able to transmt smultaneously. Thus, although the data rates could be very hgh, the fracton of tme for whch an AP transmts can be very small, havng an adverse effect on the throughput. On the other hand, f the CCA threshold of 8. MAC s set to a large value, then multple co-channel APs may transmt concurrently. The ncreased nterference can, however, nullfy the beneft of mproved sgnal strength due to sgnfcant degradaton of the recever SINR. The above descrpton clearly outlnes the comple nterdependence, between the achevable throughput, the AP densty, the avalable number of orthogonal channels, and MAC layer parameters, such as the CCA threshold n hgh densty 8. networks. Consequently, t s mperatve that a sngle unfed framework be used to study ths problem. Prevous work has typcally looked at MAC layer parameter tunng n solaton [], [3], [4] and [5].. Network Desgn Choces Based on the above, there are only a few tools at the dsposal of the network operator to avod the adverse effect of nterference n hgh densty deployments: () dentfcaton of the approprate physcal layer technology (8.g or 8.a) for the densty of the planned network, snce dfferent technologes offer dfferent coverage and spatal reuse factors, () choce of AP densty so that the desred throughput performance can be acheved, () careful selecton of the channels assgned to APs, so as to mnmze contenton among nearby APs, and (v) careful tunng of MAC parameters to mtgate nterference n the network. We call the assembly of the four aforementoned tasks as network desgn, and provde recommendatons on optmum network desgn of hgh densty 8. networks n Secton 3. Notce that the frst three tasks lsted above are smlar to the network desgn and plannng tasks carred out n cellular networks. One mportant dfference, however, s that cellular networks mtgate nterference by usng per-user power control []. However n 8., the tme granularty over whch a user s served s much smaller than n a cellular voce network, and hence per-user power control s dffcult.

3 Thus, power control n 8. s an altogether ndependent problem, and not the focus of ths work. In ths work, we only focus on the tunng of 8. MAC for nterference mtgaton, and propose an algorthm that can enable today s 8. networks to make optmal use of ther hgh densty. Note that even though both cellular and 8. networks may rely on mcro-cell deployments for hgh throughput, as we show later, the theoretcal framework borrowed from cellular network desgn needs to be adjusted to accurately ncorporate the mpact of the MAC layer..3 Hgh Densty MAC parameters Even though approprate choces n the ntal desgn of a hgh densty wreless network may be suffcent n achevng hgh performance (as wll be shown n the net secton), ths may not always be the case ether due to ncremental deployment, or less fleblty n terms of the AP placement and equpment capabltes (drectonal antennas could for nstance mtgate nterference). In settngs where nterference cannot be avoded by desgn, the behavor of a wreless transmtter and recever depends on a number of parameters whch control ther reacton to nose and nterferng sgnals, as well as ther aggressveness to seze the channel for transmsson. Wreless Transmtter: The behavor of a wreless transmtter s prmarly determned by the CCA Threshold. In 8. MAC, a transcever decdes f the wreless channel s currently busy based on the relatve value of nterference as compared to the CCA Threshold (Clear Channel Assessment Threshold). Before attemptng to transmt a frame, the transcever measures the strength of the receved nterference on the wreless channel. If the measured nterference s hgher than the CCA Threshold, the channel s assumed to be busy, and the transmsson s deferred. Wreless Recever: The behavor of the wreless recever further depends on a seres of parameters capturng the qualty of the recever s crcutry, the power of the sgnal needed for successful decodng, as well as the selectvty of the recever n terms of the transmssons that t attempts to decode. Recever Nose Power refers to the amount of nose generated n the recever crcutry. Let N denote ths quantty n db, defned as N = log S N where S N s measured n mll Watts. For typcal state-of-the-art 8. APs such as [], N s n the range of -9 to -9 db. The recever nose power drectly mpacts what s termed as Recever Senstvty, whch refers to the mnmum power of the desred sgnal at the recever, that s requred for the successful decodng of the sgnal n the presence of nose alone. The Recever Senstvty depends on the modulaton and codng scheme. If the mnmum requred SINR for successful decodng of a sgnal for a gven modulaton and codng scheme s β (n db), then the Recever Senstvty (n db) s gven by N + β. Whenever a wreless transmsson s receved by a partcular clent at a power greater than the Recever Senstvty, the clent crcutry attempts to decode the sgnal, even f that sgnal may not be addressed to the clent n queston. Any subsequent transmsson targeted to the clent wll not be decodable for the duraton of the ntal transmsson. Ths phenomenon s termed as strongest last-collson, and may occur n hgh densty envronments [4, 7]. The Recever Threshold defnes that value of receved power below whch the recever crcutry wll not attempt to decode the receved sgnal. It should be further set to be greater than the Recever Senstvty and appromately equal to the power the clent should epect from ts assocated AP. By default, the Recever threshold and the CCA threshold are set to be appromately equal to, and slghtly hgher than, the nose power []. Notce that the Recever Senstvty and the Recever Threshold are altogether dfferent quanttes. Whle the former s determned and fed by the hardware capabltes, the latter s confgurable. In Secton 3.5, we wll show that the Recever Threshold can be easly determned based on the CCA Threshold. 3. OPTIMUM NETWORK DESIGN In Secton, we dentfed the key factors mpactng the performance of hgh densty wreless networks. In ths secton, we study the nterplay between optmal network desgn and hgh densty MAC parameter tunng, dervng recommendatons on the optmal deployment and confguraton of such envronments. Optmal desgn wthn such a contet refers to the provsonng of a wreless network that covers the desred geographcal area at the smallest cost, whle offerng the best possble throughput to the users. Consequently, the metrc of nterest s what we call Throughput- Coverage. Defnton. A network provdes a of C bts per second per square meter when the total throughput delvered to all the clents n a unt area s at least C bts per second (even f the clents are located on the edge of the cell). The above defnton gves a lower bound on throughput performance. Users closer to the AP can get hgher throughput through Auto Rate Fallback, but we focus on the worst case performance when all the users are assumed to be on the cell boundary. In ths secton, our objectve s to analytcally derve the optmum AP densty, and the optmum CCA Threshold values that guarantee a desred performance. We borrow elements from cellular network desgn and provde a framework for the analyss of the performance of dense WLANs that ncorporates the effects of CSMA/CA. A common practce n cellular network desgn s the modelng of cells usng heagons. The use of a heagon pattern for a cell can be shown to be optmal n the sense that one can cover a certan geographc regon wth the smallest number of cells, whle a heagon closely appromates a crcular radaton pattern [9]. We defne a WLAN cell to be the geographc regon around an AP n whch the receved sgnal strength from the gven AP s stronger than the receved sgnal strength from any other AP. Assumng that the APs have a regular heagonal lattce placement over a twodmensonal regon, we denote the number of APs per unt area by ρ, and the number of orthogonal channels avalable for assgnment by K. Note that heagonal lattce deployment s used for clarty of nsghts. All results can be easly etended to the case of random unform AP deployment by replacng the summaton used for computng the total nterference, by an approprate ntegral n the followng arguments. 8.g has three orthogonal channels, whle n 8.a, up to orthogonal channels are avalable n US and Europe 3

4 K πρ Reuse pattern πρ (a) Reuse pattern (b) Co-channel APs Fgure : Reuse pattern and channel allocaton. Inde Rate (Mbps) SINR (db) Table : SINR requrements for dfferent data rates for 8.a/g []. For analytcal tractablty, we assume that APs operatng on a common channel also have a regular heagonal lattce placement. In such regular envronments, typcally found n enterprses, approprate reuse patterns can be desgned as long as there are at least three orthogonal channels [9]. For eample, Fg. (a) shows a channel allocaton scheme wth three orthogonal channels. We can see that the co-channel APs also have a regular lattce pattern. Gven an AP densty of ρ, and K orthogonal channels, the AP densty for each channel type s ρ. The average cell K radus, R, and the average separaton between co-channel APs, D, are gven as follows: R = πρ, D = s K πρ These dstances are depcted n Fg. (a). The three shaded heagons represent co-channel cells. The hgher the AP densty, the smaller the cell-radus, and hence the stronger the receved sgnal strength at the boundary of the cell. The hgher the number of channels, K, the larger the separaton between the co-channel APs, and hence the lower the nterference. The clent throughput depends on () the clent-ap separaton, () the amount of nterference, and () the transmsson rates supported by the AP. The largest clent-ap separaton s determned by the AP densty, whle the CCA threshold determnes the hghest co-channel nterference receved by the clent. These quanttes together determne the worst case SINR n a cell (va equaton ()). We only consder 8.a/g transmsson rates, snce these physcal layers are guaranteed to lead to hgher throughput regmes than 8.b. In 8.a/g, as Table shows, there are 8 dscrete data rates that can be supported for dfferent values of clent SINR [3]. Our objectve n ths secton s to derve the smallest AP densty that can guarantee a desred throughput-coverage performance. For ths, we take the followng approach. For each data rate n Table ( from to 8), we determne the optmum AP densty (or equvalently, the optmum cell radus R ), and the optmum CCA threshold, CCA, that can provde the desred throughput-coverage of C. We then () choose that data rate, k, for dmensonng and confgurng our network, whch requres the smallest AP densty. Together wth Defnton, ths ensures that data rate k can be supported on the cell boundary at the smallest network cost. Also note that schemes correspondng to data rates lower than that of k can also be supported for the same choce of AP densty and CCA threshold, due to ther lower SINR requrements. In Sectons 3. to 3.3, we formulate the constrants of our optmzaton problem, and then solve the problem n Secton 3.4. The only nputs to our optmzaton problem are hardware and system parameters, capturng: () the number of channels, K, () the AP transmt power, P, () the recever nose power N, and (v) a propagaton loss model P a α, where a s a fed constant, and α s the path loss eponent. 3. SINR Constrant Consder the th modulaton and codng scheme. Let C be ts data rate, and let β be the correspondng mnmum requred SINR for ths rate. Let R be the cell radus, and CCA be the CCA Threshold requred for guaranteeng the desred throughput-coverage of C wth ths scheme. Assume that the carrer sensng dstance s d,.e., two co-channel APs can transmt concurrently only f they are separated by a dstance of at least d. Note that ths does not mean that CCA = P ad α. Ths s because there are multple APs that are located at a dstance greater than d from the gven AP, and t s the cummulatve nterference from all these APs that determnes CCA. CCA also represents the mamum allowable nterference power for scheme. The worst case clent SINR s at the boundary of the cell, and s gven by SINR = P ar α, N + CCA SINR = N P ar α + CCA PaR α It s well-known that due to the strong propagaton fall-off, the total nterference n a cell s domnated by the closest ter of nterferng APs [, 3, 5]. Hence, we only consder the frst ter of co-channel APs n computng the total nterference (see Fg. (a)). By usng smple geometrc arguments, we can obtan ths nterference power as a functon of P, a, R, and d. Furthermore, f we defne an aulary varable X as follows, (3) X = d R, (4) 4

5 then we can show that (see [5]) CCA PaR α I(X ) = (X + ) α + (X ) α + X + + 3X «α + X + 3X «α In (4) and (5), X s the rato of the cell radus and the carrer sensng range, whle I(.) s a measure of the cummulatve nterference and the receved sgnal strength. Snce we want to ensure that data rate C can be supported on the cell boundary, usng (3), we get the followng SINR constrant. I(X ) + N R α Pa (5) β () 3. Constrant Snce we only allow concurrent transmssons between cochannel APs separated by at least d, crcles of radus d around concurrently transmttng co-channel APs are dsjont. Hence mamum spatal reuse s attaned when such dsjont crcles are mnmally packed over the entre regon. If the entre regon to be covered has area A, then the mamum number of APs transmttng concurrently on a gven channel s A π d = 4A πd. If we assume that the cell radus R s chosen such that data rate of C s supportable on the cell boundary, then the collectve data rate of all the APs on a gven channel s at least 4C A (even when all the users πd are on the cell boundary). Snce there are K channels, the collectve rate at whch data s transferred over the entre network s 4KC A. Hence throughput per unt area s 4KC πd. πd Note that although the data rate s C, the actual useful throughput at the applcaton layer s lower due to MAClayer and protocol-specfc overheads. For smplcty, we do not nclude these overheads. Snce we requre the throughput per unt area to be at least C, usng (4), we have the followng constrant for throughput-coverage. r KC KC π X R C X R πc (7) 3.3 Constrant on the number of Channels Note that the number of avalable channels determnes the physcal separaton of co-channel APs through (). The carrer sensng dstance d cannot be smaller than D (gven by ()), snce there are no co-channel APs at a dstance smaller than D from an AP. Hence, d K πρ (8) Combnng (), (4), and (8), we get the followng constrant. X K (9) Note that no such constrant was consdered n [], [3], [4] and [5]. The above constrant shows that the number of channels has a sgnfcant role to play n ths problem. For eample, wth channels, X.9. A choce of X for every modulaton and codng scheme must be at least as hgh as.9. Optmum values of X computed for several scenaros n [3] and [5] are much lower than ths value. Ths means that those values are not even feasble when we have a typcal 8.a settng wth at least channels. In essence, a large number of channels results n a larger separaton between the co-channel APs, and can thus reduce nterference. Hence ths constrant has to be taken nto account n determnng the optmum amount of allowable nterference,.e., the optmum carrer sensng threshold. 3.4 Optmzaton Problem and ts Soluton Combnng (7), (9) and (), the problem of optmum network dmensonng (fndng the mnmum AP densty), and optmum tunng of the carrer sensng threshold CCA, so that a throughput coverage of C s guaranteed, can be formulated as follows. Snce mnmzng AP densty s equvalent to mamzng cell radus R,.e., mnmzng R, we get: Mnmze: f(x, R ) = R () r KC Subject to: g (X, R ) = X R πc () g (X, R ) = K X () g 3 (X, R ) = I(X ) + N R α Pa β (3) where I(X ) s gven by (5). Usng the Karush-Kuhn-Tucker Theorem [], we can show that the soluton to the above optmzaton problem s as follows (we do not nclude the proof due to space constrants). (r ) R = mn C πc, ˆR where ˆR s gven by (4) = N ˆR α r! β Pa + I 4KC (5) ˆR πc X = r 4KC R () πc We solve the above optmzaton problem for each of the 8 modulaton-codng schemes, and choose that modulatoncodng scheme whch results n the largest cell radus whle provdng the desred throughput-coverage. We then choose the correspondng AP densty for network dmensonng, and set the carrer sensng threshold of the entre network, CCA thr, wth respect to ths modulaton scheme usng (5). j = argma (R ), ρ = πrj, CCA thr = P ar α j I(X j ). Notce that we use a network-wde common CCA threshold. Ths s because f the network s nterference domnated, nearby co-channel APs can hear each other. If the two nearby APs choose dfferent CCA Thresholds, then the AP wth a hgher CCA Threshold (the AP that can accept more nterference) wll acqure the channel more aggressvely than the AP wth a lower CCA Threshold. Ths may lead to starvaton of the AP that uses a lower CCA threshold. The approach of usng a common network-wde CCA Threshold s adopted n [4, 5] as well. However, the ECHOS algorthm proposed n [8], does not necessarly result n a common network-wde CCA threshold. 3.5 Numercal Results In ths secton, we obtan numercal results for the optmum network dmensonng and carrer sensng parameters as a functon of the desred throughput-coverage. In Table, we have lsted the values of the system parameters that we use n obtanng numercal results n ths secton. Propagaton loss parameters are as per ITU recommendatons 5

6 for 8.a/g n ndoor offce envronment [4]. Transmt power of the APs, nose power and number of channels n Table are typcal values for Csco []. Note that snce 8.a uses lower transmt power, and has a stronger propagaton fall-off, 8.a cells usually have smaller coverage than 8.g cells. In Table, we have lsted the mnmum requred SINR for supportng dfferent modulaton-codng schemes n 8.a/g [3]. In all the plots, the -as s the target throughput-coverage multpled by π(). Ths normalzaton constant s ncluded so that the -as can be nterpreted as the average throughput delvered to a crcular regon of radus m. We obtan numercal results for the cases when the nose power s -9 db or -9 db, and the underlyng network employees 8.a or 8.g. The reason for dscontnutes n all the plots s that there are 8 dscrete modulaton and codng schemes n 8.a/g. 8.a 8.g Transmt Power, P +7 dbm + dbm Number of Channels, K 3 Path loss eponent, α Path loss constant, a -4.5 db -4 db Table : System Parameters for Numercal Results The optmum value of cell radus and the correspondng AP densty as a functon of target throughput-coverage are plotted n Fg. (a) and Fg. (b). The plots show that to acheve hgher throughput-coverage, we must reduce the cell radus,.e., the network archtecture must comprse of a hgh densty of mcrocells. Also, the hgher the nose power, the smaller the requred cell radus,.e., the hgher the requred AP densty. In Fg. 3, we plot the data rate whch s used for system dmensonng and CCA Threshold tunng. Due to the SINR constrant n Secton 3., ths s also the data rate that can be sustaned on the edge of every cell. We can see from Fg. 3 that as the target throughput-coverage ncreases, we must employ hgher modulaton and codng schemes to satsfy the throughput-coverage requrements. We note from Fg. 3 that for 8.a, despte the fact that a data rate of 54 Mbps can be sustaned at a dstance of m [], to provde a throughput-coverage of 5, a cell radus of m (Fg. (b)), and correspondng data rate of 3 Mbps are chosen (Fg. 3). Ths s because n order to support a data rate of 54 Mbps, a substantally large number of co-channel APs need to be suppressed, and ths results n poor spatal reuse. If nstead, a data rate of 3 Mbps s used, then fewer cochannel APs need to be suppressed. Thus our analytcal and numercal results prove that n hgh densty networks the benefts of mproved spatal reuse may more than offset what we lose by usng a lower data rate. Hence, n hgh densty 8. networks, for the overall network good, usng the hghest data rates s not necessarly optmum. The optmum values of CCA Threshold as a functon of desred throughput-coverage are plotted n Fg. 4(a,b,c,d). We also plot the Recever Senstvty for the modulaton and codng scheme that can be supported on the cell boundary. There are three dstnct operatonal regons n terms of the mpact of nterference on MAC layer behavor. If the power of the nterferng sgnal s below the nose power, CCA adaptaton has no mpact n that envronment. If the power of the nterferng sgnal s above the nose power but under the recever senstvty, the sgnal can be receved but can- n Mbps a, Nose -9dB 8.a, Nose -9dB 8.g, Nose -9dB 8.g, Nose -9dB Fgure 3: Optmum Rate on cell boundary as a functon of C π() Mbps/m. not be decoded. Consequently, meda access s governed by physcal carrer sensng, and dependng on the value of the CCA threshold the transmtter wll suppress or contnue wth a transmsson. Lastly, f the nterferng sgnal s stronger than the Recever Senstvty, t can be successfully decoded. In ths case, the termnal must respect the Network Allocaton Vector feld (NAV feld) n the nterferng sgnal (f RTS/CTS s enabled), and must defer ts own transmsson for the duraton of the nterferng transmsson. Ths s the vrtual carrer sensng mechansm of 8.. Accordng to the above, we note that the optmum CCA threshold for 8.a (Fg. 4(a),(b)) s comparable to the nose level even n hghly dense scenaros. In fact, for N = 9 db, the CCA threshold eceeds the nose power by 7 db at most, and for N = 9 db, ths dfference s no more than db. Note that typcal shadow-fadng varatons are on the order of 5- db [4], and hence CCA threshold has a lmted role to play for the above settngs. We also note from Fg. 4(a),(b) that the CCA Threshold s never above the Recever Senstvty. Ths means that an AP cannot successfully decode the nterferng sgnals. Thus, we conclude that n regular hgh densty 8.a networks, the etent of co-channel nterference s almost neglgble, and the network s nose-domnated. Also note that ncreased throughput-coverage cannot be provded by tweakng the CCA threshold, an observaton that verfes the epermental results n [4], where the optmum CCA threshold for -% raw frame error rate was found to be very low (-9 db). The reason for 8.a beng nose-domnated, and not nterference-domnated, s the avalablty of a large number of orthogonal channels whch results n large nter-ap separaton for co-channel APs, and thereby substantally lower co-channel nterference. Thus, n 8.a networks, the key desgn parameter s AP densty and approprate frequency selecton for optmal spatal reuse, and not the CCA threshold. On the other hand, n 8.g networks, due to shortage of orthogonal channels, nterference plays an mportant role n determnng the optmum system parameters. From Fg. 4(c),(d), we can see that the CCA threshold s substantally hgher than the nose power for most settngs. In fact, the optmum CCA Threshold s hgher than the Recever Senstvty. Our results ndcate that n such scenaros, 8.g APs should not defer ther transmsson even f they can successfully decode the receved sgnal from an nterferng AP. Ths can be acheved as follows. The Recever Threshold (descrbed n Secton ) can be confgured to be 8

7 8.a: Optmum Cell Radus (meters) 8 4 R: Nose -9dB R: Nose -9dB AP Densty: Nose -9dB AP Densty: Nose -9dB a: AP densty (per m by m) 8.g: Optmum Cell Radus (meters) 8 4 R: Nose -9dB R: Nose -9dB AP Densty: Nose -9dB AP Densty: Nose -9dB g: AP densty (per m by m) (a) 8.a (b) 8.g 8 Fgure : Optmum Cell Radus, R, as a functon of C π() Mbps/m. n db Optmum CCA thresh Recever Senstvty Nose Power 4 8 n db Optmum CCA thresh Recever Senstvty Nose Power 4 8 n db Optmum CCA thresh Recever Senstvty Nose Power 4 8 n db Optmum CCA thresh Recever Senstvty Nose Power 4 8 (a) 8.a, N = 9 db (b) 8.a, N = 9 db (c) 8.g, N = 9 db (d) 8.g, N = 9 db Fgure 4: Optmum CCA as a functon of C π() Mbps/m. Recever Senstvty s equal to N + β, where N s the nose power, and β s the mnmum requred SINR for a gven modulaton and codng scheme. equal to the optmum CCA Threshold, so that the recever does not attempt to decode nterferng frames. Ths wll ensure that the vrtual carrer sensng mechansm of 8. s over-rdden by the physcal carrer sensng mechansm to avod the problem of strongest-last collson. Such a recommendaton s also made n [] and [4]. Also note from Fg. (b) that the optmum cell radus s almost ndependent of the nose power for 8.g; the plots for thedfferent nose powers are overlappng. Thus, n sharp contrast to 8.a networks, we note that regular 8.g networks are nterference domnated, and tunng of MAC parameters plays an mportant role n ensurng hgh network throughput. In summary, n ths secton we showed that due to dfferences n the avalable number of orthogonal channels, and due to dfferent path loss models, the desgn of 8.a and 8.g networks requres substantally dfferent approaches. Optmal AP densty and proper frequency selecton can mtgate nterference to a large etent n 8.a networks. On the other hand, the desgn of 8.g networks needs to address AP densty as well as MAC layer tunng under a unfed framework to optmze network performance. 4. OPTIMUM MAC LAYER TUNING In Secton 3, we establshed desgn recommendatons for regular dense wreless networks when one controls both, the densty of the APs, as well as the tunng of the MAC parameters. In ths secton, we rela the frst assumpton and study the tunng of MAC parameters n regular networks wth a predefned AP densty. The nsghts ganed through our analyss are then employed n Secton 5, where our solutons are generalzed to arbtrary network topologes. Another way to perceve the topc n queston s that we attempt to dentfy the regmes where CCA adaptaton can result n throughput mprovement n estng networks. As n Secton 3, we assume a regular lattce deployment of APs n our analyss. We also assume that channel allocaton has been performed n such a way that even the co-channel APs form a regular pattern. As noted n Secton 3, as long as there are at least 3 orthogonal channels, such channel allocaton s always possble n regular lattce structures. Our objectve n ths secton s to select the optmum CCA threshold, gven a fed cell radus R, so as to mamze the throughput-coverage of the network. As n Secton 3, we frst determne the optmum CCA Threshold for each of the 8 modulaton schemes, and then choose that scheme for settng the network-wde CCA Threshold whch results n the hghest throughput-coverage. Note that although we use a smlar approach to Secton 3, the constrants and the objectve functon of the optmzaton problem consdered n ths secton are dfferent. From Secton 3., the throughputcoverage of the network under the th modulaton-codng scheme s KC X R π = C X K π( R ). Snce R s fed, we have the followng optmzaton problem for the th modulatoncodng scheme. Mamze: f(x ) = C X (7) Subject to: X K (8) g (X ) = I(X ) + N R α Pa β (9) In the above, note that (9) may not be feasble n general for all modulaton-codng schemes. In other words, t may not be possble to support all the data rates on the boundary of a cell due to the non-zero contrbuton of nose. 7

8 The soluton to the optmzaton problem n (7)-(9) s as follows. For a gven network (gven R), we check f each of the modulaton and codng schemes can be supported on the cell boundary,.e., we check f for each, (9) holds for some X. If so, gven the fact that I(X ) s strctly decreasng, (9) can be rewrtten as X η () where η s a constant that depends only on R, β, N, a, P and α. Then, the soluton to the optmzaton problem n (7)-(9) s ˆX = mn n o K, η () We then choose that modulaton and codng scheme for settng CCA Threshold whch results n the hghest value of throughput-coverage,.e.,! C j = argma () ˆX where argma s taken over those modulaton-codng schemes, that satsfy (8) and (9). The CCA Threshold s then set usng (5) as follows. CCA thr = P ar α I(X j ) (3) 4. Numercal Results In ths sub-secton, we obtan numercal results for settng the optmum CCA Threshold n regular networks wth fed AP densty usng the above problem formulaton. In Fg. 5(a),(b) we plot the optmum CCA threshold as a functon of R for an 8.a network. The optmum CCA Threshold s below the nose power for a cell radus larger than 35 m. Even when the CCA Threshold eceeds the nose power, t s substantally smaller than the Recever Senstvty, and therefore nterferng sgnals cannot be decoded. These results confrm that nterference n planned 8.a hgh densty networks (where the AP deployment pattern and channel allocaton avods reuse of the same frequency n neghborng APs) has lmted mpact, and the system s nose domnated. Settng the CCA threshold optmally s crtcal only for very small cell szes ( to 3 m). In Fg. 5(c),(d), we plot the optmum CCA threshold for an 8.g network for dfferent nose powers. When N = 9 db (respectvely -9 db), the nterference s comparable to the nose power when the cell radus s smaller than 7 m (respectvely m). For a cell radus larger than these values, the system s nose domnated, and hence the CCA threshold can be set to the nose power. For small cell szes ( to m), nterference s hgher than the nose power as well as the Recever Senstvty. Hence, as n Secton 3.5, we set the Recever Threshold to be equal to the optmum CCA Threshold so that the physcal carrer sensng mechansm overrdes the vrtual carrer sensng mechansm. If, nstead of settng the CCA threshold optmally, an 8.g network were to operate wth the fed default CCA threshold, then physcal, as well as vrtual carrer sensng wll suppress concurrent transmssons n a large neghborhood, and wll brng down the throughput substantally. In Fg., we plot the percentage mprovement n throughputcoverage when the CCA threshold s set optmally, compared to the use of the default CCA threshold that s equal to the nose power. We note that there are substantal gans n throughput-coverage. For 8.g, Fg. shows that even for a cell radus of 4 m, the mprovement n throughputcoverage s as hgh as 75 to 3%. For 8.a, CCA Adaptaton s benefcal only for very small cell szes ( to 35 m). % Gan n g, Nose -9dB, CCA -9dB 8.g, Nose -9dB, CCA -9dB 8.a, Nose -9dB, CCA -9dB 8.a, Nose -9dB, CCA -9dB Cell Radus (m) Fgure : Percentage mprovement n throughputcoverage of optmum CCA selecton over the default CCA threshold. For eample, for a cell radus of m, the throughput can be mproved by 5 to 3 % by choosng the CCA Threshold optmally. Note that these results were obtaned for a regular topology wth optmal channel allocaton. However, the results strongly suggest that CCA adaptaton s benefcal. Later on, n Secton, we show that even for random deployment, CCA adaptaton results n substantal throughput mprovement. In Fg. 7(a), we plot the supportable rate on the cell boundary for 8.a and 8.g for two dfferent recever nose powers. Note that Fg. 7(a) shows rate as a functon of dstance n the presence of nose as well as nterference, and hence should not be compared to the range that s typcally advertsed by the vendors []. The latter s computed for an nterference-free scenaro. We can clearly see that the supportable rate decreases as the cell sze ncreases. Also note that the mamum cell sze for 8.a s lower than the mamum cell sze for 8.g. Ths s because 8.a uses lower transmt power and has a stronger path loss (see Table ). More mportantly, we note that hgh transmsson rates, such as 48 or 54 Mbps, are never optmal from the perspectve of overall network throughput due to ther strct requrements n terms of SINR (as n Fg. 3). In Fg. 7(b), we plot the throughput-coverage (on log scale) as a functon of the cell radus. We note that 8.a offers better throughput-coverage for smaller cell szes, however the throughput-coverage drops sharply to zero. On the other hand, 8.g provdes lower throughput-coverage for smaller cell szes, whle provdng etended coverage. 5. ORCCA: OPTIMAL-RATE CCA ADAP- TATION The analyss presented n Secton 4, even though applcable to envronments where co-channel APs are deployed n a regular lattce, offers the followng nsghts. Frst, t shows that the potental gans of usng optmum CCA Threshold n hgh densty networks are substantal (see Fg. ). Second, t provdes nsght nto desgnng an algorthm for optmally settng the CCA threshold n random topologes. In ths secton, we present ORCCA, an algorthm that sets the CCA Threshold of a gven network purely based on channel measurements. ORCCA eplots the results from Secton 4 and does not make any assumptons about the placement of 8

9 n db Optmum CCA thresh Recever Senstvty Nose Power Cell Radus (m) n db Optmum CCA thresh Recever Senstvty Nose Power Cell Radus (m) n db Optmum CCA thresh Recever Senstvty Nose Power Cell Radus (m) n db Optmum CCA thresh Recever Senstvty Nose Power Cell Radus (m) (a) 8.a, N = 9 db (b) 8.a, N = 9 db (c) 8.g, N = 9 db (d) 8.g, N = 9 db Fgure 5: Optmum CCA Threshold as a functon of cell radus R. Recever Senstvty s equal to N + β, where N s the nose power, and β s the mnmum requred SINR for a gven modulaton and codng scheme. n Mbps a, Nose -9dB 8.a, Nose -9dB 8.g, Nose -9dB 8.g, Nose -9dB Cell Radus (m) Normalzed (log scale) a, Nose -9dB 8.a, Nose -9dB 8.g, Nose -9dB 8.g, Nose -9dB 5 Cell Radus (m) (a) Optmum Rate (b) Throughput-coverage on log-scale `log(c π() ) Fgure 7: Optmal rate and throughput-coverage for dfferent cell szes. clents, APs, cell shapes, or channel assgnment. Consder an 8. a/g network whose CCA Threshold s to be optmally confgured. We make the followng assumptons n our algorthm:. Each AP keeps track of the sgnal strengths of all the cochannel APs that are operatng n ts neghborhood. Ths s requred as part of the Rado Resource Management framework of 8.k [5], and can be easly mplemented by capturng all the co-channel beacons, and passng them up to the drver for montorng purposes.. We assume that the nterference receved by a clent s appromately equal to the nterference receved at the servng AP. Whle ths assumpton mght seem restrctve at frst, n hgh densty scenaros where the cell szes are very small (-5 meters) ths assumpton s not too restrctve. To rela ths assumpton, we could nstead assume that the clent reports the receved sgnal strength of all the nterferng APs to ts servng AP, and ORCCA wll stll work under the latter assumpton. However, as of now, there s no mechansm n the 8. standard for the clent to convey a detaled nterference report. Subsequent revsons of the 8. standard may support ths feature. 3. We assume that the APs communcate wth a central controller, and report ther measured quanttes (descrbed later n ths secton). The central controller uses these measurements to compute the optmum CCA Threshold, and communcates t back to the APs. Several commercal products use a central controller for network parameter tunng [9]. Consder all the APs operatng on a certan fed channel, say channel. Assume that there are M APs n the network operatng on ths channel (not all of them may nterfere wth each other). Let varable l nde these APs. The proposed algorthm s as follows. At an AP: Each AP, l, performs the followng steps: Step : Measure the beacon strength of all the co-channel APs, sort them n decreasng order, and save them n P (l) I (k), where k vares from to M. Note that AP l may not receve measurable sgnal from all the APs, n whch case the correspondng P (l) I (k) are set to. Step : Measure receved sgnal strength of all the clents assocated wth tself (AP l), and fnd the clent whose sgnal s receved at the lowest power. Let ths power be P (l) R. Assumng a symmetrc channel, P (l) R s also the power receved by the clent from AP l. Thus, ths clent s located at the edge of the cell, and hence s used for calbratng the CCA threshold of AP l. Step 3: Let be the nde of supportable modulatoncodng schemes. Let C be the supportable data rate, and β be the requred SINR for scheme. For each scheme, AP l does the followng.. Determne! I (l) = P(l) R N β (4) Ths s the mamum allowable nterference whle stll supportng rate for the user wth the weakest receved sgnal strength. Note that f I (l) <, then ths user cannot be served at rate. If I (l) >, then the CCA Threshold requred for supportng the th data rate n cell l s:! CCA (l) = P(l) R N β = I (l) (5) 9

10 . Fnd the smallest nde m (l) such that and MX k= P (l) I (l) m X (k) = k= MX k=m (l) + P (l) I (k) + MX k=m (l) + P (l) I (k), () P (l) I (k) < I (l) (7) The above mples that f the m (l) strongest nterferng APs are suppressed, then the nterference from the remanng APs can be accommodated whle stll supportng rate for the worst case user assocated wth AP l. 3. The achevable throughput for scheme n cell l, denoted by γ (l), s gven by 8 < C γ (l) = m (l) f I (l) + >. (8) : otherwse Although the data rate C s supportable when I (l) >, there s a reducton n throughput due to tme sharng of the wreless channel by vrtue of the CCA Threshold. When the CCA Threshold s chosen such that () and (7) are satsfed, we note that AP l tme shares ts channel wth m (l) other APs. Hence the term (m (l) +) n the denomnator of (8). Note that n analyss, ths was taken nto account by the term X n the denomnator of throughput-coverage n (7). After each AP l determnes ts epected throughput γ (l), for th modulaton-codng scheme, t sends all the 8 trplets, γ (l), CCA (l) to the central controller. At the Central Controller: The central controller determnes the network-wde common CCA Threshold based on the nformaton gathered from all the APs. Assume that the central controller chooses a network-wde CCA Threshold CCA. Let the hghest supportable modulaton-codng scheme for AP l wth ths CCA Threshold be (l). Then, CCA (l) (l) CCA (9) Usng (8), the overall network throughput s gven by, Network Throughput = MX γ (l) (l) (3) The central controller determnes that value of CCA whch mamzes the above network throughput. Ths amounts to performng an ehaustve search for CCA = CCA (l) over all and l (wth M APs, at most 8M combnatons). Only those (, l) trplets are consdered for whch γ (l) >. Ths ensures that the mamzaton of network throughput does not starve any user. Note that the task of the central controller s consderably smplfed snce each AP l computes ts 8 trplets, γ (l), CCA (l). Even n a network wth M APs where M s large, the central controller just needs to perform O(M) addtons to determne the optmum CCA Threshold. Also note that ORCCA reles on measurements, and hence s not restrcted to the case of regular topologes. In fact, OR- CCA can functon n both D as well as 3D envronments. ORCCA does not assume any specfc path-loss or shadowfadng model. It can also be easly modfed to account for a heterogeneous collecton of APs n whch 8.g and 8.b APs co-est on the same channel. Ths would requre mnor modfcatons to ORCCA to take nto account the modulaton and codng schemes that 8.b supports n addton to takng nto account the 8.g modulaton and codng schemes. Ths requres performng optmzaton over schemes (8 of 8.g and 4 of 8.b) n Step 3 of the algorthm.. SIMULATION RESULTS In ths secton, we present smulaton results on ORCCA s performance. We use Opnet Modeler verson. for our smulatons. Opnet has an ecellent physcal layer model for smulatng wreless lnks. It has support for all the 8 modulaton-codng schemes of 8.a/g, and t smulates the transmsson of ndvdual bts over the wreless physcal layer. Unlke the Network Smulator ns-, t ncorporates the capture phenomenon whch s a crucal aspect of wreless communcaton n the presence of nterference. We smulate three schemes for two dfferent topologes (s scenaros n total). The three schemes are () the base scheme of CSMA/CA MAC whch uses the default CCA Threshold (equal to the nose power), () ORCCA, and () the ECHOS algorthm whch s a recently proposed algorthm for CCA adaptaton [8]. To the best of our knowledge, ECHOS and the CCA adaptaton algorthm n [4] are the only two other algorthms whch attempt to confgure the CCA threshold of a network. We do not smulate the latter algorthm, snce t reles on measurement of packet error rates for tunng the CCA threshold, and the current verson of Opnet (verson.) does not support shadowfadng whch has a sgnfcant mpact on packet error rates. We smulate the followng topologes: Regular topology: APs are deployed n a heagonal regular structure (4 4) wth each AP havng 4 clents assocated wth t. The APs have an nter-ap separaton of 7 m, whle the clent-ap separaton wthn each cell s m. Ths s equvalent to havng a regular heagonal cell pattern of 48 APs wth 3 channels (an 8.g network wth a cell radus of m). We focus on one of these three channels, and study the subset of the APs operatng on that channel. The area of the total regon covered s about 3m by 3m. Random topology: 48 APs and 9 clents (about 4 clents per AP) are deployed randomly and unformly over a regon of an area 3m by 3m. The users assocate wth ther closest AP. We assume that there are 3 orthogonal channels avalable (8.g), and the channels are allocated randomly to the APs. We consder one of the three channels, and study the subset of the network operatng on ths channel. Lnk level throughput performance s measured usng saturated UDP traffc from the APs to the clents for a duraton of mnutes. Transmt power of dbm, nose power of -9 dbm, and path loss eponent of 3. were used n the smulatons, emulatng 8.g lnks. The RTS/CTS handshake was dsabled whle rate adaptaton, and shadow fadng was not supported. The channel model conssts of path loss computed as per the ITU Recommendaton [4]. Studyng the mpact of tme-varyng channel gan on the performance More effcent channel selecton algorthms such as [8] could also be ncorporated, however channel allocaton s not the focus of ths work.