Frequency-Time Scheduling for Streaming Services in OFDMA system

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Frequency-Time Scheduling for Streaming Services in OFDMA system Mohamad Assaad Ecole Superieure d’Electricite (SUPELEC) 3 rue Joliot-Curie 91192 GIF sur YVETTE - France [email protected]

Abstract— This paper proposes a novel Frequency Time scheduler, called Frequency Time Scheduler with Delay Constraints (FTSDC), in order to handle streaming traffic in OFDMA (Orthogonal Frequency Division Multiple Access) system. Streaming technique, widely developed and used in the internet to convey multimedia application (e.g., audio, video clip, etc.), is supposed to occupy a large share of bandwidth in future wireless systems (e.g. WiMAX, LTE ”Long Term Evolution”, etc.). The stringent QoS constraints of these services may be reached at the expense of the system capacity and therefore a trade off between Fairness and capacity should be achieved. The novel opportunistic scheduler proposed in this paper balances this trade off and allows thus OFDMA system to handle streaming services without losing much cell capacity. Results afforded by this scheduler are promising and show that it outperforms the existing scheduling algorithms.

I. I NTRODUCTION OFDMA is a very promising radio access technology that has been adopted for both uplink and downlink air interfaces of WiMAX fixed and mobile standards, namely IEEE802.16d and IEEE802.16e respectively [1][2], and more recently for the downlink air interface of the Third Generation Partnership Project (3GPP) currently normalizing the Long Term Evolution (LTE) of the third generation (3G) cellular system [3]. OFDMA is based on OFDM technique; therefore it inherits the immunity to inter symbol interference (ISI) in frequency selective fading channel and offers good flexibility and performance for a reasonable complexity. The users of a same cell are multiplexed in frequency, each user’s data being transmitted on a subset of the sub-carriers of an orthogonal frequency division multiplexing (OFDM) symbol. Depending on its speed and the reliability of its channel quality indicator (CQI), a user may be allocated either a subset of sub-carriers scattered over the whole bandwidth or a subset of adjacent subcarriers. In order to achieve the challenging spectral efficiency and user throughput targets, multiple antenna schemes and fast link adaptation (Adaptive Modulation and Coding) are also used in included in the specifications. In OFDMA systems, resource allocation techniques take advantage of the frequency and time diversities of the system in order to optimize the use of the available resources. It exploits available channel state information (CSI) at the transmitter side for accomplishing an adaptive modulation and shares the resources (sub-carriers, slots) among users. A resource allocation technique is evaluated in general in terms of the maximum throughput and spectral efficiency the

system can achieves using given resources and the fairness in sharing these resources among users. fairness is defined in general by the degree of ”meeting the data rate and the delay constraints of the different services”. The resource allocation has therefore two main objectives: First maximize the system throughput by allocating the resources to the most appropriate users and second achieve fairness between the users. These two objectives are conflicting and there is a risk in achieving one at the expense of the other. Therefore, a trade-off between fairness and efficiency should be achieved. The problem of assigning the subcarriers, rates, and powers to the different users in an OFDMA system has been an area of active research. In most of the proposed studies [4-8], the problem is modeled in general as a convex optimization and solved by water-filling algorithm. Most of these studies are not suitable for implementation in practice due to high complexity implementation. To overcome this problem, few scheduling algorithms have been proposed [9-15]. Although these algorithms have a low implementation complexity, they do not achieve the best balance between fairness and capacity (sub optimal solution of the resource allocation problem). Note that most of these schedulers are suitable for non real time data. In this paper, we have conducted a study on scheduling for streaming services in OFDMA system. A new scheduler, called Frequency-Time Scheduler with Delay Constraints (FTSDC) is proposed. Link level and network level simulations are conducted to assess the performance of the proposed solution. Simulation results show that FTSDC outperforms the existing OFDMA schedulers: it allows handling streaming with fixed reading rates (Constant Bit Rate CBR traffic) and achieves a better trade off between fairness and capacity. The remainder of this paper is organized as follows: section II provides system and problem description. The state of the art on scheduling is given in section III. In section IV, the proposed scheduler is described. Simulation and results are provided in sections V and VI. Section VII concludes the paper. II. PROBLEM STATEMENT AND SYSTEM DESCRIPTION The OFDMA access technology considered in this paper relates to the downlink of 3GPP/LTE like system. In 3GPP/LTE terminology, each time frame is composed of 14 OFDM symbols and is known as Transmission Time Interval

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(TTI). The duration of TTI is 1ms. Each group of 12 subcarriers is referred to as a chunk. Two modes are adopted for mapping sub-carriers to chunks. In the first ”localized” mode, adjacent sub-carriers are mapped to chunks with the aim of almost flat fading over each chunk. In contrast, the second ”distributed” mode maps sub-carriers faraway over the whole bandwidth to each chunk in the aim of frequency diversity within the chunk. In the localized mode, a chunk is expected to experience specific propagation and interference conditions and thus a specific channel quality. This channel quality is quantified by so-called Channel Quality Indicator (CQI). The large variation of the CQI with respect to chunks allows the system to take advantage of the frequency diversity of the radio channel which makes the use of frequency scheduling greatly beneficial. However, the use of distributed mapping is more beneficial for channel with very fast variation (e.g. mobile users at high speed). In fact, the CQI estimates in this case are outdated and practically non useful. In this paper, we focus on the localized mapping mode with mobile users at low speed. Although the scheduler can assign several chunks to one user at a given TTI, one Modulation and Coding Scheme (MCS) is attributed to the user. To select a given MCS scheme for a given user, the node B determines an equivalent (or effective) CQI from the CQI values of the chunks allocated to the given user. Besides, Streaming is a popular technology widely developed and used in the internet to convey multimedia application (e.g., audio, video clip, etc.) to mobile users. This type of application is supposed to occupy a large share of the third generation (and beyond) wireless system bandwidth. The fundamental characteristic of this application class is to maintain the traffic jitter under a specific threshold. Jitter relates to the time relation between received packets. This threshold depends on the application, the bit rate and the buffering capabilities at the receiver. The use of a buffer at the receiver smoothes the traffic jitter and reduces the delay sensitivity of the application. A typical buffer capacity at the receiver is 5 s. This means that the application streams could not be delayed in the network more than 5 s. If the buffer is empty, due to jitter and delay latency, the application will be paused until enough packets to play are stored in the buffer. The streaming considered in this paper assumes that the peer streaming source transmits packets at a constant rate. Sequences are then managed by the client at the receiver that plays the sequences back at a constant rate (i.e. Constant Bit Rate CBR streaming). In order to achieve the packets delay constraint (i.e. to not have pauses in the sequences play), each user should receive during each 5 s a bit rate equal to the reading rate. Thus, in this context, the scheduling problem can be formulated as: Using the CQI values for all chunks fed back from all users, how the base station should allocate the chunks to the users at each TTI in order to achieve a good balance between capacity and fairness and respect the QoS constraints (delay and bit rate) of streaming traffic.

III. R ELATED W ORK The problem of resource allocation in OFDMA systems has attracted an enormous research interest. Three major approaches are used in designing dynamic resource allocation. The first approach is theoretical and complicated to implement. The two other approaches or classes are more suitable for implementation in practice however they do not achieve the best balance between fairness and capacity. In [4-8], the problem of resource allocation is considered as a convex optimization problem. In [6], the convex optimization problem is transformed in a min-max problem and solved by waterfilling algorithm. A lower complexity algorithm that achieves a trade off between fairness and capacity is proposed in [7]. This algorithm is issued from a Rate Adaptive optimization problem by imposing a set of nonlinear constraints. In [8], the nonlinear optimization problem is transformed into linear problem and solved by Linear Integer Programming (LIP). Even though a lot of effort is made to reduce the optimization complexity of the dynamic resource allocation, the complexity is still considerable and the proposed solutions are not suitable for implementation in practice. In addition, these optimization problems assume a continuous objective function in continuous convex sets. In practice, a limited number of Modulation and Coding Schemes (MCS) are used. The optimization should consider discontinuous sets of rates available for users. The second class of dynamic resource allocation consists in dividing the problem into two sub-problems: sub-carrier allocation and sub-carrier assignment. The sub-carrier allocation problem consists in determining the number of sub-carriers to allocate to each user, while the sub-carrier assignment consists in attributing the sub-carriers to users based on the results of sub-carrier allocation problem. Several algorithms have been proposed in this direction. In [9-10], at least one sub-carrier is allocated to each user (to ensure fairness) and the remainder of sub-carriers are allocated based on the normalized queue state of each user (i.e. by dividing the queue state of the user by the overall queue state of all users). The sub-carriers are then assigned by attributing to each user the best current subcarriers in a prioritized manner (circular order). In [11-13], the authors determine the number of sub-carrier to allocate to each user using an algorithm that balances the trade off between the channel state information and the packet delay information. The sub-carrier assignment problem is solved by an algorithm that monitors the violations of the maximal delay in all queues and by dividing the violations occurrences among all users. In [12], another sub-carrier assignment algorithm based on the exponential rule is also used. The third class of dynamic resource allocation solutions consists in merely adapting the TDMA-based discipline for scheduling traffic over time varying channels to the case of OFDMA/TDMA resource allocation problem. In other words, it consists in using the same criterion of TDMA scheduling discipline on each sub-carrier. In [14], a multi-carrier PF (called MPF) scheduling is proposed. It consists in allocating each sub-carrier to the user having the highest sub-carrier quality (in bit rate) relative to its average achieved rate. In [15],

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a similar algorithm is used where the sub-carrier is allocated to the user having the best sub-carrier quality relative to the ratio between the average achieved rate and the required bit rate. Other TDMA discipline scheduling, such as exponential rule proposed in [16], can be adapted to OFDMA system by considering the instantaneous rate on each sub-carrier. This class of dynamic resource allocation is not the optimal way to balance the trade off between the capacity and fairness since it does not consider the specificity of the OFDMA system in the scheduling discipline. Most of these scheduling studies are not suitable for streaming since they do not consider the traffic characteristics (delay, QoS) in the scheduler rule. Therefore, the use of these schedulers for streaming will result in a system throughput loss. In This paper, we propose a new scheduler able to offer streaming connections without losing much cell capacity and this by introducing new delay and QoS dependent priority in the scheduling sharing rule.

the current channel condition of a user compared to those of the other users in the system. k MCQI =

A. Novel Metrics Description As mentioned above, our scheme defines new QoS and channel quality metrics. The description of these metrics are given hereinafter: •

The first metric is the CQI metric. Our scheduler considers the instantaneous channel condition into the formulation and sets the objective to achieving the maximum k throughput in the downlink. let CQIn,t be the CQI for th th k user on n chunk at time t. The corresponding bit k rate to this CQI is denoted by rn,t and determined by attributing a given MCS to the user. The user CQI metric is defined as the average of the normalized bit rate on each chunk. This represents in some how the quality of

(1)

k parameter νn,t indicates the weight of the Channel conth dition of k user on nth chunk at time t. It represents in some how the importance of the current channel conditions on this chunk relative to the past channel conditions. If relative poor channel conditions (CQIs) are observed on a chunk in previous TTIs, a good CQI on this chunk at time t should have a high weight. Low weights is given to chunks that have poor CQIs at time t and k high CQIs in previous TTIs. νn,t is then determined as follows: k rn,t k νn,t =1+ (2) rnk

where rnk is the time average bit rate of k th user on nth chunk evaluated using a smoothed average over a time window of ² TTIs (where ² is taken in general equal to 1000). 1 k = (1 − 1 )r k + rk (3) rn,t ² n,t−1 ² n,t

IV. P ROPOSED F REQUENCY-T IME S CHEDULER WITH D ELAY C ONSTRAINTS (FTSDC) In this paper, a low computational scheduling called Frequency-Time Scheduler with Delay Constraints (FTSDC) is proposed. Our scheme relies in the second class of scheduling by decoupling the sub-carrier allocation from the subcarrier assignment. It offers several advantages by introducing new QoS metrics in the scheduling discipline. Fairness and multiuser diversity are explicitly targeted in the subcarrier assignment and allocation schemes. Streaming traffic status such as packet delay in the base station queues, rate of packet arrival/departure in the BS queues (which is extremely useful for Variable Bit Rate VBR Video traffic) as well as the instantaneous radio channel conditions on each chunk are included in the scheduling allocation rule. The scheme proposed consists in two steps: Metric Based Chunk Reservation (MBCR) and Maximum Metric Based Chunk Assignment (MMBCA) procedures. Based on the metrics defined in this paper, MBCR procedure determines the number of sub-carriers to allocate to each user. Then MMBCA procedure attributes physically and in a greedy manner the sub-carriers to users.

N k k νn,t rn,t 1 X PK j j N n=1 j=1 νn,t rn,t

•

The second metric target to provisioning the packet delay by considering the ratio between the arrival packet rate and the departure rate of packets from the queues at the base station. This metric is extremely interesting for Variable Bit Rate VBR and bursty traffic for which packets arrive to the base in burst and randomly and should be conveyed within a given time delay. This metric aims to anticipate the packets delay and buffer overflow of each user by including an information of the arrival/departure of packets in the scheduling rule. Let Stk be the data size arrived to the BS queue of k th user at time t and Qkt−1 is the data size transmitted correctly at time t − 1. The ADP (Arrival/Departure of packets) metric is defined as follows: k MA/D

•

Stk (1−F ERk )Qk t−1

=P K

Stj j=1 (1−F ERj )Qj t−1

(4)

The last metric is the metric of normalized packet delay. The packet delay is the delay between the current time and arrival time of the current Head of Line (HoL) packet. This metric does not contain any information about the delay of the other packets in the buffer since this information is contained in the previous metric (ADP metric). If dkmax is the maximal delay tolerated for the HoL packet of k th user, the delay metric can then be defined as follows: µk (1 + dk ) k MA/D = PK j j j=1 µ (1 + d )

(5)

parameter µk depends upon the service priority of user k (in this paper µk is equal to 1/dkmax .

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The overall channel and QoS metric of k th user is determined as follows: k

M =

k k k k k k (ωCQI MCQI )(ωA/D MA/D )(ωD MD )

(6)

parameters ω.k s represent the weights of previous metrics for k th user. B. Metric Based Chunk Reservation The scheduler estimates at each TTI the metrics described above for all the users. If N is the total number of available chunks, the number Nk of sub-carriers to allocate to k th user at time t is determined as: Mk Nk = b PK Nc j j=1 M

(7)

Where b.c denotes the integer part. The remainder N − Nk chunks are then allocated one by one as follows: PK While j=1 · Nj < N ¸ Mi P find user k=argmax K M j N − Ni ; j=1

Nk = Nk + 1; End(of While) C. Maximum Metric Based Chunk Assignment (MMBCA) Once the number of chunks to allocate to users is determined, MMBCA procedure allocates then physically the chunks to users. MMBCA classifies the chunks for all the users in decreased order of their metric: k k k k k k M k,n = (ωCQI MCQI,n )(ωA/D MA/D )(ωD MD )

(8)

k where metric MCQI,n is evaluated in this case for nth chunk as follows: k k νn,t rn,t k = PK j j (9) MCQI,n j=1 νn,t rn,t k parameter νn,t is determined above. Thus, the algorithm starts by classifying the users and the chunks in a descending order of the metric M k,n . Then, it constructs a table of KxN elements. The scheduler starts then with the first element of the sorted table, thus by the chunk and the user that has the maximum metric M k,n and attributes this chunk to the user. The elements corresponded to this chunk are then taken out of the table. Let use denote by i the index this chunk. The K elements corresponding to the metrics M k,i of the K users are then taken out of the table. The table is then sorted again and the same procedure is repeated. If the number of chunks to allocate to a given user (determined by MBCR) is reached, the scheduler takes the elements corresponding to this user out of the table. Let j be the index of this user, the elements corresponding to the metrics M j,i ∀ i are moved from the table. The table is sorted again and the same assignment procedure is repeated for the remainder users and chunks. After assigning all the chunks to the users, the effective CQI of each user is evaluated and a corresponding MCS with instantaneous rate rk is selected.

V. N ETWORK S IMULATION We consider a system with 10MHz of bandwidth (i.e. LTE) divided into 50 sub-carriers each having a bandwidth of 375KHz. The topology used in our simulation consists of both link level and network level simulation. The link-level simulator implements all physical layer aspects of downlink OFDMA-LTE (Long Term Evolution)as specified by 3GPP [17]. The network level focuses on MAC (Medium Access Control) and RLC (Radio Link Control). Concerning the traffic type, we assume that all the users are downloading a Constant Bit Rate (CBR) streaming traffic. The users are supposed to be uniformly distributed in the cell. Since the network simulator is static, several snapshots are simulated to cover all the possible cases or scenarios (105 snapshots simulated). Each simulation was run for 500 s giving us 500 s long traces. Note that the correlation distance of the shadowing is set to 40m and that the users are assumed to move around their geographical position within a short range and the environment is assumed to be variable, which is modeled by a fast fading with independently fading Rayleigh processes, whose power delay profile is described by the ITU Pedestrian A model. A speed dependent Doppler spectrum as given by Clarke and Jakes [17] is included in every tap of the power delay profile, and the user default speed is 3 km/h. The link level simulation delivers, at each TTI, to the network level the CQIs for all the users. The network level simulator uses these CQIs to perform scheduling and outputs the instantaneous rate allocated to each users. This procedure 5 is repeated during 500s (i.e. 5.10 TTIs) and the simulator stores the UEs rates averaged over all TTIs. Then, another snapshot starts, and so on and so forth until reaching the maximum number of snapshots (105 snapshots). In the remainder of this section, the procedure of determining the users’CQI and bit rates at a given TTI is described. The CQI value at tth TTI associated with nth chunk for k th active UE connected to j th base station is determined as follows: CQInk,j (t) =

Pjn Gjk,j |hnk,j (t)|2 PJ σ 2 (n) + l=1,l6=j Pln Gjk,l

(10)

where Pjn is the power transmitted by j th cell on nth chunk, Gjk,l is the path gain between lth NB and k th UE connected to j th NB, σ 2 (n) is the receiver noise power over nth chunk, and J is the number of cells in the cluster considered in our simulation (18 cells). The coefficient hnk,j (t) is representative of the fast fading affecting nth chunk at tth TTI for the channel between k th UE and j th base station. After evaluating the CQI values for all chunks and all active users, dynamic scheduling is performed for assigning chunks to UEs (User Equipment) in each cell. The scheduling algorithm described in previous section is implemented. Next to scheduling, the UEs instantaneous rates for the optimal allocation are outputted for the purpose of performance analysis. To that end, the base station starts first by determining the MCS (Modulation and Coding Scheme) that will attribute to each user. Since only one MCS is attributed to each user, the

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effective CQI of each over all the chunks allocated to the user should be determined. There are several forms for combining a given set of CQI values into one scalar effective CQI. Most advanced forms have been derived from performance analysis of the channel decoder. The most commonly used form in the state of the art is the Exponential Effective form. It is given by [17]: ¶ µ Nk CQI k 1 X − βn k CQIef f = −βlog e (11) Nk n=1 where β is a calibration factor dependent on the MCS used and on the codeword length, hence on the number Nk of chunks allocated to the given UE. Note that each MCS has its own specific look-up table (LUT) which is merely the mapping between BLER (Block Error Rate) and Signal to Noise Ratio (SNR) over an Additive White Gaussian Channel (AWGN). LUTs are obtained through link level simulations. Using these LUTs, the base station assigns a given MCS to each user based on its effective CQI. The MCS selected is that achieving the highest instantaneous rate of the user for the given chunks allocation. The instantaneous rate at tth TTI for k th UE connected to j th NB is then obtained as: k rk (t) = maxM CS {RM CS (1−BLERM CS (CQIef f ))} (12) k where CQIef f is the equivalent or effective CQI for the chunks allocated at tth TTI to k th user, BLERM CS is the Block Error Rate achieved with modulation and coding scheme MCS (determined using the LUT of the given MCS), and RM CS is the MCS transmission rate.

VI. R ESULTS As we mentioned throughout this paper, the application reading rate at the mobile user is constant and the buffer size is of 5 sec. This means that users should receive an average bit rate over 5 sec equal to the reading rate, Otherwise the application will be paused. Consequently, the capacity of OFDMA is determined by the maximal number of users for whose the delay limit of packets is not violated. Therefore, we depict in figure 1 the average percentage of delay limit violation vs the user required bit rate (i.e. the streaming reading rate). Two schedulers are considered: our proposed FTSDC and MPF (Multicarrier Proportional Fair proposed in [14]). Without loss of generality, we assume that all the users have the same reading rate. 40 simultaneous users are active and selected using a uniform distribution. Figure 1 shows that FTSDC allows a streaming reading rate per user equal to 470Kbps without any delay limit violation. In other word, the total cell throughput is 19Mbps. The cell throughput achieved by MPF with no delay limit violation is 14Mbps (i.e. streaming reading rate of 350Kbps per user). Note that MPF can allow higher cell throughput at the expense of delay limit violation (e.g. cell throughput of 19Mbps would generate 20% of delay limit violation which results in frequent application pauses). Note that for non real time data, MPF achieves a reasonable trade off between fairness and capacity. The fairness in this case is not perfect, i.e. MPF allocates higher bit rates to the users near the base station. This explains

the higher cell throughput achieved by MPF in this case (e.g. see [14]). For streaming services, and besides the fact that the delay constraints should be respected (which results in a loss of cell throughput), the available data in the base station buffers depends on the packet arrival rate. For CBR traffic, the arrival rate is equal to the streaming reading rate. Therefore, users near the base station, i.e. with relatively good channel conditions, can not have a bit rate higher than the packet arrival rate even if their radio channel quality allows them to have higher rates. The remainder of resources should then be allocated to the other users, i.e. with relatively bad channel conditions. Consequently, the use of MPF for streaming traffic results in a loss of cell throughput compared to the case of non real time data (especially File Transfer Protocol FTP with full queues at the base station). This explains the results obtained by MPF for streaming traffic. The QoS metrics defined in our proposed scheme seems to have an important impact on the trade off between the delay constraints and the cell throughput. VII. C ONCLUSION The natural conclusion, based on the obtained results in this paper, is that simple schedulers such as PF or MPF, that balance the trade-off between fairness and cell throughput in the case of non real time data, are not suitable for streaming services. New schedulers are then required to deal with the delay constraints of these services. The opportunistic scheduler proposed in this paper seems to be an interesting approach to handle streaming connections over OFDMA system without losing much cell capacity. Results, depicted in this paper, show that this scheduler outperforms the existing schedulers (e.g. MPF) by allowing the use of 40 simultaneous streaming connections in the cell at a reading rate of 470Kbps, in other words it allows achieving a cell throughput of 19Mbps. MPF scheduler in the same conditions allows handling 40 simultaneous streaming connections at a reading rate of 350Kbps. R EFERENCES [1] IEEE standard for local and metropolitan area networks, ”Part 16: Air interface for fixed broadband wireless access systems”, 1 October 2004. [2] IEEE standard for local and metropolitan area networks, ”Part 16: Air interface for fixed and mobile broadband wireless access systems”, 28 February 2006. [3] 3GPP TSG-RAN, ”3GPP TR 25.814, Physical Layer Aspects for Evolved UTRA (Release 7)”, v1.3.1 (2006-05). [4] E. Lawrey, ”Multiuser OFDM,” in Proc. International Symposium on Signal Processing and its Applications, pp. 761-764, Brisbane, Australia, 1999. [5] C. Y. Wong, R. S. Cheng, K. B. Letaief, and R. D. Murch, ”Multicarrier OFDM with Adaptive Subcarrier, Bit, and Power Allocation,” IEEE Journal on Selected Areas in Communications, vol. 17, no. 10, pp. 1747-1758, Oct. 1999. [6] J. Jang and K. B. Lee, ”Transmit Power Adaptation for Multiuser OFDM Systems”, IEEE Journal on Selected Areas in Communications, vol. 21, no. 2, pp. 171-178, Feb. 2003. [7] W. Rhee and J. M. Cioffi, ”Increasing in Capacity of Multiuser OFDM System Using Dynamic Subchannel Allocation,” in Proc. IEEE Int. Vehicular Tech. Conf., vol. 2, pp. 1085-1089, Spring 2000. [8] Zukang Shen, Jeffrey G. Andrews and Brian L. Evans, ”Adaptive Resource Allocation in Multiuser OFDM Systems with Proportional Fairness,” submitted to IEEE Trans. on Wireless Communications. [9] I. Kim, H. L. Lee, B. Kim, and Y. H. Lee, ”On the Use of Linear Programming for Dynamic Subchannel and Bit Allocation in Multiuser OFDM,” in Proc. IEEE Global Communications Conf., vol. 6, pp. 36483652, 2001.

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40 users per cell, streaming CBR traffic 0.2

Average %tage of delay limit violation

0.18

FTSDC MPF

0.16 0.14 0.12 0.1 0.08 0.06 0.04 0.02 0 0.25

0.3

0.35

0.4 0.45 0.5 0.55 User required bit rate (Mbps)

0.6

0.65

Fig. 1. percentage of delay limit violation vs user required bit rate (streaming reading rate or CBR traffic bit rate)

[10] J. Gross, H. Karl, F. Fitzek, and A. Wolisz. Comparison of heuristic and optimal subcarrier assignment algorithms. Proc. of Intl. Conf. on Wireless Networks (ICWN), June 2003. [11] J. Gross, J. Klaue, H. Karl, and A. Wolisz. Subcarrier allocation for variable bit rate video streams in wireless OFDM systems. Proc. of Vehicular Technology Conference (VTC), Florida, October 2003. [12] Ahmed K. F. Khattab and Khaled M. F. Elsayed, ”Opportunistic Subcarrier Management for Delay Sensitive Traffic in OFDMA-based Wireless Multimedia Networks”, Proc. of the 14th IST Mobile & Wireless Communications Summit, Dresden, Germany, June 2005. [13] Ahmed K. F. Khattab and Khaled M. F. Elsayed, ”Opportunistic Scheduling of Delay Sensitive Traffic in OFDMA-based Wireless Networks, ” Proc. of IEEE WoWMoM 2006, Buffalo-NY, June 2006. [14] A. Pokhariyal, T.E. Kolding and P.E. Mogensen, ”Performance of Downlink Frequency Domain Packet Scheduling for the UTRAN Long Term Evolution,” Proc. Of IEEE PIMRC 2006, Septembre 2006, Helsinki. [15] Lu Yanhui et. al., ”Downlink Scheduling and Radio Resource Allocation in Adaptive OFDMA Wireless Communication Systems for UserIndividual QoS,” ENFORMATIKA Trans. On Engineering and Technology, V.12, March 2006, ISSN 1305-5313 [16] S. Shakkottai and A.L. Stolyar. Scheduling algorithms for a mixture of real-time and non-real-time data in HDR. Proc. Of the 17th International Teletraffic Congress - ITC-17, Salvador da Bahia, Brazil, 793-804, September, 2001 [17] 3GPP TSG-RAN, ”System-Level Evaluation of OFDM - Further Considerations”, WG1 #35, R1-031303, Nov. 2003