Transmitting important bits and sailing high radio waves: a decentralized cross-layer approach to cooperative video transmission

Transcription

1 Transmiing imporan bis and sailing high radio waves: a decenralized cross-layer approach o cooperaive video ransmission 1 Nicholas Masronarde, Francesco Verde, Donaella Darsena, Anna Scaglione, and Mihaela van der Schaar Absrac We invesigae he impac of cooperaive relaying on uplink and downlink muli-user (MU) wireless video ransmissions. The objecive is o maximize he long-erm sum of uiliies across he video erminals in a decenralized fashion, by joinly opimizing he packe scheduling, he resource allocaion, and he cooperaion decisions, under he assumpion ha some nodes are willing o ac as cooperaive relays. A pricing-based disribued resource allocaion framework is adoped, where he price reflecs he expeced fuure congesion in he nework. Specifically, we formulae he wireless video ransmission problem as an MU Markov decision process (MDP) ha explicily considers he cooperaion a he physical layer and he medium access conrol sublayer, he video users heerogeneous raffic characerisics, he dynamically varying nework condiions, and he coupling among he users ransmission sraegies across ime due o he shared wireless resource. Alhough MDPs nooriously suffer from he curse of dimensionaliy, our sudy shows ha, wih appropriae simplicaions and approximaions, he complexiy of he MU-MDP can be significanly miigaed. Our simulaion resuls demonsrae ha inegraing cooperaive decisions ino he MU-MDP opimizaion can increase he resource price in neworks ha only suppor low ransmission raes and can decrease he price in neworks ha suppor high ransmission raes. Addiionally, our resuls show ha cooperaion allows users wih feeble direc signals o achieve improvemens in video qualiy on he order of 5 10 db peak signal-o-noise raio (PSNR), wih less han 0.8 db qualiy loss by users wih srong direc signals, and wih a moderae increase in oal nework energy consumpion ha is significanly less han he energy ha a disan node would require o achieve an equivalen PSNR wihou exploiing cooperaive diversiy. Index Terms Cooperaive communicaions, cross-layer opimizaion, decode-and-forward relaying, Markov decision process (MDP), muli-user scheduling, resource allocaion, wireless video ransmission. I. INTRODUCTION Exising wireless neworks provide dynamically varying resources wih only limied suppor for he Qualiy of Service (QoS) required by delay-sensiive, bandwidh-inense, and loss-oleran mulimedia applicaions. This problem N. Masronarde is wih he Deparmen of Elecrical Engineering, Sae Universiy of New York a Buffalo, Buffalo, NY 14260, USA ( nmasron@buffalo.edu). This work was done while he was a he Universiy of California a Los Angeles (UCLA), Los Angeles, CA , USA. M. van der Schaar is wih he Deparmen of Elecrical Engineering, Universiy of California a Los Angeles (UCLA), Los Angeles, CA , USA ( mihaela@ee.ucla.edu). F. Verde is wih he Deparmen of Biomedical, Elecronic and Telecommunicaion Engineering, Universiy Federico II, Naples I-80125, Ialy ( f.verde@unina.i). D. Darsena is wih he Deparmen for Technologies, Parhenope Universiy, Naples I-80143, Ialy ( darsena@uniparhenope.i) A. Scaglione is wih he Deparmen of Elecrical and Compuer Engineering, Universiy of California, Davis, CA , USA ( ascaglione@ucdavis.edu). The work of N. Masronarde and M. van der Schaar was suppored in par by NSF gran no Augus 30, 2011

2 2 is furher exacerbaed in muli-user (MU) seings because hey require muliple video sreams, wih heerogeneous raffic characerisics, o share he scarce wireless resources. To address hese challenges, a lo of research has focused on MU wireless communicaion [1], [2], [3], [4], [5] and, in paricular, MU video sreaming over wireless neworks [6], [7], [8], [9], [10]. The majoriy of his research relies on cross-layer adapaion o mach available sysem resources (e.g., bandwidh, power, or ransmission ime) o applicaion requiremens (e.g., delay or source rae), and vice versa. In MU video sreaming applicaions [6], [7], [8], [9], [10], for example, cross-layer opimizaion is deployed o srike a balance beween scheduling lucky users who experience very good fades, and serving users who have he highes prioriy video daa o ransmi. This radeoff is imporan because rewarding a few lucky paricipans, as opporunisic muliple access policies do [2], [3], [4], does no ranslae o providing good qualiy o he applicaion (APP) layer. Unforunaely, wih he excepion of [5], [11], he aforemenioned research assumes ha wireless users are noncooperaive. This leads o a basic inefficiency in he way ha he nework resources are assigned: indeed, good fades experienced by some nodes can go o wase because users wih higher prioriy video daa, bu worse fades, ge access o he shared wireless channel. A way o no le good fades go o wase is o enlis he nodes ha experience good fades as cooperaive helpers, using a number of echniques available for cooperaive coding [12], [13], [14]. As menioned above, his idea has been considered in [5], [11]. In [11], for example, a cross-layer opimizaion is proposed involving he physical (PHY) layer, he medium access conrol (MAC) sublayer, and he APP layer, where layered video coding is inegraed wih randomized cooperaion o enable efficien video mulicas in a cooperaive wireless nework. However, because i is a mulicas sysem, here is no need for an opimal muliple-access sraegy, and no need o worry abou heerogeneous raffic characerisics. In [5], a cenralized nework uiliy maximizaion (NUM) framework is proposed for joinly opimizing relay sraegies and resource allocaions in a cooperaive orhogonal frequency-division muliple-access (OFDMA) nework. In boh [5], [11], i is assumed ha each user has a saic uiliy funcion of he average ransmission rae, where he uiliy derived by each user in [11] is a funcion of he average received rae of he base and enhancemen layer video bisreams. Unlike he aforemenioned soluions, we ake a dynamic opimizaion approach o he cooperaive MU video sreaming problem. In paricular, unlike [5], [11], he soluion ha we adop explicily considers packe-level video raffic characerisics (insead of flow-level) and dynamic nework condiions (insead of average case condiions). Our soluion is inspired by he cross-layer resource allocaion and scheduling soluion in [10], in which he MU wireless Augus 30, 2011

3 3 video sreaming problem is modeled and solved as an MU Markov decision process (MDP) ha allows he users, via a uniform resource pricing soluion, o obain long-erm opimal video qualiy in a disribued fashion. However, alhough we use he raffic model and dual decomposiion proposed in [10], cooperaion renders our PHY/MAC model compleely differen from ha sudied in [10], hus opening addiional research issues wih respec o [10], such as how he cooperaion decision should be made, wha is he impac of cooperaion on he resource price, and wha is he impac of cooperaion on he oal nework energy consumpion. Moreover, as recenly shown in [15], augmening he framework developed in [10] o also accoun for cooperaion is challenging because of he complexiy of he resuling cross-layer MU-MDP opimizaion. The conribuions of his paper are fourfold. Firs, we formulae he cooperaive wireless video ransmission problem as an MU-MDP using a ime-division muliple-access (TDMA)-like nework, randomized space-ime block coding (STBC) [16], and a decode-and-forward cooperaion sraegy. To he bes of our knowledge, we are he firs o consider cooperaion in a dynamic opimizaion framework. We show analyically ha he decision o cooperae can be made opporunisically, independenly of he MU-MDP. Consequenly, each user can deermine is opimal scheduling policy by only keeping rack of is experienced cooperaive ransmission raes, raher han racking he channel saisics hroughou he nework. Second, in ligh of he fac ha opporunisic cooperaion is opimal, we propose a low complexiy opporunisic cooperaive sraegy for exploiing good fades in an MU wireless nework. The key idea is ha nodes can, in a disribued manner, self-selec hemselves o ac as cooperaive relays. The proposed self-selecion sraegy requires a number of message exchanges ha is linear in he number of video sources, and selecs ses of cooperaive relays in such a way ha cooperaion can be guaraneed o be beer han direc ransmission. Third, we show experimenally ha users wih feeble direc signals o he access poin (AP) are conservaive in heir resource usage when cooperaion is disabled. In conras, when cooperaion is enabled, users wih feeble direc signals o he AP use cooperaive relays and uilize resources more aggressively. Consequenly, he uniform resource price ha is designed o manage resources in he nework ends o increase when cooperaion is enabled in a nework ha only suppors low ransmission raes, bu ends o decrease when i is enabled in a nework ha suppors high ransmission raes. Fourh, we sudy he impac of cooperaion on he oal nework energy consumpion. We show ha he increased ransmission rae afforded by cooperaion requires an increase in oal nework energy relaive o he lower rae direc ransmission; however, his increase is moderae compared o he amoun of power required o ransmi direcly o he access poin a a ransmission rae equivalen o he cooperaive rae. Augus 30, 2011

4 4 The remainder of he paper is organized as follows. We inroduce he sysem and applicaion models in Secion II. In Secion III, we provide expressions for he ransmission rae, packe error rae, and nework energy consumpion in boh direc and cooperaive ransmission modes. In Secion IV, we presen he proposed MU crosslayer PHY/MAC/APP opimizaion. In Secion V, we propose a disribued proocol for opporunisically recruiing cooperaive relays. Finally, we repor numerical resuls in Secion VI and conclude in Secion VII. II. SYSTEM MODEL We consider a nework composed of M users sreaming video conen over a shared wireless channel o a single AP (see Fig. 1). Such a scenario is ypical of many uplink media applicaions, such as remoe monioring and surveillance, wireless video sensors, and mobile video cameras. The proposed opimizaion framework can also be used for downlink applicaions, where he relays can be recruied for sreaming video o a cerain user in he nework in exacly he same way ha hey can be recruied o ransmi o he AP in he uplink scenario. In Subsecion II-A, we inroduce he MAC and PHY layer models. Then, in Subsecion II-B, we describe he deployed APP layer model. A. MAC and PHY layer models We assume ha ime is sloed ino discree ime-inervals of lengh R > 0 seconds and each ime slo is indexed by N. 1 A he MAC sublayer, he users access he shared channel using a TDMA-like proocol. In each ime slo, he AP endows he ih user, for i {1, 2,, M}, wih he resource fracion x i, where 0 x i 1, such ha he user can use he amoun of channel ime R x i for ransmission. Le x (x 1, x 2,..., x M ) T R M denoe he resource allocaion vecor a ime slo, which mus saisfy he sage resource consrain x 1 = M i=1 xi 1, where he inequaliy accouns for possible signaling overhead. Each node s PHY layer is assumed o be a single-carrier single-inpu single-oupu sysem designed o handle quadraure ampliude modulaion (QAM) square consellaions, wih a (fixed) symbol rae of 1/T s symbols per second. The PHY layer can suppor a se of N + 1 daa raes β n b n /T s (bis/second), where b n log 2 (M n ) is he number of bis ha are sen every symbol period, wih n {0, 1,..., N}, and M n is he number of signals in 1 The fields of complex, real, and nonnegaive ineger numbers are denoed wih C, R, and N, respecively; marices [vecors] are denoed wih upper [lower] case boldface leers (e.g., A or x); he field of m n complex [real] marices is denoed as C m n [R m n ], wih C m [R m ] used as a shorhand for C m 1 [R m 1 ]; he superscrip T denoes he ranspose of a vecor; denoes he magniude of a complex number; x 1 is he l 1 norm of he vecor x C n, which for posiive real-valued vecors is simply he sum of he componens, whereas x 2 is he Euclidean norm of x C n ; {A} ij indicaes he (i + 1, j + 1)h elemen of he marix A C m n, wih i {0, 1,..., m 1} and j {0, 1,..., n 1}; a circular symmeric complex Gaussian random variable X wih mean µ and variance σ 2 is denoed as X CN (µ, σ 2 ); and denoe flooring- and ceiling-ineger, respecively; E[ ] sands for ensemble averaging; and, finally, [ ] + = max(, 0). Augus 30, 2011

5 5 he QAM consellaion. Hence, β 0 β 1 β N form he basic rae se B and β 0 is he base rae a which he nodes exchange conrol messages. Le d n be he minimum disance of he M n -QAM consellaion, he average ransmier energy per symbol is given by ( ) E s d 2 Mn 1 n 6 (Joules), (II.1) which is assumed o be fixed for all he nodes and daa raes, i.e., i does no depend on he indices i and n. Consequenly, he average power per symbol expended by each ransmier is P s E s /T s (Was). We consider a frequency non-selecive block fading model, where h il C denoes he fading coefficien over he i l link in ime slo, wih i l {0, 1,..., M}, and i = 0 or l = 0 corresponding o he AP. I is assumed ha all he channels are dual, i.e., h il = h li, and ha he fading coefficiens h il are independen and idenically disribued (i.i.d.) wih respec o. Moreover, we define H C M M as he marix collecing he fading coefficiens among all of he nodes and he AP, i.e., {H } il = h il, for i l {0, 1,..., M}. A he PHY layer, here are wo ransmission modes o choose from: direc and cooperaive. In he direc ransmission mode, as shown in Fig. 1, he ih source node ransmis direcly o he AP a he daa rae β i0 B (bis/second) for he assigned ransmission ime of R x i seconds. In he cooperaive ransmission mode, some nodes serve as decode-and-forward relays. Specifically, in he cooperaive mode, he assigned ransmission ime is divided ino wo phases as illusraed in Fig. 1: in Phase I, he ih source node direcly broadcass is own daa o all he nodes in he nework a he daa rae β i,1 B for R ρ i x i seconds, where 0 < ρ i < 1 is he Phase I ime fracion; in Phase II, some of he nodes overhearing he source ransmission, belonging o a cerain subse C i {1, 2,..., M} {i}, demodulae he daa received in Phase I, re-modulae he original source bis, and hen cooperaively ransmi owards he AP, along wih he original source i, a he daa rae β i,2 sequel, we denoe wih β i,coop B for he remaining R (1 ρ i ) x i seconds. In he (bis/second) he cooperaive daa rae over he wo phases, i.e., he amoun of bis ha are ransmied in a single phase divided by he overall lengh of he wo phases, which depends on he daa raes β i,1 and β i,2 aainable in each of he wo hops. The decision o ransmi in he direc or cooperaive ransmission mode depends on fading coefficiens hroughou he nework in ime slo and on he arge packe error rae (PER). Thus, he acual ransmission rae of he ih source in ime slo is dicaed by he cooperaion decision z i {0, 1}, where z i = 1 if cooperaion is chosen, and z i = 0 if direc ransmission is chosen. In Secion III, we compue he ransmission parameers β i0 and β i,coop as funcions of a subse of he enries in H, as well as he ime fracion ρ i, Augus 30, 2011

6 6 and, in Secion V, we describe how o deermine he se of cooperaive relays C i and he cooperaion decision z. i B. APP layer model and packe scheduling The source raffic can be modeled using any Markovian raffic model (e.g. [10], [19]). However, o accuraely capure he characerisics of he video packes, we adop he sophisicaed video raffic model proposed in [10], which accouns for he fac ha video packes have differen deadlines, disorion impacs, and source-coding dependencies (whereas he model in [19] does no consider hese characerisics). In his secion, we describe he key feaures of his model, bu because he problem formulaion and novely of his paper do no depend on he deployed raffic model (so long as he model is Markovian), we refer he ineresed reader o [10] for complee deails. For i {1, 2,..., M}, he raffic sae T i {F i, b i } represens he video daa ha he ih user can poenially ransmi in ime slo, and comprises he following wo componens: he schedulable frame se F i and he buffer sae b i. In ime slo, we assume ha he ih user can ransmi packes belonging o he se of video frames F i whose deadlines are wihin he scheduling ime window (STW) [, + W ]. The buffer sae b i (b i,j j F i ) T represens he number of packes of each frame in he STW ha are awaiing ransmission a ime. The jh componen b i,j of b i denoes he number of packes of frame j F i remaining for ransmission a ime. We assume ha each packe has size P bis. Fig. 2 illusraes how he raffic saes are defined for a simple IBPB GOP srucure. 2 We now define he packe scheduling acion. In each ime slo, he ih user akes scheduling acion y i (y i,j j F i ) T, which deermines he number of packes o ransmi ou of b i. Specifically, he jh componen y i,j of y i represens he number of packes of he jh frame wihin he STW ha are scheduled o be ransmied in ime slo. Imporanly, he scheduling acion y i is consrained o be in he feasible scheduling acion se P i (T i, β i ), which depends on he raffic sae T i and he ransmission rae suppored by he PHY layer β i. In paricular, he following hree consrains mus be me: 1) Buffer: Every componen of y i mus saisfy 0 y i,j bi,j. 2) Packe: The oal number of ransmied packes mus saisfy y i 1 = j F i yi,j R βi P, where βi = β i0 in he direc ransmission mode, i.e., when z i = 0, and β i = β i,coop in he cooperaive ransmission mode, i.e., when 2 In a ypical hybrid video coder like H.264/AVC or MPEG-2, I, P, and B indicae he ype of moion predicion used o exploi emporal correlaions beween video frames. I-frames are compressed independenly of he oher frames, P-frames are prediced from previous frames, and B-frames are prediced from previous and fuure frames. Augus 30, 2011

7 7 z i = 1. Noe ha β i depends on a subse of he elemens in H as described laer in Secion III. 3 3) Dependency: If here exiss a frame k ha has no been ransmied, and frame j depends on frame k (denoed ( ) by k j), hen b i,k yi,k y,j i = 0. In oher words, all packes associaed wih k mus be ransmied before ransmiing any packes associaed wih j. The sequence of raffic saes {T i : N} can be modeled as a conrollable Markov chain wih ransiion probabiliy funcion p(t i +1 T i, y i ). III. COOPERATIVE PHY LAYER TRANSMISSION In his subsecion, wih reference o he uplink scenario, we describe how he direc ransmission rae β i0 cooperaive ransmission rae β i,coop depend on a subse of he elemens in he channel sae marix H. Le us firs consider he direc i l link wih insananeous channel gain h il and daa rae β il and he B (bis/second) corruped by addiive whie Gaussian noise. The bi error probabiliy (BEP) P il (h il, β il ) a he oupu of he maximum likelihood (ML) deecor of node l, under he assumpion ha a Gray code is used o map he informaion bis ino QAM symbols and he signal-o-noise raio (SNR) is sufficienly high, can be upper bounded as (see [20]) [ ] P il (h il, β il ) 4 exp 3 γ hil 2 2 ( ), (III.1) 2 βil T s 1 where γ Es N 0 is he average SNR per symbol expended by he ransmier and N 0 is he noise power specral densiy. Each direc ransmission is subjec o a PER hreshold a he MAC sublayer, which leads o a BEP consrain P il (h il, β il ) BEP a he PHY layer. Consequenly, he achievable daa rae β il under he BEP consrain is The daa rae β i0 β il = 1 T s log 2 ( 1 + Γ h il 2), where Γ 3 γ 2 ( BEP loge 4 ). (III.2) over he link beween he source and he AP is obained using (III.2) by seing l = 0. In his case, he number of symbols required o ransmi a packe of P bis is equal o K i0 P/(β i0 T s ). Thus, neglecing receive and processing energy consumpion, he energy required for a direc ransmission of one packe is equal o E i0 K i0 E s = P E s β i0 = P P s T s β i0 (Joules). (III.3) I is worh noing ha he energy expended in direc mode is inversely proporional o he achievable daa rae β i0. 3 We do no include x i in he packe consrain y i 1 = j F i yi,j R βi P because x i is no known a he ime he scheduling decision y i 1 (see (IV.5)). y i is deermined. Once he scheduling decision is deermined, he resource allocaion x i is deermined as x i = P Rβ i Imporanly, he sage resource consrain ensures ha he scheduling decisions y i, i {1,..., M}, are seleced such ha M i=1 xi 1. Augus 30, 2011

8 8 A his poin, le us consider he cooperaive mode. Because of possible error propagaion, he end-o-end BEP for a wo-hop cooperaive ransmission is cumbersome o calculae exacly wih decode-and-forward relays; herefore, he relaionship ha ies β i,1, β i,2, and he relevan channel sae informaion, and ha guaranees a cerain reliabiliy of he overall link, is no as simple as (III.2). To significanly simplify he compuaion of β i,1 and β i,2, we use wo differen BEP hresholds BEP 1 and BEP 2 for he firs and second hops, respecively. The hreshold BEP 1 is ypically a large percenage of he oal error rae budge, say BEP 1 = 0.9 BEP, and BEP 2 = BEP BEP 1, since he firs link is he boleneck in decode-and-forward relaying. Indeed, he performance a each relay is ha of a single-inpu single-oupu sysem ransmiing over a fading channel. On he oher hand, he ransmission over he second link (from he recruied relays o he desinaion) can be regarded as a disribued muliple-inpu single-oupu sysem operaing over a fading channel; consequenly, he performance a he desinaion, which can ake advanage from cooperaive diversiy, is significanly beer han ha of each source-o-relay link, even when a small number of relays are recruied. Moreover, due o his fac and since he exponenial funcion in (III.1) decays fas as a funcion of is argumen, we reasonably assume ha he end-o-end BEP a he oupu of he ML deecor of he AP is dominaed by he BEP over he wors source-o-relay channel, i.e., he link for which h il is he smalles one. Under his assumpion, accouning for (III.2), we can esimae β i,1 = 1 T s β i,1 log 2 (1 + Γ 1 min l C i in Phase I as h il 2 ), (III.4) where Γ 1 is obained from Γ by replacing BEP wih BEP 1. In his phase, which lass R ρ i x i seconds, he number of symbols needed o ransmi a packe of P bis is equal o K i,1 = P/(β i,1 T s ) and, hus, i mus resul ha K i,1 T s = P β i,1 = R ρ i x i = P = R β i,1 ρ i x i. (III.5) Supposing ha a subse C i of he available nodes are recruied o serve as relays in Phase II, hese nodes, along wih he ih user, cooperaively forward he source message by using a randomized STBC rule [16]. More specifically, assuming error-free demodulaion a he decode-and-forward relays, if a i C Ki,2 gahers he block of i.i.d. QAM source symbols o be ransmied in Phase II of ime slo, hen a he lh node, for each l {i} C, i he vecor a i is mapped ono an orhogonal space-ime code marix G(a i ) C Q L [21], where Q is he block lengh and L denoes he number of anennas in he underlying space-ime code. During Phase II, he lh node ransmis a linear weighed combinaion of he columns of G(a i ), wih he weighs of he L columns of G(a i ) conained in he vecor r l C L. We denoe wih R (r l l C i ) C L N i he weigh marix of all he cooperaing nodes, where Augus 30, 2011

9 9 N i M is he cardinaliy of C i. 4 Under he randomized STBC rule, he AP observes he space-ime coded signal G(a i ) wih equivalen channel vecor h i,2 h i0 r i + R h i,2, where h i,2 (h l0 l C i ) T C N i collecs all he channel coefficiens beween he relay nodes and he AP (see Fig. 1). Noe ha he AP only needs o esimae for coheren ML decoding and ha he randomized coding is decenralized since he lh relay chooses r l locally. By capializing on he orhogonaliy of he underlying STBC marix G(a i ), he BEP P i,2 ( h i,2, β i,2 ) over he second hop a he oupu of he ML deecor of he AP using daa rae β i,2 h i,2 (bis/second) can be upper bounded as in (III.1) by replacing h il 2 and β il wih h i,2 2 and β i,2, respecively. By imposing he BEP consrain P i,2 ( h i,2, β i,2 ) BEP 2, he daa rae β i,2 aainable on he second hop of he cooperaing link is given by β i,2 = 1 log T 2 [1 + Γ 2 ( h i0 2 + R h i,2 2 )], (III.6) s where Γ 2 is obained from Γ in (III.2) by replacing BEP wih BEP 2. In his phase, which lass R (1 ρ i ) x i seconds, he number of symbols needed o ransmi a packe of P bis is equal o K i,2 = P/(β i,2 T s ) and, hus, i mus resul ha Q T s = P R c β i,2 = R (1 ρ i ) x i = P = R R c β i,2 (1 ρ i ) x i, (III.7) where R c K i,2 /Q 1 is he rae of he orhogonal STBC rule. From (III.5) and (III.7), he ransmission ime for he wo phase communicaion mode is R x i = P β i,1 + P R c β i,2 = P ( ) 1 β i,1 + 1 R c β i,2 = P β i,coop, (III.8) }{{} 1 β i,coop which also unveils wha is he funcional dependence of β i,coop on β i,1 and β i,2. Moreover, from (III.5) and (III.7), i is required ha R β i,1 ρ i x i = R R c β i,2 (1 ρ i ) x i = ρ i = β i,1 /(β i,2 R c ), (III.9) which shows ha, given he STBC rule, he ime fracion ρ i is deermined by he daa raes in Phase I and II. The cooperaive mode is acivaed only if he cooperaive ransmission is more daa-rae efficien han he direc communicaion, i.e., only if β i,coop > β i0, which from (III.8) leads o he following condiion 1 β i,1 + 1 R c β i,2 < 1 β i0. (III.10) 4 One specific code of he STBC marix is always assigned o he source iself, which ransmis over he cooperaive link every ime cooperaion is acivaed. This can be accouned for by simply seing r i = (1, 0..., 0) T and replacing he firs row of R wih (0..., 0), whereas he remaining enries of R are idenically and independenly generaed random variables wih zero mean and variance 1/L. Augus 30, 2011

10 10 If condiion (III.10) is fulfilled, hen he opporunisically opimal cooperaion decision is z i = 1 ; oherwise, he ih source ransmis o he AP in direc mode and z i = 0. I is ineresing o evaluae he energy consumpion in he case of a cooperaive ransmission. Neglecing receive and processing energy consumpion, he energy expended by he source i for ransmission of one packe is equal o ( ) E i,source = K i,1 + K i,2 E s = P P s β i,coop (Joules), (III.11) whereas he energy expended by each recruied relay node for ransmiing one packe of he ih source is given by E i,relay = K i,2 E s = P P s β i,2 R c (Joules). (III.12) I is noeworhy from (III.3) and (III.11) ha, since cooperaion is acivaed only when β i,coop > β i0, he energy expended by he source node i for a cooperaive ransmission is smaller han ha required by he same node for a direc ransmission. On he oher hand, he energy (III.12) expended by he relays is inversely proporional o he achievable daa rae in Phase II. Therefore, provided ha β i,2 R c β i0, over a sufficienly long period, he energy expendiure in relaying anoher node s daa can be parially compensaed for when he recruied relay acs as a source in he nework. The oal energy expended in he nework o ransmi y i 1 packes for user i can be expressed as E i ( y i, z, i C i ) y i 1 E = i0, if zi ( ) = 0 ; y i 1 E i,source + N i E i,relay, if z i = 1. The energy consumpion in he direc and cooperaive modes is numerically compared in Secion VI. (III.13) IV. COOPERATIVE MULTI-USER VIDEO TRANSMISSION Recall ha T i denoes he ih user s raffic sae and H collecs he channel coefficiens among all he nodes and he AP. Hence, he global sae can be defined as s ( T 1, T 2,..., T M ), H S, where S is a discree se of all possible saes. 5 Since: (i) he ih user s raffic sae evolves as a Markov process conrolled by is scheduling acion y i ; (ii) he ih user s raffic sae ransiion is condiionally independen of he oher users raffic sae ransiions given y i ; and (iii) he sae of each i l link h il is assumed o be i.i.d. wih respec o ime; he sequence of global saes {s : N} can be modeled as a conrolled Markov process wih ransiion probabiliy funcion M p(s +1 s, y ) = p (H +1 ) i=1 p(t i +1 T i, y i ), (IV.1) 5 To have a discree se of nework saes, he individual link saes in H are quanized ino a finie number of bins (see [24] for deails). Augus 30, 2011

11 11 where y ({y 1 } T, {y 2 } T,..., {y M } T ) T collecs he scheduling acions of all he video users. Under he scheduling acion y i, he ih user obains he immediae uiliy u i (T i, y i ) q i j y i,j, (IV.2) which is he oal video qualiy improvemen experienced by he ih user by aking scheduling acion y i in raffic j F i sae T i under he assumpion ha qualiy is incremenally addiive [17]. The objecive of he MU opimizaion is he maximizaion of he expeced discouned sum of uiliies wih respec o he join scheduling acion y and he cooperaion decision vecor z (z 1, z 2,..., z M ) T aken in each sae s. Due o he saionary Markovian ransiion probabiliy funcion, he opimizaion can be formulaed as an MDP ha saisfies he following dynamic programming equaion 6 { M U (s) = max u i (T i, y i ) + α } M p(h ) p(t i T i, y i ) U (s ), s, (IV.3) y,z i=1 s S i=1 subjec o y i P i (T i, β i ) and M x i 1 where x i is he ime-fracion allocaed o he ih user given is scheduling acion y i and ransmission rae β i, i.e., i=1 (IV.4) x i = P R β i yi 1, (IV.5) he parameer α [0, 1) is he discoun facor, which accouns for he relaive imporance of he presen and fuure uiliy, and P i (T i, H) is he se of feasible scheduling acions given he raffic sae T i and channel sae marix H. From Theorem in [26], we know ha here exiss a saionary opimal policy ha is he global opimal soluion o (IV.3). Given he disribuions p(h) and p(t i T i, y i ) for all i, he above MU-MDP can be solved by he AP using value ieraion or policy ieraion [18]. However, here are wo challenges associaed wih solving he above MU-MDP. Firs, he complexiy of solving an MDP is proporional o he cardinaliy of is sae-space S, which, in he above MU-MDP, scales exponenially wih he number of users, i.e., M, and wih he number of links in H, i.e., M 2. Hence, even for moderae sized neworks, i is impracical o compue, or even o encode, U (s). In subsecion IV-A, we show ha he exponenial dependence on he number of links in H can be eliminaed. Second, in he uplink 6 In his secion, since we model he problem as a saionary MDP, we omi he ime index when i does no creae confusion. In place of he ime index, we use he noaion ( ) o denoe a sae variable in he nex ime sep (e.g. T i, H, s ). Augus 30, 2011

12 12 scenario, he raffic sae informaion is local o he users, so neiher he AP nor he users have enough informaion o solve he above MU-MDP. In subsecion IV-B, we summarize he findings in [10] ha show ha he considered opimizaion can be approximaed o make i amenable o a disribued soluion. Addiionally, his disribued soluion eliminaes he exponenial dependence on he number of users. Noe ha he simplificaion in subsecion IV-A is very imporan, because only afer obaining his resul does i become possible o use he soluion in [10]. A. Reformulaion wih simplified nework sae The only reason o include he deailed nework sae informaion H and he cooperaion decision z in he MU- MDP is o make foresighed cooperaion decisions, which ake ino accoun he impac of he immediae cooperaion decision on he expeced fuure uiliy of he users. However, if we can show ha he opimal opporunisic (i.e., myopic) cooperaion decision is also long-erm opimal, hen he deailed nework sae informaion does no need o be included in he MU-MDP. The following heorem shows ha he opimal opporunisic cooperaion decision, which maximizes he immediae ransmission rae, is also long-erm opimal. Theorem 1 (Opporunisic cooperaion is opimal): If uilizing cooperaion incurs zero cos o he source and relays, hen he opimal opporunisic cooperaion decision, which maximizes he immediae hroughpu, is also long-erm opimal. Proof: See Appendix I. To inuiively undersand why maximizing he immediae ransmission rae a he PHY layer is long-erm opimal, consider wha happens when a user chooses no o maximize is immediae ransmission rae (i.e., does no uilize he opimal opporunisic cooperaion decision). Two hings can happen: eiher less packes are ransmied overall because of packe expiraions; or, he same number of packes are ransmied overall, bu heir ransmission incurs addiional resource coss because ransmiing he same number of packes a a lower rae requires more resources [see (IV.5)]. In eiher case, he long-erm uiliy is subopimal. A consequence of Theorem 1 is ha he cooperaion decision vecor z does no need o be included in he MU-MDP. Insead, i can be deermined opporunisically by selecing z o maximize he immediae ransmission rae. Mos imporanly, his means ha he MU-MDP does no need o include he high-dimensional nework sae. We now make wo remarks regarding Theorem 1 so ha is consequences are no misinerpreed. Firs, in he inroducion, we noed ha maximizing hroughpu is a subopimal muliple access sraegy for wireless video. This does no conradic Theorem 1 because i only saes ha he cooperaion decision should be made opporunisically Augus 30, 2011

13 13 o maximize he immediae ransmission rae. Indeed, myopic (opporunisic) resource allocaion and scheduling is subopimal because i does no ake ino accoun he dynamic video daa aribues (i.e., deadlines, prioriies, and dependencies). Second, alhough he users MDPs do no need o include he high-dimensional nework sae, he opimal resource allocaion and scheduling sraegies sill depend on i; however, insead of racking H, i is sufficien o rack he users opimal opporunisic ransmission raes provided by he PHY layer, i.e., β i for all i. Under he assumpion ha he channel coefficiens are i.i.d. random variables wih respec o, β i can also be modeled as an i.i.d. random variable wih respec o. We le p(β i ) denoe he probabiliy mass funcion (pmf) from which β i is drawn. We noe ha p(β i ) depends on p(h) and he deployed PHY layer cooperaion algorihm. Based on he second remark, we can simplify he maximizaion problem in (IV.3). Le us define he ih user s sae as s i ( T i, β i) S i and redefine he global sae as s (s 1,..., s M ) T. In Secion V, we describe how β i is deermined, bu for now we will ake for graned ha i is known. Because he opimizaion does no need o include he cooperaion decision, he maximizaion of he expeced sum of discouned uiliies in (IV.3) can be simplified by only maximizing wih respec o he scheduling acion y in each sae s, ha is, { M U (s) = max u i (T i, y i ) + α } M p(s i s i, y i ) U (s ), s, (IV.6) y i=1 s S i=1 subjec o where p(s i s i, y i ) = p(β i ) p(t i T i, y i ). B. Disribued soluion y i P i (T i, β i ) and M x i 1, i=1 (IV.7) Similar o [10], (IV.6) can be reformulaed as an unconsrained MDP using Lagrangian relaxaion. The key idea is o inroduce a Lagrange muliplier λ s associaed wih he sage resource consrain M i=1 xi 1 in each global sae s because every global sae has a differen resource-qualiy radeoff. The resuling dual soluion has zero dualiy gap compared o he primary problem [i.e., (IV.6)], bu i sill depends on he global sae so i is no amenable o a disribued soluion. However, by imposing a uniform resource price λ s = λ, s S, which is independen of he muli-user sae, he resuling MU-MDP can be decomposed ino M MDPs, one for each user [10]. 7 These local 7 We noe ha he resource price is only used o efficienly allocae he limied wireless resources among he users; i is no used o generae revenue for he AP. In oher words, i is a congesion price raher han a real price. Augus 30, 2011

14 14 MDPs saisfy he following dynamic programming equaion [ ( U i, (s i, λ) = max u i (T i, y i ) λ x i 1 ) + α y i M Û λ (s) = min λ 0 s i S M U i, (s i, λ), i=1 p(s i s i, y i ) U i, (s i, λ) ], (IV.8) subjec o y i P i (T i, β i ). Imporanly, he ih user s dynamic programming equaion defines he opimal scheduling acion as a funcion of he ih user s sae, raher han he global sae s. In his paper, he ih user solves (IV.8) offline using value ieraion; however, i can be easily solved online using reinforcemen learning as in [10] and [19]. Also, noe ha due o he disribued naure of he proposed algorihm, he sage resource consrain M i=1 xi 1 is no guaraneed o be saisfied during convergence or a seady-sae. Because he sage resource consrain may be violaed, i mus be enforced separaely by he AP, which we assume normalizes he requesed resource allocaions and, subsequenly, has he users recompue heir scheduling policies o saisfy he new allocaions. (IV.9) Alhough he opimizaion can be decomposed across he users, he opimal resource price λ sill depends on all of he users resource demands. Hence, λ mus be deermined by he AP in boh he uplink and downlink scenarios. Specifically, he resource price can be numerically compued by he AP using he subgradien mehod. The subgradien wih respec o λ is given by M i=1 Xi 1 1 α, where Xi = E [ + =0 α x i s i 0] is he ih user s expeced discouned accumulaed resource consumpion, which can be calculaed as described in [10]. Imporanly, X i can be compued locally by he ih user in he uplink scenario and by he AP in he downlink scenario. Using he subgradien mehod, he resource price is updaed as λ k+1 = [ λ k + µ k ( M i=1 )] + X i 1, (IV.10) 1 α where µ k is a diminishing sep size. Since he focus of his paper is on he ineracion beween he muliuser video ransmission and he cooperaive PHY layer, we refer he ineresed reader o [10] for complee deails on he dual decomposiion oulined in his subsecion, and he derivaion of he subgradien wih respec o λ. We noe ha a similar decomposiion has recenly been proposed for energy-efficien uplink scheduling wih delay consrains in muliuser wireless neworks using a differen MU-MDP framework [19]. Besides he fac ha [19] does no consider physical layer cooperaion or heerogeneous raffic characerisics, here is one significan difference beween he decomposiion in [19] and he one adoped in his paper. Specifically, he TDMA-like proocol in [19] assumes ha only one user can ransmi in each ime slo, whereas we consider a TDMA-like proocol in which each Augus 30, 2011

15 15 ime slo is divided ino differen lengh ransmission opporuniies for each user. Moreover, in [19], every user has a unique Lagrange muliplier associaed wih is average buffer delay consrain. In conras, in our decomposiion, all users have he same Lagrange muliplier, which regulaes he resource division among he users, raher han heir individual delay consrains. Noe ha, in his paper, delay consrains are included in he applicaion model. Imporanly, Theorem 1 applies o he MU-MDP formulaion in [19] and herefore he recruimen proocol proposed in Secion V can be used o inegrae cooperaion ino [19]. In oher words, he novely and echnical conribuions of his paper are independen of he dual decomposiion in [10], which we only use for illusraive purposes. V. RECRUITMENT PROTOCOL Wih reference o he uplink scenario, we define our opporunisic cooperaive sraegy o selec disribuively he se of cooperaive relays C i and make he decision z i a he AP. The downlink case is a minor variaion. Imporanly, he AP can exacly evaluae β i,2 in (III.6) because i can esimae h i0 and R h i,2 via raining as menioned in Secion III. However, he rouble in recruiing relays on-he-fly is ha he AP and he relays canno direcly compue β i,1 given by (III.4), since hey canno esimae he channel coefficiens h il, for all l C i. Some MAC randomized proocols have recenly been proposed [22], [23], which ge around he problem ha he AP and he relays do no have he necessary channel sae informaion o deermine β i,1. However, such proocols require he exchange and/or he racking of a large amoun of nework parameers ha may incur unaccepable delays in a wireless video nework. In paricular, he firs- and second-hop daa raes are compued in [23] by he source node using he average PER evaluaed by simulaions. To quickly seup he cooperaive ransmission and, hus, reduce he delays, we propose a much simpler recruimen scheme ha is based on he closed-form formulas (III.4) and (III.6). The proposed four-way proocol is reminiscen of he reques-o-send (RTS) and clear-o-send (CTS) handshaking used in carrier sense muliple access wih collision avoidance (CSMA/CA), which is exended o include a helperready o send (HTS) conrol message ha is cooperaively ransmied by he relays using randomized STBC and a cooperaive recruimen signal (CRS) ha is sen by he AP o recrui relays. The idea of sending he HTS frame in cooperaive mode has been originally proposed in [23]. However, apar from he use of he HTS conrol message, he proposed proocol is differen from ha of [23] because we use a compleely differen recruimen policy. All he conrol frames are ransmied a he base rae β 0 such ha hey can be decoded correcly, and he hresholds BEP 1 and BEP 2, as well as L and R c, are fixed parameers ha are known a all he nodes. Fig. 3 illusraes he signaling proocol for ime slo, which consiss of he nine seps deailed in Table I. We would like o highligh Augus 30, 2011

16 16 ha, similar o he daa ransmied in Phase II, he HTS message is a cooperaive signal, i.e., all relays joinly deliver he HTS frame using randomized STBC a he same ime and, hence, simulaneous ransmissions do no cause a collision. Wih reference o Table I, he key observaion is ha he selecion of he se C i by virue of (VII.4) is done in a disribued way and, moreover, by simply having access o he channel sae from he source i o iself, i.e., h il, he lh candidae cooperaive node can auonomously deermine if, by cooperaing, i can improve he daa rae of node i. Anoher imporan observaion is ha he recruimen of he cooperaive nodes and he assignmen of he daa raes requires only four conrol messages for each source. In paricular, he conrol informaion exchange is independen of he number of recruied relays hanks o he randomizaion of he cooperaive ransmission. Moreover, he wo parameers ξ and L need o be chosen appropriaely. The bes choice for ξ and L requires global nework informaion. A learning framework would be very appropriae for heir selecion bu we defer he reamen of his aspec o fuure work. Finally, as for he impac of L on he nework performance, i should evidenced ha randomized channels end o behave saisically like heir non-randomized counerpars [16], wih deep-fade evens ha become as frequen as hose of L independen channels, as long as he number of cooperaive nodes N i L + 1. VI. NUMERICAL RESULTS We consider a nework wih 50 poenial relay nodes placed randomly and uniformly hroughou he 100 m coverage range of a single AP as illusraed in Fig. 4. We specify he placemen of he video source(s) separaely for each experimen. Le η il denoe he disance in meers beween he ih and lh nodes. The fading coefficien h il over he i l link is modeled as an i.i.d. CN (0, (η il ) δ ) random variable, where δ is he pah-loss exponen. Addiionally, we assume ha he enries of R, defined in Secion III, are i.i.d. CN (0, 1 L ) random variables, where L is he lengh of he STBC. If an error occurs in he packe ransmission, hen he packe remains in he frame buffer o be reransmied in a fuure ime slo (assuming he packe s deadline has no passed). Due o space consrains, and because cooperaion has he same impac in boh uplink and downlink scenarios, we only presen resuls for cooperaive uplink video ransmission. In paricular, we consider four uplink scenarios: 1) Single source: In his scenario, we assume ha a single source node is placed beween 10 and 100 m direcly o he righ of he AP in Fig. 4. We use his scenario o evaluae he ransmission raes in he direc and cooperaive ransmission modes a differen disances from he AP, and o deermine a good self-selecion parameer ξ. 2) Homogeneous video sources: This scenario mimics a surveillance applicaion in which hree cameras capure correlaed video conen in an oudoor environmen and ransmi i o he AP. The video sources are placed o he Augus 30, 2011

17 17 righ of he AP as illusraed in Fig. 7. To simulae correlaed conen, we assume ha each of he hree cameras sream he Foreman sequence (CIF resoluion, 30 Hz framerae, encoded a 1.5 Mb/s) offse by several frames. Using homogeneous sources allows us o isolae he impac of cooperaion on he video sreaming performance by removing he addiional layer of complexiy inroduced by heerogeneous video sources (e.g. differen packe prioriies and bi-raes among he video users). 3) Heerogeneous video sources 1: This scenario mimics a nework in which users deploy enerainmen applicaions such as video sharing or video conferencing. To simulae his, we assume ha he hree video sources illusraed in Fig. 7 ransmi heerogeneous video conen o he AP. Specifically, we assume ha video user 1 sreams he Coasguard sequence (CIF, 30 Hz, 1.5 Mb/s), video user 2 sreams he Mobile sequence (CIF, 30 Hz, 2.0 Mb/s), and video user 3 sreams he Foreman sequence (CIF, 30 Hz, 1.5 Mb/s). 4) Heerogeneous video sources 2: This is he same as he previous scenario, bu wih video user 2 sreaming he Foreman sequence and video user 3 sreaming he Mobile sequence. We noe ha he proposed framework can be applied using any video coder o compress he video daa. However, for illusraion, we use a scalable video coding scheme [25], which is aracive for wireless sreaming applicaions because i provides on-he-fly applicaion adapaion o channel condiions, suppor for a variey of wireless receivers wih differen resource and power consrains, and easy prioriizaion of video packes. In our resuls, we deploy he proposed randomized STBC cooperaion proocol oulined in Table I and deermine he opimal resource allocaion and scheduling decisions using he disribued opimizaion inroduced in Secion IV-B. The relevan simulaion parameers are given in Table II. Noe ha, in he homogeneous and heerogeneous scenarios described above, we simulae a nework wih a high ransmission rae, using he symbol rae 1 T s = , and a nework wih a low ransmission rae, using he symbol rae 1 T s = symbols/second. A. Transmission raes and energy consumpion In his subsecion, we consider he single source scenario described above. Fig. 5 illusraes he performance of he proposed cooperaion proocol for ime-invarian self-selecion parameer values ξ = ξ {0.1, 0.2,..., 0.5}, and he performance of direc ransmission, given a single source ransmiing o he AP. Noe ha hese resuls hold regardless of he symbol rae. In paricular, he ransmission rae in Fig. 5(a) is presened in erms of he specral efficiency (bis/second/hz); he probabiliy of cooperaion in Fig. 5(b) and he average number of recruied relays in Fig. 5(c) only depend on he specral efficiency; and he energy resuls repored in Figs. 5(d-f) are normalized by Augus 30, 2011

18 18 seing he symbol energy E s = Ts P (or, equivalenly, P s = 1 P ) in (III.3), (III.11), and (III.12). From Fig. 5(a), i is clear ha nodes furher from he AP uilize cooperaion more frequenly han nodes closer o he AP. This is because, on average, disan nodes have he feebles direc signals o he AP due o pah-loss and, herefore, have he mos o gain from he channel diversiy afforded o hem by cooperaion. I is also clear from Fig. 5(a) ha cooperaion is uilized more frequenly as he self-selecion parameer ξ increases. This is because, as illusraed in Fig. 5(c), more relays saisfy he self-selecion condiion in sep 5 of Table I for larger values of ξ. However, larger values of ξ yield relay nodes for which βi0 β il is large, which leads o a bad ransmission rae over he boleneck hop-1 cooperaive link. Due o his poor boleneck rae and he large number of recruied relays, he average ransmission rae shown in Fig. 5(b) declines for ξ > 0.2 even while he oal energy consumpion increases as illusraed in Fig. 5(d). In conras, lower values of he self-selecion parameer (e.g. ξ < 0.2) lead o oo few nodes being recruied o achieve large cooperaive gains, bu yield lower energy consumpion. Ineresingly, he same properies of relay nodes ha are desirable for achieving he bes ransmission rae a balance beween he number and qualiy of relays is also imporan for achieving a high hroughpu-o-energy raio. For example, Fig. 5(e) shows us ha a 100 m from he AP, he average hroughpu-o-energy raio for cooperaive ransmission wih ξ = 0.2 is a lile less han 0.8, which is close o he hroughpu-o-energy raio of a direc ransmission, which is 1 a 100 m. Alhough he average nework energy required o suppor a cooperaive ransmission is larger han ha required for a direc ransmission, his increase is moderae compared o he amoun of energy he source node would have o expend in order o achieve he same ransmission rae as he cooperaive ransmission, i.e., o aain β i0 = β i,coop requires a large increase in he ransmission power wih respec o he cooperaive case. This is illusraed in Fig. 5(f), where, for example, i is shown ha ransmiing in he direc mode a he rae aainable under cooperaive ransmission wih ξ = 0.2 requires approximaely 13.5 normalized Joules/Packe compared o approximaely 3.5 normalized Joules/Packe in he cooperaive case shown in Fig. 5(d). 8 In he remainder of our experimens, we le he self-selecion parameer ξ = ξ = 0.2 because, as illusraed in Figs. 5(b,e), his value provides a large average ransmission rae over he AP s enire coverage range and a high hroughpu-o-energy raio. Wih ξ = 0.2, Fig. 7 illusraes he acivaion frequencies for differen relays and Fig. 6 8 The resuls in Fig. 5(f) were obained by fixing he ransmission rae and adaping he symbol energy, which is in conras o he curren problem formulaion in which we fix he symbol energy and adap he ransmission rae. Specifically, we calculaed he symbol energy Ẽs required o se β il = β i,coop by rearranging (III.2). Noe ha we could also force β i,coop = β i0 o achieve lower energy consumpion a he same ransmission rae as he direc mode. Augus 30, 2011

19 19 illusraes he average energy consumed by he source and relay nodes. Noice ha, under a cooperaive ransmission, he source node acually uses less power han under a direc ransmission, which parially compensaes for he exra energy i may expend acing as a relay for oher nodes. B. Transmission rae, resource price, and resource uilizaion Fig. 8 illusraes he average ransmission raes achieved by he video users in he homogeneous and heerogeneous scenarios in neworks ha suppor high and low ransmission raes. Recall ha he resource cos x i incurred by user i is inversely proporional o he ransmission rae [see (IV.5)], which decreases as he disance o he AP increases due o pah loss. Hence, when only direc ransmission is available, user 3 ends o resign iself o a low average ransmission rae because he cos of using resources is oo high. Cooperaion increases he average ransmission rae, hereby providing user 3 lower cos access o he channel o ransmi more daa. In he homogeneous scenario illusraed in Fig. 8(a), cooperaion ends o equalize he resource allocaions o he hree users (his is especially eviden in he cooperaive case wih a high ransmission rae). This is because he homogeneous users have idenical uiliy funcions; hus, when sufficien resources are available, i is opimal for hem o all operae a he same poin of heir resource-uiliy curves. In conras, when heerogeneous users wih differen uiliy funcions are inroduced, he ransmission raes change o reflec he prioriies of he differen users video daa. Observing Fig. 8(b,c), i is clear ha he addiional resources afforded by cooperaion end o go o he highes prioriy video user, who, in our simulaions, is he user sreaming he Mobile sequence. Recall ha users auonomously opimize heir resource allocaion and scheduling acions given he resource price λ announced by he AP. Table III illusraes he opimal resource prices in he homogeneous and heerogeneous scenarios along wih he average nework resource uilizaion, i.e. he average of M i=1 xi. There are several ineresing resuls in Table III. Firs, he average nework resource uilizaion is ofen considerably less han he oal available resources. This is due o he disribued naure of he resource allocaion and scheduling algorihm, which requires users o be conservaive in heir resource usage o ensure feasible allocaions. Second, in he cooperaive ransmission mode, he resource price ends o increase and he uilizaion ends o decrease when going from a high rae o a low rae nework, regardless of he sreaming scenario. The resource price increases because he nework suppors lower raes, bu he demand says he same, which increases congesion. The uilizaion decreases because lower raes yield a coarser se of feasible resource allocaions for each user (see (IV.5)). Third, in he high rae nework, he resource price ends o decrease and he uilizaion ends o increase when going from he direc o he cooperaive ransmission Augus 30, 2011