MAC 26.3 - Scalable Video Streaming over Fading ... - Semantic Scholar

This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the WCNC 2009 proceedings.

Scalable Video Streaming over Fading Wireless Channels Honghai Zhang∗ , Yanyan Zheng† , Mohammad A. (Amir) Khojastepour∗ , Sampath Rangarajan∗ ∗

NEC Laboratories America, Princeton, NJ – E-mail: {honghai,amir,sampath}@nec-labs.com † Stanford University, Palo Alto, CA – E-mail:[email protected]

Abstract—We consider the transmission of multiple scalable video streams from a server to multiple users over a fading wireless channel. We first present a long-term resource allocation algorithm that determines the scheduling policy and the parameters used by the scheduling policy in order to maximize the weighted sum of PSNR of all video streams. We then present an online scheduling algorithm that utilizes the results obtained by the long-term resource allocation algorithm for user and packet scheduling as well as video frame dropping strategy. Simulation results show that our proposed scheduling scheme significantly improves the video quality compared to the bestknown scheduling algorithms in the literature. Index Terms—Scheduling, video streaming, scalable video, fading channel, wireless networking

I. I NTRODUCTION Wireless video streaming is becoming increasingly popular in the past few years as both wireless networking and video coding technologies have made significant progress. On the wireless side, the data transmission rates are steadily growing. Latest WiFi networks can support data rate of more than 100 Mbps and the next generation (4G) wireless technologies are expected to achieve 1 Gbps for nomadic users and 100 Mbps for mobile users [4]. On the video coding side, H.264/MPEG4AVC[1] enables more efficient video coding and scalable video coding (SVC)[7] allows more flexible video coding. Nevertheless, it remains a challenge to adapt wireless networks to satisfy the requirements of video streaming services. In fading wireless networks, most MAC schedulers employ some type of channel-state aware scheduling algorithms (e.g., Proportional Fair Scheduling) to exploit multi-user diversity. However, these schemes often ignore the realtime QoS requirement of video traffic. In this work, we consider streaming SVC-encoded video in fading wireless networks. An SVC bitstream consists of one base layer and multiple enhancement layers. As long as the base layer is received, the receiver can decode the video stream. As more enhancement layers are received, the decoded video quality is improved. With SVC-encoded stream, the scheduler at the wireless base station can adapt to changing wireless channel conditions by transmitting a subset of enhancement layers. An important issue for the wireless scheduler is how to share the wireless radio resources in order to optimize overall streaming video quality. We first develop a model to characterize the relationship between the time-averaged data rate and the video quality (measured by PSNR), which turns out

to be a concave, piece-wise linear function. We consider a general TDMA scheduling policy: at each time slot, only one user is selected for scheduling. We then formulate the problem as a long-term radio resource allocation problem where the objective is to maximize weighted sum of the time-averaged video quality of all streaming users. We show that the optimal scheduling policy has the following property called maximal scheduling: at each time slot, the user with the largest μi Ci is selected for scheduling, where Ci is the channel capacity and μi is a parameter for user i. We then design an algorithm to find the set of parameters {μi , i = 1, · · · , n} (where n is the number of users) to maximize the weighted sum of PSNR of all n streaming users. Following that, our proposed scheduling algorithm uses the maximal scheduling policy and the computed optimal parameters μ = (μ1 , μ2 , . . . , μn ) to select the user for scheduling in each slot. We also design a frame/layer dropping strategy based on the achievable rate for each user obtained in the aforementioned long-term resource allocation algorithm. We carry out extensive simulations to validate our proposed schemes. Simulation results show that our proposed scheduling scheme achieves significant improvement over best-known real-time video scheduling algorithms in the literature. In some cases, our proposed scheme obtains an average of more than 3dB gain in a 4-user streaming system compared to the best-known existing schemes. In addition to that, when the average wireless channel conditions become weak, some video frames are not decodable with existing scheduling schemes. But with our proposed scheduling scheme, all video frames are decodable under almost all wireless channel conditions. Streaming video over wireless networks has been studied extensively. Due to space limits, we only discuss a few most relevant works. Kalman, Girod and Beek[5] studied a radio resource sharing problem among multiple users where the channel capacity for each user is assumed to be fixed. Liebl et al. [6] proposed a scheme to dynamically share the video resources by combining the SVC [7] coding scheme with an appropriate radio link buffer management for multiuser streaming services. But they did not consider the long-term radio resource allocation to optimize the overall video quality. The rest of the paper is organized as follows. In Section II, we give a brief overview of Scalable Video Coding (SVC), and develop a model to characterize the relationship between the video quality (PSNR) and the average video rate. We then discuss the long-term radio resource allocation scheme to

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This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the WCNC 2009 proceedings.

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optimize the overall video quality and the online scheduling algorithm in Section III. Simulation results are reported in Section IV and the paper is concluded in Section V. II. S CALABLE VIDEO CODING AND RATE - QUALITY MODEL In this section, we first give a brief overview of Scalable Video Coding (SVC). We then develop an empirical model to characterize the relationship between the rate and the video quality in SVC. Along with the model, we also describe a method to prioritize each layer of the SVC-encoded stream. A. Overview of Scalable Video Coding SVC can be referred to as both the general concept of scalable video coding and the special extension [7] of H.264/MPEG4-AVC [1]. An SVC stream has a base layer and several enhancement layers. As long as the base layer is received, the receiver can decode the video stream. As more enhancement layers are received, the decoded video quality is improved. The bandwidth scalability of SVC consists of temporal scalability, spatial scalability, and quality scalability. Temporal scalability refers to representing the same video in different temporal resolutions or frame rates. Spatial scalability refers to representing the video in different spatial resolutions or sizes. Normally, the picture of a spatial layer is based on the prediction from both lower-temporal layers and lower-spatial layers. Quality (or SNR) scalability refers to representing the same video in different SNR or quality level. To be precise, SNR-scalable coding quantizes the DCT-coefficients using different quantization parameters. SNR scalability in SVC includes coarse-grain scalability (CGS) and fine grain scalability (FGS). CGS is achieved using the concept of spatial scalability but with identical picture size. FGS is achieved by so-called progressive refinement (PR) slides, each of which represents a refinement of the residual signal that corresponds to a bisection of the quantization step size (QP increase of 6). In the SVC extension [7] of H.264 [1], the base layer is an H.264/MPEG-AVC bitstream for backwards compatibility. The temporal scalable bit-stream is generated using hierarchical prediction structures as illustrated in Fig. 1. SVC [7] also introduces a variation of the CGS approach called mediumgrain quality scalability (MGS), which allows a switching between different MGS layers in any access unit and the adjustment of tradeoff between drift and enhancement layer coding efficiency for hierarchical prediction structures. In this work, we only consider SVC with temporal scalability and MGS scalability. But our approach can be extended to other scalability models as well. B. Rate-quality model and prioritization of layers A natural criteria for measuring video quality is distortion, which is defined as the mean square error of the reconstructed pixel values compared to the original uncompressed pixel values. Another important metric for measuring video quality is PSNR (Peak Signal to Noise Ratio). For a single video frame, PSNR is defined as P SN R = 10 log10 (2552 /D), where D is the distortion. But for a sequence of video frames, the

SNR layer Base layer Temporal 0 level

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Fig. 1. Temporal structure of an SVC stream with SNR layers where the GOP size is 8

relationship between average PSNR and the average distortion is not direct, because both averages are taken over multiple frames with respect to their own values. Some researchers [8] have used distortion as a measure of the video quality and developed models that relate data rate and distortion. However, PSNR is more widely used as the final performance metric in the literature. Therefore, we choose to model the relationship between the average data rate and the average PSNR directly. In [8], different data rates are obtained by encoding using different quantization parameters. To serve the purpose of scalable video streaming, we obtain different data rates by sequentially truncating some layers of an SVC-encoded video stream. There are many ways to truncate an SVC-encoded video sequence, but we always truncate the frames in the same temporal layers to the same SNR layers. A layer can be specified by its temporal level t and its SNR level q. Therefore, the frames belonging to the same layer (t, q) are either all kept or all removed in a truncated video sequence. Moreover, we also need to determine the truncation order of different layers, which is based on the priority of the layers. The priority of the base layers of all temporal layers is decided by their dependence relationship; the lowest temporal base layer has the highest priority. The priority of the SNR layers is determined by the ratio of the PSNR improvement to the rate increase for each added layer. The details of the priority computation are omitted due to space limit. For each rate obtained by sequentially adding the layers with decreasing priority, we can compute the distortion and PSNR compared with the original video sequence. We now obtain a set of sample points of (rate, PSNR) for video sequences Foreman, Mobile, and Crew, all of which can be downloaded from [9]. We plot the sample points in Fig. 2. It is quite clear that the average PSNR is a piece-wise linear function of the average rate consisting of two line segments. Therefore, in our model, the PSNR value Si can be written as ⎧ 0 0 ⎪ if r ≤ ri0 ⎨Si + Li (r − ri ) Si (r) = Si0 + Ki (r − ri0 ) (1) if ri0 < r ≤ rimax ⎪ ⎩ 0 max 0 max Si + Ki (ri − ri ) if r > ri where ri0 and Si0 is the rate and PSNR of user i when only

This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the WCNC 2009 proceedings.

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where yi is the received signal, hi is the channel gain, x is the transmitted signal and z is the complex Gaussian noise with zero mean and unit variance (we assume that the transmitted and the received signal are normalized with respect to the noise). We assume a fixed transmission power |x|2 = ρ. Define the channel state h = (h1 , h2 , . . . , hn ) as the vector of all individual channel gains. We assume that the channel capacity for each user at each time slot t is

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the base layers of all temporal layers are kept, and the last line specifies the maximum encoding rate of each video1 . The regression model for each video sequence is also plotted in Fig. 2. Note that Li > Ki > 0 based on the models of these real video sequences, and the function Si (r) is therefore a concave function with respect to r. III. L ONG - TERM RADIO RESOURCE ALLOCATION AND ON - LINE SCHEDULING When multiple users request for streaming service of different video sequences concurrently through a wireless base station, the MAC scheduler in the base station needs to decide: i) how much bandwidth should be allocated to each user, ii) how to achieve the desired bandwidth, in order to optimize the overall video quality. Instead of considering the rate allocation on a short-term per-slot basis, we consider the long-term average resource allocation for each user in order to optimize average video quality under the assumption of fading wireless channels. In subsection III-A, we describe the problem formulation. To solve the problem, we first characterize the achievable long-term (ergodic) rate region in subsection III-B, and then in subsection III-C, we develop a scheduling policy together with the parameters to maximize the video quality. Finally we discuss how to utilize the obtained results to devise an online scheduling algorithm in subsection III-D. A. Problem formulation We assume that the link from the base station to each mobile client is fading with a known distribution. We consider a block fading model where the fading is constant in each time slot and changes independently from one time slot to the other. The complex baseband model of the ith user channel is given by y i = hi x + z (2) 1 In practice, we may also need a minimum coding rate to maintain a minimum video quality. But we assume that such a requirement can be achieved by admission control. For example, if the resulting data rate of user i is less than its minimum rate requirement, user i will be rejected for admission.

C(hi (t)) = B log(1 + ρ|hi (t)|2 )

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where B is the channel bandwidth. We assume a discrete time system with a TDMA transmission strategy: at each time slot, the server picks only one user (which may depend on the channel states of all the users) and sends information with the supportable rate of the channel of this scheduled user. Our objective is to maximize the weighted sum of average PSNR of all users: n  wi Si (ri ) max s.t.

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r∈R

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where n is the number of users, Si is the PSNR of user i as modeled in Eq. (1), wi is the weight of user i, r = (r1 , · · · , rn ) and R is the achievable ergodic rate region. The major challenge in solving problem (4) is that the achievable rate region R cannot be explicitly specified in a fading environment. We next address this challenge by characterizing the achievable rate region R and its property. B. Achievable rate region R Let C(h) = B log(1 + ρ|h|2 ) denote the instantaneous capacity of the single link with the channel gain h. The achievable rate region for a TDMA strategy is given by R = {r : ri ≤ Eh [I{s(h) = i}C(hi )], 1 ≤ i ≤ n}

(5)

where s(h) is the index of the scheduled user for channel state h, and I{s(h) = i} is an indicator function which is one if s(h) = i and zero otherwise. We note that for the TDMA strategy, the scheduling function s(h) in general can be randomized. We show later that for any continuous distribution for the channel state h, each rate tuple in the boundary B can be achieved with a static scheduling function s(h) that returns only one index for a given channel state. Nonetheless, we consider the general randomized scheduling function to first show the convexity of the achievable rate region and then obtain the boundary points. Suppose that r(1) and r(2) are in the achievable rate region R and are obtained by two scheduling functions s(1) (h) and s(2) (h). In other words, (k)

ri

= Eh [I{s(k) (h) = i}C(hi )], 1 ≤ i ≤ n, k = 1, 2. (6)

Thus, any intermediate point τ r(1) + (1 − τ )r(2) , 0 ≤ τ ≤ 1 also belongs to the region R by considering the randomized scheduling function  s(1) (h) with probability τ s(h) = . s(2) (h) with probability (1 − τ )

This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the WCNC 2009 proceedings.

Therefore, we have proved that the achievable rate region R is convex. Next we define the boundary of the achievable rate region as B = {r ∈ R : there exists no r ∈ R such that r ≺ r } where r ≺ r means that all components of r is less than or equal to r and at least one component in r is less than the corresponding one in r . In other words, the boundary B is the set of the Pareto-optimal achievable rate tuples. Because of the non-decreasing property of the PSNR function Si (r), there must exist optimal solution to problem (4) in the boundary region B of the achievable rate region. Therefore, to solve the PSNR optimization problem (4), it is sufficient to look for solution on the boundary B. The boundary surface B can be obtained by solving the following optimization problem max r∈R

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μi ri

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for all μ = (μ1 , μ2 , . . . , μn ) that is a unit norm vector with positive real elements. To solve the above problem, for each channel state h we have n  μi Pr{I{s(h) = i}}C(hi ). (8) max s(h)

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Therefore, the solution for the scheduling function is given by s(h) = i ⇔ h ∈ {h : μi C(hi ) > μk C(hk ), ∀k = i}.

(9)

In the solution given by (9) we have ignored the set of channel states h for which μi C(hi ) = μk C(hk ) which in fact has zero probability if the distribution of h is continuous. We call the scheduling policy defined by s(h) in (9) as maximal scheduling policy, due to the fact that this scheduler only obtains the set of rates in the boundary which are the set of Pareto-optimal rate tuples. C. Solution to Problem (4) We can now view a boundary point r = (r1 , · · · , rn ) as a function of the parameter set μ = (μ1 , · · · , μn ), where the average rate ri of user i can be written as ri = E[C(hi )I(μi C(hi ) > μk C(hk ) for all k = i)].

(10)

Let γi = ρ|hi |2 denote the SINR of the user i with PDF function fγi (γ) and CDF function Fγi (γ). Let R(γi ) = C(hi ) = B log(1 + γi ). Thus, the rate ri can be computed as  ∞ R(x)Πk=i Fγk (R−1 (μi R(x)/μk ))fγi (x)dx (11) ri (μ) = 0

Now our objective is simply to maximize

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Note that Si (ri ) is a non-decreasing concave function of ri . A general approach to solve an optimization problem is the gradient-based method: we start with some point μ0 , and in

each step k we find the gradient and update the vector μ along a direction d that is related to the gradient: μ(k+1) = μ(k) + α(k) d(k)

(13)

where d(k) = D(k) ∇Y (μ(k) ), D(k) is a positive definite symmetric matrix and ∇Y (μ(k) ) is the gradient of Y with respect to μ(k) . But the challenge with problem (12) is that the function Y is not differentiable at the points where ri = ri0 or ri = rimax for some user i. To resolve the issue, we note that although Si is not differentiable at ri = ri0 or ri = rimax , it has one-sided derivatives. Now with the one-sided partial derivative, we can obtain a modified gradient-based solution by choosing an (k) (k) (k) ascent direction d(k) = (d1 , d2 , ..., dn ) in each iteration k as follows. (k)

di

⎧ ⎪ 0, ⎪ ⎪  ⎨ Yi+ (µ(k) ), = ⎪ ⎪ ⎪ ⎩Y  (µ(k) ), i−

  if Yi+ (µ(k) ) ≤ 0 and Yi− (µ(k) ) ≥ 0  (k) if Yi+ (µ ) > 0 and   (µ(k) ) ≥ −Yi− (µ(k) ) Yi+ otherwise

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  where Yi+ (μ(k) )( Yi+ (μ(k) )) is the right-sided (left-sided) (k) partial derivative of Y with respect to μi . Stepsize selection using modified Armijo Rule: In any gradient-based approach, we also need to choose the step size α(k) appropriately in order for the algorithm to converge to a local maximum. Armijo rule [3] is a simple but effective rule to choose the step size when the gradient exists. For fixed scalars α0 , σ, β, Armijo rule chooses the minimum non-negative m such that α(k) = α0 β m and

Y (μ(k) + α0 β m d(k) ) − Y (μ(k) ) ≥ σα0 β m ∇Y (μ(k) )T d(k) (15) where ∇Y (μ(k) )T is the transpose of the gradient of Y with respect to μ. In our problem, the gradient ∇Y (μ(k) ) may not exist, so we define a modified Armijo rule using d(k) to replace the gradient ∇Y (μ(k) )T in Eq. (15). The pseudo-code of our algorithm is listed next. A1: Pseudo-code to find the optimal solution for problem(12) /* , σ, α0 are constant values.  is a positive value close to 0, and 0 < σ < 1.*/ (0) 1: Select a starting point μi = 1 for all 1 ≤ i ≤ n. (0) 2: Compute d according to Eq. (14) 3: k = 0; (k) 4: while Exists i such that di ≥  do 5: /* Choose the step size */ 6: α = α0 7: while Y (μ(k) + αd(k) ) − Y (μ(k) ) < σα · |d(k) |2 do 8: α=α·β 9: end while 10: μ(k) = μ(k) + α · d(k) 11: k = k+1 12: Recompute d(k) from μ(k) according to Eq. (14) 13: end while With the choice of the gradient-based approach and the modified Armijo rule, it can be shown that the algorithm converges, which is omitted due to space limit.

This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the WCNC 2009 proceedings.

D. Online scheduling Algorithm An online scheduling algorithm for real-time video applications needs to address three issues: 1. User scheduling: at each time slot, which user should be scheduled? 2. Frame scheduling: after a user is selected, which packets/frames of the selected user should be transmitted? 3. Dropping strategy: when does it need to drop frames and which frames should be dropped? The long-term resource allocation algorithm presented in the previous section produces two results: 1) the choice of μi for each user i, 2) the achievable average rate ri for each user i. We next design a scheduling scheme for video streaming using these results. For the user scheduling, we use the maximal scheduling policy: at each time slot the user with the maximum μi Ci is selected for scheduling where Ci is the channel capacity of user i and the vector μ = (μ1 , · · · , μn ) is computed from the long-term resource allocation algorithm in the previous subsection. Note that when users leave or join, or when the channel statistics of some users change significantly, the vector μ need to be re-computed. Frame scheduling for the selected user is based on both the deadline and priority of the packets. We differentiate two types of deadlines. Playout deadline is the time a frame need to be displayed. Decoding deadline is the earliest time that a frame is needed for decoding itself or other frames. The decoding deadline of a frame can be computed as the earliest playout deadline of all frames that depend on it. Note that if a frame is dropped, the decoding deadlines of the frames it depends on need to be updated. We then schedule packets of a given user in the order of their decoding deadline. Those packets with the same decoding deadline are scheduled in the order of their priority. As to the dropping strategy, there are two types of dropping. The first is late dropping, which happens when the playout deadline of a packet is passed. If the base layer of a frame is dropped, all dependent frames are dropped too. Note that when all packets of a frame are either successfully transmitted or dropped, the decoding deadline of the frames that it depends on need to be re-computed. The second type of dropping is early dropping. With the achievable rate computed from the previous subsection, we can pre-determine which layers should be dropped based on the rate requirement. We find the minimum priority such that the average data rate of the packets with priority higher than or equal to the minimum priority does not exceed the achievable rate computed from the previous section. All packets with priority lower than the minimum priority are dropped. In our simulations, we observe that the second type of dropping is essential to ensure that the packets with higher priority are not blocked by those with lower priority. IV. S IMULATION R ESULTS For the simulations, 4 videos are encoded with the SVC extension [7] of H.264/MPEG4-AVC: Foreman, Mobile, Har-

TABLE I S IMULATION PARAMETERS Video Sequence Channel SINR (dB) Initial buffer duration (ms)

User 1 Foreman 5 711

User 2 Mobile 12 762

User 3 Harbour 10 782

User 4 Crew (4CIF) 17 792

TABLE II S UM PSNR ACHIEVED Proposed Scheduling Maximum capacity Proportional fairness M-LWDF

Y-PSNR 143.6 142.0 141.2 138.4

U-PSNR 167.2 166.1 166.0 164.2

V-PSNR 170.3 167.4 167.1 165.2

bour at CIF resolution and Crew at 4CIF resolution, all of which can be downloaded from [9]. All video sequences are encoded at 30Hz with GOP size of 16 pictures and an intra period of 64 frames (about 0.5Hz). The initial buffer duration is randomly generated from 700 milliseconds to 800 milliseconds and for fair comparison, we use the same initial buffer duration for different schemes and the values are listed in Table I. Wireless channels are generated based on Rayleigh fading model. Channel bandwidth is assumed to be 1MHz and slot duration is set to 2ms. The average SINR of four users are listed in Table I. For the simulations, our objective is to maximize the sum Y-PSNR2 of all users. In other words, the weights for all users are set to 1. We consider three reference schemes. The first is the scheme in [6] where the user selection is based on maximum channel capacity, and the packet drop is based on buffer overflow. The buffer limit for each link is 110KBytes as used in [6]. Packets with the lowest priority are dropped first at the time of buffer overflow. This scheme is termed as “Maximum capacity” scheduling. The other two reference schemes are based on the one in [6] but with a different user scheduling. The second scheme uses proportional fairness scheduling and the third uses Modified Largest Weighted Delay First (MLWDF) scheduling [2]. Figure 3 shows the obtained average PSNR of Y,U,Vcomponents of all four video sequences for different schemes (we connect the points that belong to the same scheme with lines simply to group them together). Although our algorithm is applied to improve the Y-PSNR in the simulations, it actually improves the PSNR of all other components. The sum PSNR obtained is summarized in Table II. Our proposed scheme achieves 1.6-4.8 dB gain for the Y-component and 1-5 dB gain for the U and V-components compared with existing schemes. In the second set of experiments, we use the same 4 video sequences but assume that the average channel SINR for all four users is equal. We then investigate the video quality when 2 In video encoding, video signals are decomposed into three components: Y stands for luma component (for brightness), U and V are the chrominance components (for color). Among the three components, Y-component is the most important one as human eyes are most sensitive to the brightness information.

This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the WCNC 2009 proceedings.

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the heavy packet loss3 . But because of the early dropping strategy employed, our scheme can decode all four video sequences even if the average SINR of all users is 5dB. Figure 5 shows the number of video sequences that are not decodable under each scheduling algorithm for different SINR values. It demonstrates the robustness of our proposed scheduling scheme in comparison to that of the existing schemes.

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the average channel SINR varies. Figure 4 shows the sum of the Y-PSNR of all four video sequences under different SINR values. When the channel conditions are good, all schemes achieve similar performance although our proposed scheme and the M-LWDF scheduling algorithm obtains slightly higher PSNR than the other two schemes. This is not surprising because when the channel conditions of all users are good, any scheduling algorithm can fulfill the realtime requirement of the video streams. But when the channel conditions become worse, our scheme is much better than all the other schemes. In the best case, our scheme achieves an average gain of over 5.5 dB compared to the proportional fairness scheduling, and over 3 dB compared to the M-LWDF scheduling, which is the best among the reference schemes. Moreover, when the SINR is low, most other schemes cannot decode the video sequences completely because of

V. C ONCLUSION In this paper we study the scheduling issue for scalable video streaming in fading wireless environments. We first develop a model to characterized the relationship between the average rate and average PSNR of a video stream. We then devise a scheduling policy to maximize the weighted sum of PSNR of all video streams. Simulation results show our scheme achieves much better performance than existing schemes. R EFERENCES [1] Advanced video coding for generic audiovisual services. ITU-T Recommendation H.264-ISO/IEC 14496-10(AVC), ITU-T and ISO/IEC JTC 1, 2003. [2] M. Andrews, K. Kumaran, K. Ramanan, A. Stolyar, R. Vijayakumar, and P. Whiting. Providing quality of service over a shared wireless link. IEEE Communication Magazine, Feb. 2001. [3] D. Bertsekas. Nonlinear Programming. Athena Scientific, 1999. [4] J.M. Costa. More frequencies needed for mobiles - terrestrial spectrum sought for imt. ITU News, No. 3, April 2007. [5] M. Kalman and B. Girod. Optimized transcoding rate selection and packet scheduling for transmitting multiple video streams over a shared channel. Proc. IEEE International Conference on Image Processing, ICIP-2005, September 2005. [6] G¨ unther Liebl, Thomas Schierl, Thomas Wiegand, and Thomas Stockhammer. Advanced wireless multiuser video streaming using the scalable video coding extensions of h.264/mpeg4-avc. In IEEE ICME 2006. [7] H. Schwarz, D. Marpe, and T. Wiegand. Overview of the scalable video coding extension of the h.264/avc standard. 17(9), Sep. 2007. [8] K. Stuhlm¨ uller, N. F¨arber, M. Link, and B. Girod. Analysis of video transmission over lossy channels. IEEE Journal on Selected Areas in Communications, 18(6):1012–1032, June 2000. [9] SVC test sequences. ftp.tnt.uni-hannover.de/pub/svc/testsequences/. 3 The PSNR values plotted in Fig. 4 are the average values of the frames that can be successfully decoded. If we account for the frames that are not decodable, the actual PSNR of other schemes is even lower.