Video-Quality-Driven Resource Allocation for Real-Time ... · Video-Quality-Driven Resource Allocation for Real-Time Surveillance Video Uplinking Over OFDMA-Based Wireless Networks

IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 64, NO. 7, JULY 2015 3233

Video-Quality-Driven Resource Allocation forReal-Time Surveillance Video UplinkingOver OFDMA-Based Wireless Networks

Po-Han Wu, Chih-Wei Huang, Jenq-Neng Hwang, Fellow, IEEE, Jae-Young Pyun, Member, IEEE, and Juan Zhang

Abstract—This paper proposes an effective real-time video up-link (UL) framework for mobile wireless camera networks (WCN)over an orthogonal frequency-division multiple access (OFDMA),based infrastructure. Mobile wireless camera stations (CSs) trans-mit their videos in real time to a base station (BS) so that these livevideo streams can be archived or fed to subscribers to facilitatereal-time video monitoring. Based on the utility function drivenby video quality, the target bit rate resulting in the highest pos-sible utility is quickly set for each UL video. To optimize systemperformance, a real-time video packet scheduler and a spectral-efficient resource-allocation policy are derived. This scheduleris also capable of exploiting the inherent diversity gain due tochannel variations. Using fourth-generation (4G) mobile networkprotocols and a realistic wireless channel model, it is demonstratedthrough our extensive simulations that our proposed method cansignificantly enhance utility, boost spectral efficiency, and stabilizevideo quality.

Index Terms—Cross-layer design, Long-Term Evolution (LTE),mobile surveillance system, video quality driven (VQD), videouplink (UL), Worldwide Interoperability for Microwave Access(WiMAX).

I. INTRODUCTION

W IRELESS or mobile surveillance systems that integratewireless cameras or ad hoc wireless video sensor net-

works with moving vehicles or mobile devices have becomereality [1], [2]. As shown in Fig. 1, video streams capturedby wireless or mobile camera stations (CSs) are uploaded viauplink (UL) wireless channels to a control center where theacquired videos can be archived, analyzed, and/or distributed.

Surveillance systems of this kind have numerous applica-tions, including real-time traffic monitoring, facility monitor-

Manuscript received August 27, 2013; revised March 15, 2014 and June 20,2014; accepted July 30, 2014. Date of publication August 20, 2014; date ofcurrent version July 14, 2015. The review of this paper was coordinated byDr. L. Zhao.

P.-H. Wu is with T-Mobile USA Lab, Bellevue, WA 98006 USA (e-mail:[email protected]).

C.-W. Huang is with the Department of Communication Engineering, Na-tional Central University, Jhongli 32054, Taiwan (e-mail: [email protected]).

J.-N. Hwang is with the Department of Electrical Engineering, University ofWashington, Seattle, WA 98105 USA (e-mail: [email protected]).

J.-Y. Pyun is with the Department of Information Communication Engineer-ing, Chosun University, Gwangju 501-759, Korea (e-mail: [email protected]).

J. Zhang is with the Shanghai University of Engineering Science, Collegeof Electronic and Electrical Engineering, Shanghai 201620, China (e-mail:[email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TVT.2014.2350002

Fig. 1. Real-time video surveillance system over mobile networks.

ing, combat/rescue operation monitoring, disaster relief anddamage assessment, etc. Depending on specific applicationscenarios, different quality of service (QoS) requirements mayhave to be imposed on the design of such systems. For example,video streams that report critical unfolding events will requirehigh QoS levels compared with streams that contain no events.

Recent advances in the fourth-generation (4G) wireless broad-band networks, such as IEEE Worldwide Interoperability for Mi-crowave Access (WiMAX) and Third-Generation PartnershipProject’s Long-Term Evolution (LTE), have adopted many QoS-enabling technologies such as orthogonal frequency-divisionmultiple access (OFDMA), single-carrier frequency-divisionmultiple access (SC-FDMA), and multi-input–multi-output(MIMO). In particular, OFDMA offers an elegant way of radioresource partition and supports QoS optimization.

Many cross-layer (physical (PHY) and medium-access-control layers) QoS-guaranteed scheduling schemes forIEEE 802.16 (WiMAX) systems have been reported [3]–[7].The method proposed in [3] requires a significant overhead fora low-power mobile station (MS) to upload status information,such as delays of all packets and requirements of bandwidth[7]. Several efficient user/connection-based schemes have sub-sequently been proposed and claimed to be more suitable forUL scheduling [4]–[7]. The proportional fair scheme (PFS) [8]has been widely used in mobile networks with the objectiveof maximizing the long-term fairness and throughput. How-ever, it has no mechanism to guarantee the QoS for real-timeservices. Later, an improvement is proposed in [9] that jointlyconsiders PFS, capacity prediction, and video rate adaptation tosupport the QoS requests of UL videos. Well-known schedul-ing strategies, such as maximum-largest weighted delay first(M-LWDF) and exponential fairness (EXP) [10]–[12], facilitatereal-time video streaming by guaranteed minimum throughputand enhanced MS priority scheduling. These existing works

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3234 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 64, NO. 7, JULY 2015

focused on QoS parameters in physical-layer performancemetrics, such as packet loss rate, throughput, and jitter. Yet,these communication oriented metrics do not directly reflect theperceptual quality experienced by the subscribers.

Recently, the perceived quality of video networking appli-cations, commonly formulated as a utility function to be opti-mized, has been promoted as a more appropriate performancemetrics for wireless video streaming [13]–[16]. These works fo-cused on the downlink (DL) radio resource allocation problems.The greedy method in [16] has been extended to the scenarioof UL video scheduling [17], [18]. However, these algorithmsdo not scale up well with increasing users due to the need oftracking resource and utility variations. In [19], a frameworkfor joint DL and UL real-time mobile video transmission in awireless camera network (WCN) is proposed. The videos fromUL CSs are scheduled according to the feedback of quality ofexperience (QoE) aggregated from all DL multicast MSs.

In this paper, we consider the scenario where multiple livesurveillance videos, from either fixed or mobile CSs, competefor wireless channels to upload their videos to the BS. Thekey innovation of this framework is to use video-quality-driven(VQD) utility function to decide how the long-term UL videobit rate and the real-time UL radio resource are to be assigned.

In a realistic wireless environment, the radio spectrum islimited, and the channel conditions of UL CSs vary frequentlyover time and space. For efficient video UL delivery in a WCN,the target bit rate for all CSs should be decided according tothe available resource and corresponding utility. Furthermore,service scheduling and modulation coding scheme (MCS)should be chosen to facilitate real-time delivery. Based onthese settings, UL resource allocation problems are formulatedand optimized in this paper. There are two key objectives ofthis paper. First, to maximize the system utility, a long-termencoding rate assignment problem has to be formulated todecide the target bit rates for all CSs. Toward this goal, a fastand effective VQD algorithm is proposed to quickly obtainthe best utility and bit rates for all CSs. The complexity andapproximation analysis results of this algorithm indicate thatthe solution is in a close proximity to the optimum and canbe achieved in polynomial time. Second, To achieve each CS’starget utility and bit rate obtained from the first objective, areal-time scheduling problem needs to be solved. Toward thisgoal, a utility-based priority function that is able to exploit thediversity gain embedded in channel variations is designed as thescheduler. By incorporating it in the proposed slot assignmentpolicy, not only each CS can achieve its target utility and bitrate but also can the system improve its overall throughput.Advantages of the proposed algorithms for both the first andsecond objectives, including some 80% more enhanced utility,extremely low packet loss, much higher throughput, and morestable video quality, are all demonstrated in simulations utiliz-ing the realistic wireless channel model and the 4G networkprotocol parameters.

The remainder of this paper is organized as follows. Theproblem formulation is discussed in Section II. The proposedsolutions including the video-quality-driven (VQD) fast-bit-rate assignment algorithm and the utility-based scheduler alongwith the efficient slot allocation method are detailed and ana-

TABLE IMCS (m), SLOT CAPACITY (C), AND NORMALIZED CAPACITY (b) IN [20]

lyzed in Sections III and IV, respectively. The simulation resultsand discussions are in Section V, followed by the conclusion inSection VI.

II. UPLINK RESOURCE MANAGEMENT PROBLEM

In this paper, UL resource allocation problems are formu-lated and optimized by two key steps. First, to maximize thesystem utility, a long-term encoding rate assignment problemhas to be formulated to decide the target bit rates for all CSs.Second, since each CS’s target bit rate along with the targetutility are determined in the first step, to achieve each CS’starget, a real-time scheduling problem needs to be solved. Wewill describe and formulate the first and second objectives inSection III-B and C, respectively.

A. OFDMA Uplink Transmission Resources

For OFDMA systems, such as WiMAX, the radio resourceis organized and allocated in both frequency and time do-mains. In the frequency domain, the subcarriers are groupedto form subchannels (SCHs) according to different permutationschemes. In particular, the so-called band adaptive modulationand coding (AMC) scheme groups adjacent subcarriers (eightdata subcarriers and one pilot subcarrier) into a frequency bin.One, two, or three adjacent frequency bins over, respectively,six, three, or two consecutive OFDM symbol frames in timeform a slot, which is the basic unit of radio resources that maybe assigned to any specific user (in this case, a CS). AMCpermutation enables multiuser diversity by choosing the SCHwith the best frequency response and is adopted in this paper.

A slot may be modulated at one of M different rates{C(m); 1 ≤ m ≤ M} according to a specific MCS m (seeTable I). For IEEE 802.16e [20], M = 7, and C(m) =[9.6 14.4 19.2 28.8 28.8 38.4 43.2] Kb/s/slot, m = 1, 2, . . . , 7.The total amount of radio resource is limited to G0 slots perOFDMA UL frame. The modulation rate is chosen to ensurethat the bit error rate is kept below a preset SNR threshold(TH) for a given channel quality index (CQI). Thus, given aCQI (b(t)), the corresponding highest possible modulation rate,noted as m(b(t)), can be uniquely determined.

CQIs are frequently estimated by the BS based on receivedpilot subcarriers. Due to fast and slow fading, the CQIs betweena CS and the BS vary over different frequency bands. In thispaper, we use the normalized capacity b(t) to serve as a goodapproximation to the instantaneous CQI at time t when aspecific MCS is chosen.

WU et al.: VQD RESOURCE ALLOCATION FOR REAL-TIME VIDEO UPLINKING OVER OFDMA NETWORKS 3235

Over a longer period of time (e.g., for couple seconds in areal-time application), the average CQI of the vth CS up totime t, i.e., bavgv (t), is evaluated using an exponential windowas follows:

bavgv (t) = (1 − ρ) · bavgv (t− 1) + ρ · bv(t) (1)

and ρ is empirically set as 1/50 for real-time services [21], [22].

B. Long-Term Video Rate Assignment Problem

Assume V video streams, each captured by a CS, are tobe uploaded to the control center via OFDMA-based wirelessULs. Each uploading video is assigned a target bit rate bythe BS from L different encoding rate modes. More specif-ically, we denote R0 = [Rv, l] (in b/s) to be an L× 1 vec-tor consisting of the L allowable target bit rates, e.g., R0 =[500 700 1000 1200]T Kb/s, l = 1, . . . , 4, and each CS needsto be assigned a bit rate from R0 for uploading. Further, wedefine an 1 × L assignment vector av = [av, l]. If the vth CS isassigned with the lth rate mode, av, l is set as 1, and the otherelements in av are all 0. Thus, the bit rate assigned to the vthCS, noted as Rv , can be expressed as

Rv = avR0 =L∑

l=1

av, l ·Rv, l. (2)

Define the average slot capacity Cavgv (t) = 9.6 ∗

bavgv (t) Kb/s/slot [20], as shown in Table I. This value isinstrumental in the task of estimating the average slots requiredwhen a bit rate Rv, l (Kb/s) is assigned to a CS by the BS.For the lth bit rate mode, the average number of slots requiredis Gv, l = �Rv, l/C

avgv �. Thus, the average number of slots

needed by the vth video stream is expressed as

Gv =L∑

l=1

av, l ·Gv, l. (3)

In OFDMA, the total number of slots available at eachOFDM burst is capped at G0 slots. Hence, the radio resourceconstraints can be represented by

V∑v=1

Gv =V∑

v=1

L∑l=1

av, l ·Gv, l ≤ G0. (4)

The utility function of networking applications in generalshould directly tie together expectations to applications anduser perception [35]. In the video UL systems, for the purposeof qualitative analysis, a common approach is to representthe utility as a function of both video quality metrics andsubjectively calibrated parameters [17], [31]. The calibratedparameters can be assigned by different criteria [23], [31] ofapplications. In this paper, we assign a weight factor wv toreflect the importance of a video that is a situation-dependentsubjective criterion that ties closely to visual quality perceptionof surveillance systems. For example, a video showing an emer-gency event should have a higher priority, i.e., higher wv , thanother videos. The design of wv depends on specific operating

scenarios and will not be elaborated upon here. Instead, we willfocus on solving the optimization problem to be discussed later.Further, we define uv, l to be the video quality if the vth videostream is assigned to the lth bit rate, where uv, l > uv, l−1 anduv, l can be directly tied to the subjective or objective qualitymetrics. In the simulations of this paper, we use peak signal-to-noise ratio (PSNR) to approximate the values of uv, l becauseof its simplicity and low complexity [37], [38] for UL CSs andreasonable degree of correlation with subjective video quality[32], [33] so that it can also be translated to subjective metrics,e.g., mean opinion score, using various methods when needed[32], [39], [40]. In line with these discussions, the overallutility function for long-term UL bit-rate assignment can beexpressed as

U =

V∑v=1

wv ·(

L∑l=1

uv, l · av, l

)=

V∑v=1

Uv (5)

where Uv is the long-term utility to be generated by vth CS.Equations (4) and (5) lead to the following problem formulation.

P1. A Long-Term Bit-Rate Assignment Problem: Given R0,wv , bv , and uv, l, find the assignment av = [av, l] for all CSsthat maximizes the total long-term utility U defined in (5). Thiscan be expressed as

maxU =

V∑v=1

Uv

subject to the constraints in (4) and

L∑l=1

av, l = 1, 1 ≤ v ≤ V. (6)

It implies that each CS will be assigned to a designated bitrate, i.e., at least the lowest rate has to be assigned to a CS toensure the minimum quality for each UL video because of thenature of surveillance applications. The solution to P1 is theassignment {a∗v} for all V CSs. It will then be substituted into(2) to calculate the optimal bit-rate assignment for each CS as

R∗v = a∗vR0 =

L∑l=1

a∗v, l ·Rv, l.

Further, the video quality assignment, i.e., the targeted videoquality, for each CS can be noted as

u∗v =

L∑l=1

a∗v, l · uv, l. (7)

Thus, the targeted utility of each CS can be expressed as

U ∗v = wv · u∗

v.

Problem P1 [see (4) and (5)] is the classical 0–1 knapsackproblem with additional constraints described in (6), which hasthe worst-case complexity LV .


C. Real-Time Packet Scheduling Problem

Solution to problem P1 yields an optimal targeted averagebit-rate assignment R∗

v and an optimal targeted utility U ∗v for

each CS. To achieve the targeted U ∗v and R∗

v, an effective packetscheduler is essential. The video streams are allocated withG∗

v slots in each OFDMA frame. However, bit-rate assignmentdoes not bind the CS to any particular slot of any specificSCH (frequency band). Moreover, for live video streaming,each packet has a deadline Dv,max and should be deliveredbefore the Dv,max. Otherwise, it will be discarded and result inutility degradation. Thus, to achieve the U ∗

v obtained from P1,the objectives of real-time packet scheduling is to assign slotsto each CS such that 1) the real-time constraints are met, and2) the average bit rates will be as close to those assigned bitrates as possible.

For a particular OFDMA frame, CQIs between the CSs andthe BS vary among SCHs. This information is represented bybv, k, which is the number of bits that a subcarrier can betransmitted if the kth SCH is assigned to the vth video stream.

In an OFDMA UL subframe, there are G0 slots and K SCHs.Thus, each SCH has G0/K = GK slots. The task of the BS isto assign SCHs and the number of slots in each SCH to eachof the V video streams. Define Sv, k as the number of slots inthe kth SCH allocated to the vth video stream at the current ULsubframe. Summarizing above notations, for the vth CS, thenumber of bits that are allocated at the tth OFDMA frame canbe expressed as

rv(t) =K∑

k=1

Sv, k · (bv, k(t) · scr)

where scr is the number of data subcarriers in each slot.Moreover, for the kth channel

V∑v=1

Sv, k ≤ GK . (8)

Each CS maintains a buffer of video packets ready to betransmitted to the BS. For real-time video streaming, eachpacket has a deadline (Dv,max) timestamp. If the packet isnot delivered before the deadline, it becomes expired and willbe discarded. Packets in the buffer can be divided into twocategories: time critical versus time less critical. Time-criticalpackets, with its size denoted by rv, c(t), have pressing dead-lines and must be transmitted immediately. Otherwise, utility ofthe upload video will be compromised, diminishing the utilityvalue due to the packets discarded. Less-critical packets havemore relaxed deadlines and may remain in the buffer for a shorttime without causing utility reduction if resource is insufficientthen. Clearly, it is desired that

rv(t) ≥ rv, c(t) ≥ 0 (9)

where rv(t) is the actual number of packets (bits) of the vthvideo that are transmitted at time t. The quality generated by theuploaded rv(t) can be noted as uv(t). If the actually assignedbit rate rv(t) < rv, c(t), then the overall utility value will be

reduced by a nonnegative amount αv(t) for failing to meet thereal-time constraint, which can be shown as

αv(t) = wv · (u∗v(t)− uv(t))

where u∗v is as defined in (7).

Now, we define the indicator function J(a, b) = 1, if a > b;otherwise, J(a, b) = 0. Then, the penalty of the utility valuediscussed above may be expressed as

αv(t) · J (rv, c(t), rv(t)) .

As for less-critical packets, they should be transmitted if thereare still slots available after all critical packets are allocated.Above discussions lead to a cost function at time t

E(t) =

V∑v=1

αv(t) · J (rv, c(t), rv(t)) . (10)

More specifically, the reduced utility is the difference betweenthe targeted utility and the generated utility. The packet sched-uler has to make the utility uploaded by each CS be as close toU ∗v as possible so that the utility reduced can be minimized.Now, we are ready to present the problem formulation.P2. A Real-Time OFDMA Slot Assignment Problem: Find

Sv, k for each (v, k) such that E(t) in (10) is minimized, whichis formulated as

minE(t)

subject to constraints (8) and (9).In this paper, after P1 is solved, any procedure applied to P2

is to reach the targeted U ∗v found in P1 and will not change

the determined P1 solution; therefore, the optimization of P2 isregarded as a finer search of detailed parameters.

In a mobile network, it is difficult to allow UL users to uploadall their packet information to the BS due to the fact that theresource for feedback is limited. Thus, a BS actually cannothave all the information from CSs for UL scheduling [7], [9].Because of this, the feedback information used in our solutionto P2 along with its practical availability in a BS is consideredas follows. For 802.16 and LTE, the number of critical packetsand the total number of packets in the buffer (queue length) canbe reported by CSs to the BS via the information of bandwidthrequest and buffer status through the control channel [24]–[26]. Further, head-of-line (HOL) delay τv(t), i.e., the waitingtime of the first packet of the vth video in the transmit buffer,is used to determine if a CS has critical packets. The τv(t)must be lower than the highest allowable delay Dv,max toprevent packets from being dropped. It can also be fed backto the BS via control channel [4], [25]. The notations used aresummarized in Table II for convenience.

In this paper, a cross-layer algorithm, called VQD schedul-ing, is proposed to solve P1 and P2. As shown in Fig. 2,this systematic method intelligently considers the interactionbetween the application and MAC/PHY layers to search theoptimal solutions for P1 and P2. Further discussions for VQDare detailed Sections III and IV.


TABLE IILIST OF NOTATIONS

Fig. 2. VQD System: In BS, the VQD module is for optimal UL utility.

III. LONG-TERM VIDEO ENCODING RATE ADAPTATION

AND RESOURCE ALLOCATION

A. Long-Term Uplink Bit-Rate Assignment

To solve the problem of P1, we first define per-slot utilitygain φv, l = wvuv, l/Gv, l and rewrite (5) as follows:

U =

V∑v=1

L∑l=1

Gv, l · φv, l · av, l (11)

where φv, l is the unit utility gain when video stream v is as-signed with bit rate #l. Denote Umax to be the maximum utilitythat can be achieved with G0 or fewer slots. Clearly, the per-unitutility gain Umax/G0 will also be the largest. This observationleads to the first two steps of the bit-rate assignment heuristicalgorithm. To obtain the optimal utility gain, we introduce thenotion of incremental utility. For a video stream, the changeof utility value due to change of bit rate levels from l − 1 to lis noted as δUv, l = wv(uv, l − uv, l−1), and the change of slotdemand is δGv, l = Gv, l −Gv, l−1. Thus, one can define theincremental unit utility gain as

ηv, l =wv(uv, l − uv, l−1)

Gv, l −Gv, l−1=

δUv, l

δGv, l, 1 ≤ l ≤ L (12)

where uv,0 and Gv,0 are both defined as zero. Then, thealgorithm proceeds with bit-rate assignment as follows.

Step 1. Compute and then sort {ηv, l; 1 ≤ v ≤ V, 1 ≤ l ≤L} to yield a mapping of index (v, l) to an ordered list{(v′(f), l′(f)); 1 ≤ f ≤ F} such that

ηv′(1),l′(1) ≥ ηv′(2), l′(2) ≥ · · · ≥ ηv′(F ), l′(F )

where f is the rank index for ordered list, and F = V × L.Step 2. Set Gu(0) = 0.

For f = 1 to F ,Compute Gu(f) = Gu(f − 1) +Gv′(f), l′(f)

If Gu(f) ≤ G0,set av′(f), l′(f) = 1 and av′(f), l′(f)−1 = 0, ifl′(f)− 1 > 0

Else Gu(f) = Gu(f − 1)J = f − 1, then break the for loop

End for loopStep 3.

For f ∗ = J + 1 to F ,If δUv′(f∗),l′(f∗) >

∑Jf=1 δUv′(f), l′(f)

(i) reset {av′(f),l′(f) = 0, Gu(f) = 0; 1 ≤ f ≤ J}(ii) set av′(f∗),l′(f∗) = 1(iii) Redo Steps 1 and 2 for the rest (v, l) with

Gu(0) = Gv′(f∗),l′(f∗)

End for loop

If Gu(J) < G0, perform Steps 4 and 5. Otherwise, exit.With the Steps 1 and 2 in this greedy heuristic, each video

stream is assigned with the most efficient transmission bit ratein terms of utility value per slot, starting from the most efficientvideo stream. Note that not all video streams may be assignedwith a bit rate. Step 3 guarantees the algorithm performance bypreventing any extremely high utility video but with lower perslot usage, from being discarded.

On the other hand, it is possible that Gu(J) < G0. In thissituation, even if each video stream is assigned a bit rate that hasmaximum unit utility gain, there might be still slots left. Hence,it is possible to transmit some videos at even higher bit rates tomaximize the overall utility. To do this, one may apply selectionprocedures as Steps 3 and 4 to select the video streams to trans-mit at higher rates. More specifically, we have the following:

Step 4. Find each CS’s mode by l∗(v) = argmax{av, l; 1 ≤ l ≤L} and then sort {δUv,l∗(v); 1 ≤ v ≤ V } to yield a mapping ofindex v to an ordered list {v∗(q); 1 ≤ q ≤ V } with rank indexq so that

δUv∗(1),l∗(v∗(1))≤δUv∗(2), l∗(v∗(2)) ≤ · · · ≤ δUv∗(V ), l∗(v∗(V )).

Next, for all nonselected higher modes # (l∗(v) + 1), where1 ≤ l∗(v) + 1 ≤ L, sort {δUv,l∗(v)+1; 1 ≤ v ≤ V } to yield amapping of index v to an ordered list {v′′(q′′); 1 ≤ q′′ ≤ V }such that

δUv′′(1), l∗(v′′(1))+1 ≥ δUv′′(2), l∗(v′′(2))+1 ≥ · · ·≥ δUv′′(V ), l∗(v′′(V ))+1.


Step 5.For q′′ = 1 to V ,

For q = 1 to V ,Compute δG=δGv′′(q′′),l∗(v′′(q′′))+1−δGv∗(q),l∗(v∗(q))

If δUv′′(q′′), l∗(v)+1 > δUv∗(q), l∗(v∗(q)) && Gu(J) +δG ≤ G0,set av′′(q′′),l∗(v′′(q′′))+1=1 and av′′(q′′),l∗(v′′(q′′))=0.

av∗(q), l∗(v∗(q)) = 0 and av∗(q), l∗(v∗(q))−1 = 1.Gu(J) = Gu(J) + δG

Then redo Steps 4 and 5.End if

End forEnd for loop

B. Analysis for VQD Algorithm to Solve P1

We now provide an analysis of VQD algorithm proposed forlong-term bit-rate assignment. As described in Section II-B, theP1 is closely related to the 0–1 knapsack problem and is NP-hard. In general, the method to optimize unit resource usage,known as the greedy heuristic method, can potentially resultin poor performance for 0–1 knapsack problem. Thus, we firstshow that our proposed algorithm can at least guarantee 1/2-approximation in this type of problem.

Theorem 1: For long-term resource allocation, the VQD canat least achieve the 1/2-approximation of optimal performancefor a 0–1 Knapsack problem.

Proof: See Appendix A.Theorem 1 gives a loose lower bound for the VQD algorithm

in this 0–1 knapsack problem. In the VQD, we assign bit rateaccording to δG, which is the slot demand when bit rate isincreased from (l − 1)th to lth. By keeping this δG small (asin comparison with G0) and iteratively allocating this smallportion of resource to CSs while deciding their bit rates, the per-formance of VQD can be further enhanced. More specifically,define

ε = maxv, l

(δGv, l

G0

)where ε denotes the maximum ratio of slots demand for higherbit rate over total slots for UL. Then, a stronger performancebound that VQD can provide within a factor of (1 − ε) of theoptimal solution is stated in Theorem 2.

Theorem 2: For allf , if δG(f) ≤ ε ·G0, the VQD algorithmguarantees a solution that is at least (1 − ε) of the optimalvalue. That is, OPTVQD ≥ (1 − ε) · OPT.

Proof: See Appendix B.

C. Complexity of VQD Algorithm to Solve P1

The complexity of using VQD algorithm to solve P1 isassessed as follows. First, O(V L) is needed to find out allηv, l. Steps 1 and 2 take O(V L · log V L) operations for sortedscheduling. Step 3 may have O(V L) as the highest amountof operations. After this stage, the worst case for Steps 4and 5 is O(V · log V ) and O(V 2), respectively. Since in gen-eral, V � L, the overall complexity is max{O(V L), O(V L ·

log V L), O(V L), O(V · log V ), O(V 2)} = O(V 2). Consider-ing that P1 needs to be solved only once every few seconds,it is reasonable to assume that VQD can solve P1 in real time.

IV. REAL-TIME SCHEDULING AND

RESOURCE ALLOCATION

A. Frame-by-Frame Packet Scheduling Algorithm

Once long-term bit-rate assignment problem is solved, eachCS will upload video stream according to the assigned bit rate.However, due to frame-by-frame variations of CQI, it is neces-sary to solve the real-time OFDMA slot assignment problem P2.As discussed earlier, P2 involves three tasks: 1) Decidethe scheduling priority for each CS; 2) allocate time-criticalpackets to meet real-time constraints; and 3) allocate less-critical packets to meet the target bit rate for each video.

For the first task, a utility-based priority function is proposedin this paper to assign scheduling priority for each CS in anOFDMA frame. This priority function is based on the unitutility gain, average throughput of individual CSs, and thequeuing delay. Specifically, the priority function defined is

φkv(t)=

⎧⎨⎩Uv, norm

sv, k

1Fv

1Cmax , if F delay

v (t)≥1 and bv, k(t) =0

1, if F delayv (t)<1 and bv, k(t) =0

0, otherwise(13)

where

Uv,norm =L∑

l=1

(wv · uv, l) · av, l/U

Fv(t) =F delayv (t) · F rate

v (t) (14)

F delayv (t) =

(Dv,max − τv(t))

Γs(15)

F ratev (t) =

rv(t− 1)Rv,min

. (16)

Note that φkv is the priority of the vth CS on SCH k; Uv,norm

is the vth utility normalized by U in (5); sv, k = �Rv/Cv, k� isthe estimated slots consumption when CQI is bv, k; F delay

v isthe delay factor [3] with Dv,max and τv(t); and Γs is the guardtime and usually is the same as the scheduling period. WhenF delayv < 1, it implies that the queue in the vth CS has the

critical packet and should be served at time t. Thus, the φkv is

assigned with the highest priority. This mechanism is criticalfor reducing packet loss and maintaining satisfactory utility.F ratev is the ratio of the average upload bit rate to the

minimum throughput required to maintain utility. The averagebit rate of the vth video is evaluated by

rv(t) = (1 − ρ) · rv(t− 1) + ρ · rv(t) (17)

where ρ is set as 1/50 for real-time application [21], [22]. WhenF ratev < 1, φk

v should be increased to make up the deficiency.Cmax is the highest MCS in Table I and is used to normalizethe φv value within (0, 1).


The steps for frame-by-frame scheduling are as follows.

1) For each CS, assess {φ′s} for all the K SCHs by (13) as

follows:

Φv={k1, k2, . . . , kK : φk1

v ≥ · · · ≥ φkKv

}; v=1, . . . , V

(18)

where φv, k will be deleted from Φv if there is no moreslots available for upload in the kth SCH.

2) Set the priority Pv as

Pv = max{Φv}; v = 1, 2, . . . V. (19)

3) The CS with the maximum Pv will be scheduled first andallocated to the available SCH ksch, where

(vsch, ksch) = argmax(v,k)

{Pv}. (20)

The instant CQI assigned to vsch at frame t can be shown as

bvsch(t) = bvsch, ksch(t).

This assigned CQI can be mapped to the corresponding MCSm, as shown in Table I, and the MCS adopted by CS vsch is thusobtained. The average CQI is then updated by (1).

In our system, we iteratively schedule the CS and selectthe allocated SCH along with the corresponding MCS usingSteps 1–3 above for every OFDMA frame until no more slotsare available or all payloads have been allocated.

Intuitively, to obtain the optimal utility, the CSs with higherunit utility gain should have higher priority to be scheduled.However, scheduling decisions relying on utility gain only areinsufficient to support real-time video service due to its strictdelay and throughput constraints, as well as instantaneous vari-ations in compressed videos. Hence, the Fv factor is includedin the proposed function (13), where once critical packets existin a CS, the priority of this CS is raised to the highest value fortimely transmission.

However, such an arrangement may lead to a critical ques-tion: For CSs with no critical packets, will the policy articulatedby (13) favor CSs with high utility or good instant CQI andbecome highly unfair?

To answer this question, we offer the following analysis.Without loss of generality, let us assume the best SCH is usedand both F delay

v > 1 and bv > 0 are held for each CS. We alsodenote sv = Rv/Cv for brevity of notations. From (13), (15),and (16), one has

φv(t) =Uv,norm

sv

1F ratev

1

F delayv

1Cmax

=Uv,norm

sv

Rv,min

rv(t− 1)

1

F delayv

1Cmax

.

The average bit rate rv(t− 1) in (16) can be derived as Cavgv

and Savgv , where Cavg

v and Savgv are average slot capacity and

average slot assigned, respectively. Then, the priority functionabove becomes

φv(t) =Uv,norm

Rv

Cv

Rv,min

Cavgv Savg

v

1

F delayv

1Cmax

=Uv,norm

Savgv

Cv

Cavgv

Rv,min

Rv

1

F delayv

1Cmax

. (21)

In (21), the Cv/Cavgv indicates that the BS tends to schedule

a CS when its instantaneous CQI is high enough relative to itsown average CQI over a specific timescale. In short, a CS isallowed to upload data when its CQI is near its own peak. Thisconcept is consistent with the proportional fair or opportunisticscheduling in [8]; and thus (21) shows that fairness is infact already embedded in the proposed algorithm of (13). Inaddition, the spectrum usage efficiency is also sustained byusing (13) since multiuser diversity can still be benefited byusing proportional fair scheduling, as shown in [8].

The complexity for scheduling by VQD priority function in(13) is assessed as follows. In (18), for each CS, the priorityin (13) needs to be evaluated for all K channels and theseK results in turn need to be sorted. Thus, (18) has O(V K) +O(V K · log V K) operations. In regard to (19) and (20),both require O(V ) operations. Therefore, the complexityfor scheduling is max{O(V K), O(V K · log V K), O(V )} =O(V K · log V K), which is polynomial time. It is hence justi-fiable to apply the proposed algorithm to real-time application.

B. Real-Time Slot Assignment

When a CS is scheduled based on its priority, the number ofslots allocated to this CS also needs to be decided. The allocatedbandwidth must satisfy the rc, v(t) constraint in (9) to minimizethe cost function E(t) defined in (10). Besides, for live video,the required rate Rv,min must be guaranteed while assigning theUL rate of rc, v(t) and less-critical bits in case the videosbecome useless due to insufficient bandwidth [30].

Thus, [5], [6], and [11] proposed that the average assignedbit rate at time t, as shown in (17), should fulfill the condition

rv(t) ≥ Rv,min. (22)

In [5] and [6], the amount of bits to be uploaded by eachCS is evaluated every OFDMA frame. When the average ratebefore frame t, i.e., rv(t−1), is smaller than Rv,min, the bits to beuploaded should be increased and assured to satisfy the Rv,min.Otherwise, no resource is needed. It can be expressed as

Δv(t)=

⎧⎨⎩(Rv,min−rv(t−1)) · tc+ rv(t−1), if rv(t−1)<Rv,min

0, otherwise(23)

where Δv(t) is the rate required to assure Rv,min, andtc = 1/ρ.

However, the instantaneous channel condition of a mobileclient is time-varying, and a CS may temporarily suffer fromunexpected serious channel fading. In case of slow stations,with high scheduling priority, if too many packets are trans-mitted through the poor-quality channels in order to meet


Fig. 3. Pseudocode for proposed resource allocation method.

the Rv,min requirements, they will definitely consume evenmore resource than fast stations do due to poor CQI and thelow-efficiency MCS. Under this circumstance, the resourceusage efficiency is decreased, and other CSs will suffer fromresource shortages because of the slot exhaustion caused byslow stations. Thus, the performance of each UL CS and thesystem throughput are all negatively affected or sacrificed.To overcome this issue, we propose the resource allocationalgorithm, shown in Fig. 3, by modifying (23) as follows.

Two situations are considered in our method: 1) when theinstantaneous UL CQI bv(t) measured by the BS [24] is lowerthan the average CQI bavgv ; or 2) bv(t) ≥ bavgv , but rv(t−1) ≥Rv,min. Then, Gv , derived from (3), is imposed as the upperbound for the amount of slots to be assigned to each (e.g.,the vth) CS in each frame. Otherwise, if the bv(t) is higherthan the average, the number of bits allowed for the vth CS’stransmission should be assured to satisfy the Rv,min. Theprocedure above can be shown by (C1) listed in Fig. 3.

By imposing the Gv in the first situation, the system canprevent the scheduled CSs with deep channel fading fromsevere exhaustion of the available slots during transmission [9].For the second situation, although the average uploaded ratealready satisfies the Rv,min, the bandwidth Gv can still beallocated to scheduled CSs in view of its ability to efficientlydecrease the amount of buffered data and the critical packets.

After Δv(t) is found, we should assure that constraint in (9)is guaranteed. Thus, the rv(t) is determined by

rv(t) = max (Δv(t), rv, c(t)) (24)

and the number of slots assigned at time t(Sv(t)) is

Sv(t) =

⌈rv(t)

(scr × bv(t))

⌉. (25)

If the available slots on SCH ksch in (20) is not enough, thesecond best SCH for the CS vsch is selected, and the remainingbits are allocated [6]. The details for real-time slot assignmentare summarized in Fig. 3.

V. SIMULATION AND PERFORMANCE COMPARISON

A. Utility-Driven Greedy Algorithm

The performance of the proposed VQD algorithm is eval-uated through extensive simulations using realistic wirelesschannel models. Specifically, for bit-rate assignment in P1,

VQD will be compared with a baseline utility-driven greedyalgorithm over various scenarios [16]–[18].

The baseline greedy algorithm is initialized by assigningequal amount of resource Gv to each UL CS. The utility Uv

and rate Rv of each CS are thus obtained based on Gv andits average CQI, as shown in (4). Then, the greedy algorithmiteratively takes away a small amount of assigned slots ΔGfrom the CS identified to be least sensitive to the utility decreasedue to this reduction in slots and then continuously assigns thisΔG to the other CS that can generate the highest utility benefituntil no improvement is obtainable.

Let ΔUv denote the change of utility for the vth CS due toa change of slot ΔG. This algorithm can be expressed as aniterative maximization of the incremental utility by adding ΔGof CS n+ and decreasing ΔG from CS n−, such that

n+ = argmaxv

(ΔUv|Gv ← Gv +ΔG)

n− = argminv

(ΔUv|Gv ← Gv −ΔG).

After the rate Rv is assigned, two well-known schedulers,i.e., M-LWDF and EXP [10]–[12], along with the slot assign-ment strategy in (23), are incorporated with utility greedy tofacilitate live video packet scheduling in P2. M-LWDF andEXP are adopted because of their great QoS performances forreal-time flows in cellular systems [10], [29], where the formerperforms well for systems with lower loads, and the latter isrecommended for those with higher loads [29].

B. Simulation Configuration and Channel Model

In this paper, the simulations are performed strictly accordingto [20], [27]. The simulated WCN includes one UL BS in thecenter of cell, and the connected UL CSs are all mobile anduniformly distributed within the cell. To simulate each mobileCS’s CQI, the channel propagation loss is estimated based onthe COST 231 suburban model, and the small-scale fadingeffect is measured employing the ITU Veh-A multipath model[27] corresponding to 30 Km/h. Simulations I and II in thefollowing are set to work on bandwidth of 5 and 10 MHz witha 5-ms OFDMA frame [27], respectively, and both adopt theband-AMC permutation [20] for subchannelization.

C. Simulation I: Packet Scheduler Performance

In the first simulation, we only compare the performance ofdifferent packet schedulers, including VQD, and the M-LWDFand EXP in Section V-A. We assume that six CSs are uniformlyscattered in a WCN, which is a 5-MHz OFDMA system.Each CS has a constant bit rate (CBR) video with 1 Mb/s.Without loss of generality, we use the normalized utility, i.e.,uv, l = 1 since only one rate mode is used. To ensure real-time streaming, the Dv,max = 50 ms for each packet [9], [36].Moreover, three resource scenarios (176, 154, and 198 slots forUL) are used for comparison. In the first scenario, 176 slotscan be considered as 50% of total slots in a 5-MHz OFDMAframe and is abundant for all six CBR videos being uploaded if


TABLE IIIAVERAGE THROUGHPUT (KB/S)

TABLE IVAVERAGE PACKET LOSS (%)

Fig. 4. Quality (uv, l)—Rate models for the five videos used in simulation.The “�” denotes the quality of each R0,l [28], [34].

the resource is efficiently assigned. The other two scenarios,with lower and higher resource budgets, are also tested formore comparisons. The experimental results are summarizedin Tables III and IV. It is evident that by jointly considering thefactors in (14), the concept of opportunistic scheduling, and theslot assignment method in Fig. 3, the VQD packet schedulercannot only effectively enhance the throughput but also greatlydecrease the system packet loss, even if the available slot budgetis tight.

D. Simulation II: Systematic Method Performance

In this simulation, a WCN with 20 uniformly distributed ULmobile CSs is considered. Each CS is assigned to a weightinteger wv within the range from 1 to 3, which is an empiricaland reasonable range, and provided with a live video encodedby H.264/AVC with L = 4 allowable target bit rate modes, i.e.,R0 = [Rv, l] = [500, 700, 1000, 1200] Kb/s. The PSNR, whichis an objective quality measurement, is adopted to assess thevideo quality (uv, l) at different bit rates in our simulation.Fig. 4 shows the quality-rate curves, obtained by using themodel in [28] and quality-rate data in [34], for five differentvideos encoded with the H.264 AVC codec at common inter-mediate format resolution and a frame rate of 30 frames/s. Each

CS is randomly assigned to one of the compressed videos (withdifferent quality-rate model) to be uploaded to the BS, and then,the video quality and utility to be uploaded to the BS can beevaluated by these models based on the target bit rate, as in [16],[17], and [32]. Again, to ensure real-time video streaming, theDv,max = 50 ms is used.

Four UL systematic algorithms are compared: 1) the pro-posed VQD method; 2) the utility-driven greedy method incor-porated with M-LWDF; and 3) the utility-driven greedy methodwith an EXP scheduler; and 4) the globally optimal utility byexhaustive search. Each method needs to solve P1 to decide theRv and target utility for each CS, and then real-time schedulersadopted in the first, second, and third algorithms have to solveP2 to find the utility actually being generated. As for the fourthalgorithm, we assume the target Rv and utility can be perfectlyreached to the optimum; thus, no scheduler is needed to solveP2. The utility produced by each CS is updated every 3 s. Thetotal slots per frame reserved for UL video (G0) is 495.

The overall system performance are summarized inFigs. 5–7. Fig. 5(a) shows the average utility comparisons in30 s, and both the target and generated utility by VQD beingmuch closer to the optimum by the fourth algorithm than thoseby the other methods. Fig. 5(b) shows the normalized results,i.e., the generated utility normalized by the optimum, whichfurther indicates that the utility of VQD is close to the optimumconsistently.

Furthermore, for each method, the G0 in the simulation isin fact allowing all CSs to upload videos by using a basic bitrate of 500 Kb/s to generate the basic utility. Therefore, thereal meaningful aspect here is to compare the enhanced utility,i.e., the increased utility obtained by each method above thebasic utility portion. Fig. 6(a) shows that the enhanced utilityproduced by VQD is consistently far better at each moment,and Fig. 6(b) exhibits the enhanced utility by VQD is some 80%higher on average than those obtained by other methods.

Fig. 7 shows system loss rate by the proposed VQD packetscheduler and Utility Greedy with different schedulers. TheVQD packet scheduler maintains better performance because itassigns the highest priority to the CS with time-critical packets,consequently providing better QoS than the others, as has beencovered in [4]. According to [29], the M-LWDF provides betterQoS to systems with lower loads, and the EXP is recommendedfor those with higher loads. Since the utility greedy assigns thebit rate based on the available slots and the capacity of eachCS, the UL traffic is basically appropriately allocated; thus, theresults for method 2 and 3 are similar.

In addition, the utility greedy method needs to search themost appropriate CS pairs to exchange the assigned resourcefor the optimal utility. This task becomes more complicated dueto the fluctuating or changing channel qualities of mobile CSs.Since the best CS pairs and the slots exchanged may not bethat easy to obtain, it thus takes longer execution time to findthe optimum, as shown in Fig. 6. VQD simply assigns resourceaccording to the ηv, l in (12), and then enhances the results byapplying steps 3 to 5 in Section III-A when needed. Using thissimpler procedure, the VQD can quickly find the near-optimalsolution and can be easily implemented in the wireless ULscenario.


Fig. 5. Comparisons of different Methods. 1: VQD; 2: utility greedy with M-LWDF; and 3: Utility greedy with EXP. (a) Average utility: optimum versus targetversus generated in 30 s. (b) Average normalized utility: every 3 s.

Fig. 6. (a) System enhanced utility every 3 s. (b) Enhanced utility in 30 s by method 1: VQD; method 2: Utility Greedy with M-LWDF; and method 3: UtilityGreedy with EXP.

Fig. 7. (a) System packet loss every 3 s. (b) Packet loss in 30 s by 1: VQD; 2: utility greedy with M-LWDF; 3: utility greedy with EXP.

Fig. 8 shows the results averaged over all CSs with differentwv , including the normalized utility and packet loss rate. Figs. 9and 10 display the performance of CSs randomly selected fromthe highest and the lowest weighted CSs. The comparisons inFigs. 8–10 further demonstrate that the VQD provides higherand more stable utility, as well as lower packet loss for all thedifferent weighted videos.

VI. CONCLUSION AND PERSPECTIVES

We have proposed a novel VQD algorithm that yields near-optimal solutions to both the long-term bit-rate assignmentand the real-time packet scheduling for the UL wireless mul-timedia system over the mobile network of next generation.The simulation results indicate that VQD is able to deliversuperior performances in a good many aspects, including higher


Fig. 8. Average (a) normalized utility and (b) packet loss for CSs in different weight (wv).

Fig. 9. (a) Utility and (b) Packet loss every 3 s. A CS with highest weight is randomly selected.

Fig. 10. (a) Utility and (b) packet loss every 3 s. A CS with lowest weight is randomly selected.

spectrum efficiency and throughput, much lower packet loss,more stable video quality, around 80% more enhanced utility,etc., as compared with the baseline methods. This proposedsystem can be applied to various real-time monitoring scenariosand is readily applicable to any OFDMA 4G technologies, suchas WiMAX and LTE.

In view of the practical limitations of feedback resource formobile UL systems, we presented the VQD packet schedulerusing only the allowable number of the actual feedback infor-mation from CSs, such as HOL and bandwidth request, in the

OFDMA systems. This proposed scheme can also be applied toLTE type of networks, which use SC-FDMA in the uplinking,and will require different radio resource allocation policy.

Further extension of this work resides in adopting more infor-mation from videos, such as the type of video frame, to adjust thescheduling priority, e.g., the I-frame packets in a higher weightedCS should have the higher priority than P-frame packets ofothers. In addition, the design for scheduler in mobile CS, allo-cating the bandwidth required from a BS to adequate packets inits queue for uploading, should be worth investigating as well.


APPENDIX APROOF OF THEOREM 1

Denote {(δU(f), δG(f)); 1≤f≤F =V ×L} as the utility–resource pairs evaluated from all eligible (v, l) by Step 1 ofVQD method, where f is the rank index reflecting the sortedresults of all ηv, l in descending order, i.e., δU (1)/δG(1) >δU (2)/δG(2) > · · · > δU (F )/δG(F ). SupposeJ items are sche-duled in total by Step 2, and assume

δU (1)

δG(1)>

δU (2)

δG(2)> · · · > δU (J)

δG(J)>

δU (J+1)

δG(J+1).

The index J + 1 represents the first item not be selected due toinsufficient slots, which means the following condition holds:

δG(J+1) > G0 −J∑

f=1

δG(f). (A.1)

If we assume the OPT is the global optimal solution for P1,then

J∑f=1

δU (f) + δU (J+1) ≥ OPT (A.2)

since the LHS has the largest unit utility gain. Denotes thesolution obtained from VQD as OPTVQD. The performance ofVQD algorithm can be demonstrated in two phases.

Phase I: In Step 3, if an item f ∗ with the highest δU (f∗)

results in

δU (f∗) >

J∑f=1

δU (f)

where J + 1 ≤ f ∗ ≤ F , OPTVQD can be expressed as

OPTVQD=δU(f∗)+

J′∑f′=1

δU(f′)≥δU(f∗)>

j−1∑f=1

δU(f) (A.3)

where f ′ and J ′ is, respectively, the index of sorted resultand the number of items scheduled after f ∗ is scheduled.

Since δU (f∗) >∑J

f=1 δU(f) and δU (f∗) ≥ δU (J+1),

from (A.2), one has

OPT≤J∑

f=1

δU (f)+δU (J+1)≤δU (f∗)+δU (f∗)=2 · δU (f∗).

Substituting (A.3) to above, we conclude

OPT≤J∑

f=1

δU (f)+δU (J+1)≤2·δU (f∗)≤2·OPTVQD. (A.4)

This immediately implies OPTVQD≥(1/2)OPT in Phase I.Phase II: If there is no item f ∗ with highest δU(f∗), i.e., Step 3

is not triggered and δU (J+1) ≤∑J

f=1 δU(f), by Step 4

and 5, we obtain

OPTVQD=

J∑f=1

δU (f)−δU (i)+δU (f ′′)≥J∑

f=1

δU (f) (A.5)

where {δU (f ′′) > δU (i) : 1 ≤ i ≤ J, J + 1 ≤ f ′′ ≤ F}.Since δU (J+1) ≤

∑Jf=1 δU

(f) (A.2) becomes

J∑f=1

δU (f)+δU (J+1)≤J∑

f=1

δU (f)+

J∑f=1

δU (f)=2 ·J∑

f=1

δU (f).

Substituting (A.5) into the earlier equation, we have

OPT ≤J∑

f=1

δU (f) + δU (J+1) ≤ 2 ·J∑

f=1

δU (f) ≤ 2 · OPTVQD.

(A.6)

This immediately leads to OPTVQD≥(1/2)OPT in Phase-II,and (A.4) and (A.6) complete the proof of Theorem 1. �

APPENDIX BPROOF OF THEOREM 2

For 1≤f≤J , δU (f)/δG(f)>δU (J+1)/δG(J+1). Therefore

δG(1) δU(1)

δG(1)+ δG(2) δU

(2)

δG(2)+ · · ·+ δG(J+1) δU

(J+1)

δG(J+1)

≥(δG(1) + δG(2) + · · ·+ δG(J+1)

)· δU

(J+1)

δG(J+1)

⇒ δU (1) + δU (2) + · · ·+ δU (J+1)

≥(δG(1) + δG(2) + · · ·+ δG(J+1)

)· δU

(J+1)

δG(J+1).

By applying (A.1), this inequation can be simplified as

δU (1) + δU (2) + · · ·+ δU (J+1) ≥ G0 ·δU (J+1)

δG(J+1). (B.1)

Since for all f , δG(f) ≤ εG0, it follows from (B.1) that

δU (J+1) ≤ ε ·(δU (1) + δU (2) + · · ·+ δU (J+1)

)≤ ε

1 − ε·(δU (1) + · · ·+ δU (J)

).

By using (A.2), it can be easily deduced that(δU (1) + δU (2) + · · ·+ δU (J)

)≥ (1 − ε) · OPT. (B.2)

Recall that in (A.3) and (A.5), we already know thatOPTVQD ≥ δU (1) + δU (2) + · · ·+ δU (J), and we apply it to(B.1). This completes the proof. It thus indicates that theOPTVQD is extremely close to the OPT since the δG is verysmall, as compared with the total UL slots G0. �

ACKNOWLEDGMENT

The authors would like to thank the editor and the anonymousreviewers for their many insightful comments and constructivesuggestions. The perspective in Section VI is inspired by thereviewers.


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Po-Han Wu received the B.S. degree in mechan-ical engineering from National Central University,Chungli, Taiwan, in 2002; the M.S. degree in electri-cal engineering from New York University Polytech-nic School of Engineering, New York, NY, USA, in2005; and the Ph.D. degree in electrical engineeringfrom the University of Washington, Seattle, WA,USA, in 2014.

In 2006, he was an Intern Researcher with theInstitute of Information Science of Academia Sinica,Taipei, Taiwan, and a Graduate Co-Op Intern with

Network Data Planning Team, Verizon Wireless, Walnut Creek, CA, USA,and Bellevue, WA, USA, in 2012. He is currently with the Lab Group,T-Mobile USA. His research interests include multimedia networking, orthogo-nal frequency-division multiplexing mobile systems, real-time video transmis-sion, optimization for wireless communication systems, video processing, andsignal processing.

Chih-Wei Huang received the B.S. degree fromNational Taiwan University, Taipei, Taiwan, in2001; the M.S. degree from Columbia University,New York, NY, USA, in 2004; and the Ph.D. degreefrom the University of Washington, Seattle, WA,USA, in 2009, all in electrical engineering.

From 2006 to 2009, he was an Intern Researcherwith Siemens Corporate Research and Microsoft Re-search. Since 2010, he has been with the Departmentof Communication Engineering, National CentralUniversity, Jhongli, Taiwan, where he is currently an

Assistant Professor, heading the Information Processing and CommunicationsLaboratory. He is the author of papers in a broad range of areas, includingwireless networking, multimedia communications, digital signal processing,and information retrieval.


Jenq-Neng Hwang (F’01) received the B.S. andM.S. degrees in electrical engineering from the Na-tional Taiwan University, Taipei, Taiwan, in 1981and 1983, respectively, and the Ph.D. degree fromthe University of Southern California, Los Angeles,CA, USA.

Since 1989, he has been with the Department ofElectrical Engineering, University of Washington,Seattle, WA, USA, where he was promoted to FullProfessor in 1999. He is currently the AssociateChair for Research with the Department of Electrical

Engineering. He has a close working relationship with industry on multimediasignal processing and multimedia networking. He is the author of more than300 journal and conference papers, book chapters, and the book MultimediaNetworking: from Theory to Practice (Cambridge University Press). His re-search interests include multimedia signal processing and multimedia systemintegration and networking.

Dr. Hwang is a founding member of the Multimedia Signal Processing Tech-nical Committee of the IEEE Signal Processing Society and was the Society’srepresentative to IEEE Neural Network Council from 1996 to 2000. He was theProgram Cochair of the 1998 International Conference on Acoustics, Speech,and Signal Processing and the 2009 International Symposium on Circuits andSystems. He is currently a member of the Multimedia Technical Committeeof the IEEE Communication Society as well as a member of the MultimediaSignal Processing Technical Committee of the IEEE Signal Processing Society.He served as an Associate Editor for the IEEE TRANSACTIONS ON SIGNAL

PROCESSING, the IEEE TRANSACTIONS ON NEURAL NETWORKS AND

LEARNING SYSTEMS, the IEEE TRANSACTIONS ON CIRCUIT SYSTEMS FOR

VIDEO TECHNOLOGY, the IEEE TRANSACTIONS ON IMAGE PROCESSING,and IEEE SIGNAL PROCESSING MAGAZINE. He is currently on the EditorialBoards of Electronics and Telecommunications Research Institute, the Interna-tional Journal of Data Mining and Bioinformatics, and the Japan Society for thePromotion of Science journals. He received the 1995 IEEE Signal ProcessingSociety’s Best Journal Paper Award.

Jae-Young Pyun (M’03) received the B.S. degreefrom Chosun University, Gwangju, Korea; the M.S.degree from Chonnam University, Gwangju; and thePh.D. degree from Korea University, Seoul, Korea, in1997, 1999, and 2003, respectively, all in electronicsengineering.

From 2003 to 2004, he was with Samsung Elec-tronics, where he was involved in the research anddevelopment of mobile phone communication sys-tems. Since 2004, he has been with the Departmentof Information and Communication Engineering,

Chosun University, where he is currently a Professor. His research interestsinclude network protocols over wireless sensor networks, indoor positioning,and video communication.

Dr. Pyun is a member of the Institute of Electronics, Information, andCommunication Engineers; the Institute of Electronics Engineers of Korea; andKorean Institute of Communications and Information Science.

Juan Zhang received the B.S. and M.S. degrees incomputer science from Jiangxi Normal University,Jiangxi, China, in 1997 and 2005, respectively, andthe Ph.D. degree in computer science from ShanghaiUniversity, Shanghai, China, in 2012, respectively.

From 2012 to 2014, she was a Postdoctoral Fellowwith the School of Communication and InformationEngineering, Shanghai University. She is currentlya junior faculty with the College of Electronic andElectrical Engineering, Shanghai University of Engi-neering Science. Her research interests include soft-

ware testing and computer graphics.

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