A User-Centric Approach for Dynamic Resource Allocation in CDMA systems based on Hopfield Neural Networks

Transcription

1 A User-Centrc Approach for Dynamc esource Allocaton n CDA systems based on Hopfeld eural etworks. García. Agustí J. érez-omero Unverstat ompeu Fabra (UF) Unverstat oltècnca de Catalunya (UC) Barcelona Span emal: nura.garca@upf.edu ramon@tsc.upc.edu orperez@tsc.upc.edu Abstract hs paper ntroduces a novel approach for consderng the Dynamc esource Allocaton (DA) n a mult-rate DS-CDA wreless network supportng non realtme () communcaton. he allocated bt rate obeys to a user-centrc approach by ntroducng a non-satsfacton user probablty that has to be mantaned below ts targeted value whle stll keepng the best explotaton of the mum avalable bandwdth. o ths purpose dfferent classes of users wth dfferent Contracted User rofles are ntroduced and a Hopfeld eural etwork optmzaton methodology s used under both user and network restrctons. Sgnfcant and promsng results are fnally shown for a sngle solated cell DS- CDA scenaro ncludng realstc propagaton and moblty models. Index terms CDA Hopfeld eural etworks esource Allocaton I. IODUCIO esearch n mult-rate drect-sequence code-dvson multple access (DS-CDA) networks for future wreless communcaton systems has recently attracted a lot of attenton n the lght of the new hgh bt rate data servces that wll be provded through 3G and 4G systems ncludng vdeo multmeda crcut and packet mode data together wth the tradtonal speech servces and low bt rate data. In such a scenaro t becomes crucal a proper management of the avalable rado resources n order to beneft from the traffc multplexng to mse the channel utlsaton whle at the same tme keepng the specfc servce requrements. Specfcally n a DS-CDA system the amount of rado resources allocated to each user s controlled by regulatng the transmsson powers and the spreadng gans (equvalently the transmsson rates). he problem of dynamc resource allocaton (DA) n a mult-servce DS-CDA wreless network supportng non real-tme () communcaton servces has been wdely treated n the lterature (see [][] and references theren). However n most of the cases a network-centrc vson has been the common way to face the DA usually wth the obectve of mzng the aggregate throughput under dfferent network constrants. As a consequence of that n many cases users are treated accordng the propagaton losses they suffer so that throughput s msed by allowng the transmssons of the users wth the lowest path loss. herefore statc and pedestran users located far from the base staton could be dscrmnated aganst other closer users. In ths paper a user-centrc approach s ncorporated n the dynamc resource allocaton problem meanng that the users needs expectatons and requrements are consdered and supported by the wreless network. In ths way the system can contnue provdng an optmzed throughput but now ncludng users servce profles. Specfcally users wll be servced accordng to the bt rates that they have contracted wth ther moble operator n an uplnk CDA wreless network. he actual bt rate allocated wll be granted accordng to a far mechansm. oreover the closed loop power control algorthm wll provde to each user the requred Eb/o target regardless of ts poston n a gven nstant. An solated cell and realstc propagaton and moblty models wll be consdered to llustrate these concepts. On the other hand n such user-centrc approach wth dfferent users servce profles performance ndcators other than the tradtonal ones (e.g. outage probablty BLE etc.) must be consdered to capture the degree of fulflment of the contracted bt rate. Specfcally n ths paper the probablty that a user s not satsfed wth the obtaned bt rate wll be retaned as a mechansm to assess the system performance [3]. he remander of the paper s organzed as follows. In Secton II we descrbe the system model and formulate the resource allocaton problem by ntroducng the farness crteron and some DS-CDA wreless network restrctons. In Secton III we present an optmzaton procedure able to allocate as many resources as possble but stll guaranteeng a certan user satsfacton probablty n agreement wth the user profle. A Hopfeld eural etwork wll be used for that purpose. In Secton I we present numercal results and n Secton conclusons are summarsed. II. DA OBLE FOULAIO In ths work a CDA wreless network s consdered where specfc bt rates have to be allocated to a set of users already admtted n the network. Dfferent types of users wth dfferent rghts coexst n the system accordng to ther user profles. In partcular each user belongs to a user class charactersed by the contractual bt rate whch s the mum bt rate that can be allocated to the user.

2 In partcular t s assumed that the allocaton process s carred out perodcally n perods of a s denoted n the followng as frames. Let assume that there are users =... n the cell n the current frame and that the -th user has a set of possble bt rates. he obectve of the DA problem s then to select for each user an optmum allocated bt rate takng nto account a set of constrants as explaned n the followng. he optmzaton approach s performed through the use of Hopfeld eural etworks (H) already addressed n multmeda reless A [4] and n Dynamc ado lannng [5]. H can actually be mplemented n hardware devces at a low complexty cost thus consttutng an effcent approach to deal wth the DA problem n real tme compared wth other approaches lke genetc algorthms whch may have more lmtatons [4][6]. As CDA s an nterference-lmted technque the am of the DA algorthm s to allocate the hghest possble bt rate per user subect to a mum planned uplnk cell load factor whch allows keepng the total nterference under certan lmts [7]. A fast closed loop power control strategy s assumed lke n US [8] amng to keep the requred Eb/o target. he user s satsfacton degree wth the experenced servce s measured wth the non-satsfacton probablty whch s defned for the -th user as: ns r b () D where s the bt rate experenced by the -th user s the mum contractual bt rate for the -th user accordng to ts user class and D s a parameter to be selected accordng to the user contract and represents the fracton of the mum bt rate wth whch the user s satsfed. A plausble farness rule wll be ncluded n the H formulaton n order to guarantee the above probablty ns accordng to the agreed user contract. On the other hand the CDA technque mposes certan restrctons to the above optmzaton as follows: A. Load estrcton In any CDA system t s requred to lmt the mum amount of nterference generated by the dfferent transmssons. hs can be acheved by lmtng the so-called uplnk load factor UL to a mum value UL. In the case of a sngle solated cell the load factor s related to the number of nstantaneous transmssons by means of the followng expresson [7]. the (E b / ) target provded that t has enough power to acheve t. hat means t s not unfarly treated. he above expresson () can be approxmated assumng that usually t holds: (3) E b It s worth mentonng that when ncreasng the bt rate the last approxmaton becomes less vald. evertheless t holds reasonably well even for the hghest bt rates that wll be consdered n ths paper. hen assumng for smplcty that the (E b / ) target s the same for all the users the sum of allocated bt rates must fulfl the followng nequalty: UL B (4) Eb otce that B can be regarded as the total bandwdth to be parttoned among the dfferent users. B. ower estrcton hs condton takes nto account the fact that the mum avalable power n a moble termnal s lmted and therefore some bt rates may not be achevable for termnals located at the cell edge. In partcular the power requrement of a termnal s gven by [9] : Lp Eb o Lp UL Eb b o where L p s the path loss correspondng to the -th user and s the background nose. Consequently assumng a mum avalable power of the bt rate allocaton must take nto account the followng constrant for the -th user: E b o L p UL UL (5) (6) UL Eb UL where s the total transmsson bandwdth (E b / ) s the target for the -th user and s the bt rate allocated to the -th user. he power control ensures that each user attans () III. OIIZAIO FOULAIO he DA problem formulated n the prevous secton turns nto the requrement to fnd the optmal bt rate allocaton for the dfferent users gven the avalable bandwdth B the user satsfacton degree and the constrants posed by the CDA technque gven by (4) and (6). In partcular the effcent explotaton of the avalable

3 bandwdth B n terms of the allocated bt rate to the -th user can be obtaned by mnmzng: B (7) b whch ensures that the mum aggregated throughput s stll attaned n ths scenaro. he bt rate allocated to one user should be one out of possble bt rates. In the followng the notaton () wll be used ndcatng the allocaton of the -th bt rate =... to the -th user =.... Accordng to () the -th user s not satsfed n the k-th () frame whenever the allocated bt rate s below the satsfacton bound /D. hen the farness rule takng nto account the user satsfacton degree s formulated k through a sutable cost functon C assocated to the -th user n the k-th frame and for an allocated -th possble bt () rate as: C k p ns pˆ k ns f f pˆ f pˆ k ns k ns p p ns ns () D () and D () and D where p ns s the target probablty that the -th user s not satsfed. In turn p ˆns k s an estmaton of the current nonsatsfacton probablty measured up to frame k-. It s computed as the rato of non-satsfed users belongng to the same user class of the -th user wth respect to the total number of users of ths class. otce that for bt rates above the satsfacton bt rate bound /D the cost functon s low (.e. ) meanng that these bt rates are sutable for the -th user. In turn for lower bt rates t depends on the non-satsfacton experenced by the user up to frame k-: f the nonsatsfacton s above the desred target the cost s hgh (.e. ) meanng that hgher bt rates are desrable whle f the non-satsfacton s below the target the cost decreases meanng that the user could stll accept these low bt rates. he above optmzaton problem subect to the mentoned restrctons can be formulated n terms of a fast and parallel combnatonal optmser known as Hopfeld eural etwork (H) []. In partcular a two-dmensonal L= neural network can be consdered for ths problem. In a D H each neuron s modelled as a nonlnear devce wth a sgmod monotoncally ncreasng functon defned by the logstc functon: U e (8) f ( U ) (9) where U and are the nput and output respectvely of the -th neuron and s the correspondng gan of the amplfer of the neuron. he optmzaton process of the H s carred out on a frame bass and reles on mnmzng an energy functon E through the convergence of the expresson: du dt U E () whch characterzes the H behavour []. he mnma of the Energy occur at the L corners nsde the L- dmensonal hypercube defned on {} []. By solvng numercally () and after reachng a stable state each neuron s ether O (.e. f s greater or equal than.5) or OFF (.e. f lower than.5). Accordng to [4][5] a vald expresson for the energy functon E follows as: E 3 k C 4 ( ) B 5 () he mnmsaton of ths functon provdes the allocaton of the -th user gven by whch takes the value for the -th bt rate (.e. () ) and for the rest of bt rates. he frst summand n () contans the cost functons defned n (8). In turn the second summand ncludes the exponent: ( ) u () B where u(.) s the unt step functon. hs summand penalzes the undesred stuatons n whch: ( ) B (3) and at the same tme t drves the above expresson to the equalty. he thrd summand smply penalzes non allowed bt rates accordng to the contractual user profle. hat s for the allowed bt rates () of the -th user = whle for the non allowed bt rates = thus ncreasng ther contrbuton to the energy functon and then brngng these bt rates out of the energy mnma. he non-allowed bt rates nclude both those gven the user profle and those caused by the power constrants gven n (6). hat fourth and fve summands were ntroduced n [5] n order to ensure rapd convergence to correct and stable states of neurons. Specfcally the fourth term forces convergence towards {} and the last term forces the

4 physcal condton that only one bt rate () s possble for the -th connecton. I. ESULS hs secton presents some llustratve results obtaned wth the proposed allocaton strategy. he CDA wreless network scenaro conssts of one solated crcular cell wth radus km. he propagaton and moblty models defned n [3] are consdered. In partcular the path loss at dstance d(km) s gven by L(dB)= log (d) wth a lognormal dstrbuted shadowng wth devaton db. he moble speed s 6 km/h and the shadowng decorrelaton length s m. he wrap-around technque s consdered n the smulatons n order to avod that termnals leave the smulated scenaro due to moblty. he transmsson bandwdth s =3.84 chps/s and the mum load factor s UL =.7. Furthermore the Eb/o target s 5 db whch leads to an avalable bandwdth B =85 kb/s. he avalable set of bt rates s gven by: {56 kb/s 8 kb/s 64 kb/s 3 kb/s and 6 kb/s}. he nose power s - dbm. he selected parameters appearng n the formulaton of the H are µ = µ =4 µ 3 =8 µ 4 =8 µ 5 =6 = =. and =. hese values have been set based on [4]. In turn the non-satsfacton probablty s the same for all the users p ns =% and s measured wth respect to the fracton D = of the mum bt rate. A user s blocked whenever the mum allowed bt rate takng nto account transmsson power constrants s below the mnmum of 6 kb/s. A blockng stuaton would also occur n H enabled systems when all the actve users were assgned the mnmum 6 kb/s bt rate occupyng all avalable bandwdth B and a new user requested a lnk to get through. he sesson duratons are exponentally dstrbuted wth average duraton m =.5 s for the -th user. It s assumed that the sesson duraton s ndependent of the allocated bt rate lke n e.g. streamng servces. Furthermore the average sesson arrval rate s gven by: (4) m where =.3s s the average tme between the end of one sesson and the begnnng of the next one for the -th user also exponentally dstrbuted. hen the total traffc s gven by: m m m m m (5) he allocaton algorthm s executed n frames of a =. s and the bt rate s kept durng the whole frame tme although t can change from frame to frame. So at the begnnng of each actve frame a Hopfeld optmzaton s carred out. hen a user fnshes a sesson t s moved randomly to another locaton wthn the scenaro ust to smulate a dfferent user when t comes to actvty. It s worth mentonng that the computatonal complexty assocated wth H s small enough to be executed n very short perods of tme so that the consdered update perod of a =.s has been manly chosen n accordance wth the tme requred to sgnal the users the new bt rate to be used and not wth the executon tme of the H algorthm much lower than.s. In that sense some studes regardng the executon tme of H algorthms are presented n [3]. wo scenaros are consdered n the smulatons: - Homogeneous scenaro: All the users belong to the same user class. he mum bt rate s 56 kb/s. - Heterogeneous scenaro: In ths case two dfferent user classes are consdered. Class users have a mum bt rate of 56 kb/s and class users of 8 kb/s. % of the users n the scenaro belong to class and 8% to class. AB (% b) = ath Loss (db) Fg. Average Bt ate (AB) for the Homogenous scenaro measured as the percentage of the mum bt rate Fg. shows the average bt rate allocated dependng on the propagaton loss for the homogenous case wth =6.5 correspondng to = users. It can be notced the shrnkng effect for propagaton losses above 35 db approxmately wth a reducton n the average bt rate Hstogram b =56kb/s Class Bt rate (b/s) Hstogram b =8kb/s Class Bt rate (b/s) (%) Fg. Hstogram and of the allocated bt rates for the two user classes wth =6.5 (%)

5 In turn for the heterogeneous scenaro Fg. shows the hstogram and the cumulatve dstrbuton functon () of the bt rate allocated to Class and users for a moderatehgh load of =6.5. It can be notced n the that the non-satsfacton probablty (.e. the probablty of havng a bt rate below 8 kb/s for class users and 64 kb/s for class users) s below the target value of % and the allocated bt rates are most of the tme the mum permtted. In turn n Fg. 3 the load has sgnfcantly ncreased up to =8.5 and the mum permtted bt rates are allocated n a lower number of stuatons but the target obectve of % non-satsfacton probablty s stll kept. In all the cases the blockng probablty results n very low values below.5% Hstogram b =56kb/s Class Bt rate (b/s) Hstogram b =8kb/s Class Bt rate (b/s) Fg. 3 Hstogram and of the allocated bt rates for the two user classes wth =8.5 It can be notced n the above fgures that a trade-off appears resultng from the Cost functon (frst term n ()) and the best bandwdth parttonng among users (second term n ()). In other words the algorthm tends to explot the mum avalable bandwdth (.e. allocatng the mum permtted bt rates whenever possble) whle keepng at the same tme the target non-satsfacton probablty. (%) (%) contracted user profle. For ths purpose a Hopfeld eural etwork optmzaton methodology has been retaned wth the ntroducton of a proper cost functon charactersng the user requrements. It has been shown that the consdered approach s able to mantan the so-called non-satsfacton user probablty below ts targeted value whle stll keepng a good explotaton of the mum avalable bandwdth. Sgnfcant and promsng results have been obtaned revealng that the proposed strategy performs satsfactorly. ACKOLEDGEES hs work has been carred out n the framework of the European etwork of Excellence ECO (Contract number 5735) and s partally funded by the Spansh esearch Councl under the COSOS grant. EFEECES [] S.A.Jafar A. Goldsmth Adaptve ultrate CDA for Uplnk hroughput axmzaton IEEE ransactons on reless Communcatons ol. o. arch 3 pp [] Seong-Jun Oh Danlu Zhang and Kmberly. asserman Optmal esource Allocaton n ultservce CDA etworks IEEE ransactons on reless Communcatons ol. o. 4 July 3. [3] US 3.3 v3.. Selecton procedures for the choce of rado transmsson technologes of the US ESI Aprl 998. [4] C..Ahan.S.amakrshna QoS rovsonng Dynamc Connecton-Admsson Control for ultmeda reless etworks Usng Hopfeld eural etworks IEEE ransactons on ehcular echnology ol 53 Jan 4 [5] E. Del e. Fantacc L. onga A Dynamc Channel Allocaton echnque Based on Hopfeld eural etworks IEEE ransactons on ehcular echnology February 996. [6].. Sherf I.. Hab. agshneh. Kerman Adaptve allocaton of resources and call admsson control for wreless A usng genetc algorthms IEEE Journal on Selected Areas n Communcatons vol. 8 pp. 6-8 February. [7] H. Holma A. oskala CDA for US John ley & Sons nd edton. [8] 3G S 5.4 hyscal layer procedures (FDD) [9] J. érez-omero O. Sallent. Agustí. A. Díaz-Guerra ado esource anagement Strateges n US John ley & Sons 5. []J.J. Hopfeld eural etworks and physcal systems wth emergent collectve computatonal abltes roc. at.acad. Sc.98 vol 79 pp []Haykn eural etworks. A Comprehensve Foundaton ew York: ac llan994 []S J.J. Hopfeld etworks wth graded response have collectve computatonal propertes lke those of two state neurons roc. at. Acad. Sc. vol 8 ay 984 [3]C..Ahn.S. amakrshna C.G. Kang I.C.Cho Shortest path routng algorthm usng Hopfeld neural network IEE Electroncs Letters vol. 37 no. 9 pp COCLUSIOS hs paper has presented a novel Dynamc esource Allocaton approach for a mult-rate DS-CDA wreless network supportng non real-tme communcaton. A usercentrc nstead of a network-centrc approach has been consdered amed at developng a far mechansm that allocates the avalable resources accordng to the specfc