Crosslayer optimization for streaming scalable video over fading wireless networks
ABSTRACT We present a crosslayer design of transmitting scalable video streams from a base station to multiple clients over a shared fading wireless network by jointly considering the application layer information and the wireless channel conditions. We first design a longterm resource allocation algorithm that determines the optimal wireless scheduling policy in order to maximize the weighted sum of average video quality of all streams. We prove that our algorithm achieves the global optimum even though the problem is not concave in the parameter space. We then devise two online scheduling algorithms that utilize the results obtained by the longterm resource allocation algorithm for user and packet scheduling as well as video frame dropping strategy. We compare our schemes with existing video scheduling and buffer management schemes in the literature and simulation results show our proposed schemes significantly outperform existing ones.

Article: Reliabilityoriented ant colony optimizationbased mobile peertopeer VoD solution in MANETs
Shijie Jia, Changqiao Xu, Athanasios V. Vasilakos, Jianfeng Guan, Hongke Zhang, GabrielMiro Muntean[Show abstract] [Hide abstract]
ABSTRACT: Mobile peertopeer (MP2P) has emerged as a stateoftheart technology for video resource sharing in mobile adhoc networks (MANETs), building on the advantages of P2P data exchange and providing a feasible solution for largescale deployment of media streaming services. Fast search for video resources and low maintenance overhead of overlay networks to support the mobility of nodes are key factors in MP2P video on demand solutions. In this paper, we propose a novel reliabilityoriented ant colony optimization (ACO)based MP2P solution to support interactivity for video streaming in MANETs (RACOM). RACOM makes use of highly innovative algorithms such as the peer statusaware mechanism and peercentric overlay maintenance mechanism to support highefficiency video resource sharing. The peer statusaware mechanism includes the user reliability measure model which is used to identify the peers having reliable playback status in order to find stable potential resource suppliers and a new ACObased prediction model of playback behavior which provides the accurate prediction of playback content in the future to ensure the smooth experience and optimize the distribution of resources. In order to balance the fast supplier discovery and low maintenance overhead, RACOM makes use of peercentric overlay maintenance mechanism composed of the time windowbased detection strategy and encounterbased synchronization strategy to reduce the maintenance overhead of reliable peers, obtain quasi realtime status of peers and support the mobility of mobile nodes. Simulation results show how RACOM achieves higher hit ratio, lower seek delay, lower server stress, lower peer load and less overlay maintenance overhead in comparison with another state of the art solution.Wireless Networks 07/2013; 20(5):11851202. · 1.06 Impact Factor 
Conference Paper: Crosslayer radio resource allocation for multiservice networks of heterogeneous traffic
[Show abstract] [Hide abstract]
ABSTRACT: A crosslayer design framework, in the sense of maximizing sumthroughput, is proposed for a multiservice network of heterogeneous traffic. Considering different prescribed target packet loss rates and maximum automatic repeat request (ARQ) delays for the services in the data link control (DLC)layer, we derive the respective optimum signaltointerferenceplusnoise ratio (SINR)targets and variable spreading factor (VSF)s of the services in the physical (PHY)layer, analytically as functions of the multiuser interference (MUI) and fading fluctuations. A multidimensional Markov chain is employed to model the packet traffic characteristics in the network. Performance of the proposed optimized crosslayer system is demonstrated and compared to stateoftheart universal mobile telecommunication system (UMTS) standard, with conventional power, rate, and error control, for various practical system settings using theoretical and simulation results. Considerable improvement in sumthroughput performance of the multiservice mobile communication network is achieved through joint optimization of PHYlayer and DLClayer parameters, whilst satisfying unique quality of service (QoS) constraints of different traffic types.2014 International Conference on Computing, Networking and Communications (ICNC); 02/2014 
Conference Paper: Receiverdriven adaptive layer switching algorithm for scalable video streaming over wireless networks
[Show abstract] [Hide abstract]
ABSTRACT: This paper considers a receiverdriven adaptive rate control scheme for scalable video streaming over wireless networks by jointly utilizing the channel condition and the receiver buffer state. In order to adjust the source video layers based on the feedback received from the enduser, we define buffer overflow probability (BOP) and buffer underflow probability (BUP) as metrics to characterize the degree of matching between the source video bitrate and the channel throughput. Thus, the problem is formulated as maximizing the attainable video quality while keeping BOP and BUP in an acceptable range. Based on the large deviation principles, we derive a probability estimation model for BOP and BUP. Relying on this estimation model, an online adaptive layerswitching algorithm is designed in order to adapt the video bitrate to the available channel throughput. Simulations are conducted with video trace and the results illustrate that the proposed policy is capable of accommodating different channel qualities without any prior knowledge.2014 IEEE 11th International Conference on Networking, Sensing and Control (ICNSC); 04/2014
Page 1
1
Crosslayer Optimization for Streaming Scalable
Video over Fading Wireless Networks
Honghai Zhang, Member, IEEE, Yanyan Zheng, Mohammad A. (Amir) Khojastepour, Member, IEEE,
and Sampath Rangarajan, Senior Member, IEEE
Abstract—We present a crosslayer design of transmitting
scalable video streams from a base station to multiple clients
over a shared fading wireless network by jointly considering the
application layer information and the wireless channel conditions.
We first design a longterm resource allocation algorithm that
determines the optimal wireless scheduling policy in order to
maximize the weighted sum of average video quality of all
streams. We prove that our algorithm achieves the global op
timum even though the problem is not concave in the parameter
space. We then devise two online scheduling algorithms that
utilize the results obtained by the longterm resource allocation
algorithm for user and packet scheduling as well as video frame
dropping strategy. We compare our schemes with existing video
scheduling and buffer management schemes in the literature
and simulation results show our proposed schemes significantly
outperform existing ones.
Index Terms—Scheduling, video streaming, scalable video,
fading, wireless networks
I. INTRODUCTION
Recent years have witnessed increasing popularity of
streaming video over wireless networks as both wireless data
communication and video compression techniques undergo
significant progress. On one hand, the data transmission rates
of wireless networks are steadily growing, e.g., 1Gbps target
rate for nomadic and 100Mbps for mobile users in 4G systems
[9]. On the other hand, H.264/MPEG4AVC [1] achieves
more efficient video compression and the Scalable Video
Coding (SVC) extension [16] of H.264/MPEG4AVC obtains
both high coding efficiency and high scalability. Nevertheless,
because the wireless medium is often shared by many users,
it is still important to adapt to the wireless channel conditions
in order to satisfy stringent bandwidth and delay requirement
of video traffic.
Streaming video over wireless networks has been studied
extensively by many researchers, but much of the previous
work ([7], [8], [25], [15], [22], [26] and the references
therein) has focused on the singlestream scenario where the
transmitter of a video streaming service adaptively adjusts its
transmission rate, retransmission, videotruncation, Forward
Error Correction (FEC) and/or Hybrid ARQ (HARQ) policy
in order to optimize the received video quality. Multiuser
streaming where the wireless radio resources are shared by
multiple streaming users has also been considered in [24],
[10], [11], [13], [14], [12]. However, none of them considered
Manuscript received 19 March 2009; revised 20 October 2009.
Honghai Zhang, Mohammad A. Khojastepour, and Sampath Rangarajan
are with NEC Laboratories America (email:{honghai,amir,sampath}@nec
labs.com.)
Yanyan Zheng is with the Electrical Engineering Department of Stanford
University(email:yyzheng@stanford.edu)
exploiting the fading wireless channel characteristics and the
scalable video encoding jointly.
Realtime radio resource scheduling algorithms have been
studied in [17], [3], [18] by considering the delay requirement
and channel conditions. An alternative formulation based on
optimizing a concave utility function and rate control over a
fading wireless networks has been considered [6], [19], [4].
However, these algorithms only warrant asymptotic conver
gence without explicitly considering video applications (such
as the hard deadline constraint and bursty rate requirements).
In this work, we considerthe crosslayeroptimization of rate
adaptation and exploiting the multiuser diversity for video
streaming using scalable video coding over a shared fading
wireless channel. In a fading wireless channel, it is important
to exploit the multiuser diversity, i.e., by scheduling users
in relatively good channel conditions. With SVC [16], it is
possible to adapt the video transmission rate to the wireless
channel capacity.
We first develop an empirical model to relate the aver
age video quality (measured by PSNR (Peak SignaltoNoise
Ratio)) and the average throughput based on SVC [16]. We
then formulate the following crosslayer problem: maximizing
the weighted sum of video quality of all users subject to
the achievable longterm (ergodic) rate constraint under a
fading wireless channel model. To solve the problem, we
develop a longterm radio resource allocation algorithm which
determines the wireless scheduling policy and the parameters
used by the scheduling policy. We prove the convergence
and the optimality of the proposed algorithm under mild
conditions.
Aiming to exploit multiuser diversity, we propose two
online scheduling algorithms that meet the realtime video
traffic QoS (Quality of Service) requirement. The Static
scheduling algorithm only uses the results obtained from
the aforementioned longterm resource allocation algorithm.
And, the Dynamic scheduling algorithm further adapts the
scheduling parameters to meet the instantaneous rate, deadline
requirement of video traffic and wireless channel conditions.
The underlying objective function for the optimal scheduling
problem is nonconvex/concave and nondifferentiable. We
transform the problem to an equivalent, but differentiable
one. We then develop a gradientbased approach to solve the
problem and prove that it converges to the optimal solution
even though the objective function is nonconvex/concave. We
also design frame dropping strategies that determine when and
which frames will be dropped.
We carry out extensive simulations to validate our proposed
schemes using SVCencoded real video sequences. Simulation
results show that our proposed scheduling schemes achieve
significant improvement over existing realtime video schedul
Page 2
ing algorithms in the literature. Our proposed schemes obtain
up to 810 dB gain of average video quality compared to
several wellknown existing schemes. Moreover, our proposed
schemes are much more robust under weak wireless channel
conditions. At low SINR, some videos are not decodable with
existing video scheduling schemes because of heavy packet
drop, while nearly all videos are decodable even at very weak
channel conditions by using the dynamic scheme. Finally, our
proposed algorithms are robust to channel estimation errors.
Our main contributions are threefold. First, we design a
longterm radio resource allocation algorithm and prove that it
achieves the global optimum of the objective function. Second,
we design two online scheduling algorithms and also prove the
optimality of the obtained scheduling parameters used by the
dynamic scheduling algorithm. Third, we develop intelligent
frame/layer dropping strategies based on both the longterm
resource allocation algorithm and the dynamic scheduling
algorithm.
The rest of the paper is organized as follows. In Section
II, we discuss SVC and the ratequality model. The proposed
longterm radio resource allocation scheme is given in Section
III. We present two algorithms for online scheduling of video
streaming traffic in Section IV. Simulation results based on
SVCencoded real video sequences are reported in Section V
and the paper is concluded in Section VI.
II. SCALABLE VIDEO CODING AND RATEQUALITY
MODEL
SVC can be referred to as both the general concept of
scalable video coding and the special extension [16] of
H.264/MPEG4AVC [1]. As a general concept, 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. For a detailed overview of SVC,
please refer to [16].
As in [27], we use PSNR (Peak Signal to Noise Ratio) as a
measure of video quality and develop a model to characterize
the relationship between the rate and PSNR. It turns out
that the relationship between the PSNR Si of video stream
i and the video rate r can be described as a piecewise linear
function:
where r0
quality layers are included, and the last line specifies the
maximum encoding rate of a video sequence. In figure 1,
we plot both the sample points of rate and PSNR and the
model we have obtained for eight video sequences: News,
Hall, Silent, City, Foreman, Crew, Harbour, and Mobile, all
of which can be downloaded from [21] (more video sequence
models are obtained but are omitted for the clarity of the
figure). The points in the figure show the sample points of
the rate and PSNR and the lines show the regression models
we obtained based on Eq. (1). It can be seen that our model
is quite accurate. Note that Li> Ki> 0 based on the models
of the real video sequences, so the function Si(r) is concave,
continuous, and nondecreasing with respect to r.
Si(r) =
S0
S0
S0
i+ Li(r − r0
i+ Ki(r − r0
i+ Ki(rmax
i)
i)
− r0
if r ≤ r0
if r0
else
i
i< r ≤ rmax
i
ii)
(1)
i,S0
iare the rate and PSNR when only the base
020040060080010001200140016001800
15
20
25
30
35
40
45
rate (Kbps)
PSNR (dB)
News
Hall
Silent
City
Foreman
Crew
Harbour
Mobile
Fig. 1.Sample points and linear regression models of the rate and PSNR.
Along with the model, we also obtain the priority of
different video layers. Note that a layer can be specified with
a temporal level t and quality level q (when the video is
encoded with temporal and quality scalability). We use q = 0
to represent a base (quality) layer. We then determine the
priority of each layer based on the average ratio of the PSNR
drop to the rate decrease for each truncated layer; the details
are omitted due to space limit. Once the priority is determined,
we can drop video layers in ascending order of their priority
to obtain any desired transmission rate and the corresponding
PSNR can be obtained based on the model (1).
Stuhlmuller [20] et al. also proposed a ratedistortion model.
The major difference between our model and their model is
that the different rates in the model in [20] are obtained by
encoding with different source coding rates and INTRA rates
while those in our model are obtained via dropping layers in
the increasing order of layer priority. As a result, our model
is more appropriate in wireless networks where video packets
may be dynamically dropped depending on wireless channel
conditions.
III. LONGTERM RADIO RESOURCE ALLOCATION FOR
STREAMING VIDEO
When a wireless base station receives multiple requests
for streaming service of different video sequences, it has to
decide i) how much radio resources should be allocated to
each user in order to maximize the overall video quality, ii)
how to achieve the desired radio resource allocation. In a non
fading wireless network, these problems can be simply solved
by Time Division Multiple Access (TDMA) (e.g. [11], [12]).
But mobile networks often experience fast fading. In a fading
wireless network, channel state dependent scheduling is often
used to exploit multiuser diversity.
We describe the problem formulation under a fading channel
in subsection IIIA. In subsection IIIB, we develop an algo
rithm to find the optimal scheduling policy and the associated
parameters. In subsection IIIC, we rigorously prove that
the obtained scheduling policy and its parameters achieve
the global optimum of the overall video quality defined in
subsection IIIA under mild conditions.
2
Page 3
A. Problem formulation
We assume that the instantaneous transmission rate for each
user i at each time slot t is
C(hi(t)) = B log(1 + ρhi(t)2/Γ)
(2)
where B is the channel bandwidth,ρ is the transmission power,
hi(t) is the channel gain of user i, normalized with respect
to the standard deviation of noise (and interference), Γ ≥ 1
represents the gap between the actual coding scheme and
the Shannon capacity. We assume discrete time system and
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:
max
n
?
i=1
r ∈ R
wiSi(ri)
s.t. (3)
where wiis the weight of user i, Siis the PSNR of user i as
modeled in Eq. (1), r = (r1,··· ,rn) and R is the achievable
ergodic (longterm average) rate region.
The major challenge in solving problem (3) is that the
achievable rate region cannot be explicitly specified in a
fading environment. We next develop an algorithm to solve
the problem.
B. Algorithm to solve problem (3)
We first consider a randomized channelstatedependent
TDMA scheduling strategy (which is also called static service
split (SSS) in [2]): given the channel states h of all users at
a time slot, the scheduler picks user i with probability πi(h)
and?n
randomized TDMA strategy is decided by the randomized
scheduling function π(h):
i=1πi(h) ≤ 1. The achievable rate region under this
R = {r : ri≤ Eh[πi(h)C(hi)],1 ≤ i ≤ n}
(4)
It was shown in [19] that the achievable rate region under this
randomized TDMA strategy is convex, bounded, and closed.
Because the PSNR function Si(r) is a nondecreasing
function of the rate r, there must exist an optimal solution
to problem (3) on the boundary of the achievable rate region
(i.e., which is Paretooptimal). It was proved in [2] that for
any achievable rate vector r on the boundary of the achievable
rate region, there exists a vector µ = (µi> 0,i = 1,··· ,n)
such that the rate vector r can be achieved by the following
scheduling function:
πi(h) > 0 ⇒ h ∈ {h : µiC(hi) ≥ µkC(hk),∀k ?= i}.
(5)
The solution in (5) is essentially a deterministic scheduling
function: at each time slot, the user with the largest µiCi
is chosen for scheduling, if we ignore the set of channel
states h for which µiC(hi) = µkC(hk) which in fact has
zero probability if the distribution of h is continuous. We
call the scheduling policy defined by s(h) in (5) as maximal
scheduling policy, due to the fact that this scheduler only
obtains the set of rates in the boundary which are Pareto
optimal.
We can now view a boundary point r = (r1,··· ,rn) as
a function of the parameter set µ = (µ1,··· ,µn), where the
average rate riof user i can be written as
ri= E[C(hi)I(µiC(hi) > µjC(hj) for all j ?= i)].
(6)
where I is an indicator function.
Let γi = ρhi2denote the SINR (SignaltoNoiseRatio)
of the user i with PDF (Probability Density Function) func
tion fγi(γ) and CDF (Cumulative Density Function) function
Fγi(γ). Let R(γ) = B log(1+γ/Γ). Thus, the rate rican be
computed as
ri(µ) =
?∞
0
R(γ)Πj?=iFγj(R−1(µiR(γ)/µj))fγi(γ)dγ
(7)
Now our objective is simply to
maximize
Y =
n
?
i=1
wiSi(ri(µ))
(8)
Note that Si(ri) is a nondecreasing concave continuous
function of ri.
A general approach to solve an optimization problem is the
gradientbased method. But the challenge with problem (8)
is i) the function Y is not differentiable at the points when
some ri = r0
i
, ii) the function Y is generally
not concave (or convex) with respect to µ. When a function is
not concave or convex, the solution generated by the gradient
based approach is often only a local maximum (or minimum)
but not a global maximum. In the following we develop an
algorithm and prove that the limit point of the algorithm is
the global maximum of problem (8) under mild conditions.
To resolve the first issue, we note that although Si is
not differentiable at ri = r0
sided derivatives. For functions with onesided derivatives, the
following lemma is a simple generalization of the firstorder
necessary optimality conditions.
ior ri = rmax
ior ri = rmax
i
, it has one
Lemma 1 If µ∗is a local maximum of Y , then
Y′
i+(µ∗) ≤ 0 and Y′
i−(µ∗) ≥ 0
(9)
for all 1 ≤ i ≤ n, where Y′
sided partial derivative and Y′
partial derivative.
i+(µ∗) =
i−=
∂Y
∂µi+(µ∗) is the right
∂Y
∂µi−(µ∗) is the leftsided
Now with the onesided partial derivative, we can obtain an
iterative modified gradientbased solution as follows. First we
compute the modified gradient g(k)= (g(k)
each iteration k:
1,g(k)
2,...,g(k)
n ) in
g(k)
i
=
8
<
:
0,
Y′
Y′
if Y′
if Y′
otherwise
i+(µ(k)) ≤ 0 and Y′
i+(µ(k)) > 0 and Y′
i−(µ(k)) ≥ 0
i+(µ(k)) ≥ −Y′
i+(µ(k)),
i−(µ(k)),
i−(µ(k))
Let i0 = argmax(g(k)
be d(k)= (0,··· ,g(k)
direction d(k)is all zero except the i0th element, which takes
the value g(k)
direction but d(k)is unless d(k)is zero.
i
). The ascent direction is chosen to
i0,··· ,0). In other words, the ascent
i0. Note that g(k)is not necessarily an ascent
3
Page 4
TABLE I
ALGORITHM A1
A1: Pseudocode to find the solution to problem(8)
/* ǫ,σ,α0 are positive constant values. ǫ is close to 0, and 0 < σ <
1.*/
1: Select a starting point µ(0)
i
= 1 for all 1 ≤ i ≤ n.
2: Compute d(0)from µ(0)
3: k = 0;
4: while d(k)2≥ ǫ do
5: /* Choose the step size */
6:
α = α0
7:
while Y (µ(k)+ αd(k)) − Y (µ(k)) < σα · d(k)2do
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)
13: end while
Stepsize selection using modified Armijo Rule: In any
gradientbased approach, we also need to choose the step size
α(k)appropriately in order for the algorithm to converge to a
local maximum. For this purpose, we apply a modified Armijo
rule [5] where the gradient ∇Y (µ(k)) is replaced with d(k)
because the gradient ∇Y (µ(k)) may not exist. The pseudo
code of our algorithm A1 is listed in Table I.
We can now show the convergence of the algorithm, which
is summarized next. The proof follows similar ideas in the
standard proof of the limit points of the stationary points for
gradientbased methods (see e.g., [5]) and is omitted.
Lemma 2 Algorithm A1 converges to a point µ∗satisfying the
necessary conditions of a local maximum in Eq. (9), assuming
that the finite stopping condition (in line 4 of Algorithm A1)
is removed.
C. Optimality of the algorithm A1
For all practical purpose, we can assume that the PSNR
function Y is continuously differentiable, nondecreasing and
concave with respect to r (we can always connect the two line
segments using a smooth curve to make the function continu
ously differentiable). Under this assumption, we can prove that
the limit point of algorithm A1 is a global maximum. This is
quite significant as the function Y is generally not concave
with respect to the controlling variable µ. We first prove the
following lemma.
Lemma 3 For any rate vector r(µ) achieved using the max
imal scheduling policy (5) with parameter µ, all achievable
rate region is below the hyperplane defined by
{r(µ) +∂r
∂µµu : u ∈ Rn}
(10)
where
column is
rate vector r′, we can find a vector u ∈ Rnsuch that r′≤
r +∂r
∂r
∂µµ is a matrix whose element at i’th row and j’th
∂ri
∂µjµ). More precisely, for any other achievable
∂µµu element wise.
Proof. The intuition is quite clear. At any point r that is
achieved by the maximal scheduling scheme with parameter
vector µ, there is a tangent hyperplane. All the achievable
rate region is below the tangent hyperplane. Next we give a
rigorous proof.
Since r is on the boundary of the achievable rate region,
which is convex, from Proposition B.12 in [5], there is a vector
b ?= 0 such that
bT(r′− r) ≤ 0
(11)
for any r′in the achievable rate region. We now show two
properties of the vector b. First, bT ∂r
be the rate achieved using parameter set µ′= (µ′
where µ′
of Eq. (11) by µ′
µ′
we let µ′
r is continuously differentiable with respect to µ, we obtain
bT ∂r
The second important property is b ≥ 0 element wise.
Suppose b = (b1,··· ,bn). We choose r′
for all j ?= k. Clearly, r′is a achievable rate vector. So from
Eq. (11), we get 0 ≥ bT(r′−r) = bk(r′
we have bk≥ 0.
We now look at the intersection point of the line {r′+bt :
t ∈ R} and the hyper plane (10). At the intersection point, we
have
r′+ bt = r +∂r
∂µk= 0 for all k. Let r′
1,··· ,µ′
n)
j= µj for all j ?= k and µ′
k− µk we obtain that bT (r′−r)
k> µk and µ′
k< µk and µ′
k> µk. Divide both sides
k−µk≤ 0. Let
∂µk≤ 0. Similarly, if
k→ µk−, we get bT ∂r
µ′
k→ µk+, we have bT ∂r
∂µk≥ 0. Since
∂µk= 0 for all 1 ≤ k ≤ n.
k< rk and r′
j= rj
k−rk). Since r′
k< rk,
∂µµu
(12)
Multiplying both sides by bTfrom the left and doing a little
rearrangement, we get
bTbt = bT(r − r′) + bT∂r
∂µµu = bT(r − r′) ≥ 0
where the second equality is because of the first property of
vector b and the last inequality is from Eq. (11). Since bTb >
0, we obtain t ≥ 0. Therefore, the intersection point r′+ bt
is on the hyper plane (10) and is larger than or equal to r′
element wise (because t ≥ 0 is a scalar and bj≥ 0 for all j).
?
Next we prove the main theorem. Note that we can always
connect the two line segments of the function Si(ri) with a
smooth curve such that the function Si(ri) is continuously
differentiable.
(13)
Theorem 1 The limit point of the algorithm A1 is a global
maximum of function Y assuming that the PSNR function
Si(ri) is nondecreasing, concave, and continuously differen
tiable with respect to ri.
Proof. Let µ and r(µ) be the limit point of the algorithm
A1. Clearly r(µ) is a boundary point of the achievable rate
region. Applying Lemma 3, for any achievable rate vector r′,
there exists a vector u such that r′≤ r +∂r
wise. Because of the nondecreasing property of the function
Y over each ri, we have
Y (r′) ≤ Y (r +∂r
∂µµ u element
∂µµu)
(14)
We next show that, for any point r +
hyperplane (10),
Y (r(µ) +∂r
∂r
∂µµu on the
∂µµu) ≤ Y (r(µ)),
(15)
4
Page 5
012345
µ2
678910
45
50
55
60
65
70
75
80
Sum PSNR (dB)
Fig. 2. Sum PSNR vs. µ2 while µ1= 1
given that µ is the limit point of algorithm A1. With the
assumption that Y is continuously differentiable with respect
to both r and µ, from Lemma 2, the limit point µ of algorithm
A1 satisfies, for any 1 ≤ k ≤ n,
0 =∂Y
∂µk
=
n
?
i=1
∂Y
∂ri
∂ri
∂µk,
(16)
where the second equality is from the chain rule of partial
derivative.
Because of the concavity of Y over r,
Y (r +∂r
∂µµu)≤Y (r) + ∇Y (r)T∂r
∂µµu
n
?
k=1
∂Y
∂rj
=Y (r) +
n
?
j=1
n
?
k=1
∂Y
∂rj
n
?
j=1
?
∂rj
∂µkuk
=Y (r) +
∂rj
∂µk
???
=0
uk
=Y (r)
(17)
where the last equality is from Eq. (16).
Combining Eq. (14) and (17), we obtain that Y (r′) ≤
Y (r(µ)) for any achievable rate vector r′provided that µ is
the limit point of the algorithm A1.
In general, for a nonconvex (or nonconcave) problem,
a stationary point is only a local maximum (or minimum).
It appears surprising that although the objective function Y
is not a concave function with respect to µ, the stationary
point is the global maximum of Y . To further understand the
problem, we consider a twouser scenario and fix µ1 = 1.
The objective function Y is then the function of µ2. Using
parameters derived from two real video sequences, we plot
the sum PSNR of the two users vs µ2 in Fig 2. We can
observe from the figure that the function Y is neither convex
or concave, and that the stationary points of the function are
not even unique. However, all the stationary points are indeed
the global maximum of Y .
?
IV. ONLINE SCHEDULING FOR SVC VIDEO STREAMING
An online scheduling algorithm for realtime video appli
cations 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 pack
ets/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 resource allocation algorithm presented in the section
produces two results: 1) the vector µ used for userscheduling,
2) the achievable average rate rifor each user i. We next de
scribe two online scheduling schemes exploiting these results.
In the first scheme, we simply apply the results obtained from
the resource allocation algorithm. In the second scheme, we
also consider the bursty and dynamic arrival and the deadline
of video frames.
A. Static scheduling scheme
In this first scheme, the vector µ is computed from the
previous section and is fixed during the process of streaming (µ
may be recomputed when new users join or some users leave).
At each time slot, the user with the largest µiCiis chosen for
scheduling, where Ci is the current channel capacity of user
i, and the vector µ = {µ1,µ2,··· ,µn} is computed from
the longterm resource allocation algorithm in the previous
section.
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 minimum playout
deadline of all frames that depend on it. 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, which is obtained in Section II.
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 recomputed.
The second type of dropping is early dropping. With the
achievable rate computed from the previous subsection, we
can predetermine 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 at the
beginning of the video streaming.
B. Dynamic scheduling scheme
The dynamic scheduling is built on top of the static
scheduling scheme with two additional enhancements. The
first enhancement is on the user scheduling. At each time slot,
still, the user with the largest µiCiis selected for scheduling.
However, the vector µ is periodically updated to reflect both
the bursty arrival and the deadline of video traffic.
5
Page 6
Assume that for user i, the size of total packets that need
to be transmitted before the deadline Tjis Qj. We define the
target rate ¯ rifor user i to be
¯ ri=
n
max
j=1
Qj
Tj− t
(18)
where t is the current time.
Now with the target rate ¯ rifor each user i, we ask whether
there exists a vector of µ such that the target rate ¯ ri can be
satisfied for every user i. We consider the following maxmin
problem.
maximize minri(µ)
¯ ri
(19)
over all possible choices of µ. Clearly, if the optimal value
of Eq. (19) is larger than or equal to 1, the target rate ¯ r is
schedulable and vice versa. The problem (19) is not easy to
solve as i) the problem is nonconvex and ii) the derivative
does not exist and the gradientbased approach cannot be
directly applied. But the following result was obtained in [6]:
Lemma 4 Solving problem (19) is equivalent to solving the
following problem: find µ such that
r1(µ)
¯ r1
=r2(µ)
¯ r2
= ... =rn(µ)
¯ rn
,
(20)
assuming that the channel distribution function fγi(γ) is a
continuous function of γ for all i.
To solve problem (20), we define g = (g1,···gn), ¯ g, and
h(µ) as follows:
gi(µ)=ri(µ)/¯ ri
n
?
i=1
1
2
i=1
¯ g=
gi(µ)/n
h(µ)=
n
?
(gi(µ) − ¯ g)2.
(21)
In each iteration k, we compute ¯ g(k)and treat it as a fixed
value during the iteration. We then solve the problem of
minimizing the function h(µ) in Eq. (21) using GaussNewton
method. To do so, we choose the direction
d(k)= (∇g(µ)∇g(µ)T)−1∇g(µ)(g(µ) − ¯ g(k)).
(22)
and update µ(k)as
µ(k+1)= µ(k)− α(k)d(k)
where α(k)is the step size chosen by Armijo rule. The
pseudocode of the algorithm A2 is presented in Table II. The
following lemma follows from the stationarity of limit points
of gradientbased approach (see e.g. [5], page 43).
Lemma 5 Algorithm A2 converges to a stationary point of
the function h(µ) (defined in Eq. (21)) assuming that the finite
stopping condition in the outerloop is removed.
In general, the stationary point of a function h(µ) is not
necessarily a global minimum of the function because of the
nonconvexity of the function. But, surprisingly, we can prove
that the limit point of the algorithm A2 is a global minimum
TABLE II
ALGORITHM A2
A2: Pseudocode to solve problem (20)
/* ǫ,σ,α0 are positive constant values. ǫ is close to 0, and 0 < σ <
1.*/
1: Select a starting point µ(0)
i
= 1 for all 1 ≤ i ≤ n.
2: Compute g(µ(0)), ¯ g(0), and h(µ(0)) using Eq. (21).
3: Compute d(0)according to Eq. (22)
4: k = 0;
5: while g(µ(k)) − ¯ g(k)2≥ ǫ do
6:/* Choose the step size */
7:
α = α0
8:
while h(µ(k))−h(µ(k)−αd(k)) < σα·(∇h(µ)T)d(k)do
9:
α = α · β
10:
end while
11:
µ(k+1)= µ(k)− α · d(k)
12:
k = k + 1
13:Recompute d(µ(k)),g(µ(k)), ¯ g(k)and h(µ(k)).
14: end while
(i.e., 0) of the function h(µ), which is also the unique solution
to problems (19) and (20), even though the function h(µ) may
not be convex. The result is stated in the following theorem.
The proof is presented in the appendix.
Theorem 2 Algorithm A2 converges to the optimum solution
to the problems (19) and (20) assuming that the finite stopping
condition in the outerloop is removed.
The second enhancement of this dynamic scheduling
scheme is on the frame dropping strategy. Note that the algo
rithm A2 not only produces the new vector µ that is used for
user scheduling, but also the value η = maxminn
1, it indicates that the target rate vector ¯ r = (¯ r1, ¯ r2,··· , ¯ rn)
is achievable in long term. If η < 1, it indicates that the
target rate vector ¯ r is unachievable and some video frames
need to be dropped. To overcome the shortterm uncertainty
of wireless channels, in this dynamic scheduling scheme, we
maintain a target range (η, ¯ η) of η. During the periodic re
evaluation of the vector µ and η, if η < η, we will start to
drop packets, and if η > ¯ η, we will put some dropped packets
(whose playout deadline is not passed yet) back to the queue.
To support the function of putting dropped packets back to
the queue, we do not really drop a packet unless its playout
deadline is passed. Instead, we simply mark it to be dropped.
When we need to drop some packets (i.e., η < η) or need
to put some dropped packets back to the queue (i.e., η > ¯ η),
we first choose the user using round robin. After the user is
selected, we choose the packets that have the lowest priority
within a window from now when droppingpackets, and choose
the packets that have the highest priority among those marked
as dropped when putting dropped packets back to the queue.
Then we recompute the vector µ and η using Algorithm A2
and repeat the process until the value η falls between η and
¯ η. We use the final result µ for subsequent user scheduling.
i=1
ri
¯ ri. If η >
V. SIMULATION RESULTS
The following settings are used for simulations. All video
sequences are encoded at 30Hz with GOP size of 16 pictures
and an intra period of 64 frames (about 0.5Hz). Wireless
channels are generated based on Rayleigh fading model unless
specified otherwise. Channel bandwidth is assumed to be
6
Page 7
1MHz unless specified otherwise and slot duration is set to
2ms. For the dynamic scheme, dynamic procedure is activated
once every 4 video frames. Our objective is to maximize the
sum YPSNR1of all users. In other words, the weights for all
users are set to 1. All results are average of ten simulation
runs.
We consider three reference schemes. The first is the scheme
in [14] where the user selection is based on maximum channel
capacity and packets are dropped based on their priority at
the time of buffer overflow. The buffer limit for each link is
110KBytes as used in [14]. Packets with the lowest priority
are dropped first at the time of buffer overflow. This scheme
is termed as Maximum capacity scheduling w/ FD (FD refers
to frame dropping). The other two reference schemes are
enhanced version of the Maximum capacity w/ FD where a
different user scheduling algorithm is employed. The second
scheme uses proportional fairness scheduling [23] and the
third uses Modified Largest Weighted Delay First (MLWDF)
scheduling [3]. Note that in all the reference algorithms we
employ the same frame prioritization and dropping strategy
as in [14]. We choose these two enhanced scheduling al
gorithms because i) the Proportional Fairness scheduling is
very widely used in wireless access networks, and ii) the
MLWDF scheduling is designed for realtime traffic and is
shown in [13] to be one of the best scheduling algorithms for
video streaming. In the following we evaluate the developed
algorithms under four scenarios.
A. Variable mean SINR and different video sequences
In this scenario, we encode 8 video sequences with the SVC
extension [16] of H.264/MPEG4AVC: News, Hall, Silent,
City, Foreman, Crew, Harbour, and Mobile, all of which
are downloaded from [21]. The average SINR value of each
user is uniformly distributed from 5dB to 20dB. The initial
buffer duration is randomly generated from 700 milliseconds
to 800 milliseconds. For fair comparison, we obtain the same
initial buffer duration and the same SINR values for different
schemes by using the same pseudo random number seed.
Figure 3 shows the obtained average PSNR of Y,U,V
components of all eight video sequences for different schemes
(we connect the points that belong to the same scheme with
lines simply to group them together). Although our algorithms
are applied to improve the YPSNR in the simulations, they
actually improve the PSNR of all other components.
The average PSNR over all all video sequences is sum
marized in Table III. It can be seen that both of our pro
posed schemes achieve significant gains over existing schemes.
For the YPSNR, the static scheme achieves a gain of 1.5
5.4 dB and the dynamic scheme achieves a gain of 2.2
6.1 dB compared to the existing schemes. The improvement
on UPSNR and VPSNR is less because i) it is not our
objective to optimize the U and Vcomponents, and ii) the
color components appear less affected by dropping frames.
1In 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, Ycomponent is the
most important one as human eyes are most sensitive to the brightness
information.
02468
20
25
30
35
40
45
User index
Y−PSNR (dB)
Dynamic scheduling
Static scheduling
Maximum−capacity w/ FD
Proportional Fairness w/ FD
M−LWDF w/ FD
02468
30
35
40
45
50
U−PSNR (dB)
02468
25
30
35
40
45
50
V−PSNR (dB)
Fig. 3.Average PSNR of different schemes for each user
TABLE III
AVERAGE PSNR ACHIEVED BY EACH SCHEME
YPSNR
Dynamic Scheduling
Static Scheduling
Maximum capacity w/ FD
Proportional fairness w/ FD
MLWDF w/ FD
UPSNR
42.5
42.3
39.9
41.1
41.7
VPSNR
43.5
42.9
36.6
40.1
41.7
38.0
37.3
31.9
34.3
35.8
B. Same mean SINR, different video sequences
In the second scenario, we use the same 8 video sequences
as in the previous scenario, but choose the average channel
SINR for all users to be equal. We then investigate the video
quality when the average channel SINR varies. Figure 4(a)
shows the sum of the YPSNR of all eight video sequences
under different SINR values. We can see that the proposed
dynamic scheme always achieves the best video quality and the
static scheme is slightly worse the the dynamic scheme. When
the channel conditions are good, the MLWDF scheduling
algorithm with frame dropping obtains slightly higher PSNR
than the static scheduling algorithm. However, when the
average channel SINR decreases, the video quality obtained
by all reference schemes including MLWDF degrades very
quickly. This is because at bad channel conditions, all refer
ence schemes do not perform early dropping and may end
up dropping important (lowlayer) frames, which affects the
decoding process of highlayer video packets. In the case of
very low SINR, both of our schemes achieve an average gain
of more than 6 dB compared to the three reference schemes.
Moreover, when the SINR is low, most other schemes
468 101214 16 18 20
26
28
30
32
34
36
38
40
SINR (dB)
Y−PSNR (dB)
Dynamic scheduling
Static scheduling
Maximum−capacity w/ FD
Proportional Fairness w/ FD
M−LWDF w/ FD
(a)
46810121416 1820
0
1
2
3
4
5
6
SINR (dB)
Average number of un−decodable sequences
Dynamic scheduling
Static scheduling
Maximum−capacity w/ FD
Proportional Fairness w/ FD
M−LWDF w/ FD
(b)
Fig. 4.
of undecodable sequences for each scheme.
(a) Average PSNR of all users for each scheme; (b) Average number
7
Page 8
2468
Number of users
10121416
22
24
26
28
30
32
34
36
38
Average Y−PSNR (dB)
Dynamic scheduling
Static scheduling
Maximum−capacity w/ FD
Proportional Fairness w/ FD
M−LWDF w/ FD
Fig. 5.
the number of users varies.
Average PSNR when all users request Mobile video sequence but
cannot decode the video sequences completely because of
the heavy packet loss2. Figure 4(b) shows the number of
video sequences that are not decodable under each scheduling
algorithm for different SINR values. Because of the early
dropping strategy employed, the dynamic scheme can decode
all video sequences for all SINR values greater or equal to
4dB, and the number of undecodable sequences for the static
scheme is much smaller than that of all reference schemes
at the low SINR regime. For the static scheme, occasionally
some video sequences may not be decoded completely. This
is because the static scheme does not consider the instanta
neous deadline requirement, which indicates that the dynamic
scheme is required in order to have the best performance.
C. Variable mean SINR, same video sequences
In this set of simulations, all the users request the same
Mobile video sequence (but the content is transmitted through
unicast) and we let the number of users vary. The average
SINRs (in dB) of the users are generated randomly using
uniform distribution from 5dB to 20dB. To accommodate more
users, we set the channel bandwidth to be 2.5MHz. Figure
5 shows the average PSNR of different schemes when the
number of users ranges from 2 to 16. When the number of
users is small, all scheduling algorithms perform very well
except for the Maximumcapacity algorithm w/ FD. But when
the number of users increases, our proposed schemes perform
much better than the reference schemes. The static scheme
and the dynamic one improve the average video quality by
8 dB and 10 dB, respectively, compared to the best of the
three reference schemes when there are 16 users. This again
demonstrates the efficacy of our proposed schemes.
D. Robustness under inaccurate channel model
In Sections III and IV, we assume precise information on
the fading distributions. We now evaluate the performance
of the algorithms when the fading distribution information is
inaccurate. We assume Rayleigh distribution in our scheduling
algorithms but let the actual fading distribution be Rician
2The PSNR values plotted in Fig. 4(a) 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.
00.10.20.30.40.5
v2/σ2
0.60.70.80.91
31
32
33
34
35
36
37
38
39
40
Average Y−PSNR (dB)
Dynamic scheduling
Static scheduling
M−LWDF w/ FD
Proportional Fairness w/ FD
Maximum−capacity w/ FD
Fig. 6.
Rician distribution.
Average PSNR vs. v2/σ2where v and σ are the parameters in the
with PDF function f(xv,σ) =
where I0(z) is the modified Bessel function of the first kind
with order zero. When v = 0, the distribution reduces to a
Rayleigh distribution. A nonzero v indicates the deviation
from Rayleigh distribution, and normally v2≤ σ2. Other
simulation setups are identical to those in Section VA.
Figure 6 shows the average PSNR of the eight video
sequences vs. v2/σ2. We maintain fixed SINR values when
v2/σ2changes. We can see that with the static scheme, the
average PSNR drops about 0.8dB when v = σ, and there is
nearly no drop in the PSNR values for the dynamic scheme.
Therefore, our algorithms (especially the dynamic one) is
robust to the channel distribution errors.
x
σ2exp(−(x2+v2)
2σ2
)I0(xv
σ2),
VI. CONCLUSION
In this paper we study the problem of scalable video
streaming in fading wireless environments. We exploit both the
application layer video characteristics and the wireless channel
fading information to obtain a crosslayer solution. We first
develop a model to characterize the relationship between the
average rate and average PSNR of a video stream. We then
formulate the problem as a longterm radio resource allocation
problem in a fading environment in order to maximize the
weighted sum of average PSNR of all users. We develop
an algorithm to find the optimal scheduling policy and the
parameters used by the scheduling policy, and rigorously prove
the optimality of the solution. We next design two scheduling
algorithms based on the results of the longterm resource
allocation scheme. Simulation results show that our scheduling
algorithms are much superior to existing solutions and are
robust to channel estimation errors.
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APPENDIX
Proof of Theorem 2
We first prove a technical lemma.
Lemma 6 For any 1 ≤ i ≤ n,?n
To prove the lemma, notice that if we rescale the vector
µ by a constant, the function gi(µ) remains fixed. In other
words, gi(µ) = gi(τµ). Now consider the partial derivative
(letting τ = µ1/µ′
j=1µj
∂gi(µ)
∂µj
= 0.
1)
∂gi(µ)
∂µ1
= lim
µ′
1→µ1
gi(µ′
1,µ2,...,µn) − gi(µ1,µ2,...,µn)
µ′
1− µ1
= lim
µ′
1→µ1
gi(µ1,τµ2,...,τµn) − gi(µ1,µ2,...,µn)
µ′
1− µ1
n
?
j=2
∂µj
n
?
j=2
∂µj
µ1
n
?
j=2
∂µj
= lim
µ′
1→µ1
∂gi(µ)
µj(τ − 1)
µ′
1− µ1
= lim
τ→1
∂gi(µ)
−µjτ
=−
∂gi(µ)
µj
µ1.
(23)
Rearrange the equations, we obtain the result in the lemma.
?.
We now prove theorem 2. From Lemma 5, algorithm A2
converges to a stationary point of the function h(µ). That
means at the limit point µ,
∇g(g(µ) − ¯ g) = 0,
(24)
In order to show the limit point µ is the optimal solution to
problem (19) and (20), it is sufficient to show that gi(µ) = ¯ g
for all 1 ≤ i ≤ n. We prove using contradiction. Suppose
that there exist gi(µ)’s that are not all equal and satisfy Eq.
(24). Denote wi = gi(µ) − ¯ g and w = (w1,··· ,wn), and
we have ∇g · w = 0 where w is a vector with zero mean.
Without loss of generality, we can assume wi’s are sorted in
the decreasing order. Because w is a zeromean vector and
its elements are not all equal, at least one element of w is
positive. Now suppose that k is the index such that w1 ≥
··· ≥ wk ≥ 0 ≥ wk+1 ≥ ··· ≥ wn. For simplicity, we use
the matrix A to represent ∇g and aij=
matrix A = ∇g, the diagonal elements are positive and the rest
are negative. If k = 1, the first element of Aw cannot be zero
because it is equal to?n
negative and the first term is positive. This is a contradiction.
For k > 1, we look at the ith (i ≤ k) element of Aw, which is
?n
?k
matrix form, we obtain
∂gj
∂µi. Note that in the
j=1a1jwj where all terms are non
j=1aijwj= 0. Note that aijwj> 0 for j > k. Therefore,
j=1aijwj< 0 and aiiwi<?k
j=1,j?=iwjaij. Writing it in
Diag(w1,··· ,wk)[a11,a22,··· ,akk]T< Akw[k],
where Ak is a matrix with k rows and k columns and the
element at the ith row and jth column of Ak is aij except
that the diagonal elements are zero, w[k]is a vector with the
first k elements of w, and the sign “<” is elementwise.
Since w1,··· ,wkare all positive, we have
[a11,a22,··· ,akk]T< Diag(w1,··· ,wk)−1Akw[k].
(25)
If we write the results of Lemma 6 in matrix form and
note that A = ∇g, we have µTA = 0 and so ATµ = 0.
Still look at the ith (i ≤ k) element of ATµ, and we have
?n
(because µj> 0 and aji< 0 for j > i). So the summation of
the first k terms must be positive. That is,?k
Therefore, µiaii >?k
matrix form, we obtain (recall the definition of Ak, and µ[k]
is a vector containing the first k elements of µ)
j=1ajiµj = 0. Note that all terms for j > k are negative
j=1ajiµj > 0.
j=1,j?=iµjaji. Again, writing them in
Diag(µ1,··· ,µk)[a11,a22,··· ,akk]T> AT
kµ[k].
9
Page 10
Since µi’s are all positive, we have
[a11,a22,··· ,akk]T> Diag(µ1,··· ,µk)−1AT
kµ[k].
(26)
Combining the two equations (25) and (26), we have
Diag(µ1,··· ,µk)−1AT
kµ[k]< Diag(w1,··· ,wk)−1Akw[k](27)
Multiplying both sides in the left by Diag(µ1w1,··· ,µkwk),
andnote
µ[k]
=Diag(µ1,···µk)J
Diag(w1,···wk)J where J = [1,1,··· ,1]Thas k elements,
we obtain
and
w[k]
=
Diag(w1,··· ,wk)AT
< Diag(µ1,··· ,µk)AkDiag(w1,··· ,wk)J
kDiag(µ1,··· ,µk)J
(28)
Let B = Diag(µ1,··· ,µk)AkDiag(w1,··· ,wk). Eq. (28)
can be written as
BTJ < BJ.
Thus, sum(BTJ) < sum(BJ). However, sum(BTJ) =
sum(BJ) because both are equal to the summation of all
elements in the matrix B. Therefore, this is a contradiction
and the proof is complete.
?
10