ECast: An enhanced video transmission design for wireless multicast systems over fading channels

Transcription

1 1 ECast: An enhanced vdeo transmsson desgn for wreless multcast systems over fadng channels Zhlong Zhang, Danpu Lu, Xaol Ma, and Xn Wang Abstract Conventonal wreless vdeo multcast schemes face a challenge due to ther star-shaped performance curves called clff effect [1] and the lmted ablty to accommodate multple users wth dverse channel condtons. Recently, a seres of analog vdeo codng approaches amng to solve the problem has been proposed. In ths paper, our goal s to enhance such schemes through a novel cross-layer desgn. A jont subcarrer matchng and power allocaton scheme whch s proved to be optmal n terms of mnmzng the mean square error s proposed. The scheme can dynamcally adapt to both channel condtons and vdeo contents, and at the same tme mantan contnuous qualty scalablty. Furthermore, the feedback overhead of the channel state nformaton from multple users s addressed and a novel analog feedback method s proposed. The vdeo qualtes at varous recevers are controllable through assgnng dfferent weghts to dfferent users. Therefore, ths scheme s sutable for wreless vdeo multcast systems. Smulaton results valdate the effectveness of our proposal. Index Terms Analog vdeo codng, power allocaton, subcarrer matchng, wreless vdeo multcast, analog feedback. I. INTRODUCTION In tradtonal wreless vdeo multcast systems, the vdeo codng layer and the wreless transmsson layer are often desgned separately. Source codng and channel codng are employed as ndvdual unts. Lttle nformaton s exchanged between the two layers. Most of the systems, such as dgtal vdeo broadcastng (DVB)[2] and some adaptve cross-layer proposals[3, 4], have star-shaped performance curves and are fragle to transmsson errors. When castng vdeo sgnals, a transmtter encodes vdeo sources at a specfc codng rate to serve all the users n a multcast cell. Users under weak channel condtons cannot reconstruct vdeos correctly whch causes the severe degradaton of qualty of experence (QoE); meanwhle, those under strong channel condtons cannot obtan further mproved performance. Although by adoptng scalable vdeo codng (SVC) [5], weak recevers can afford low resoluton vdeo sgnals whle strong recevers can decode hgh qualty vdeo sgnals, SVC cannot serve well all users wth varous channel condtons. SVC only replaces one large Ths work was funded by NSFC under grant and Part of the thrd authors work was supported by NSF grant ECCS Zhlong Zhang and Danpu Lu are wth Bejng Key Laboratory of Network System Archtecture and Convergence, Bejng Unversty of Posts and Telecommuncatons, Bejng , Chna (e-mal: jerome.zl.zhang@gmal.com, dplu@bupt.edu.cn). Xaol Ma s wth the School of Electrcal and Computer Engneerng, Georga Insttute of Technology, GA Atlanta, USA (e-mal: xaol@ece.gatech.edu). Xn Wang s wth the Department of Electrcal and Computer Engneerng, Stony Brook Unversty, NY 11790, USA (e-mal: xwang@ece.sunysb.edu). star wth multple small stars, and does not entrely mtgates the clff effect[6]. Recently, a novel vdeo codng technque called SoftCast was proposed n [7 9]. SoftCast adopts a specal analog vdeo codng structure. Vdeo data are frst compressed by 3D-Dscrete Cosne Transform (DCT). DCT coeffcents are grouped nto chunks and dfferent amounts of power are allocated to mnmze the mean square error (MSE). Every two DCT coeffcents from the same chunk are mapped nto one dense quadrature ampltude modulaton (QAM) symbol and are transmtted drectly through an OFDM-based physcal layer. Unlke n conventonal vdeo codng schemes, such as H.264 and MPEG, the entropy codng part s absent n the framework, because t makes the vdeo qualty senstve to transmsson errors. The key dea of SoftCast s to mantan the lnear relaton between pxel values and transmtted samples. The graceful desgn leads to a roughly lnear relaton between the peak sgnal to nose rato (PSNR) and the sgnal to nose rato (SNR), and makes the system robust and scalable. After SoftCast, a large number of proposals have amed to mprove the orgnal analog codng scheme n varous ways. To reduce nterframe redundancy, 3D-DCT s replaced wth 3D wavelet n [6] and employed moton estmaton s ntroduced n [10]. A wreless vdeo transmsson framework called DCast whch was proposed n An mproved scheme called SIRCast based on DCast was proposed n [11]. In [12], Xong et al. proposed an adaptve chunk dvson method whch adapted well to the energy dstrbuton of DCT coeffcents. WSVC whch presented a hybrd dgtal-analog jont source-channel codng scheme that ntegrated the advantages of dgtal codng and analog codng was proposed n [13]. The analog codng part was smlar to SoftCast. On the other hand, many efforts have been devoted to mprovng the orgnal wreless transmsson scheme. A collson preventon mechansm was proposed to allow SoftCast to operate effcently n IEEE networks n [14]. ParCast [15] was proposed to enhance vdeo transmsson by ntroducng MIMO. ParCast appled MIMO precodng to mprove the lnk qualty and mapped mportant vdeo components to more relable channels. Cooperatve communcatons were ntroduced n [16] whch extended the work of [13]. Recevers could transmt messages between each other, and those wth better SNR served as relays. The aforementoned results provded varous ways to mprove the performance of SoftCast. Gaussan channels were assumed n most proposals. However, sgnals often experence fadng durng wreless propagaton. In the OFDMbased physcal layer, a large frequency band s dvded nto

2 2 multple narrowband subcarrers wth dfferent channel fadng factors. Subcarrers, as sgnfcant wreless resources, should be allocated properly. Among these proposals, only ParCast mentoned mappng mportant vdeo components to more relable channels, but t focused only on vdeo uncast. The method was not applcable for multcast systems because of the hgh channel state nformaton (CSI) feedback overhead from multple users. In addton, the optmalty of ts mappng scheme was not proved. In ths paper, we focus on how to optmally allocate subcarrer and power accordng to both vdeo contents and channel condtons, whle copng wth the large feedback overhead. Through a cross-layer desgn of both the vdeo layer and the OFDM-based physcal layer, an enhanced vdeo multcast scheme called ECast s proposed. The man contrbutons are threefold. Frst, a cross-layer resource allocaton problem s formulated, and a jont carrer matchng and power allocaton scheme s derved whch s proved to be optmal; Second, an analog feedback method s proposed to lmt the feedback overhead for vdeo multcast; Thrd, a qualty-controlled method s ntroduced. By assgnng dfferent mportance factors consderng farness or pad prortzaton, we can ether protect users wth poor channel condtons or enhance the performance of hgh-payng users. Smulaton results show that the proposed scheme outperforms the performance of typcal analog vdeo codng systems sgnfcantly and s sutable for wreless vdeo multcast. The remander of ths paper s organzed as follows. Secton II descrbes the system desgn. Secton III elaborates the problem settng and the optmal soluton of jont carrer matchng and power allocaton. The system model s smplfed, where the number of chunks s assumed to be equal to the number of subcarrers. Secton IV extends the smplfed model to a general scenaro where the two numbers are unequal. Bandwdth adapton and user moblty are also consdered. In Secton V, the LLSE decoder s ntroduced and a novel analog feedback scheme s proposed based on the theoretcal results of Secton III-C. Smulaton results verfy our proposal n Secton VI and a summary concludes the paper n Secton VII. II. DESIGN OVERVIEW In ths secton, we llustrate the system desgn of the consdered wreless vdeo multcast system. The system s composed of one servce access pont (SAP) as the transmtter and multple users as the recevers. Tme dvson duplexng (TDD) s assumed. Both downlnk and uplnk channels are based on OFDM. All users share an uplnk feedback channel, through whch CSI s fed back to the SAP. Meanwhle, vdeo data are transmtted from the SAP to multple users through a downlnk multcast channel. There are two categores of vdeo data n the downlnk: content data and meta data. Only a small amount of mportant nformaton s treated as meta data. Meta data are transmtted through tradtonal communcaton methods wth hgh redundancy, such that the transmsson obtans more protecton and s nearly lossless. The majorty of vdeo data are content data whch are transmtted n lossy mode. They are more tolerant to nose, fadng and nterference. The content data to be transmtted are dvded nto chunks wth equal szes. Symbols n the same chunk are carred by at most one subcarrer wthn a channel coherent tme, so that they experence smlar channel attenuaton. Fg. 1 depcts the framework of the proposed system. Modules that make the approach outperform others are hghlghted n the fgure and wll be detaled n the followng sectons. Meanwhle, gven that the system s based on the structure of SoftCast 1, for ntegrty, modules that are smlar to those adopted by SoftCast are also brefly descrbed below. The rest of ths secton overvews how to transmt dfferent categores of data based on the framework. Note that the proposed scheme can also be used n vdeo systems that ncorporate an analog codng part, such as WSVC [13]. A. Content data transmtted n lossy mode Content data are the domnant data whch are transmtted n lossy mode. The man components for transmttng content data are descrbed as follows. For the transmtter: Lnear Transform: Lnear transform s appled to a group of pctures (GOP) to compress vdeo sgnals. The transform matrx could be 2D/3D DCT[8], 3D wavelet[6] or any other operator matrxes wth good performance for compresson. Channel Adapton: The role of channel adapton s to adapt the vdeo layer to the transmsson layer. Coeffcents obtaned after the lnear transformaton are grouped nto chunks. Source bt rates, wreless channels and user moblty are jontly consdered. The mean and the varance of each chunk and a btmap that ndcates the dscarded chunks are sent as meta data. The detal of channel adapton wll be elaborated n Secton IV. Subcarrer Matchng and Power Allocaton: Subcarrer matchng and power allocaton (or power scalng) are performed at chunk level. The SAP collects channel condtons from each user, determnes the optmal subcarrer matchng order and calculates the amount of power allocated to each chunk. Matchng nformaton and power scalng factors are transmtted as meta data. The jont subcarrer matchng and power allocaton scheme s the key technology we focus on n ths paper, whch wll be detaled n Secton III. Dense QAM Mappng: A par of two coeffcents n the same chunk after power scalng s mapped to a 64K- QAM symbol. Specfcally, each coeffcent s quantzed nto an 8-bt nteger and every two ntegers compose one complex number of 64K possble values. The dense QAM mappng wthout channel codng makes the end-to-end MSE roughly lnear to the mpact of wreless channels. 1 Compared wth tradtonal wreless vdeo transmsson systems, the proposed scheme has the same lmtaton and beneft as SoftCast as dscussed n [8]. We have not stated them n the paper.

3 3 meta data VLC FEC BPSK meta data Input GOP Lnear Transform Channel Adapton Subcarrer Matchng and Power Allocaton Dense QAM OFDM Process Channel State Informaton (CSI) Fadng Channels Output GOP Inverse Lnear Transform Chunks Combnaton Demodulaton and CSI Feedback Inverse QAM Inverse OFDM Process meta data meta data VLC FEC BPSK Fg. 1. System Model for ECast. It s an enhanced structure of SoftCast as well as other systems adoptng a smlar analog codng part, such as WSVC. The specal modules n our system are hghlghted n ths fgure. OFDM process: 64K-QAM symbols are allocated to subcarrers accordng to the optmal matchng soluton. Subsequently, symbols of each subcarrer undergo the IFFT and D/A processes. Then the obtaned analog sgnals are modulated wth carrer waves to generate the fnal transmtted vdeo sgnal. A recever performs the nverse processes of the transmtter: Inverse OFDM: A recever receves the sgnal and reconstructs the modulated complex symbols of both the content data and the meta data. To assst the decoder n nvertng the receved sgnal, meta data are decoded frstly. Inverse QAM: Scaled coeffcents are reconstructed by nverse dense QAM. Each complex value s decoupled back nto two real values. Demodulaton and CSI feedback: Coeffcents are demodulated by LLSE (see Secton V-A). The CSI feedback scheme wll be brefly descrbed n Secton II-C and detaled n Secton V. Chunks combnaton: Demodulated chunks are combned nto a group of transformed coeffcents. Those dscarded at the transmtter are set to zero at ther GOP postons. Inverse Transform: The coeffcents are transformed by the nverse lnear transform, and a reconstructed GOP s fnally obtaned. Wthout any nonlnear processes n our system, the end-toend performance has a nearly lnear relaton wth the SNR. As wll be shown, the performance s largely mproved by adoptng the proposed scheme. B. Meta data transmtted n lossless mode Meta data assst recevers n decodng the receved sgnals. They are generated n dfferent vdeo encodng processes, consstng of the mean and the varance of each chunk, a btmap that ndcates the dscarded chunks, chunk mappng nformaton and scalng factors. Meta data are coded usng conventonal dgtal communcaton schemes consstng of varable length codng (VLC), forward error correcton (FEC) and bnary phaseshft keyng (BPSK) mappng, and decoded by recevers wth the nverse processes. C. CSI transmtted n analog mode The CSI feedback from multple users s transmtted through a shared uplnk channel. As the upcomng WF standard and LTE both use the channel feedback, assumng the avalablty of channel condtons at the SAP s reasonable. However, the problem s not about the avalablty of CSI but how to lmt the large overhead of feedback from numbers of users. In our proposal, users do not transmt channel states themselves, but transmt the strengths of channel gans through parallel tone sgnals. All feedback from dfferent users s transmtted smultaneously. They are superposed at the SAP. The SAP does not need to separate each tone from others, but uses the superposed feedback drectly. The detal of ths lmted feedback scheme and the reason why t works wll be descrbed n Secton V. III. JOINT SUBCARRIER MATCHING AND POWER ALLOCATION In ths secton, we dscuss the jont subcarrer matchng and power allocaton scheme and analyze ts benefts to the entre system. Frstly, a non-lnear zero-one optmzaton problem for vdeo uncast s formulated and the optmal soluton s obtaned. Then, the results for uncast are extended to multcast. We focus only on the system wth equal number of chunks and subcarrers n ths secton. It s a smplfed and basc model, and can be easly extended to a more general case (see Secton IV). A. Problem formulaton for uncast Power scalng or power allocaton s a key component n tradtonal analog vdeo codng schemes[7 9]. DCT coeff-

4 4 cents are scaled before transmsson and the scalng factors are obtaned by solvng an optmzaton problem. In general, the transmtted chunks are often assumed to experence AWGN channels n the system desgn and wreless fadng s handled by the OFDM-based physcal layer tself. When consderng channel fadng, we have to derve a new method to calculate the scalng factors and at the same tme determne how to match the chunks to the subcarrers. We address the jont resource allocaton problem for the system wth equal number of chunks and subcarrers n ths subsecton. Assume N chunks should be transmtted and N subcarrers are avalable. Each subcarrer carres only one chunk,.e. only one-to-one matchng s allowed. A coeffcent n the th chunk s selected as a typcal value. Assume t s scaled from x to y = g x before transmsson, where g s the scalng factor for ths chunk. Defne the power of a chunk as ts varance. We denote by λ the varance of chunk and µ ts power after applyng the gan. Assumng the mean of each chunk has been removed to get a zeromean dstrbuton, we obtan that λ = E[x 2 ], µ = E[y 2] and g = µ λ. All coeffcents of the chunk are allocated to the j th subcarrer and experence the same fadng durng transmsson. The recever receves ŷ j = a j y + n, where a j s the channel fadng coeffcent 2 of the j th subcarrer, and n s a random Gaussan varable wth zero mean and varance σ 2. The recever decodes ˆx j = ŷj = x + n, (1) a j g a j g and the expected MSE of the th chunk carred by the j th subcarrer s obtaned by e j =E [(ˆx j x ) 2] = λ σ 2 a j 2. (2) µ Gven that larger λ contrbutes more to the MSE, λ can be consdered as the mportance of the th chunk. The end-to-end MSE of a GOP s expressed by MSE = b j e j = b j λ σ 2 j j a j 2, (3) µ where b j s a bnary value denotng whether the th chunk s allocated to the j th subcarrer. b j = 1 means that the th chunk s allocated to the j th subcarrer and b j = 0 means the opposte. Let P tot be the total power budget. An optmzaton problem s formulated as mnmze subject to b j λ σ 2 j a j 2, µ µ P tot, b j = 1, j b j = 1, b j {0, 1}, µ 0, whch s a mxed bnary programmng problem. Obtanng a global optmal soluton s dffcult because of the computatonal complexty. However, when {b j } s gven, the problem s reduced to a smple convex optmzaton problem λ σ 2 mnmze, c µ subject to µ P tot, (5) µ 0, where {c } s a rearrangement of { a 2 } dependng on the subcarrer matchng scheme. The optmal power allocaton of (5) can be obtaned by KKT condtons[17] as µ = P λ c and scalng factors are calculated accordngly: µ P g = = λ (4) λ c, (6) λ c λ c. (7) Therefore, the optmal jont subcarrer matchng and power allocaton can be obtaned by fndng the mnmal objectve functon among all subcarrer matchng possbltes, and the correspondng subcarrer matchng and power allocaton are jontly optmal. Unfortunately, the complexty s O(N!). In ths paper, a low-complexty matchng scheme s proposed and ts optmalty can be proved. B. Problem soluton for vdeo uncast 2 Wreless fadng ncludes large scale fadng (path loss), shadow fadng and small scale fadng (multpath effect). Here, the channel coeffcent s the product of all fadng factors. In order to obtan the optmal soluton, a system ncludng only two chunks and two subcarrers s consdered frstly. Then, ths system s extended to a system ncludng N chunks and N subcarrers, where 2 N <. When the numbers of chunks and subcarrers are both two, solvng the problem (4) s equvalent to obtanng the mnmum of the followng two optmzaton problems, each of whch

5 5 ndcates a subcarrer matchng scheme: P1: P2: mnmze err 1 = λ 1σ 2 + λ 2σ 2, h 1 µ 1 h 2 µ 2 subject to µ 1 + µ 2 P, µ 1 0, µ 2 0, mnmze err 2 = λ 1σ 2 + λ 2σ 2, h 2 µ 1 h 1 µ 2 subject to µ 1 + µ 2 P, µ 1 0, µ 2 0, where h 1 = a 1 2 and h 2 = a 2 2 denote the two channel gans; λ 1 and λ 2 are the varances of the two chunks; P s the system power constrant. Wthout loss of generalty, we assume that h 1 h 2, λ 1 λ 2 and P > 0. Thus, P1 denotes that the chunk wth small varance λ 1 s matched to the subcarrer wth small gan h 1, and accordngly λ 2 to h 2. P2 denotes another matchng that λ 1 s matched to h 2 and λ 2 to h 1. Lemma 1. For the system ncludng only two subcarrers and two chunks, the optmal subcarrer matchng matches the chunk wth large varance to the subcarrer wth large gan and the chunk wth low varance to the subcarrer wth small gan. Together wth the optmal power allocaton for ths subcarrer matchng, the optmal jont subcarrer matchng and power allocaton scheme s obtaned. Proof. Under the assumpton of two subcarrers and two chunks, all the possbltes can be enumerated. Assume the optmal soluton of P1 and P2 are (µ 1, µ 2) and (µ 1, µ 2), respectvely. In the followng, we wll prove that P1 always has a better soluton than P2,.e. err 1 (µ 1, µ 2) err 2 (µ 1, µ 2). The whole proof s dvded nto two cases accordng to the relatonshp between h 2 µ 1 and h 1 µ 2. Case 1: h 1 µ 2 h 2 µ 1 Let ˆµ 1 = µ 2 and ˆµ 2 = µ 1. Obvously, ( ˆµ 1, ˆµ 2 ) s a feasble soluton of P1. The dfference between err 1 ( ˆµ 1, ˆµ 2 ) and err 2 (µ 1, µ 2) s calculated by err 1 ( ˆµ 1, ˆµ 2 ) err 2 (µ 1, µ 2) = λ 1σ 2 h 1 µ + λ 2σ 2 2 h 2 µ λ 1σ 2 1 h 2 µ λ 2σ 2 1 h 1 µ 2 = σ2 (λ 2 λ 1 )(h 1 µ 2 h 2 µ 1) (h 1 µ 2 )(h 2µ 1 ) 0. (8) (9) (10) Note that the MSE err 1 ( ˆµ 1, ˆµ 2 ) s even larger or equals the optmal MSE err 1 (µ 1, µ 2), from whch we obtan that err 1 (µ 1, µ 2) err 1 ( ˆµ 1, ˆµ 2 ) err 2 (µ 1, µ 2). Case 2: h 1 µ ( 2 > h 2 µ ) 1 Let ˆµ 1 = µ h1 h 2 µ 2 and ˆµ 2 = h1 h 2 µ 2. Obvously, ˆµ 1 + ˆµ 2 = P. Due to the relatonshp that 0 < h 1 < h 2 and 0 < µ 1, µ 2 P, t s obtaned that 0 < ˆµ 1, ˆµ 2 P. Therefore, ( ˆµ 1, ˆµ 2 ) s one of the feasble solutons of P1. The dfference of err 1 ( ˆµ 1, ˆµ 2 ) and err 2 (µ 1, µ 2) s calculated by err 1 ( ˆµ 1, ˆµ 2 ) err 2 (µ 1, µ 2) λ 1 σ 2 = ( ) ) + h 1 µ 1 (1 + h1 h 2 µ 2 λ 2 σ 2 h 2 ( h 1 h 2 µ 2 = λ 1σ 2 1 h 2 (h 2 h 1 )(h 2 µ 1 h 1 µ 2) ( ) ) h 1 µ 1 (1 + h1 h 2 µ 2 h 2 µ 1 = λ 1σ 2 (h 2 h 1 )(h 2 µ 1 h 1 µ 2) h 1 h 2 2 µ 1 ˆµ. 1 ) λ 1σ 2 h 2 µ 1 λ 2σ 2 h 1 µ 2 (11) Gven that h 1 µ 2 > h 2 µ 1 and h 1 < h 2, (11) has a non-postve value. As a result, t s fnally obtaned that err 1 (µ 1, µ 2) err 1 ( ˆµ 1, ˆµ 2 ) err 2 (µ 1, µ 2). The above two cases all ndcate that P1 has a better soluton than P2. Therefore, P1 s the optmal matchng scheme, and the optmal soluton of P1 s also optmal for problem (4). Next, we extend the method to the system ncludng N subcarrers and N chunks. Denote the subcarrer gans and the chunk varances by {h } and {λ }, respectvely. Here, wthout loss of generalty, t s stll assumed that h h j and λ λ j, f j. For the global optmum, the followng proposton gves the jont power allocaton and subcarrer matchng approach. Theorem 1. For the system ncludng N subcarrers and N chunks, the optmal subcarrer matchng matches the th chunk to the th subcarrer where both {λ } and {h } have been arranged n a decreasng order, respectvely. Together wth the optmal power allocaton for ths subcarrer matchng, the optmal jont subcarrer matchng and power allocaton scheme s obtaned. Proof. The theorem wll be proved n a contrapostve form. Suppose that there exsts a subcarrer matchng method whose matchng result ncludes the followng two pars that λ s matched to h j and λ k s matched to h l, where λ < λ k and h j > h l. Under ths supposton, the mnmal MSE obtaned by adoptng ths matchng method s lower than that by adoptng Theorem 1. Fx the matchng result and the amounts of power allocated to other subcarrers. The total MSE of the above two pars can be further reduced accordng to Lemma 1. Thus, the total MSE of all the chunks can be reduced by rematchng subcarrers and the matchng method s obvously not optmal, whch s contrary to the supposton. Therefore, the optmal matchng result should nclude no such matchng pars. Snce only the method denoted by Theorem 1 satsfes the requrement, ths subcarrer matchng and correspondng optmal power allocaton are the optmal jont subcarrer matchng and power allocaton. So far, the optmal jont subcarrer matchng and power allocaton for uncast s provded. The optmal scheme matches the subcarrers by the order of the channel gans and chunk

6 6 varances, and allocates optmal power under ths matchng accordngly. The scalng factors can be calculated by (7). Thus the mxed nteger optmzaton problem (4) s reduced to a smplfed form (5) by adoptng Theorem 1. Frequency (subcarrer) GOP perod C. Extenson to vdeo multcast In ths subsecton, the results of uncast are extended nto multcast. To make the vdeo qualtes at varous recevers controllable, dfferent weghts or mportance factors are assgned to multple users. Defne the new optmzaton objectve as the weghted sum of all users MSEs. By mnmzng the objectve, users wth hgh weghts wll get large performance mprovement. We can enlarge the weghts for users at cell edge or some mportant users to enhance ther performance. Assumng K users locate randomly n a wreless vdeo multcast cell and the k th user s weght s β k, a new optmzaton problem for vdeo multcast s formulated as mnmze subject to b j λ σ 2 β k a k j jk 2, µ µ P, b j = N, b j = N, j µ 0, b j {0, 1}, (12) where a k 2 denotes the th channel gan of the k th user, whch can be obtaned from the feedback channel. We defne the vrtual gan of the j th subcarrer as the weghted harmonc mean of all users j th channel gans as follows: ã j 2 1 = β k. (13) k a jk 2 Accordng to the above defnton, the objectve of (12) s rewrtten as b j λ σ 2 ã j 2. µ (14) j Note that by replacng the objectve wth (14), (12) has the same form as (4) and thus can be solved by the proposed method. In concluson, the SAP collects all users CSI and calculates the vrtual channel gans denoted by (13). Then, the jont carrer matchng and power allocaton scheme s appled n the same way as vdeo uncast: the varances of chunks and the vrtual channel gans are arranged n a decreasng order, respectvely, and then matched by ths order; subsequently, the optmal power s calculated for ths subcarrer matchng accordngly. Ths scheme s the optmal carrer matchng and power allocaton scheme for vdeo multcast n terms of mnmzng the weghted sum of the end-to-end MSEs. IV. CHANNEL ADAPTION In the proposed real-tme wreless vdeo multcast system, the role of channel adapton s to adapt the vdeo layer to Chunks carred by one subcarrer tme slot 1 tme slot 2 tme slot Ns Tme Fg. 2. Illustraton of chunks, tme slots, subcarrers and GOP perod n the resource allocaton process. the transmsson layer. The bt rate of the vdeo source, the avalable bandwdth and user moblty are jontly consdered, whch are all n the scope of channel adapton. Another goal of ths module s to extend the results n Secton III nto a general case where the number of chunks s unequal to the number of subcarrers. Assume that the tme s slotted and the length of a tme slot s less than the channel coherence tme. As a result, channel states stay nearly unchangeable wthn one tme slot. In order to smplfy the resource allocaton process, a proper chunk sze s determned such that each subcarrer carres an ntegral number of chunks n one tme slot. As shown n Fg. 2, for real-tme transmsson, chunks n a GOP should be transmtted wthn a GOP perod, whch s determned by the number of frames per GOP and the frame rate. Assume that N s tme slots are needed to transmt a GOP. Gven that future channel states are unknown n advance at the SAP and only nstantaneous values are fed back from recevers, the jont carrer matchng and power allocaton scheme has to be appled ndependently n each tme slot. A. Bandwdth adapton The amount of nformaton that can be transmtted s lmted by the capacty of the PHY layer. When the bandwdth s larger than needed, the transmtter skps a certan number of weak subcarrers and allocate chunks to strong subcarrers n each tme slot; otherwse, the least mportant chunks are dscarded at the transmtter and reconstructed wth zero values at the recever. The chunks wth least varance are consdered as least mportant chunks, because they contrbute the least to the vdeo qualty. After channel adapton, we ensure that the number of reserved chunks s an nteger multple of the number of selected subcarrers. B. Moblty adapton When a recever s movng, the channel status changes fast and the SNR also fluctuates. To adapt user moblty, shot tme slots are needed. Assume a GOP s transmtted n N s tme slots. Then, the reserved chunks should be dvded nto N s groups wth one group transmtted n one tme slot. To dsperse the mportance of vdeo data across all tme slots, let the N s groups have a nearly equal average varance. Therefore,

7 7 chunks N-6 N-5 N-3 N-2 N-1 N subcarrers tme slot 1 Fg. 3. Map chunks to multple tme slots by adoptng the nterleavng method tme slot 2 tme slot 3 packets mssng or dstorton leads to the least vdeo qualty degradaton. A chunk nterleavng method s proposed n ths paper. It can be vewed as a chunk nterleaver whch has the same effect as that of the Hadamard transform n SoftCast. Gven that the chunks are sorted accordng to ther varances, the (2N s + n) th and the (2N s + N s n) th chunks are assgned to the n th tme slot, where = 0, 1, 2,. Fg. 3 llustrates the method where N s s set to 3. The (6 + 1) th and (6 + 6) th chunks are allocated to the frst tme slot, (6 + 2) th and (6 + 5) th chunks to the second tme slot and (6 + 3) th and (6 + 4) th chunk to the thrd tme slot, respectvely. C. Extenson for unequal numbers of chunks and subcarrers The one-to-one matchng constrant n Secton III s a smplfed assumpton. However, n a more general case, the numbers of chunks and subcarrers are unequal. As dscussed above, the number of chunks s an nteger multple of the number of subcarrers by proper system parameter settng. Therefore, we can assume that m chunks are carred by one subcarrer n each tme slot, where m s an nteger and m 1. To satsfy the one-to-one matchng condton, each channel gan s duplcated m tmes. Then, the number of chunks equals that of the subcarrers, and the approach descrbed n Secton III s applcable. V. DEMODULATION AND ANALOG FEEDBACK A recever decodes QAM symbols and feeds CSI to the SAP n ths module. A. Demodulaton A lnear least square estmator (LLSE) decoder s employed at the recever. Unlke the LLSE decoder n SoftCast[8], wreless fadng s consdered n our system. For the th chunk, denote by λ the varance, g the scalng factor and a the channel coeffcent. The k th sample n the th chunk s decoded by: ˆx [k] = λ g a λ a 2 g 2 + σ2 y [k], where y [k] s the receved sample, σ 2 denotes the nose power and a s the complex conjugate of a. B. Analog feedback scheme Gven that TDD s assumed, wthn channel coherence tme, the states of the uplnk channels are nearly the same as that of the downlnk channels. Therefore, the CSI feedback from users can be used drectly n the downlnk. In vdeo uncast, the overhead of feedng CSI s low and can be nearly neglected. However, n vdeo multcast, the overhead scales to the number of users. As a result, how to lmt the overhead s a sgnfcant problem. In ths subsecton, a novel lmted feedback scheme s nvestgated to deal wth the large overhead. Accordng to (13), feedng CSI back to the SAP exactly s unnecessary for users, because what the SAP actually needs are the weghted harmonc means of channel gans. Tradtonal lmted feedback methods [18] whch often quantze and compress the CSI before transmsson are not adopted n our system. Because the overhead grows lnearly wth the number of users, whch s not scalable n multcast scenaros. In order to reduce the overhead, we desgn a novel scheme, whch allows the SAP to obtan the vrtual channel gans drectly from a shared uplnk feedback channel. In the proposed scheme, each user transmts a group of tone sgnals n the feedback tme slot smultaneously. One tone sgnal s carred by one subcarrer and the ampltude refers to the channel condton of the subcarrer. For user k, F jk s sent as the power of the tone sgnal n the j th subcarrer: F jk = β k a jk 4. (15) The SAP sees the superposton of multple tone sgnals from the same subcarrer. The total power of the superposed sgnals n the j th subcarrer s F j = k F jk a jk 2 + σ 2 = k β k a jk 2 + σ2, (16) where σ 2 s the nose power. Although the SAP cannot dstngush each of the channel gans, t drectly obtans an nverse of (13). As a result, the SAP only needs to lsten to the

8 8 Parameters TABLE I TEST SEQUENCES akyo bus cty coastguard crew flower football foreman harbour ce moble news soccer stefan tempete waterfall TABLE II SIMULATION PARAMETERS Descrpton number of chunks per frame 64 number of data subcarrers 64 wreless channel Raylegh fadng channel vdeo resoluton vdeo frame rate 30 frames/s number of frames per GoP 32 rato of reserved chunks 75% pathloss factor α 4 Gaussan nose transmsson power 90 dbm 5 dbm feedback tme slot and obtans the detected power of sgnals over each subcarrer. When only one user exsts, the feedback that the SAP receved n uncast and multcast s unfed. The effect of nose power wll be analysed n Secton VI-C. As wll be shown, the system s not senstve to nose. VI. SIMULATION RESULTS In ths secton, the performance of our method s evaluated. Vdeo algorthms often perform dfferently when tested wth dfferent vdeo sequences. Thus, 16 common vdeo sequences wth resolutons of 228 pxels 352 pxels as shown n Table I are combned to form an ntegrated test sequence. The proposed method s compared aganst two baselnes: SoftCast and WSVC. All schemes are mplemented usng MATLAB. SoftCast: SoftCast s a tradtonal analog codng system and s often adopted as a baselne n performance comparson. WSVC: WSVC s one of the most popular state-of-the-art approaches. It s a hybrd dgtal-analog codng scheme. A group of pctures s frst decomposed by 2D-DWT. Then, the dgtal codng part encodes the base layer and the analog codng part encodes the enhancement layer. In our smulaton, the analyss and the synthess flter coeffcents of DWT are set accordng to Table I n [13]. JSVM [19] s adopted to generate H.264/AVC streams. Gven that the denosng part of WSVC s optonal and leads to a slght PSNR loss, t s not mplemented n the smulatons. Both SoftCast and the analog part of WSVC can be mproved by adoptng our approach. The structure of WSVC s P S N R (d B ) S N R (d B ) Fg. 4. Performance comparson of vdeo uncast. E C a s t E C a s t w /o c a rre r m a tc h n g S o ftc a s t w /o H S o ftc a s t w / H W S V C E n h a n c e d W S V C analog codng part s smlar to that of SoftCast. Our proposed jont subcarrer matchng and power allocaton can be appled on the I and Q components of WSVC, respectvely. To dstngush the two enhanced versons of SoftCast and WSVC, we use ECast to denote the former and enhanced WSVC to denote the latter n the followng smulaton results. Gven that the performance of WSVC s not entrely determned by ts analog part, we compare t only to the pure analog codng scheme,.e. SoftCast, n some results to llustrate the characterstcs of our proposed scheme. Some common parameters are summarzed n Table II. A total of 32 vdeo frames are grouped nto a GOP. DCT (3D-DCT for SoftCast and temporal DCT after 2D-DWT for WSVC) s appled on each GOP. Coeffcents of each frame are dvded nto 64 chunks. An OFDM-based PHY layer wth 64 subcarrers s adopted. We assume that the vdeo sgnal experences Raylegh fadng and path loss durng transmsson. For Raylegh fadng, ZMCSCG random varables wth unt varance are adopted as fadng coeffcents. For path loss, when a user s located at a dstance r k from the SAP, the receved sgnal power s attenuated by r α k, where α s the path loss factor and s set to 4 n our smulatons. Dfferent schemes are compared usng a standard metrc PSNR, whch s defned as ( 2 L 1 ) 2 P SNR = 10 log 10 MSE, where L s the number of bts used to encode each pxel and s typcally 8 bts. A. Uncast Performance Comparson Fg. 4 shows the performance comparson of vdeo uncast. ECast has a 4 db - 6 db gan compared to SoftCast wth Hadamard transform n a large SNR range from 0 db to 30 db. Hadamard transform provdes a 2 db - 3 db precodng gan n low SNR ranges n fadng channels. However, our proposal outperforms Hadamard transform. When SNR tends to be hgher, the dstorton caused by wreless transmsson errors s smaller and chunk dscardng n bandwdth adapton becomes the domnant reason for performance loss. As a result, the gan tends to be small n hgh SNR ranges. ECast wthout subcarrer

9 9 S N R & P S N R (d B ) S N R S o ftc a s t w / H S o ftc a s t w /o H E C a s t Schemes TABLE III MOBILITY SIMULATION RESULTS Number of percevable changes SoftCast w/ H 17 SoftCast w/o H 69 ECast fra m e n d e x Fg. 5. Performance varaton under large moblty. The SNR vares unformly from 6 db to 12 db. matchng assgns chunks to subcarrers randomly but calculate the scalng factors accordng to the optmal power allocaton scheme consderng fadng. The performance gan s about 1 db n low SNR ranges and 2 db - 3 db n hgh SNR ranges. From these curves, we obtan that subcarrer matchng s the man reason for the performance enhancement. It domnates the proposed jont subcarrer matchng and power allocaton scheme. By adoptng the proposed method n the analog part of WSVC, the performance s mproved by 2 db n average. Gven that the performance of WSVC s determned by both the analog codng and dgtal codng parts, the mprovement s a slghtly smaller. The enhanced WSVC outperforms pure analog schemes n low SNR ranges, because some mportant components are protected well by the dgtal codng part. However, wth the ncreasng SNR, the performance ncreases slowly n PSNR. Ths s because the data generated by the dgtal part are over-protected n hgh SNR ranges. Nonscalablty s nevtable because the dgtal part of WSVC adopts tradtonal vdeo codng and wreless transmsson schemes whch are not scalable. B. Moblty test The performance s evaluated under user movement. We run a smple uncast experment wth one SAP and one movng user to compare our proposal aganst SoftCast. Wth the help of Hadamard transform whch redstrbutes the mportance of vdeo coeffcents, SoftCast performs well n user movement scenaros. By contrast, the moblty adapton n our scheme has a smlar effect to that of Hadamard transform. We assume that each subcarrer carres only one chunk wthn a tme slot, and the SNR vares unformly from 12 db to 6 db and changes at every tme slot. As depcted n Fg. 5, the PSNR fluctuaton of SoftCast wthout Hadamard s more volent than ECast and SoftCast wth Hadamard. Both ECast and SoftCast wth Hadamard have a smlar fluctuaton, but ECast outperforms SoftCast n PSNR. In addton, the performance of dfferent schemes s also compared numercally. As ntroduced n [20], temporal vdeo qualty fluctuaton s percevable only f the change exceeds a certan threshold. In our smulaton, f the PSNR change between two consecutve frames exceeds 0.5 db, t s consdered as a vsble change[21]. A total of 720 frames are smulated. The results are shown n Table III. The number of percevable changes for SoftCast wth Hadamard, SoftCast wthout Hadamard and ECast are 17, 69 and 18, respectvely. ECast and SoftCast wth Hadamard have a smlar PSNR fluctuaton. Both of them outperform SoftCast wthout Hadamard n terms of qualty fluctuaton. C. Inaccurate feedback Fg. 6 shows the performance degradaton caused by naccurate CSI. The naccuracy s nvolved n both the channel estmaton and the channel feedng processes. We assume that the mnmum mean square error estmator s adopted to estmate channel states. The estmaton errors can be modeled as..d. ZMCSCG varables[22]. The noses n feedback tones are also..d. ZMCSCG varables. They are ndependent from each other. As a result, a combned Gaussan nose can be used to model the naccuracy of each feedback tone. The SAP recevng naccurate CSI s equvalent to recevng accurate CSI plus the Gaussan nose. Fg. 6 shows the performance of naccurate CSI feedback under dfferent nose powers. We plot three curves wth SNR 5 db, 8 db and 11 db, respectvely. The estmaton error rato s the varance rato of the estmaton error and the Raylegh fadng coeffcent. In all cases, wth the rato ncreasng, the PSNR of the system degrades smoothly. No sharp drops of these performance curves have been found. Therefore, the analog feedback scheme s not senstve to nose. D. Multcast Performance Comparson The performance of recevers at varous dstances from the SAP s compared. We assume that the SAP serves a group of three recevers. The dstance between the k th recever and the SAP s r k, where r 1 = 100 m, r 2 = 134 m and r 3 = 167 m. Due to large scale fadng, the three users receve dfferent average sgnal powers. The transmttng power target s set to 5 dbm. The receved power for the k th user s approxmately 5 10 log(rk α ) dbm. We further set the nose and nterference power to 90 dbm. Then, the correspondng SNRs for the users are 15 db, 10 db and 5 db, respectvely. Smulaton results are gven n Fg. 7. The ECast (uncast) means that only one user exsts n the multcast cell, so the SAP transmts vdeo sgnals only accordng to ths user s channel condtons. Obvously, the user obtans best performance mprovement. It provdes an upper bound of performance mprovement for users n a multcast cell. In addton, we assgn the weghts of the three users to 0.01, 0.1 and 0.89 from near to far, respectvely. Users that are remote from the

10 S N R = 5 d B S N R = 8 d B S N R = 1 1 d B P S N R (d B ) P S N R (d B ) u s e r1 (S N R = 1 1 d B ) u s e r2 (S N R = 1 7 d B ) e s tm a to n e rro r p o w e r ra to (% ) Fg. 6. Performance degradaton due to naccurate feedback w e g h t o f u s e r1 Fg. 8. The effect of mportance factors E C a s t (u n c a s t) E C a s t (m u ltc a s t) S o ftc a s t P S N R (d B ) P S N R (d B ) S N R (d B ) Fg. 7. Multcast to three recevers n u m b e r o f u s e rs Fg. 9. Performance changes wth an ncreasng number of users. SAP obtan lager performance mprovement, whereas those near the SAP obtan less or even negatve gans. As a result, the scheme provdes an effectve way to guarantee farness by assgnng large weght to users at the cell edge. E. Effect of mportance factors The effect of mportance factors s evaluated. Two users wth SNRs 11 db and 17 db are smulated. Let 0 < ω < 1 denote the weght of user 1 and 1 ω the weght of user 2. As shown n Fg. 8, wth ω ncreasng, the PSNR of the frst user ncreases rapdly between 0 and 0.1 and gradually between 0.1 and 1. At the same tme, the performance curve of user 2 declnes gently between 0 and 0.9 and steeply between 0.9 and 1. As a result, assgnng an mportance factor larger than 0.1 s suggested; otherwse, the performance may decrease largely. A crossover pont exsts when ω approaches 1. Ths fndng mples that the vdeo qualty s affected by the weght, and a user wth hgh weght but low SNR can have better performance than that wth hgh SNR but low weght. F. Performance changng wth an ncreasng the number of users We assgn the same weght to each user n ths smulaton and evaluate how a user s performance changes wth the number of users. The SNR s set to 11 db. As shown n Fg. 9, wth the ncreasng number of users, the performance of ECast decreases. If the number of users s large enough and the same weght s assgned to each user, then ECast wll perform smlarly as SoftCast and all vrtual channel gans obtaned by the SAP wll be nearly equal to 1. VII. CONCLUSION In ths paper, a cross-layer desgn for wreless vdeo multcast systems s proposed. It s an enhanced analog vdeo codng scheme. We take advantage of the SoftCast framework and focus on the jont subcarrer matchng and power allocaton method. Wth analytcal argument, a low-complexty and optmal scheme s provded. Channel adapton s consdered to make the scheme applcable and robust n real-tme wreless vdeo systems. Fnally, a novel analog method s proposed to lmt the overhead of channel feedback. Smulaton results show that the proposed approach outperforms SoftCast and WSVC, and provdes flexble enhancement for dfferent users. Therefore, the proposed approach s sutable for wreless vdeo multcast applcatons. REFERENCES [1] M. Skoglund, N. Phamdo, and F. Alajaj, Hybrd dgtal analog source channel codng for bandwdth compresson/expanson,

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Goldsmth, Capacty and power allocaton for fadng mmo channels wth channel estmaton error, Informaton Theory, IEEE Transactons on, vol. 52, no. 5, pp , Zhlong Zhang receved the B.E. degree n communcaton engneerng from the Unversty of Scence and Technology, Bejng, Chna n 2007, and the M.S. degree n communcaton and nformaton systems from Bejng Unversty of Posts and Telecommuncatons, Bejng, Chna n He s currently pursung hs Ph.D. degree at Bejng Unversty of Posts and Telecommuncatons. Durng 2010 to 2012, he was a software engneer n TD Tech Ltd., Bejng, Chna. Durng 2014 to 2015, he was a vstng Ph. D student at Stony Brook Unversty, NY, USA. Hs research nterests nclude optmzaton theory and ts applcatons n wreless vdeo transmsson, cross-layer desgn and wreless networks. Danpu Lu receved the Ph.D. degree n communcaton and electrcal systems from Bejng Unversty of Posts and Telecommuncatons, Bejng, Chna n She was a vstng scholar at Cty Unversty of Hong Kong n 2002, Unversty of Manchester n 2005, and Georga Insttute of Technology n She s currently workng at the Bejng Key Laboratory of Network System Archtecture and Convergence, Bejng Unversty of Posts and T- elecommuncatons, Bejng, Chna. Her research nvolved MIMO, OFDM as well as broadband wreless access systems. She has publshed over 100 papers and 3 teachng books, and submtted 26 patent applcatons. Her recent research nterests nclude 60GHz mmwave communcaton, wreless hgh defnton vdeo transmsson and wreless sensor network. Xaol Ma receved the B.S. degree n automatc control from Tsnghua Unversty, Bejng, Chna n 1998, the M.S. degree n electrcal engneerng from the Unversty of Vrgna, Charlottesvlle, n 2000, and the Ph.D. degree n electrcal engneerng from the Unversty of Mnnesota, Mnneapols, n From 2003 to 2005, she was an Assstant Professor of Electrcal and Computer Engneerng at Auburn Unversty. Snce 2006, she has been wth the School of Electrcal and Computer Engneerng at Georga Insttute of Technology, Atlanta, where she s currently an Assocate Professor. Her research nterests nclude transcever desgns and dversty technques for wreless fadng channels, cooperatve communcatons, UWB communcatons, synchronzaton for mult-carrer systems, and channel modelng, estmaton, and equalzaton for wreless systems.

12 Xn Wang receved the B.S. and M.S. degrees n telecommuncatons engneerng and wreless communcatons engneerng respectvely from Bejng Unversty of Posts and Telecommuncatons, Bejng, Chna, and the Ph.D. degree n electrcal and computer engneerng from Columba Unversty, New York, NY. She s currently an Assocate Professor n the Department of Electrcal and Computer Engneerng of the State Unversty of New York at Stony Brook, Stony Brook, NY. Before jonng Stony Brook, she was a Member of Techncal Staff n the area of moble and wreless networkng at Bell Labs Research, Lucent Technologes, New Jersey, and an Assstant Professor n the Department of Computer Scence and Engneerng of the State Unversty of New York at Buffalo, Buffalo, NY. Her research nterests nclude algorthm and protocol desgn n wreless networks and communcatons, moble and dstrbuted computng, as well as networked sensng and detecton. She has served n executve commttee and techncal commttee of numerous conferences and fundng revew panels, and s the referee for many techncal journals. Dr.Wang acheved the NSF career award n 2005, and ONR challenge award n