Equalization of Packet Delays in OFDMA

Scheduling of Real-Time Video Calls

Alexander X. Han, I-Tai Lu

Department of Electrical and Computer Engineering

Polytechnic Institute of New York University

5 Metrotech Center, Brooklyn, NY 11201

ihanxiao@gmail.com; itailu@poly.edu

Abstract—This paper studies the scheduling of multiple real-time

unicast videos (e.g. video calls) over the Orthogonal Frequency

Division Multiple Access (OFDMA) air interface. Modified

Largest Weighted Deadline First (M-LWDF) and Exponential

Rule (EXP) were proposed to schedule traffic with quality-of-

service constraints in shared-channel systems. Both have been

proven to be throughput optimal and EXP also possesses delay

optimality in a sense. This paper proposes several techniques that

modify M-LWDF to further improve users’ 99% packet delays

over M-LWDF and EXP. An interesting phenomenon of

simultaneous reduction in latencies and bandwidth usages is

demonstrated in various comparisons, which contradicts with the

conventional observation that giving unequal weights to users

sacrifices spectral efficiency. Our study shows that a better

scheduling policy often improves both spectral efficiency and

user latencies simultaneously in the scheduling of real-time

traffic. Under the same user latency constraints, the proposed

scheduler also improves the Peak-Signal-to-Noise-Ratio (PSNR)

of received videos considerably under moderate system load.

Keywords- OFDMA; real-time; video calls; QoS; latency; 99%

packet delay; M-LWDF; EXP rule; scheduling; delay equalization;

PSNR; H.264/AVC

I. INTRODUCTION

Voice call service has successfully migrated from circuit-switched network to IP-based network in the past few years. The majority of content delivered over next generation cellular networks will be video [1], including real-time conversational video calls (packet switched video telephony, PSVT). In contrast to voice calls, video calls exhibit much higher data rates, e.g. 128-384 kbps for a mere 352 × 288 (CIF) resolution [2]. Meanwhile, the delay constraints of video calls are comparable to those of voice calls, e.g. the 99% percentile packet delay of a video call should be ideally less than 150 milliseconds and no more than 300 milliseconds [3]. Quality-of-Service (QoS) is a major research topic in the current 3GPP development of next generation cellular network (LTE-A) [4].

The downlink of LTE-A employs the orthogonal frequency division multiple access (OFDMA) air interface and performs link adaptation based on the feedback of channel quality indicators (CQIs) from users to enhance throughput [5]. Observing that the base station to user link is a bottleneck in the end-to-end packet delays and the scheduler has a lot of freedom in manipulating the packet delays, we propose several

techniques in this paper to improve the QoS of real-time video calls by OFDMA scheduling.

The QoS of a service is typically given by a) minimum average data rate, b) the (100-x)% tail packet delay if x% packet loss rate at the IP layer is acceptable to the application. The acceptable packet loss rate for video calls is on the order of 1% depending on the error correction code applied in higher layers [3, 4]. Assuming the base station delivers all the incoming traffic to the receiving users, requirement a) is automatically satisfied as long as the tail packet delay in b) is maintained stable over time.

In the case of real-time videos, assuming successive video frames are generated and supposed to be played back at equispaced time instants (e.g. every 67 milliseconds at 15 frames per second), each receiver uses a finite time window to wait for all the packets of a given video frame. The packets that belong to the video frame but are delayed by more than the time limit are excluded during the decoding of the video frame and this causes distortion in the decoded video. Assuming the length of the window is adapted to maintain x% packet loss, the (100-x)% tail packet delay of a user determines the latency of the real-time video. Because of this, this paper focuses on reducing the 95-99% tail packet delays of real-time videos. However, we find that bandwidth usage and packet delay can often be reduced simultaneously using a better scheduling policy, which is surprising as traditionally tradeoffs must be made between the two. The lower bandwidth usage of real-time services leaves more resources to other lower priority (e.g. best effort) services, leading to higher total system throughput.

The delays of each user’s video packets follow a certain distribution under a scheduling policy. To reduce the tail packet delays, it would be desirable to reduce the delays of the longer delayed packets at the cost of increased delays of the less delayed packets, i.e. equalize the delays of a user’s video packets.

The organization of this paper is as follows: Section II analyzes the factors in designing an OFDMA scheduler for real-time services and discusses previous work related to this problem. Section III describes our proposed techniques and demonstrates them by simulations. The causes of the improvements by the proposed techniques are also explained in this section. Section IV concludes this paper. Details on our simulation setup is given in appendix A.

This work is sponsored by InterDigital, Inc. in part.

The 2011 Military Communications Conference - Track 4 - Middleware Services and Applications

978-1-4673-0081-0/11/$26.00 ©2011 IEEE 1547

II. OFDMA SCHEDULING OF REAL-TIME SERVICES

A. Opportunistic Scheduling

Consider a system where multiple users are multiplexed over the same carrier by time division. The channels between the base station (BS) and the users are in general asynchronously time-varying due to the fading of wireless channels. The channel capacity is related to a user’s Signal to Interference-plus-Noise Ratio (SINR) by Shannon’s channel capacity formula:

2log (1 )C SINR (1)

In practice, a user’s data rate is determined by the modulation and coding scheme (MCS) level (corresponds to a CQI value in LTE-A). User equipments (UE) report the CQIs of their channels to the BS and the BS performs link adaptation based on the CQI feedback to achieve some target block error rates.

Opportunistic scheduling exploits the fading channels to enhance system throughput. Maximum throughput scheduler allocates a time slot to the user with the highest instantaneous capacity:

arg max ( )ii

j t (2)

to enhance system throughput. Here ( )i t is user i ’s

instantaneous channel capacity in the time slot. Assuming all users have infinitely backlogged data to transmit, this scheduler maximizes the system throughput. The throughput improvement over conventional systems is called the “multi-user diversity gain”. Because of the monotonic relationship between capacity and SINR, this scheduler is also called the MaxSINR scheduler.

But MaxSINR scheduler is highly unfair to the users with worse channel conditions. To achieve proportional fairness (PF) in the infinitely backlogged data case, proportional fair scheduling gives lower data rate users higher weights. It schedules the user with the highest weighted instantaneous capacity:

arg max ( ) ( )i ii

j t R t (3)

where ( )iR t is user i ’s past average data rate [5]. Due to the

unequal weights 1 ( )iR t , PF scheduling loses some degree of

“multi-user diversity” and achieves lower system throughput and spectral efficiency than MaxSINR [5]. But we will show in the next section that unequal weights do not necessarily lead to lower spectral efficiency in the real-time service case.

B. Weights to Compensate for Different Channel Conditions

The goal of a real-time service scheduler is to satisfy the QoS of as many users as possible. To achieve this goal, it is reasonable to apply weights that are proportional to the users’ demands to average channel capacity ratios. In the following we assume all involved users are of the same service class (QoS requirement) and data rate level, i.e. the traffic models are symmetric between users, as is conventionally done in many studies [6-11]. Since supporting the same high data rate for users at cell edges (with very low SINRs) can be impractical, we also restrict the involved users in a smaller

range, e.g. all users are within 200 meters of the base station. Following this model, the weights to compensate for different channel conditions are inversely proportional to the users’ average channel capacities, i.e. the “Fixed Weight” scheduler allocates a time slot to user

arg max ( )i ii

j K t (4)

where ( )i iK f SINR is user i ’s average spectral efficiency in

a system with many users of the same SINR. Note that it includes the multi-user diversity gain due to opportunistic scheduling and does not depend on time t. The process to determine these weights are not specified in many related works [11]. Our study finds the fixed weights

iK defined in this

way equalize the mean packet delays of users. However, the tail packet delays in general are still in favor of the users with better channel conditions. We argue that there is no need to compensate more for the worse channel users, e.g. by using the users’ average channel capacities without multi-user diversity considered

1

1

1( )

T

i i

t

K tT

(5)

which favors the worse channel users even more. In the latter case, better channel users would get longer mean packet delays, which is unreasonable in practice.

Lastly, the rationale behind using such fixed weights instead of the PF weights are given in [7]. Indeed, since we require the scheduler to deliver all the users’ traffic while satisfying packet delay constraints, the user’s past average data rates would be approximately equal if long averaging windows are used. Then the PF weights cannot compensate for the worse channel users effectively.

C. Weights to Prioritize Packets with Longer Delays

To make packets arrive at destinations in time, it is intuitive to prioritize packets that are delayed by longer at the BS. Conventionally, packets for a given user are organized in a FIFO queue and priorities are given to the user’s queues. The Modified Largest Weighted Deadline First (M-LWDF) scheduler allocates a time slot to user

arg max ( ) ( )i i ii

j K W t t (6)

where ( )iW t is the waiting time of user i ’s head-of-line (HOL)

packet at the base station, and is an arbitrary positive

number. M-LWDF achieves throughput optimality in this sense: it ensures that all queues are stable as long as the vector of average arrival rates is within the system's maximum stability region [7]. A problem with the delay dependent weight in M-LWDF is that with practical values of power , the

weight difference is too dramatic between large and small delays and too small between large delays, e.g. the weight only increases by 5% from a delay of 180 ms to 200 ms with

0.5 . Too dramatic weight differences result in loss of

multi-user diversity since only the few users with large weights compete for a time slot given the limited range of the capacity differences. On the other hand, suppose the maximum

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allowable packet delay is 200 ms, the scheduler does little to ensure the packet is delivered before deadline.

The exponential rule (EXP) is proposed to improve tail delay properties over M-LWDF. EXP schedules user

arg max exp ( ) 1 ( ) ( )i i i i i ii

j K aW t aW t t

(7)

where log( )i i ia D and

1

1( ) ( )

M

i i i i

i

aW t aW tM

, M is the

number of real-time service users in the system. Parameter i

is the target probability of a user’s packets being delayed by more than a threshold

iD . Suppose we aim to control the 99%

tail delay and take 0.01i , then 4.6i ia D . The authors

recommend 0.5 . The exponential term in the EXP rule

grows more dramatically than M-LWDF with large delays, yet the increases become less dramatic when the users’ average delays are large. It also possesses “throughput optimality” as M-LWDF [8] and is proved to maximize the tail decay rate of the delay distribution [9]. Under certain conditions, the maximization of tail decay rate is approximately equal to “delay optimality” [9]. Thus the EXP rule possesses both “throughput optimality” and “delay optimality”. Other related works on the maximization of tail decay rate include [10]. The “Log rule”, proposed to minimize average packet delays [11], did not produce better tail packet delay performance than the EXP rule and M-LWDF in our studies. Indeed, as is pointed out in [10], to reduce tail packet delays, the scheduler should put less emphasis on delay balancing when the average delays are small and more emphasis on delay balancing for large delays. In this sense, the “Log rule” works in the opposite direction of our goal.

However, all the proofs of the above “throughput optimality” and “delay optimality” were obtained in the large deviations sense, i.e. when the queue lengths approach infinity, thus they are not necessarily optimal for practical queue sizes. Furthermore, the proofs were obtained assuming traffics arrive at constant rates. In the case of varying instantaneous data rates such as variable bit rate video, EXP might not be the optimal scheduler to minimize the 99% tail packet delays. Lastly, we argue that the “throughput optimality” is a sense of “robustness” in maximizing the stability region. Although in doing so, M-LWDF and EXP maximize the system capacity, given the traffic to deliver and the channel conditions, the bandwidth usages might not be minimized by either scheduler.

In section III, we will show that given the particular situations, we can modify the M-LWDF scheduler so that it outperforms both the M-LWDF and EXP, even though both M-LWDF and EXP use optimized parameters.

D. Extension from Single-Carrier to Multi-Carrier System

Note that all of the aforementioned schedulers were designed for single-carrier systems. A simple extension from single-carrier to multi-carrier system is to schedule the carriers one by one in each time slot [12]. In this case, it is necessary to update the weights after the allocation of each carrier. However, even if the weights are updated in this way, the schedulers still might not hold their optimality, as is

demonstrated using the PF scheduler [13] when traffic arrivals are considered. Furthermore, it is pointed out in a system with sufficiently many carriers, scheduling in time domain and resource allocation in frequency domain probably can be decoupled due to frequency diversity [14].

In this study, the scheduling policies are applied on the carriers in each time slot one by one, and the weights of schedulers are updated after the allocation of each carrier.

III. PROPOSED TECHNIQUES FOR DELAY EQUALIZATION

AND DEMONSTRATIONS

This section proposes and demonstrates three techniques that take different characteristics of scheduling real-time videos into account. Before we propose these techniques, comparisons between MaxSINR, Fixed Weight and M-LWDF with default and optimized parameters are made to establish baseline performance references. The system setup of the simulation is described in appendix A. Note that the performance metric that is used here to evaluate delay properties is the users’ latencies (99% packet delays) instead of the delay distributions that include the delays of all the packets of all users commonly used in other work.

Figure 1: Performance of MaxSINR, Fixed Weight, M-LWDF with 1 , and

M-LWDF with 0.5 . 10 realizations involving a total of about 230 users.

Figure 1 shows that MaxSINR has the lowest spectral efficiency (higher bandwidth usage in delivering the same amount of data) and the worst delay properties. The users’ latencies (99% packet delays) vary wildly from about 80 milliseconds to 1200 milliseconds, with 10% of the users’ latencies longer than 500 milliseconds. Fixed Weight scheduler significantly outperforms MaxSINR resulting in much better latency distribution (lower on average, fairer between users) and about 3% lower bandwidth usage. M-LWDF further reduces the latencies significantly at the cost of slight increases in bandwidth usage. It is interesting to note that M-LWDF with

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0.5 results in both lower latencies (about 20 milliseconds

on average) and lower bandwidth usage (about 0.7 percentage) than M-LWDF with 1 . From these results, it can be

inferred that in the scheduling of real-time services, user latency and spectral efficiency do not necessarily tradeoff each other. A better scheduling policy may improve both metrics simultaneously. Such a phenomenon is also observed in our proposed modifications to M-LWDF.

An intuitive explanation to the surprising result is: since the amounts of data to deliver for each user is already given, prioritizing best channel users in MaxSINR results in few users left in the system after the best channel users have completed transmission, hence reducing multi-user diversity gain.

Note that the better scheduling policies compress the probability density function (pdf) of the users’ latencies (99% packet delays). To further improve the delay properties of the scheduler, it is desirable to compress the pdf of users’ latencies or move the pdf to the left. To achieve this, it also helps to compress the pdf of the delays of each individual user’s all packets. Hence our objective in designing a better scheduler is to “equalize” the delays of packets.

A. Using End-to-end Delays Instead of Queuing Delays

Assuming the sender-to-BS delay can be evaluated by the base station, e.g. by applying timestamps on the IP packets, the total delay of a HOL packet is

( ) ( ) ( )abs

i i iW t W t S t (8)

where ( )iS t is the sender-to-BS delay of user i ’s HOL packet.

Replacing ( )iW t with ( )abs

iW t in the M-LWDF scheduling

policy (6), our proposed scheduling policy “Abs” assigns a time slot to user

arg max ( ) ( ).abs

i i ii

j K W t t (9)

Such a scheduling policy accounts for the unequal sender-to-BS delays and aims to balance the end-to-end delays instead of just the queuing delays of packets inside the base station.

B. Accounting For the Variable Video Frame Sizes

Frame sizes in video applications can vary significantly depending on the encoding options. The larger frames are typically the more important intra-frames (“I” frames) and the last few packets of such frames experience the longest delays, compared to the packets of smaller predicted-frames (“P” frames), assuming the video frames are played back at equispaced time instants. Hence to improve the users’ latencies (99% packet delays), it is essential to improve the delays of these packets. Since all the packets within the same video frame are decoded and played back at the same time, we propose to correct the delay of a HOL packet using the predicted delay of the last packet within the same video frame. Assuming each packet in a video frame is delayed by more

milliseconds (when it is delivered to the destination) than the previous packet that belongs to the same video frame (if it exists), the delay of a HOL packet is corrected by a term

max hol

i i iPC pn pn (10)

where “PC” means “predictive correction”, max

ipn is the packet

number (numbered from 1 at the beginning of each video frame and increments by 1 when the video frame is packetized into

one more packet) of the HOL packet, max

ipn is the maximum

packet number of packets in the queue belonging to the same video frame as the HOL packet. Putting (8) and (10) together, our proposed scheduling policy “Abs-PC” assigns a time slot to user

argmax ( ) ( ).abs pc

i i ii

j K W t t (11)

where

( ) ( ) ( ) ( ).abs pc

i i i iW t W t S t PC t (12)

This scheduling policy further improves the performance of M-LWDF as is shown in Figure 2. Compared to M-LWDF, the user latencies (99% packet delays) are reduced by 0-30 ms (about 20 ms on average), while the bandwidth usages are also reduced significantly (0.8 percentage on average). Compared to EXP, Abs-PC outperforms EXP (lower average latencies and bandwidth usage) except that it is not as fair as EXP in that some users experience latencies longer than 230 ms under Abs-PC while all users have latencies less than 220 ms under EXP.

C. Urgency Based Scheduling to Meet Delay Targets

M-LWDF is unaware of the users’ 99% delay targets, while EXP determines its fixed parameters

ia based on the 99% delay

targets but does not treat packets approaching the delay targets differently by giving them temporarily larger weights. Simulations show that the users’ 99% packet delays vary significantly depending on the system load, instead of being maintained at the 99% delay targets. In practice it is possible to estimate such delay targets quite accurately. Even if the system load varies significantly due to changes in data rates and channels, it is still possible to adaptively adjust the estimation of delay targets. Assuming the delay targets can be estimated to reasonable accuracy (e.g. within 10% of the actual 99%

packet delays), we propose to give packets approaching deadlines temporarily larger weights based on urgency:

( ) exp max 0, ( ) 0.9abs pc

i i i iU t D W t D (13)

where is an arbitrary positive number. Taking 10 gives

an additional multiplicative weight of 1 to exp(1) as the (“Abs-

PC”) delay of the HOL packet grows from 0.9 iD to iD .

Putting together (11-13), our proposed scheduling policy “Abs-PC-DD” (DD means “delay approaching deadline”) assigns a time slot to user

argmax ( ) ( ) ( ).abs pc

i i i ii

j K W t U t t (14)

Compared to M-LWDF, Abs-PC-DD reduces the users’ latencies by about 10-30 ms (about 20 ms on average), and achieves lower bandwidth usage (about 0.7 percentage). Compared to EXP, Abs-PC-DD reduces the users’ latencies by about 0-30 ms (about 13 ms on average), and achieves lower bandwidth usage (about 0.5 percentage). The results show that by setting an accurate target, the scheduler can perform better

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than EXP that does not set explicit delay targets. In this sense, the EXP rule that works well without explicit delay targets is robust, while our proposed technique improves upon optimality with explicit delay targets. An explanation to the improvement in spectral efficiency is: due to equalized packet delays, more queues remain active and non-empty at the same time.

Using a Ffmpeg decoder modified to indicate the frames discarded due to errors during decoding, the received videos are aligned in time with the transmit videos and the Peak Signal-to-Noise Ratios (PSNR) [15] of the received videos are evaluated under the M-LWDF, EXP, Abs-PC and Abs-PC-DD schedulers. The evaluation assumes no error correction applied in higher layers, i.e. the received raw video data are directly passed to the Ffmpeg decoder. It also assumes that packets delayed by more than the deadline (200 ms) are not included in decoding and causes PSNR degradation. The packet loss rates of the users are found to vary from 0% to 3%. All of the best channels users have packet loss ratios of 0% and perfect PSNRs (equal to 36.36 dB using the particular video sample). From Figure 3, Abs-PC outperforms M-LWDF and Abs-PC-DD outperforms both M-LWDF and EXP in the users’ PSNRs. Comparing Abs-PC-DD and M-LWDF, Abs-PC-DD reduces the number of users with packet losses by about 50%, and of those users affected by packet losses under both schedulers, Abs-PC-DD reduces the PSNR degradations by about 50%. The typical PSNR improvement is on the order of 1 dB.

Figure 2: Performance of M-LWDF, EXP, Abs-PC, and Abs-PC-DD.

0.5 , 200iD . 10 , 8 for Abs-PC and Abs-PC-DD. 0.01i ,

0.5 for EXP. 30 realizations involving a total of about 700 users.

Figure 3: PSNR distribution of users under M-LWDF, EXP, Abs-PC, and Abs-PC-DD. Parameters and realizations are the same as in Figure 2.

IV. CONCLUSION

We found by simulations the phenomenon that in the scheduling of real-time services, spectral efficiency and users’ latencies (each user’s 99% packet delays) can be improved simultaneously using better scheduling policies, e.g. the Fixed Weight scheduler improves both metrics substantially over the MaxSINR scheduler, which has been established as yielding the maximum spectral efficiency in the infinitely backlogged data case. The same phenomenon repeats during the optimization of the parameter of M-LWDF, and our

proposed scheduling policies also improve both metrics compared to M-LWDF with optimized parameters, as well as the EXP rule which is established as the scheduling policy that is both “throughput optimal” and “delay optimal”. In terms of PSNR improvement given the same latencies, compared to M-LWDF, the proposed scheduler reduces the number of users affected by packet losses by about half, and reduces the PSNR degradation of the users with packet losses under both schedulers by about half. The studies in this paper considers only single-input-single-out (SISO) links between the base station and users, and does not consider adaptive power loading based on users’ QoS demands. We expect future study considering multiple-input-multiple-output (MIMO) links and adaptive power loading to yield even better compression of users’ packet delays, leading to better user latencies.

APPENDIX A: SYSTEM SETUP OF THE SIMULATIONS

A single cell with 5 MHz downlink bandwidth is considered. The UEs are uniformly distributed in the cell and

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move in random directions at 1 m/s. Their distances to the BS are less than 200 meters and greater than 35 meters. The links between the UEs to the BS are single-input-single-output (SISO) without power adaptation. The path loss model is the Urban Hata model. The CQI mapping table is as follows:

SINR Modulation Coding Rate RB Capacity

< 3 dB N/A N/A 0 bits

3 – 6 dB BPSK 1/2 64 bits

6 – 8.5 dB QPSK 1/2 128 bits

8.5 – 11.5 dB QPSK 3/4 192 bits

11.5 – 15 dB 16QAM 1/2 256 bits

15 – 19 dB 16QAM 3/4 384 bits

19 – 21 dB 64QAM 2/3 512 bits

> 21 dB 64QAM 3/4 576 bits

Table 1: CQI mapping table used in the simulation

The video sample used is “Foreman” of CIF resolution downsampled to 15 frames per second (fps). The video is encoded in AVC/H.264 format at 340 kbps with a group of picture (GoP) length of 4. Intra (I) and Prediction (P) frames are used. Users wait for a packet for no more than 200 milliseconds from the time the video frame is encoded at the sender. The base station transmits 90 video frames to each UE in each realization. The number of realizations is 10 for the baseline comparison, and 30 for the comparison between M-LWDF, EXP, Abs-PC and Abs-PC-DD. The delays from senders to BS are 30 milliseconds for all users.

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