IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 25, NO. 3, APRIL

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1 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 25, NO. 3, APRIL Mechansm-Based Resource Allocaton for Multmeda Transmsson over Spectrum Agle Wreless Networks Ahmad Reza Fattah, Student Member, IEEE, Fangwen Fu, Mhaela van der Schaar, Senor Member, IEEE, Fernando Pagann, Senor Member, IEEE Abstract We propose to add a new dmenson to exstng wreless multmeda systems by enablng autonomous statons to dynamcally compete for communcaton resources through adjustment of ther nternal strateges and sharng ther prvate nformaton. We focus on emergng spectrum agle wreless networks, where developng an effcent strategy for managng avalable communcaton resources s of hgh mportance. The proposed dynamc resource management approach for wreless multmeda changes the passve way statons are currently adaptng ther jont source-channel codng strateges accordng to avalable wreless resources. Each wreless staton can play the resource management game by adaptng ts multmeda transmsson strategy dependng on the experenced channel condtons and user requrements. The resource allocaton game s coordnated by a network moderator, whch deploys mechansm-based resource management to determne the amount of transmsson tme to be allocated to varous users on dfferent frequency bands such that certan global system metrcs are optmzed. Subsequently, the moderator charges the varous users based on the amount of resources t has allocated to them, n order to dscourage them from beng dshonest about ther resource requrements. We nvestgate and quantfy both the users and the system performance when dfferent cross-layer strateges, and hence users levels of smartness, are deployed by wreless statons. Our smulatons show that mechansm-based resource management outperforms conventonal technques such as arfar tme and equal tme resource allocaton n terms of the obtaned system utlty. They also provde nsghts that can gude the desgn of emergng spectrum agle network protocols and applcatons. Index Terms Spectrum Agle Wreless Networks, Resource Management, Wreless Multmeda Streamng, Game Theory, Mechansm Desgn I. INTRODUCTION EMERGING wreless networks provde dynamcally varyng resources wth only lmted support for the Qualty of Servce (QoS) requred by the delay-senstve, bandwdthntense and loss-tolerant multmeda applcatons. Ths varablty of resources does not sgnfcantly mpact delaynsenstve applcatons (e.g., fle transfers), but has consderable consequences for multmeda applcatons and often leads Manuscrpt receved February 1, 2006; revsed October 12, Ths work s n part supported by NSF under grant ECS Ahmad Reza Fattah, Fangwen Fu, and Mhaela van der Schaar are wth the Electrcal Engneerng Department, Unversty of Calforna, Los Angeles (e-mal: {ahmad,fwfu,mhaela}@ee.ucla.edu). Fernando Pagann s wth the Unversdad ORT, Uruguay (e-mal: pagann@ort.edu.uy). Dgtal Object Identfer /JSAC /07/$25.00 c 2007 IEEE to unsatsfactory user experence. Exstng algorthms and protocols for wreless transmsson do not provde adequate QoS support for multmeda applcatons n crowded wreless networks or when the nterference s hgh. In partcular, ndoor wreless technologes are overcrowdng the unlcensed spectrum whle the lcensed spectrum goes wthout much utlzaton [1]. To fulfll the necessary QoS requrements under such condtons, wreless statons (WSTAs) need to dynamcally and cogntvely harvest addtonal resources as well as optmally adapt ther cross-layer strateges based on the avalable resources. A. Spectrum Aglty and ts Challenges A possble way of obtanng addtonal resources s to deploy an Opportunstc Spectrum Agle Rado (OSAR) network nfrastructure [2][3][4][5][6][1], where WSTAs can beneft from the opportunstc deployment of unused spectral opportuntes from varous frequency bands that were ntally allotted to prmary users (.e., users for whch the spectrum was orgnally assgned such as emergency servces, polce, etc.). Whle conceptually smple, the realzaton of OSAR has shown to be hghly challengng. Whle deployng these emergng OSAR networks can allevate to some extent the need for wreless resources, the problem of effcently dvdng the addtonal avalable resources among competng, autonomous WSTAs becomes hghly mportant and s the subject of ths paper. In a recent IEEE Spectrum ssue, Robert W. Lucky [8] argued for the need for new and proactve resource management schemes that are able to prevent competng users from msusng the common (shared) network resources. Importantly, he mentoned the lack of ncentves for the WSTAs n current wreless networks to adhere to farness or courtesy rules: Today we worry whether W-F wll exhbt the same meltdown. There s no ncentve, other than the ultmate survval of the system, for users to lmt ther use. Naturally, each WSTA tres to acqure as much of the network resources as possble (see e.g. [7]), unless a preemptve mechansm exsts n the network [8]. Even when such preemptve mechansms exst, the problem of determnng optmal utltes and strateges for allocatng the transmsson opportuntes among varous WSTAs streamng delaysenstve multmeda stll remans unsolved. The complexty of ths problem s further exacerbated by the fact that the cross-layer optmzaton at each WSTA nvolves numerous

2 602 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 25, NO. 3, APRIL 2007 tme-varyng parameters and nteractons among layers. Ths makes the nteractons among WSTAs and the resultng utltyresource tradeoffs very dffcult to model. Moreover, WSTAs are consdered autonomous enttes that separately determne and optmze ther deployed cross-layer strateges. Hence, another nherent property of the consdered OSAR system s ts dstrbuted nature, both n nformaton and actons. Last but not least, for wreless multmeda applcatons, the resource management s further complcated by the delaysenstve nature of the applcaton,.e. multmeda data that s receved after ts delay deadlne s useless. B. Exstng Solutons and Ther Lmtatons To solve the aforementoned OSAR resource management problem, several strateges can be envsoned [9], ncludng equal-tme, ar-far tme, and admsson-control (reservaton) based schemes. In the equal-tme scenaro, the avalable tme on a channel s equally dvded among all present users. Whle ths allocaton strategy mght seem far, t s nether effcent nor far, snce t does not consder the content characterstcs, channel condtons, and the applcaton constrants of each user. In ar-far tme allocaton, each user announces a measure or request of the amount of tme (or rate) t requres over the next perod of servce called servce nterval. Then, each user receves an amount of tme proportonal to the requested amount. Ths strategy represents an mprovement to the equaltme method because t explctly consders the rate requrements and, nherently, the vdeo content characterstcs of dfferent users. Nevertheless, not only the entre performance of the network heavly depends on the truthfulness of the users, t effectvely persuades users to le! There are multple ncentves for WSTAs to le about ther requrements n addton to mere qualty mprovements. For nstance, they mght want to be able to cope wth sudden varatons n channel condtons or content characterstcs. Moreover, WSTAs can lower ther power usage va over-provsonng because t allows them to deploy lesssophstcated codng and protecton schemes. Alternatvely, n admsson-control schemes such as the IEEE e [10], the resources are allocated on a frst-come frst-served bass. In ths scenaro, users wll ether be admtted at ther exact resource requrement or they wll be dened any servce. In congested networks, ths scheme s neffcent because t does not scale well wth the number of users. For nstance, n [7] t has been shown that a consderable number of users may be dened any servce n a congested IEEE e network. Moreover, as n the case of ar-far tme allocaton, there are multple ncentves for the users to le about ther requrements. C. The Proposed Novel Paradgm To overcome the aforementoned lmtatons of exstng allocaton schemes, we propose a new paradgm for resource management n OSAR networks that allows WSTAs to dynamcally compete and pay for avalable spectral opportuntes. In the OSAR transmsson scenaro, the transmsson opportuntes (shown as TXOPs and defned as the smallest unt of transmsson tme nterval) avalable on the multple channels need to be allocated to the varous competng WSTAs. Our paper s based on the observaton that wreless devces currently operate n such a passve manner that degrades the whole network s performance. We propose to change the passve resource management n whch wreless statons currently nteract, by allowng them to bd for the avalable TXOPs. For ths, we assume the presence of a central spectrum moderator (CSM) (smlar to [11]) that manages the avalable TXOPs and dvdes them among the varous users; Hence, n ths part the algorthm s centralzed. To enforce autonomous self-optmzng WSTAs to act n a socally optmal way, the CSM adopts a tool called transfers through whch t charges WSTAs based on the nconvenence they cause to others by usng common resources. Each WSTA transmts to the CSM a vector of prvate nformaton that quantfes ts expected utlty as a functon of potental allocated tme. In ths sense, the nformaton and decson-makng process s decentralzed. The avalable TXOPs n the network are then allocated to the WSTAs by the CSM n a way that the aggregate utlty gets maxmzed. The transfers are computed n such a way that encourages the WSTAs to declare the truth. Gven the current condtons of dfferent channels and source, each WSTA has to adopt the optmal cross-layer strategy n order to maxmze ts own expected utlty. In ths stage, our method performs n a decentralzed way. Hence, the proposed algorthm partly reles on the ratonalty and smartness of WSTAs (e.g. how good the cross-layer strategy, compresson, or protecton schemes are, etc.) to play the resource management game. Therefore, the burden of optmzng the transmsson parameters s shared by all WSTAs. In ths paper, we wll not thoroughly dscuss the mpact of the varous cross-layer strateges on the user s performance, whch s defned n terms of experenced vdeo qualty. Instead, we wll use our pror cross-layer strategy desgn results [12], [13], [9] and focus on how to manage the resultng network resources. To recap, our approach ensures truthfulness and dynamc adaptaton of users strateges based on tme-varyng channel and content characterstcs. In other words, t promotes collaboraton n an ndrect way through chargng WSTAs based on the nconvenence they cause to other users rather than the used resources. In ths way, WSTAs wll naturally tend to dstrbute ther requests over tme n an effcent manner to avod crowded ntervals as much as possble. D. Related Work and Paper Organzaton To enable the resource exchanges among WSTAs as requred by the proposed resource management, we rely on recent developments on cross-layer optmzaton for multmeda transmsson (see [9] for a revew of the topc). However, n pror work, the optmzaton has been performed n solaton, at each ndvdual staton, and does not consder ts mpact on the overall wreless system. Game theory has been used n prevous research to resolve resource allocaton ssues for wreless networks n a dstrbuted and scalable manner [14][15][16]. However, prevous research has not consdered the benefts of dynamc and compettve resource management among WSTAs; Such a management regmen reles on users ablty to adapt ther cross-layer

3 FATTAHI et al.: MECHANISM-BASED RESOURCE ALLOCATION FOR MULTIMEDIA TRANSMISSION 603 Channel 5 Channel 4 Channel 3 Channel 2 Channel 1 Fg. 1. frequency t SI t SI t SI t SI t SI t TXOP Spectrum opportuntes for OSAR users. tme Channel occuped by prmary users Channel avalable for secondary users strateges to changng source propertes and varyng channel condtons. In [17], the authors proposed a dscrete resourceutlty functon and maxmze the aggregate utlty by dynamcally assgnng network resources. However, ths centralzed allocaton method passvely adjusts the allocaton based on the prevous observatons and does not take nto account the dynamc user behavor. In [18], prcng schemes are ntroduced from the pont of vew of the servce provder, by consderng the requested qualty of servce and the wllngness to pay. However, the relatonshp between the assgned resources and the ganed utlty s not thoroughly studed. The proposed framework reles on related work n OSAR network development, multmeda compresson, streamng, cross-layer desgn, and game-theory. In ths paper we rely on exstng research on OSAR network nfrastructure [1]. The US Federal Communcatons Commsson (FCC) has ssued a Notce of Publc Rulemakng and Order regardng the socalled OSAR or cogntve rado technologes [5]. The Defense Advanced Research Projects Agency (DARPA) has also started the next Generaton (XG) Communcatons Program to develop new technologes that allow multple rado systems to share the spectrum through adaptve mechansms [2]. For more detals on the OSAR nfrastructure, the nterested reader s referred to [2][3][4][5][6][1]. The paper s organzed as follows. In Secton II, we ntroduce the nvestgated OSAR system and ts parameters. Secton III presents the transmsson strateges that are deployed by the users n playng the resource management game. The users and system utltes s ntroduced n secton IV. Secton V proposes the mechansm for tme allocatons and computngtransfers. Numercalresults are presented n secton VI followed by conclusons and future work n Secton VII. II. OSAR SYSTEM DESCRIPTION We consder an OSAR wreless communcaton network system, where two types of users co-exst, namely prmary and secondary users. (In ths paper, the expressons user and WSTA are nterchangeably used). Prmary users have exclusve access to desgnated spectral bands, whle secondary users only access spectral bands when the prmary users do not use that band. To realze such an opportunstc use of dle spectral resources, secondary users need to possess spectral aglty [3], enabled for nstance by software-defned rados. The network moderator can then locate and dstrbute avalable resources among the varous secondary users, n both spectral and temporal domans (see Fgure 1). The wreless spectrum that can be accessed by the secondary users s dvded nto channels, whch represent the smallest unt of a spectral band. As n [4], we dfferentate two types of spectrum agle rados, referred to as type I and type II users. The type I WSTAs use a fxed spectral bandwdth to transmt ther data, but they may effectvely explot the avalable spectrum opportuntes by dynamcally hoppng between the varous channels. For nstance, the WLANs that exst today are examples of type I agle rado WSTAs. In the type II case, the WSTAs can dynamcally expand and contract ther bandwdth and also adapt ther physcal layer and modulaton strategy based on the vacant spectral opportuntes present on all the avalable channels. In our paper, we assume that all WSTAs are type II users; In a smulaton case we show the effects of sudden presence of a type I user on type II users performances and resource allocatons. Note that n our analyss, we assume that each secondary user can scan a channel, swtch to a channel, and vacate a channel nstantly (when clamed by the prmary network) wthout ncurrng any control overhead or delay. In the nvestgated communcaton system, we assume that each WSTA s transmttng multmeda btstreams to a sngle WSTA connected to the same OSAR nfrastructure. However, as mentoned n [3], one of the most challengng tasks n realzng a spectral-agle network s to mantan the connectvty among the communcatng WSTAs. Hence, an mportant role of the CSM s not only to determne the TXOP assgnments per channel for the varous transmt-receve WSTA pars, but also to dssemnate these assgnments to both nvolved WSTAs, such that they can mantan ther connectvty. Defnng effcent protocols for communcatng spectrum opportuntes among WSTAs and dssemnatng TXOP assgnments between the CSM and the users are beyond the scope of ths paper, but they represent an mportant topc for further research as ther overheads and latency may sgnfcantly mpact the performance of the system. In ths paper, we assume that the varous spectrum-aglty functonaltes are already mplemented usng e.g. the system descrbed n [3][4]. Hence, we do not consder here the mportant problems of spectral opportunty dscovery or management. We assume that based on e.g. [3], each WSTA and network moderator can mantan a spectral opportunty map, whch stores the status of each channel n the consdered wreless spectrum. We assume that whle the network moderator has full knowledge about the avalable resources, the spectrum maps of the varous WSTAs s n general a subset of all the avalable channels and/or spectral opportuntes. Moreover, the avalable opportuntes are characterzed dfferently by the WSTAs based on ther experenced channel condtons. Hence, the spectrum opportunty maps of the varous WSTAs wll be dfferent. However, t s not essental for all nodes to mantan an dentcal spectrum map as long as the network moderator coordnates ther channel assgnments. The resource allocaton mechansm for OSAR has to fulfll several mportant propertes. It needs to scale to a varyng number of users havng dfferent requrements and adapt to the dynamc nature of the wreless envronment and the tme-

4 604 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 25, NO. 3, APRIL 2007 varyng vdeo source characterstcs. Moreover, due to the dstrbuted property of nformaton, we need to adopt a dstrbuted optmzaton model, n whch the CSM does not need to be aware of the transmsson strateges, requrements, or capabltes of the varous users. Thus, a consderable porton of the complexty of the OSAR system optmzaton resdes at the user sde (.e. they need to adapt ther cross-layer strateges accordngly and determne what are the resultng utltes for dfferent resource allocatons) rather than the CSM s. We assume that the proposed game-theoretc resource management strategy s mplemented usng a reservaton (pollng)- based MAC, where a CSM s allocatng tme slots to the varous wreless statons every servce nterval (SI). The CSM has suffcent authorty to allocate TXOPs to users, charge users f necessary, and deny servce to WSTAs whch do not comply wth network regulatons. The number of TXOPs n each SI equals Q; Hence, the relaton t TXOP = tsi Q holds where t SI and t TXOP are the duratons of each SI and TXOP, respectvely (See Fgure 1). Each WSTA can potentally be allocated q number of TXOPs per channel per SI (where q {1, 2,,Q}). The consdered OSAR network has N channels avalable whereas there are M secondary users competng for these resources. All secondary users are assumed to be of type II. In addton, we assume that the performance of each channel s characterzed by each user based on the experenced Sgnal to Nose Rato (SNR). Hence, each WSTA, =1, 2,,M s assumed to be capable of measurng the SNR of channel j, j =1,,N, represented by SNR,j. III. USERS STRATEGIES In ths secton we wll analyze the actons and strateges that a WSTA can deploy. Snce the network s consdered a compettve adversaral envronment, the way users wll play the game wll be of paramount mportance for ther own performance, as well as the overall system performance. We wll frst nvestgate and defne the space of feasble strateges for a WSTA. In the followng sectons, based on the strateges defned n ths secton, we wll defne the utltes and show results about the game outcomes. We assume that each user has a multmeda content to be transmtted through the wreless network. We also assume that each WSTA has nformaton about the spectral opportuntes on the varous channels, as well as about ther qualty represented by SNR,j. Gven the multmeda content and channel condtons, the WSTA should decde about two major set of strateges: Internal Strateges: Ths set of strateges, represented by S nt for user, ncludes the cross-layer transmsson parameters and strateges used by each WSTA. External Strateges: As shown later n ths paper, each user has to announce a vector of prvate nformaton to the CSM at the begnnng of each SI. External strateges, whose space for user s represented by S ext, determne how each WSTA decdes about the nformaton to be transmtted to the CSM such that t results n the most avalable expected payoff for that user. In the followng two subsectons we dscuss these two sets of strateges n detal. A. Internal Strateges The beneft or utlty that user gans by successfully transmttng the k-th packet from transmsson queue, shown here by v k, s denoted as k ;Itsdefnedasthedstorton reducton at the vdeo recever n case the vdeo data of packet number k s correctly decoded at the recever. The utlty k s expressed n our paper as the expected mean square error (MSE) reducton at the vdeo decoder nstead of the vsual dstorton reducton, snce the latter s harder to quantfy. Ratedstorton (R-D) models can be used for modellng the utlty as a functon of rate/tme. These models are codec specfc and such R-D models can be found for example n [19]. Let s =[phy l macm app n ] Snt, =1, 2,,M be a nomnal vector of cross-layer adaptaton strateges feasble to the -th WSTA, where S nt = S PHY S MAC S AP P and the three sets S PHY, S MAC,andS AP P are the strategy spaces of user n physcal (PHY), medum access control (MAC), and applcaton layers (APP), respectvely. We also assume that the three strategy spaces above have a fnte number of elements, wth N PHY S MAC, and N AP P = S AP P = S PHY, N MAC =. In general, the sze of the strategy space s very large. However, n ths paper we consder only the optmzaton of a lmted set of parameters and strateges at varous layers. For nstance, at the PHY, we only allow users to adjust ther modulaton and codng schemes and assume that other parameters are fxed. Hence, S PHY = {phy 1 PHY,, phyn } represents the nomnal PHY strategy space of user, =1, 2,,M where each element phy k shows a partcular vector of modulaton and channel codng strateges feasble to user on N channels. In the same manner, n the MAC layer, we only consder adaptve retry-lmt adaptaton per packet and hence, the strategy space MAC,, macn }, represents a vector of maxmum retransmsson can be defned as S MAC = {mac 1 where mac k numbers per packet per channel for user. In the APP layer, users can adapt the transmsson rate or schedulng strategy, S AP P = {app 1,, AP P appn }, where app k shows a specfc packet schedulng n the transmsson queue of user based on the contrbuton of the packets n vdeo qualty, delay constrants, etc. The SNR of channel j seen by the -th WSTA together wth ts physcal layer strategy phy determne the bt-error probablty of user on channel j whch s represented by e(snr,j, phy ) and s assumed ndependent and smlar for all bts. Then the packet-loss probablty for user over channel j wll be computed as: e,j (L, phy ) = 1 (1 e(snr,j, phy )) L (1) where L s the average packet sze of user n bts. We also assume that through a sngle SI, the changes n channel qualty are neglgble and therefore the SNR,j, =1,,M; j = 1,,N s constant over a certan SI. For OSAR networks that deploy smlar modulaton and codng schemes lke IEEE e networks, t can be shown [20] that the physcal-layer throughput of channel j can be approxmated by: R phy,j (SNR,j, phy )= Rphy max (phy ) (2) 1+e µ(snr,j δ)

5 FATTAHI et al.: MECHANISM-BASED RESOURCE ALLOCATION FOR MULTIMEDIA TRANSMISSION 605 where Rmax phy (phy ) s the maxmum achevable data rate for the physcal layer strategy phy and µ, δ are constants whose values for each modulaton and codng strategy phy can be determned as n [20]. We assume that each packet s retransmtted untl t s receved or ts deadlne s expred. Gven the modulaton, the maxmum number of retransmssons (ncludng the ntal transmsson) of packet v by user on channel j can be dynamcally computed as: T,j max (L,v) = R,j phy (tdelay (v) t trans (v)) (3) L where t delay (v) = mn{the deadlne of packet v, t SI } and t trans (v) s the expected tme that user begns the frst transmsson attempt of packet v. If a number of packets are ordered n the transmsson queue of user, then for the frst packet, t trans (v) s the current tme whle for the next packets the expected transmsson tmes of prevous packets should be accounted for (based on the average number of transmssons each packet takes untl successfully transmtted as n equaton (5) below and channel rate computed by equaton (2)). Then the probablty of successfully recevng these packets can smply be computed as [21]: P,j succ (s) = 1 [e,j (L, phy )] T max,j (L,v) (4) The average number of transmssons untl the packet s successfully transmtted, or the retransmssonlmt s reached, can be calculated as [21]: Ntr mean (phy,t,j max (L,v)) = 1 [e,j(l,phy )] T,j max (L,v) 1 e,j (L,phy ) (5) Hence, the average number of packets that can be correctly transmtted durng the tme t TXOP by user over channel j can be computed as p,j (t TXOP ): p,j (t TXOP ) = max{p t TXOP p 1 L Ntr mean (phy,t,j max (L,v k R phy (phy,snr,j ) ))}(6) k=1 n whch we smply counted the number of packets whch can be successfully transmtted before the current TXOP s over [7]. Fnally, the total number of packets that could on average be transmtted by user over all channels n one TXOP s equal to: p tot = N p,j (t TXOP ) (7) j=1 The above ntermedate parameters wll be used later to calculate the users utltes and the method to choose them s called lnk adaptaton and s dscussed n detal n [9]. The nternal strateges for our delay-senstve vdeo transmsson nclude modulaton and codng mode selecton at the PHY layer, adaptng the number of retransmssons at the MAC layer and adaptve packet schedulng at the APP layer (consult [13], [1] for more detals on the varous cross-layer strateges that can be deployed by the WSTAs and ther mpact on the resultng vdeo qualty). Hence, the nternal strateges determne the expected vdeo qualty at the recever sde as a functon of the allocated tme. Ths, n turn, determnes the prvate nformaton characterzng the utlty functon for each WSTA. These vectors of prvate nformaton wll be revealed to the CSM as the external strateges whch are descrbed n secton III-B. The form of the nformaton space s dscussed n sectons IV and V. In the next subsecton we ntroduce the external strateges of users. B. External Strateges After each user decdes about ts nternal strategy and calculates ts ntermedate parameters, t has to announce a functon of them to the CSM accordng to certan protocols defned n secton V. These protocols determne the form or space of the messages and consttute a consderable porton of the contrbutons of ths paper whch are dscussed rgorously n secton V. On the other hand, the role of external strateges s to determne the content of what s to be sent to the CSM such that the expected utlty gets maxmzed. Snce the network s assumed compettve and the resources are scarce, n general, there s no guarantee that users do not le about ther prvate nformaton n a way that leads to more payoff for them. However, as we show n secton V, the best external strategy for all users s to announce the true prvate nformaton; Hence, we say that our mechansm s ncentve compatble. Besdes, truthfulness s the domnant strategy regardless of what strategy other users take; In more techncal terms we say that announcng the truth, s mplemented n domnant strateges. Snce there s no reason for users to announce other than ther true prvate nformaton, we content our strategy analyss manly to nternal strateges. Ths fact leads to a very useful separaton prncple: At frst, each user s nterested n nternal strateges and afterwards, t has to decde, based on ts decson n frst stage, how to play the game. The fact that announcng the truth s the equlbrum of the game mplemented n domnant strateges, mples that further analyss of the external strateges s unnecessary. In the next secton we wll compute the expected utlty of a WSTA resultng from the tme allocaton vector on the network channels. IV. UTILITIES Gven the space of strateges of the WSTAs n the network, we wll dscuss the nature of the utlty functons that WSTAs and the CSM seek to separately maxmze. Ths paper s focused on vdeo applcatons and therefore, we assume that all users are nterested n transmttng vdeo data. However, the utlty and mechansm formulaton n the sequel, s general enough to make the CSM capable of handlng varous user types. The fact that we only defne the utlty functons for vdeo, s just for length lmts; The only expectaton from a user of any knd s that t calculates ts own utlty functon. On the other sde, the CSM even does not care about any specfc applcaton as long as each user announces some utlty values. A. Users Utltes The vector of allocated network tme to each user s a column vector of tmes, t R N, whch represents the tme

6 606 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 25, NO. 3, APRIL 2007 ntervals allocated to user on the N channels avalable n the network (Fgure 1). We also defne the collecton of the allocated tmes to all M users as an accumulated column vector of sze M N as t =[t T 1, tt 2,, tt M ]T R M N.In the followng we wll defne user s utlty as a functon of the vector of allocated tmes to all users, t.defnesze queue as the sze of the transmsson queue of the -th WSTA n packets. Next we defne the dscrete dstorton reducton functon of user as a functon of the number of transmtted packets, V : N {0} R +, as the followng: { 0 for n =0 V (n) = n k=1 q+k 1 for n>0 where q s the place-holder ndex of user whch ponts to the top of user s queue, q+k s the dstorton reducton of the packet n place q +k when q +k sze queue,and q+k =0 otherwse. Snce n ths paper we do not consder any temporal effects on the value of packets (.e. how close a packet s to ts deadlne), the correspondng value ndex (utlty) that s attached to each packet s assumed equal to the dstorton reducton resultng from that packet. Therefore the packet utlty, for each certan packet, s assumed fxed over tme. The dscrete dstorton reducton functon V (n) represents user s dstorton reducton resultng from successfully transmttng the frst n packets from ts transmsson queue. We proceed to defnng user s contnuous verson of the dstorton reducton functon,v cont : R + R +,as: V cont (η) = { V (η), for η nteger V (n +1)(η n) V (n)(η n 1), o.w. where n s nteger and n<η<n+1. The functon V cont s the lnearly-nterpolated verson of the orgnal V. Lemma 1: In the above setup f the dstorton reductons n user s transmsson queue are sorted n descendng order,.e., k k+1, = 1, 2,,M and k = 1, 2,,sze queue 1, then the contnuous dstorton reducton functon V cont (η) s concave n η over R +. Proof: Due to the fact that the dstorton reductons n the queue are sorted n descendng order, the functon V cont can alternatvely be expressed as the pont-wse mnmum of sze queue +1 affne functons over R + : V cont (η) = mn{l k (η),k = 1, 2,,szequeue +1} where the affne functons are defned as: l k (η) = (η k)[v (k) V (k 1)] + V (k), for k {1,,sze queue +1} (8) Hence V cont s concave n η over R + [22]. The next step s to state the utlty of each user drectly n terms of the allocated network resources, whch n ths case s transmsson tme. For an arbtrary vector w, we show ts j-th element by w(j). Based on the defntons of the parameters p,j and t SI,theeffectve number of packets that user can successfully transmt on average, usng tme vector t,s: NoP (t ) = N t (j) p,j t j=1 TXOP = α T t (9) where the column vector α R N s defned as α = 1 t TXOP [p,1,, p,n ] T. Hence, user s utlty functon U (t) :R M N R s defned as the expected dstorton reducton resultng from transmttng over the correspondng N channels n the allocated tmes as: U (t) = V cont (α T t ) (10) Note that the utlty functon of each user seems to depend only on user s strategy. However, the dependency of user s utlty on all other users strateges s mplct through the allocated tme t whch n turn s a drect functon of all users strateges. Fnally, the parameters, whch shape the utlty, and the parameters α are transmtted to the CSM n the mechansm desgn whch wll be dscussed n detal n secton V. functon V cont B. System Utlty Havng defned the utlty of every ndvdual user, we dscuss the utlty functon of the whole system. The goal of the CSM s n general dfferent from that of the ndvdual users. In ths paper, we propose a CSM whose goal s to maxmze the followng system utlty functon: U SY S (t) = M U (t) (11) =1 In other words, the CSM cares about the aggregate utlty of all users present n the network. The followng proposton paves the way for performng effcent maxmzaton of the U SY S (t) over t as wll be shown n the sequel: Proposton 2: The system utlty functon U SY S (t) as defned above s concave n the vector of tme allocatons t. Usng Lemma 1 and observng that α T t s a lnear functon of t, proves that each user s utlty functon U (t ) s concave n t. Therefore, by defnton, U SY S (t) s concave n t because t s the sum of M concave functons. In the next secton we wll synthesze a mechansm based on whch WSTAs and the CSM nteract n a way that the system utlty wll get maxmzed. V. MECHANISM DESIGN In ths secton we desgn a mechansm to moderate the network comprsed of selfsh users. The key problem for mechansm-based resource management s how the CSM should allocate the tme slots to users n an effcent and far way. Assumng that WSTAs announce correct nformaton, one could be optmstc that solvng some sort of optmzaton program over users utltes mght be feasble. Unfortunately, that s a nave assumpton because selfsh users by defnton am at mprovng ther own utlty. Hence, they are prone to le about ther nternal parameters to the CSM. The queston s thus how the penalty of a selfsh user should be desgned such that t refrans from requestng unnecessary transmsson tme? The basc tool to prevent the lyng/exaggeraton problem assocated wth selfsh users, deployed by a CSM, s the so-called mechansm from the game theory lterature [23], [24]. Generally speakng, a mechansm s a tool for

7 FATTAHI et al.: MECHANISM-BASED RESOURCE ALLOCATION FOR MULTIMEDIA TRANSMISSION 607 Fg. 2. The block dagram of the whole system over one SI. effcent resource management n cases where users are noncollaboratve and the nformaton s decentralzed. A mechansm has three man components: () The envronment whch n ths case s the source and channel characterstcs. The envronment can not be affected by the users or the CSM. () The message space whch descrbes the structure of the prvate nformaton to be exchanged by the users and the CSM. Ths choce plays a very mportant role n the resultng outcome of the mechansm and composes one of the key contrbutons of ths paper. For the problem n hand, t s rgorously defned n secton V-A.1. () The outcome correspondence whch determnes the outcome gven the messages from the users. The outcome for our problem s the vector of tme allocatons, t, and the vector of the transfers to be charged to all users, τ R M. The nformaton space together wth the outcome correspondence are decsve factors as to what propertes a certan mechansm possess. Determnng the outcome s rendered by the CSM whch does so based on the nformaton receved from WSTAs. Both t and τ are functons of the vectors of prvate nformaton or types, represented by θ,=1,,m, sent to the CSM from WSTAs. The transfers dscussed n ths paper could be monetary charges or other resources avalable at the WSTAs (e.g. computatonal resources). In the followng subsectons we formalze the arguments above. A. The Mechansm The goal of ths subsecton s to calculate the allocaton of TXOPs on all N channels to M users such that the system utlty, U SY S (t), becomes maxmzed. The followng three steps form the resource management mechansm whch take place at the begnnng of every servce nterval. Exchangng Informaton: Each user, transmts a vector of prvate nformaton θ, to the CSM. We represent the vector of all transmtted nformaton to the CSM by θ. Allocatng Tmes: The CSM decdes about the tme allocatons on all N channels n a way that maxmzes the system utlty U SY S. Computng Transfers: The CSM calculates the transfers to be charged to users to prevent them from lyng. Fgure 2 depcts the block dagram of the system. In the followng we descrbe the three phases. 1) Exchangng Informaton: We assume that the nformaton transmtted from user to the CSM at the begnnng of each SI s captured n the followng two vectors: δ and α defned as follows: The vector of vdeo dstorton reductons that would result from the successful transmsson of dfferent packets n user s transmsson queue of sze Q p tot : δ = [ q v,, q v +Q p tot 1] T R Q ptot. All packets are assumed to have the same delay constrant. The CSM sorts each vector of dstorton reducton n descendng order upon recept; The vector α of sze N as defned n secton IV. The content of the nformaton conveyed to the CSM s formed and sorted based on user s dscreton and crosslayer strategy; e.g. how to schedule the packets and calculate correspondng dstorton reductons n δ or how to calculate accurate parameters p,j and P,j succ s fully dependng on users dscreton. 2) Allocatng Tmes: The optmzaton program of the CSM, represented by [OPT({1,2,,M})], can be shown by: max U SY S (t) s.t. t (j) 0 (12) M =1 t (j) =t SI j =1,,N (13) where the optmzaton varables are t (j), =1, 2,,M and j =1, 2,, N whch represent the tme allocated to user on channel j. The objectve functon s the system utlty whch shows that, by defnton, the optmzaton s amed at maxmzng the aggregate utlty. Constrant (12) smply enforces nonnegatve allocated tmes whle constrant (13) enforces that the sum of allocated tmes on each channel equals the length of a servce nterval t SI. Usng proposton 2, the problem [OPT({1,2,,M})] s a convex optmzaton program whch could be solved very effcently [22]. We represent the soluton to the above optmzaton by t.wealso note that the optmzaton varables above are contnuous tmes on each channel. In realty, after solvng ths optmzaton, we wll round all allocated tmes to the closest nteger multple of t TXOP. In other words we approach the problem by solvng a convex relaxaton of the orgnal optmzaton whch s n the number of TXOPs and hence, non-convex. Ths approxmate approach s legtmate because of the followng two reasons: Frst, the dstorton reducton values are sorted n the decreasng order, and hence our pece-wse lnear relaxaton of the utlty functon s equvalent to ther convex hull. Second, the number of packets n the queue s generally of the order of tens or hundreds. Ths makes the relatve error ncurred, n case of consderng the convex relaxaton of the problem, very small. 3) Computng Transfers: The next task of the CSM s to compute and announce the vector of transfers. The dea s that each user s charged based on the amount of net utlty loss t causes other users. Formally, the CSM computes each transfer τ as follows: τ (θ) = k U k (t (θ)) max ˆt R N (M 1) k U k (ˆt), =1, 2,,M (14) The frst term s the sum of real utltes that other users are makng n presence of user. The second summaton however s the best aggregate utlty that others would have made, had not user been present at all. It s n fact the soluton to

8 608 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 25, NO. 3, APRIL 2007 For the current SI do: TABLE I THE RESOURCE ALLOCATION ALGORITHM 1) For every WSTA =1, 2,,M do Poll WSTA about ts prvate nformaton θ =[δ, α ]; 2) Compute the optmal tme allocaton by solvng [OPT({1,2,,M})] and calculate t 3) For every WSTA =1, 2,,M do Compute WSTA s transfer, τ, accordng to (14); 4) Announce tme allocatons, t, and transfers, τ, toallwstas. 5) Transmsson phase begns [OPT({1,, 1, +1,,M})]. The dfference, whch s always by constructon non-postve, s the transfer assocated wth user. Defnton: The mechansm n whch the nformaton exchange, decson on tme allocaton, and transfers are rendered accordng to the three steps descrbed above s called Clarke pvotal mechansm. There are two man reasons why we choose the Clarke mechansm. The frst reason s that the transfers are computed n a very ntutve way. The ntuton s that each user s beng penalzed for the nconvenence t causes to all other WSTAs. The second reason s that because τ 0 for =1, 2,,M, the transfers n ths mechansm are always n the form of charges and not ncentves and therefore the mechansm s always feasble n terms of transfers,.e. there wll be no need for outsde funds. The followng proposton shows why the Clarke pvotal mechansm leaves no ncentve for users to le about ther prvate nformaton. Frst defne θ as the vector of nformaton of all WSTAs except for user. Proposton 3: Assume that n our OSAR resource management problem, the Clarke pvotal mechansm s appled. Then no WSTA wll have any ncentve to le about ts real nformaton regardless of what other WSTAs announce. In other words, t s domnant strategy ncentve compatble. Proof: Let us assume t s not true. Then, f WSTA s real nformaton vector s represented by θ there should exst an nformaton vector ˆθ such that user receves more payoff by announcng ˆθ rather than the true nformaton θ.inother words, U (t (θ, ˆθ ), θ )+τ (θ, ˆθ ) > U (t (θ, θ ), θ )+τ (θ, θ ) (15) Replacng τ from (14), we get: U (t (θ, ˆθ ), θ )+ j U j (t (θ, ˆθ ), θ j ) > U (t (θ, θ ), θ )+ j U j (t (θ, θ ), θ j ) (16) whch s clearly a contradcton to the defnton of t. Hence, such ˆθ can not exst for any. Thus, we can predct that every ratonal WSTA wll announce the true nformaton. TABLE II USERS SPECIFICATIONS FOR SIMULATION 1 Rate Sequence Resoluton Channels SNRs User kpbs Foreman [24dB 24dB] User kpbs Foreman [24dB 24dB] B. Implementng the Mechansm In ths subsecton we wll focus on more practcal aspects of mplementng the Clarke pvotal mechansm. The algorthm n table I recaps the mplementaton of the algorthm. The frst step ncludes nformaton exchange between each user and the CSM. Analyzng the tradeoff between more granular nformaton and more overheads s the topc of our future research. The next steps n the algorthm are the computaton of the optmal tme allocaton and transfers. Ths amounts to solvng M +1 convex optmzaton programs. In the frst optmzaton, that fnds the optmal tme allocaton, there are MN varables, MN lnear nequaltes, and N lnear equaltes whle calculatng every transfer requres solvng an optmzaton program wth N(M 1) varables, N(M 1) nequaltes, and N equaltes. Usng an nteror-pont optmzaton method [22] wth a logarthmc barrer functon, the complexty of solvng such optmzaton programs s of order MN Newton teratons for an unconstraned convex optmzaton. Hence, the number of Newton teratons per SI s of order M MN. In a deeper analyss of the complexty of the mechansm, we also fnd the growth of the number of basc operatons per Newton teraton. Because of the very smple form of the equalty and nequalty constrants of the optmzaton program, whch are lnear and sparse, each Newton teraton takes basc operatons of order MN. VI. SIMULATION RESULTS In ths secton, we present our smulaton results. In order to acheve effcent streamng of vdeo over OSAR networks, the applcaton layer needs to accommodate nstantaneous bandwdth varatons due to tme-varyng channel condtons, network congeston, and/or the sudden emergence of prmary users. Non-scalable vdeo codng algorthms do not provde graceful degradaton and adaptablty to a large range of wreless channel condtons. Hence, although the concepts proposed n ths paper can potentally be deployed wth state-of-the-art non-scalable codng wth btstream swtchng, ths usually entals hgher complexty and smaller granularty for real-tme bandwdth adaptaton and packet prortzaton [25]. Consequently, n ths paper we use recently-proposed scalable vdeo codng schemes based on Moton Compensated Temporal Flterng (MCTF) usng wavelets [26]. Such a 3D wavelet vdeo compresson s attractve for wreless streamng applcatons snce t provdes on-the-fly adaptaton to channel condtons, support for a varety of wreless recevers wth dfferent resource capabltes and power constrants, and easy prortzaton of varous codng layers and vdeo packets. More detals about the deployed 3D wavelet vdeo coder can be found from [27].

9 FATTAHI et al.: MECHANISM-BASED RESOURCE ALLOCATION FOR MULTIMEDIA TRANSMISSION 609 TABLE III USERS AVERAGE EXPERIENCED PSNR FOR SIMULATION 1 User 1 User 2 Sum Ar-Far Tme 28.8dB 38.1dB 67.0dB Mechansm 33.8dB 36.4dB 70.2dB TABLE IV SIMULATION SETUP N M t SI t TXOP ms 10ms Fg. 3. Transmtted bts per GOP and PSNR for user 1 n the 2-user example. dfferent packets, ts performance s worse than our dynamc mechansm-based resource allocaton method. Partcularly, we consder the sudden drop n user 1 s PSNR below 10dB n ar-far, whch practcally causes frozen vdeo, at about frame number 160. The reason s that, due to sudden changes n vdeo, user 1 temporarly needs more rate at around frame 160. The comparson shows how our mechansm handles ths change dynamcally and smoothly whle ar-far tme fals offerng acceptable qualty of servce to user 1. The average experenced PSNRs of two users are reported n table III. Fg. 4. Transmtted bts per GOP and PSNR for user 2 n the 2-user example. A. A Smple Motvatng Example The frst smulaton, focuses on the comparson between the ar-far tme paradgm and our mechansm on a specfc OSAR network setup and ams at showng the ncapablty of the arfar paradgm to adapt dynamcally to users needs. Table II lsts the specfcatons of the 2 users present n the network. We assume that the network conssts of 2 autonomous WSTAs transmttng real-tme vdeo over 2 OSAR transmsson channels. We also assume t SI = 100ms and t TXOP =10ms. The sequences selected are CIF ( ) wth 288 frames at 30 frames per second. The packet deadlnes are assumed 533ms for all packets. We use a Group Of Pctures (GOP) structure wth 16 frames n each GOP, and a temporal decompostons wth 4 temporal levels. We assume that no user les about ts rate requrement. Fgures 3 and 4 depct the performance of the ar-far and Clarke mechansm. For reference, the graph for an deal case s also shown, whch corresponds to a case n whch there s no resource lmt and each WSTA can transmt at any arbtrary rate. The reported result s the nstantaneous experenced PSNR (Peak Sgnal-to-Nose Rato) and number of transmtted bts per GOP for each user. Snce the ar-far tme paradgm s a statc tme-allocaton method, whch does not take nto account the relatve mportance of B. More Users and Spectrum Aglty In the next smulatons, we consder a specfc OSAR network nfrastructure and quantfy the performance of varous resource management schemes: equal-tme, ar-far tme, and the proposed Clarke mechansm. We assume that the network conssts of 5 autonomous WSTAs transmttng real-tme vdeo over 2 OSAR transmsson channels. Other user and network specfcatons are the same as last smulaton unless otherwse stated. We consder two congeston scenaros: In the frst scenaro, the network s mldly congested,.e., the rato of the aggregate requred rate to the total avalable channel rate s close to 1, whle n the second scenaro, the network s more congested and the above rato s much larger than 1. The experenced SNRs on the two channels for all users vary between 18dB and 29dB. Tables IV and V show the specfcatons of the smulaton. Case I: In the frst smulaton, we compare the performances of the three above resource management paradgms when user 1 announces ts utlty exaggerated by 30%. In other words, WSTA 1 s not a ratonal user and devates from ts own optmal strategy. In ths case, WSTA 1 s penalzng other users by makng them receve less resources; e.g. user 2 s recevng an unacceptable vdeo qualty of less than 25dB n the ar-far case. Fgure 5 depcts the results. Ths undesrable penalty, s mtgated by the use of mechansm as compared wth the two other cases: The Equal-tme scenaro, s clearly not effcent especally for hgh-demandng users; e.g. users 4 and 5, whch need the largest amounts of resource, are allocated nsuffcent number of TXOPs and hence, they experence less than 24dB n the sense of PSNR. However, the proposed mechansm, performs much better than both aforementoned scenaros n whch all users receve close to 27dB or more n terms of PSNR. Ths s a result of the hgh level of the contentawareness of the CSM. Case II: In ths case, we focus only on our mechansm and analyze the effects of changes n varous assumptons that we

10 610 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 25, NO. 3, APRIL 2007 TABLE V USERS SPECIFICATIONS FOR SIMULATIONS 2,3,4, Rate Sequence Resoluton User kpbs Foreman User kpbs Foreman User kpbs Coastguard User kpbs Moble User kpbs Moble PSNR (db) PSNR (db) Ideal Mechansm User 5 Nave Strategy User 5 Erroneous Info User Number Fg. 6. Low Congeston Case: Comparng experenced average PSNR of users n cases of smple-strategy user and erroneous data user Ideal Ar Far Equal Tme Mechansm User Number Fg. 5. Hgh Congeston Case: Comparng experenced average PSNR for equal-tme, ar-far tme, and Clarke mechansm wth user 1 lyng. made about users. We generally assume the followng about the users: all users schedule ther packets n the decreasng order of dstorton reducton and they keep retransmttng a packet untl t s successfully receved or t s expred, and also users adjust ther modulaton scheme n the physcal layer based on channel condtons. The above assumptons state to what extent a user s capable of dong lnk adaptaton and takng the rght strategy n playng the resource allocaton game. We show through smulaton results that the more advanced a user can adapt ts strategy, the better vdeo qualty t can expect. Ths way the need for more advanced vdeo coders and cross-layer strategy s well-justfed. In the model we used, the mldly-congested network s chosen. Fgure 6 depcts the experenced PSNRs of all users. In one scenaro, user 5 has no packet schedulng, no retransmsson of unsuccessful packets, and deploys a fxed modulaton and codng schemes;.e., ths user s not smart compared to other WSTAs. From the graph t s clear that user 5 s dong worse than other users due to ts lack of good strategy; t s experencng more than 12dB loss n PSNR compared to the smarter strategy scenaro. In the same fgure we also show the results for another scenaro where user 5 suffers from a bad estmaton of channel SNRs. We smulated user 5 n a way that t always underestmates the qualty of channels by about 10dB. Ths defcency n ts nformaton about channels, results n flawed strateges and eventually consderable loss n the resultng PSNR whch s more than 2dB compared to the true channel nformaton. Case III: In the next set of smulatons we pck the hghly-congested network as opposed to the last case. In two cases, agan user 5 suffers from bad strategy, and flawed channel estmaton as n the prevous case. In the above two PSNR (db) Mechansm User 5 Nave Strategy User 5 Erroneous Info User 1 Exaggerates User Number Fg. 7. Hgh Congeston Case: Comparng experenced average PSNR of users n cases of smple-strategy user, erroneous data user, and exaggeratng user. scenaros, smlar to case II, user 5 loses about 6dB and 2dB, respectvely. Fgure 7 shows the results. In a thrd scenaro we assume that, even though the best external strategy for all users s to announce the real utlty, user 1 announces an exaggerated verson of ts expected dstorton reducton to the CSM; t always announces a constant number even when t has no packets to transmt. In ths scenaro, user 1 receves better PSNR whch s a reasonable observaton due to exaggerated announcements. Fgure 8 shows that however user 1 s experencng better PSNR, by payng more transfers, t s penalzed for the extra resource t s clamng. Accordng to proposton 3, the extra PSNR does not compensate the extra ncurred charges. Case IV: In ths scenaro, we consder a mldly-congested network where the specfcaton of the users and the network s the same as before (as shown n tables IV and V) except for users 1 and 2, whch now have hgher rate requrements,.e. ther requred rate equals 512kbps nstead of 384kbps. A more dynamc network stuaton s consdered here: the