Optimal Resource Allocation in Wireless Multiaccess Video Transmissions

Transcription

1 Optmal Resouce Allocaton n Weless Multaccess Vdeo Tansmssons Cong Shen and Mhaela van de Schaa Electcal Engneeng Depatment Unvesty of Calfona, Los Angeles Los Angeles, CA Emal: {congshen,mhaela@ee.ucla.edu Abstact We study the poblem of optmal esouce allocaton fo mult-use weless vdeo tansmssons fom an nfomatontheoetc pont of vew. We show that the pevously known optmal ate allocaton soluton n weless multaccess whch maxmzes the weghted sum ate s suboptmal n weless vdeo communcatons. We futhe deve the optmal vdeo esouce allocaton by jontly consdeng the Applcaton-MAC- PHY layes. Ths optmal scheme maxmzes the weghted sum vdeo qualty of all vdeo uses fo any feasble powe contol polcy. We efe to ths polcy as Lagest Qualty Impovement Hghest Possble Rate (LQIHPR). We popose a smple geedy algothm fo mplementaton. Wth the help of the nheent potzaton mechansm of vdeo codes, we show that LQIHPR s unvesally optmal fo all vdeo codng schemes. Smulaton esults demonstate the sgnfcant mpovement LQIHPR leads to as opposed to the conventonal one. I. INTRODUCTION It has been ntensvely agued that coss-laye esouce allocaton can lead to sgnfcant pefomance gans n weless netwoks [1]. Howeve, n most of the exstng woks, thee mpotant poblems have not been well addessed. 1) Most esouce allocaton focuses on the nteacton only among PHY, MAC and Netwok layes. Nevetheless, snce geneally hghe laye metcs such as the end-toend pefomance n the Applcaton (APP) laye ae the ultmate goal of the oveall system, solutons should also be deved dectly fo hghe-laye objectves. 2) The fundamental pefomance lmts have not been vey well studed. The queston of what s the pefomance lmt we can expect by esouce allocaton needs to be answeed. 3) Vdeo tansmsson n weless netwoks has emeged nto an mpotant applcaton. Due to the seveal unque chaactestcs of vdeo tansmsson such as hgh bandwdth, hgh data ate and dynamc delay constant, coss-laye esouce allocaton s a pomsng means to mpove the end-to-end pefomance n weless vdeo tansmssons [2]. Thee have been some woks addessng the afoementoned poblems. Fo example, thee ae some nfomaton-theoetc studes n the fundamental lmts of jont PHY, MAC and Netwok layes. Stablty and delay ssues of a multaccess channel wth andom packet avals have been studed n [3], [4]. The optmal esouce allocaton fo multaccess/boadcast fadng channels s addessed fom a combnaton of nfomaton theoy and queueng theoy n [5], [6]. Ths soluton s named Longest Queue Hghest Possble Rate (LQHPR). All these woks, although studyng the nfomaton-theoetc lmts, only dealt wth seveal lowe layes. On the othe hand, thee ae also many eseaches on cosslaye desgns fo multmeda weless communcatons. In [7], [8], scalable codng s combned wth adaptve modulaton and channel codng at the PHY laye to povde obust multmeda tansmsson. Coss-laye esouce allocaton fo effcent vdeo steamng ove weless netwoks can be found n [2], [9]. Nevetheless, t should be ponted out that whle many contbutons have been made to enhance the sepaate pefomance of the vaous OSI layes, o jontly fo the MAC and PHY o APP and Tanspot layes, no ntegated and ealstc coss-laye optmzaton famewok exsts to suppot effcent weless multmeda tansmsson. Also, the optmzaton has been pefomed n solaton at each ndvdual staton, and does not consde ts mpact on the oveall weless system. In ths pape, we wll focus on the poblem of optmal esouce allocaton fo multple vdeo uses fom an nfomaton-theoetc pont of vew. The novelty of ths wok s the followng. Fst, we explctly consde APP laye vdeo chaactestcs, whch eques a consdeably dffeent cosslaye optmzaton [10] [2]. Second, we take an nfomatontheoetc appoach n the esouce allocaton poblem. We use capacty egons as the lowe laye constants. Snce the capacty egon s the fundamental chaactezaton of the achevable ates, the solutons developed n ths pape povde the fundamental opeatonal lmt of achevable vdeo qualty n a multaccess fadng channel. We wll fst show that the pevous nfomaton-theoetc appoach whch maxmzes the weghted sum ate of all uses s suboptmal fom a vdeo pespectve. We then poceed to develop the optmal vdeo ate allocaton polcy 1. By adoptng a geneal opeatonal Qualty-Rate (Q-R) model fo vdeo codes, we dentfy the esouce allocaton scheme that maxmzes the weghted aggegate vdeo qualty of all vdeo uses fo any gven feasble powe contol polcy. We 1 Ths poblem has been patally consdeed n [11], but the study was only pelmnay and ncomplete /07/$ IEEE

2 tem the optmal polcy Lagest Qualty Impovement Hghest Possble Rate (LQIHPR). Ths polcy has a vey smple geedy algothm: tansmt an ncementally lage amount of vdeo bts/packets untl the capacty egon s eached. We wll explan the optmalty of the poposed polcy by utlzng the concept of bt steam potzaton. Also wth the help of potzaton, we ae able to ague that the optmalty of the poposed algothm does not depend on any specfc Q- R model beng adopted, but athe comes fom the essental vdeo chaactestcs. Thus, ths polcy s optmal fo all vdeo codes. The est of ths pape s oganzed as follows. Secton II defnes the system model fo coss-laye desgn. Secton III fomulates the poblem and addesses the suboptmalty of the conventonal polcy. In Secton IV we pesent the optmal esouce allocaton polcy togethe wth a smple mplementaton algothm. In ths secton we also show that the poposed polcy s optmal to any vdeo codes wth the nheent potzaton mechansm. Secton IV-C gves numecal esults to llustate the beneft of the poposedpolcy ove the conventonal one. Fnally, Secton V concludes the pape. Due to space lmtaton, we omt poofs n ths confeence pape. Inteested eades can efe to the jounal veson [12]. II. SYSTEM MODEL FOR CROSS-LAYER DESIGN In the PHY laye, we adopt the same model as n [5], [6], [13]. Specfcally, we consde an I-use Gaussan multaccess channel wth bandwdth W. The dscete-tme channel model used n ths pape s Y (n) = I H (n)x (n)+w(n) =1 whee X (n) and H (n) ae the tansmtted symbol and the flat-fadng pocess of use at tme n, espectvely. W (n) s the eceve addtve whte Gaussan nose (AWGN) wth vaance N 0 /2 pe dmenson. Each use s subjected to a longtem aveage powe constant: E[ X (n) 2 ] P. The tmevayng fadng pocesses {H (n), =1,,I ae assumed to be jontly statonay and egodc as well as symmetc [5], and the channel coheent tme s suffcently lage such that H can be consdeed constant ove a vey long block length. We futhe assume that the fadng pocesses of the uses ae ndependent of each othe. We consde the case whee both the eceve and the tansmttes know the channel state nfomaton (CSI) pefectly. Unde ths assumpton, both ends can be desgned to explot the beneft of CSI. Fo example, we can utlze ths nfomaton to pefom powe and ate allocaton n the MAC laye to optmze the system pefomance. Resouce allocaton s done by a cental contolle whch takes the jont fadng state h as an nput, and outputs the powe allocaton P(h) = (P 1 (h),,p I (h)) and ate allocaton R(h) = ( 1 (h),, I (h)). Fomally, a esouce allocaton polcy s a mappng f( ) fom the fadng state space H to R I + R I +:... Tansmtte 1 (P1(h),1(h)) Tansmtte 2 (P2(h),2(h))... Tansmtte I (PI(h),I(h)) (P(h), R(h)) h2(n)... h1(n) hi(n) Fg. 1. Cental Contolle w(n) System dagam. y(n) h Receve f(h) =(P(h), R(h)). The system dagam s shown n Fg. 1. In the Applcaton laye, all the I uses ntend to send vdeos to a common eceve. These vdeos could be ndependent o coelated. Fo compessng the vdeo, we adopt a stateof-the-at H.264 based vdeo code [14]. Howeve, note that ths code s smply used fo llustaton puposes and the poposed famewok can be appled usng any altenatve vdeo codng scheme (e.g. a hybd vdeo code such as MPEG-2, MPEG-4 o a 3D wavelet vdeo code). The vdeo code output wll dvde packets of each encoded vdeo steam nto seveal potes. We can detemne the poty classes by jontly consdeng the contbuton of the packets to the econstucted vdeo qualty and the delay deadlnes. Fo smplcty, we assume that all the packets coespondng to a specfc Goup Of Pctues (GOP) that ae n a cetan class have the same qualty contbuton and delay deadlne. We use the Peak Sgnal-to-Nose Rato (PSNR) as a measue of vdeo qualty, as ths s the only wdely accepted metc fo quantzng the vdeo qualty. The opeatonal Q-R model adopted s a wdely used one [15] whee fo use we use N lne segments wth slopes λ (k),k =1, 2,,N, each of whch coesponds to a ate nteval of length (k) : { 0, mn Q ( )= q (k) + λ (k) ( (k) ), (k) whee q = q mn, q (k),k > 1 s the connecton of two lne segments, and stats wth mn. Notce that as shown n [15], λ k λ k+1,.e., the slope deceases as ate nceases. Ths s a dect esult fom the potzaton of vdeo packets, as each (k) can coespond to a vdeo packet. Also we want to pont out that the specfc opeatonal Q-R model s not fundamental n devng the poposed optmal soluton, and that othe opeatonal Q-R models, such as the one n [16], could also be used. Instead t s the vdeo potzaton mechansm that s fundamental. Ths wll be llustated n Secton IV-B. III. PROBLEM FORMULATION AND PREVIOUS RESULTS Fom the nfomaton theoetc pont of vew, geneally t s of nteest to maxmze the weghted sum ate fom all uses [13], [17]. To be moe specfc, gven a jont fadng

3 state h = (h 1,,h I ), fo any feasble powe allocaton p(h) =(p 1 (h),,p I (h)), the queston s how to detemne the best opeaton pont n ths capacty egon C g (h, p(h)) that maxmzes the weghted sum ate: max µ s.t. C g (h, p(h)) whee µ s the weght vecto, P µ 0, and by defnng. C (S) = 1 2 (1+ log S hp(h) N 0 ), the MAC capacty egon s C g (h, p(h)) = { : (S) C (S), S {1,,I. Due to the polymatod popety of C g (h, p(h)), thesoluton to ths poblem s gven by one specfc vetex of C g (h, p(h)) whch coesponds to the same pemutaton π : µ π1 µ π2 µ πi [13]. We wll efe to ths soluton as the Sum-Rate-Maxmzng (SRM) polcy. An mpotant obsevaton hee s that SRM always opeates at one cone pont of the capacty egon, and thus successve decodng s suffcent to acheve ths vetex; thee s no need fo tme shang. The poblem consdeed n ths pape, howeve, ams at optmzng the Applcaton laye utlty functon (vdeo qualty). In othe wods, we focus on how to allocate the ate to dffeent uses such that the weghted aggegate vdeo qualty s maxmzed. Ths poblem can be fomally casted as max I w Q ( ) s.t. C g (h, p(h)), =1 whee w 0 s the weght coeffcent fo use. Note that the afoementoned soluton whch only consdes the lowe laye paametes s suboptmal fo vdeo applcatons. Ths s because that even f two uses have the same ate, the vdeo qualty mght dffe sgnfcantly. As an example, we use the state-of-the-at AVC/H.264 encode [14] to compess both Moble and Coastguad vdeos at CIF esoluton 30 Hz, and epot the qualty (PSNR) vs. ate n Fgue 2. Obvously, f two vdeos ae gven the same ate (say, 1500 kbts/s), the qualty wll not be the same (Moble has PSNR of appoxmately 33.1dB, whle Coastguad has aound 35.4dB). Thus, due to the nonlneaty of the Q-R model, SRM s not optmal n tems of vdeo qualty. In next secton we wll addess poblem n detals. IV. OPTIMAL RESOURCE ALLOCATION FOR WIRELESS VIDEO TRANSMISSIONS A. Lagest Qualty Impovement Hghest Possble Rate To solve poblem, fst we need to detemne n whch aea of the MAC capacty egon the optmal soluton s n. Fo ths, we cte the defnton of bounday suface fom [13, Defnton 3.9]. Defnton 1: The bounday suface of the MAC capacty egon C g (h, p(h)) s the set of ates such that no component can be nceased wth the othe components emanng fxed whle n the capacty egon. PSNR (db) Moble Coastguad Rate (kbt/s) Fg. 2. PSNR vs. ate usng AVC/H.264 encode fo Moble and Coastguad vdeos. The followng theoem gves the possble postons of the optmal opeaton pont wthn the MAC capacty egon. Theoem 1: The soluton to the optmzaton poblem must be at the bounday suface of the MAC capacty egon: I Cg { bs (h, p) = : = C ({1,,I), =1 (S) C (S), S {1,,I (6) The emanng poblem s how to fnd the opeaton pont at the bounday suface. We popose a smple geedy algothm to solve ths poblem. Fst, we can ncopoate the weght w nto the slopes of of each use s Q-R functon. Thus, wthout loss of genealty we assume all w to be equal to 1 fo the emanng of ths pape. Secondly, each use has ts own dsageement pont, whch s a mnmum qualty equement: { mn,q mn, =1,,I.Thssbasedon the obsevaton that below ths pont, the tansmsson esults n unacceptable vdeo qualty and hence, Q s set to be zeo. We assume that each use has an ndvdual ate lmt whch s lage than the mnmum ate equed n ts Q-R model : C ({) > mn. Ths s easonable because othewse we can allocate zeo ate to the use. The geneal algothm that solves poblem fo I uses s fully descbed n Algothm 1. We name ths algothm Lagest Qualty Impovement Hghest Possble Rate (LQIHPR), as we always ncease the ate of the use who has the lagest qualty mpovement wth the same ate ncease. The optmalty of Algothm 1 s poven n [12]. LQIHPR algothm s bette undestood f we look at a two-use example. Fom Theoem 1 the soluton to max 1, 2 Q 1 ( 1 ) + Q 2 ( 2 ) s.t. C g (h, p(h)) must le n the lne segment {( 1, 2 ): = C ({1, 2), C ({),=1, 2. By notcng that the slopes of each use s Q-R model ae monotoncally deceasng as ts ate nceases, a

4 Algothm 1 I-Use Geedy Rate Allocaton Algothm fo Lne-segment Q-R Models Input: C g (h,{ P) ; Use s Q-R model wth slope set λ, λ,, λ (N) and ate nteval set {,,, (N), =1,,I. Intalzaton: { Sot the slopes fom all uses I λ, λ,, λ (N) n descent ode and fom the =1 { odeed slope set Λ ode = λ (kj 1 ) j 1 λ (kj 2 ) j 2 { wth the coespondng ate nteval set ode =, (kj 1 ) j 1, (kj 2 ) j 2, ; Allocate use wth an ntal ate = mn, =1,,I. Repeat: 1) Select the fst avalable slope λ (k) j fom the odeed slope set Λ ode, and detemne the coespondng use j; 2) Incease the ate j of use j untl the ate nteval (k) j s fulflled, o any ate lmt s eached; 3) Delete λ (k) j / (k) j fom sets Λ ode / ode. In case that any ate lmt s eached, delete all emanng slopes/ate ntevals assocated wth the coespondng use(s) fom sets Λ ode / ode. Untl: Λ ode / ode s empty, o the oveall I-use sum ate lmt s eached. Retun: =( 1,, I ). typcal { odeed slope set Λ ode could be Λ ode = λ 1 λ 2 λ 2 λ 1, and the assocated ate { nteval set s ode = 1, 2, 2, 1,. Fgue 3 gves two examples showng how the geedy ate allocaton s pefomed based on the stuaton descbed n the pevous paagaph. Rate s allocated to uses accodng to the slopes odeng. In example Fgue 3 (a), use 1 and 2 ncease the ate n the ode of 1, 2, 2, 1, 2 untl use 1 fst stops at ts ndvdual maxmum ate C ({1), and then use 2 contnues beng allocated moe ate untl the maxmum sum ate lmt C ({1, 2) s eached. The example n Fgue 3 (b) shows anothe possblty that nethe use s ndvdual ate lmt s eached, but the sum ate lmt C ({1, 2) s met. In ths stuaton the optmal opeaton pont s not at any vetex. Agan ths demonstates that the conventonal SRM polcy whch opeates at one vetex s suboptmal n vdeo tansmssons. Snce LQIHPR and SRM geneally opeate at dffeent ponts n the capacty egon bounday suface, the methods to acheve them ae also dffeent. As we have mentoned befoe, to maxmze the sum ate one has to opeate at a specfc cone pont of the capacty egon, and successve decodng can acheve the coespondng ate pa. In LQIHPR we geneally opeate wthn the bounday suface, whch means tme shang s necessay. B. Unvesal optmalty of LQIHPR fom vdeo potzaton At ths moment t seems that the optmalty of the LQIHPR polcy depends on the lne-segment Q-R model. Howeve, we ague that the optmalty s not dependng on any specfc Q-R model beng used, but athe ognates fom the essental vdeo chaactestcs whee cetan bts/packets ae moe mpotant than othes, and that potzaton mechansm s deployed. One dect example wll be to change the Q-R model to anothe vey popula one [16]: ( ) D() = θ 0 + d 0,Q() =10log D() whee D() s the Mean-Squae-Eo (MSE) as a functon of ate, andθ, 0,d 0 ae known paametes. It t easy to see that ths s a contnuous Q-R functon wth a contnuously deceasng slope. We can show that a slghtly modfed LQIHPR polcy [12] s optmal fo ths model by a smla agument. Due to the space lmtaton we wll not dscuss the detal on LQIHPR fo geneal Q-R models. Inteested eades can efe to [12]. The key eason that makes the LQIHPR polcy unvesally optmal s the monotoncally deceasng slope popety of the Q-R model. It s mpotant to notce that all the vdeo codes desgned so fa, wthout consdeng any esouce allocaton ssues, geneate a Q-R functon wth deceasng slopes by bts/packets potzaton. Fo moe nfomaton on vaous potzaton schemes fo hybd vdeo codes and wavelet codes, the eade s efeed to [18] and [19], espectvely. As the ganulaty of the vdeo packets becomes fne and fne, the oveall Q-R functon becomes moe smooth. Ideally, we wll have a contnuous Q-R functon: the ate of vdeo code can be made nceasng contnuously and ts qualty wll also ncease contnuously, and due to potzng bts/packets accodng to the descent mpact on the oveall vdeo qualty, the ncease of qualty wll become smalle as the ate nceases. Ths dectly tanslates to an eve deceasng slope n the Q-R functon. Mathematcally, the LQIHPR polcy s optmal as long as the functon Q() s contnuous (o has a fnte set of dscontnuous ponts) wth nonnceasng slopes. Fotunately, all vdeo codes beng used nowadays satsfy these equements, and thus the optmalty of LQIHPR s unvesal to all vdeo codng schemes. C. Numecal Examples In ode to access the pefomance dffeence between the SRM polcy and the optmal LQIHPR, we povde the followng fou sets of smulatons. The esults ae summazed n Table I and II. We fst smulate a two-use Raylegh fadng symmetc multaccess channel wth aveage channel powe 1. Each use s assumed to have an aveage eceve SNR of 10 db and bandwdth 1 MHz. Ths bandwdth s used thoughout ths secton. Use 1 wants to tansmt the Moble vdeo, whle use 2hastheCoastguad vdeo fo tansmsson (the same settng as n Fgue 2) 2. AVC/H.264 encode s used thoughout all 2 The vdeos used thoughout all smulatons ae standad ones n vdeo codng communty. All vdeos have CIF esoluton 30 Hz. (7)

5 Qualty Qualty Use 1 Use 1 Use 1 maxmum ate eached Use 1,2 maxmum sum ate eached Use 1,2 maxmum sum ate eached Use 2 Use 1,2 maxmum sum ate eached Use 2 mn,2 mn,1 C ({1) C ({2) C ({1, 2) Rate mn,2 mn,1 C ({1) C ({2) C ({1, 2) Rate (QUIT) 4 4 X X (a) (QUIT) X X X X (b) Fg. 3. Two examples llustatng the Geedy Rate Allocaton Algothm. (a) ndvdual ate lmt s eached; (b) sum ate lmt s eached. In the table below each plot, the fst ow shows the slop odeng, and the second ow ndcates the deleton odeng as n Step 3 of Algothm 1. Hee C (S) means the sum ate constant fo the ente set S s tght. TABLE I SIMULATION RESULTS FOR TWO-USER FADING MULTIACCESS. PSNR IN DB AND RATE IN MBPS. Polcy sum PSNR PSNR 1 PSNR 2 sum ate ate 1 ate 2 Symmetc MAC LQIHPR SRM Asymmetc MAC LQIHPR SRM TABLE II SIMULATION RESULTS FOR THREE-USER FADING MAC. PSNR IN DB AND RATE IN MBPS. Symmetc MAC Asymmetc MAC Polcy sum PSNR PSNR 1 PSNR 2 PSNR 3 sum ate ate 1 ate 2 ate 3 LQIHPR SRM LQIHPR SRM smulatons. LQIHPR s mplemented wth all weghts equal to 1 and compaed wth SRM. As we have poved, each exteme pont of the MAC capacty egon s an optmal soluton of SRM fo cetan weghts. We smply choose one out of all the I! exteme ponts whch gves the lagest sum of vdeo qualtes. Notce that ths s the hghest sum vdeo qualty SRM can povde. Smulaton shows that the LQIHPR polcy, whch ams at maxmzng the sum qualty, has an aveage sum PSNR of 71.8 db, whle the SRM polcy only povdes 69.3 db: thee s an appoxmately 2.5 db aveage qualty gan n ths smulaton settng. It s nteestng to exploe how the SRM polcy esults n such a suboptmal vdeo pefomance. SRM always opeates at one exteme pont, whee only one use gets ts maxmum ate, and thus ts best possble vdeo qualty. Howeve, ths selfsh allocaton leaves vey small oom fo the othe use to ncease ts qualty. Heustcally, f the fst use can gve some ate to the second one wthout deceasng the sum ate, the fst use mght expeence vey lmted qualty dop, but at the same tme the vdeo qualty of the second use mght ncease sgnfcantly due to the nonlnea elatonshp between ate and qualty, and thus the sum of vdeo qualtes can be nceased. The second smulaton has the same envonment as the fst one, except that the channels ae asymmetc. We assume that use 1 has an aveage eceve SNR of 10 db, whle use 2 has 15 db. Ths models the stuaton whee one use has a bette channel than the othe, possbly due to the nea-fa effect. In ths smulaton, SRM gves an aveage PSNR of 66.5 db, and

6 LQIHPR povdes 73.9 db. Thee s a 7.4 db pefomance dffeence. It can be noted that n ths asymmetc stuaton the beneft of LQIHPR s even lage, whch can be explaned as followng. The fact that use 2 has hghe eceve SNR means use 2 wll typcally have a bette channel than use 1. Tanslatng nto the MAC capacty egon, the ate of use 2 s much lage than that of use 1 at the bounday suface. In ths egon, typcally the vdeo qualty of use 2 has aleady satuated, whle use 1 may opeates aound ts mnmum atequalty pont such that ts vdeo qualty can be sgnfcantly mpoved by a vey small ate ncease. In othe wods, the same ate s much moe mpotant to use 1 than to use 2 n tems of vdeo qualty. Also notce that f use 1 cannot get enough ate to pass ts mnmum ate-qualty pont, the qualty s zeo. SRM opeates at the exteme pont whee the ate of use 2 s maxmzed, whle LQIHPR, by notcng the fact that ate s moe mpotant to use 1 than to use 2, deceases the ate of use 2 and allocates t to use 1, and maxmzes the sum of vdeo qualtes. The thd and fouth smulatons nclude thee uses. Use 1 and 2, same as n the fst smulaton, want to tansmt the Moble and Coastguad vdeos, espectvely. Use 3 has a dffeent vdeo Stefan fo tansmsson. In the thd smulaton we smulate a Raylegh fadng symmetc multaccess channel, wth the same paametes as n the fst smulaton. LQIHPR esults n an aveage sum PSNR of db, whle SRM gves db. The last smulaton ncludes a thee use asymmetc Raylegh fadng multaccess channel. Use 1 has an aveage eceve SNR 15 db, whle use 2 and 3 has 18 and 13 db, espectvely. The othe paametes ae the same as befoe. In ths settng LQIHPR gves an aveage sum PSNR db, compaed wth db fom SRM. V. CONCLUSION In ths pape, we addess the poblem of mult-use vdeo tansmsson ove a weless multaccess fadng channel. We show how the MAC laye esouce allocaton should be pefomed by jontly consdeng the APP-MAC-PHY layes. 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