Joint Space-Frequency-Power Scheduling Algorithm

Joint Space-frequency-power Scheduling Algorithm for Real Time Service in Cellular MIMO-OFDM System Feng Jiang, Jianchi Zhu, Guona Hu, Ying Wang, Guangyi Liu, and Ping Zhang Key Laboratory of Universal Wireless Communications, Ministry of Education WTI Institutes, Beijing University of Posts & Telecommunications, Beijing, 100876, P. R. China Email: [email protected] Abstract—To meet the increasing demand of wireless services associated with the scarcity of the radio spectrum and the trend to provide end to end quality of service (QoS), on the one hand advanced technologies that harness the available resource efficiently should be developed, on the other hand the collaboration of different layers such as physical (PHY) layer and medium access control (MAC) layer is needed. In this paper, we propose a joint space-frequency-power scheduling algorithm (JSFP) for real time service in multiuser cellular MIMO-OFDM system which jointly optimizes the subcarrier, bit and power allocation in the PHY layer along with the scheduling in the MAC layer to exploit the multiuser diversity. This algorithm considers both the user equipments (UE)’ QoS requirements (such as packet delay and packet loss ratio) and the UEs’ channel conditions and includes three parts: packet scheduling, subcarrier allocation and antenna selection, power allocation. Numerical results show that the proposed algorithm achieves significant system performance improvement compared with the conventional methods.

I. I NTRODUCTION As MIMO-OFDM system can provide better system performance by exploiting both antenna diversity and frequency diversity, it has been identified as one of the leading candidates for future wireless communication systems. Through adapting bandwidth and power allocation as well as transmission strategies jointly across the protocol stack, the resource utilization efficiency of the MIMO-OFDM system can be significantly improved and a predetermined QoS requirement can be effectively guaranteed. However, resource allocation in cellular MIMO-OFDM systems is much challenging because of the following reasons [1]: • Inter-cell interferences make the optimization problem combinatorial and complex. Adjusting the data transmission on one subcarrier affects the co-channel interference to other subcarriers in the adjacent cells which in turn change the optimal transmission scheme of all UEs. • The achievable spatial subchannel gain is a function of the set of the UEs that share the subcarrier. To maximize the spectral efficiency optimal set of UEs should be identified for each subcarrier based on the UEs’ channel attenuation and the spatial correlation the between the channels. • MIMO-OFDM system is able to multiplex the UEs in both the space and frequency domains. The scheduler should decide which dimension should be occupied by which set of UEs.

978-1-4244-1645-5/08/$25.00 ©2008 IEEE

•

QoS requirements impose additional constraints on the optimization problem. How to utilize smart scheduling mechanisms to improve utilization efficiency of the resource based on UE’s demand and channel state is essential for the next generation wireless communication systems.

In [2], the authors studied the joint problem of resource allocation and transmit beamforming in the context of an OFDM-SDMA system from an information theory point of view, and this algorithm can not guarantee the UEs’ instantaneous QoS requirements. In [3], an adaptive resource allocation algorithm with QoS provision is proposed, but the scheduler works with two implicit assumptions that there is no constraint on the maximum size of the transmission buffer and the scheduled UEs always have data to transmit, which may make this algorithm not applicable for a realistic scenario. The scheduling algorithm proposed in [4] jointly implements the scheduling in the link layer and the subcarrier, bit and power allocation in the physical layer, and can achieve significant improvement in throughput and packet delay, but this algorithm fails to consider the stringent QoS requirements of real time service, such as packet loss ratio and the maximum allowable packet delay. As the objective of resource allocation is to maximize the number of UEs that share the system resources while ensuring their QoS requirements, a well designed scheduling algorithm should provide a good match between the randomness of the traffic patterns and that of the radio environment. This paper is intended to provide such a scheduling algorithm, namely joint space-frequency-power scheduling algorithm (JSFP), for real time service in the cellular MIMO-OFDM system. This algorithm can fully exploit the multiuser diversities in the frequency and space domains to satisfy the stringent packet delay and packet loss ratio constraints while obtaining a high system spectral efficiency. The rest of this paper is organized as follows: section II presents the assumed system model. In section III we propose the JSFP algorithm. Section IV provides the simulation results which compare the system performance between the proposed algorithm and the conventional algorithms. Conclusions are drawn in section V.

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II. S YSTEM M ODEL A. MIMO channel model We consider the downlink of a multi-cell multi-user MIMOOFDM system. In each cell, there is one Base Station (BS) equipped with MT transmit antennas and K UEs with MR receive antennas. Using zero-forcing beamforming (ZFB) [5] at the transmitter. The received signal can be expressed as y = HWDx + n

(1)

where x ∈ CMT ×1 is the transmitted signal vector, y ∈ CMT ×1 is the received signal vector and n ∈ CMT ×1 is the additive white Gaussian noise (AWGN) vector with variance σ 2 . H is the MIMO channel matrix between the MT transmit antennas and the MT receive antennas selected from the K UE. The size of H is MT × MT and the entries of H are i.i.d. Gaussian random variables with zero mean and unit variance. W is the transmit zero-forcing beamforming matrix which is given by W = H† = HH (HHH )−1

(2)

where (·)† denotes the pseudo-inverse operation, (·)H denotes the conjugate transpose. And D = diag{d1 , d2 , . . . , dMT } is a diagonal matrix which keeps the transmit power unchanged after beamforming. The ith diagonal elements di is defined as
  −1 . 1/ (HHH ) i,i

B. Multi-user interferences In the multicell MIMO-OFDM system, as the downlink scheduling of the adjacent cells are distributed, the BS can not exactly estimate the inter-cell interference, and the system capacity of the downlink multicell MIMO-OFDM system is significantly limited by the inter-cell interference. In the presence of the inter-cell interference, when the scheduler at the BS allocates the subcarriers to active UE, the scheduled data rate of the UE may be larger than the actually achievable rate which depends on the UE’s channel quality and the inter-cell interference, thus the packet transmission will be corrupted and packet outage occurs and this is called misscheduling problem. In order to effectively estimate the intercell interference and avoid the mis-scheduling problems, in this paper the total transmitted power is equally assigned to all the traffic subcarriers, which guarantees that the estimated inter-cell interference is higher than or equal to the actual interference, thus the systems transmission efficiency can be enhanced. Define N to be total subcarrier number and Pmax to be the total transmit power, under the above inter-subcarrier power distribution strategy, the UE k’s SINR on the spatial subchannel of the nth subcarrier can be approximately denoted as SIN Rk,n =

h2n,k pn,k M σ 2 + i=1 Ii

where hn,k is the UE k’s spatial subchannel gain on the nth subcarrier, pn,k is the allocated power for UE k on the nth N K subcarrier, pn,k ≥ 0 and n=1 k=1 pn,k = Pmax , Ii is the intercell interference from the adjacent cells, and M is the number of the cells in the interference tiers. In this paper, we mainly consider the real time traffic for which packets must be delivered to the destination before certain delay upper bound. As the estimated intercell interference is definitely greater than the UE’s real received interference, we assume that if the packets have been transmitted before the maximum allowable delay Wmax , this packet will be successfully received by the UE; otherwise the packet will be discarded. As for packet based real time data service the packet arrival rate is constant and when UE’s packet loss ratio is larger than the maximum allowable packet loss ratio plrthreshold for a continuous period of time T , this UE will drop out of the system and the dropped UE will have no contribution to the system effective capacity, so the effective system capacity is given by

(3)

Cs =

K 

(1 − pk,drop )Rk

(4)

k=1

where pk,drop and Rk are UE k’s drop rate and data rate respectively. From formula (4), we would like to find the scheduling algorithm so that the effective system capacity is maximized under a total power constraint. Finding the optimal scheduling algorithm can be written as the following optimization problem max

K 

(1 − pk,drop )Rk

(5)

k=1

Subject to Pmax , N = p{plrk ≥ plrthreshold }, Pn =

pk,drop

k Ndiscard k k Nsend +Ndiscard

n = 1, . . . , N

(6)

k = 1, . . . , K

(7)

where plrk = is the UE k’s packet loss ratio, pk,drop is the drop out rate which is the probability of plrk k larger than the plrthreshold , Nsend is the number of the total k is the number of the packets transmitted to UE k, Ndiscard discarded packets due to the expiration of Wmax , and Pn is the transmit power on the nth subcarier. The optimization problem in (5-7) can equivalently be stated as: finding the scheduling algorithm so that the UEs’ drop out rate can be minimized. As the optimal solution for the problem is not known, we propose an algorithm for obtaining an approximate solution, called joint space-frequency-power scheduling algorithm (JSFP). The proposed resource allocation scheme involves the joint optimization of three parts: packet scheduling, subcarrier allocation and spatial power distribution. The structure of the proposed scheduler is illustrated in Fig. 1. On arriving at the BS, the packets for different UEs are buffered in separate queues. Within one queue the packet are served in a first-in first-out order and across the queues packets

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Packet arrival qi(t)

qj(t)

qk(t)

qm(t) ...

BS

Step 3: UEm

QoS Queuing states

Scheduler

CSI

Packet scheduling

Data

UEk

Subcarrier allocation

Step 4:

Spatial subchannel selection UEj

Spatial power allocation UEi

Fig. 1.

Structure of the proposed scheduler.

are served according to the proposed scheduling algorithm which is based on the UEs’ QoS requirements, queuing states observed in the MAC layer and channel state information (CSI) observed in the PHY layer. The basic idea of this algorithm is to serve the most urgent packet with the best subcarrier in the channel capacity sense. III. PACKET S CHEDULING A ND R ESOURCE A LLOCATION In JSFP, the UE k’s scheduling priority is described as follows µk = wk rk,max f (plrk )

(8)

Step 5: Step 6:

and k ∈ C, select j = arg maxk∈C uk , and allocate the ith subcarrier corresponding to rj,i to the jth UE. On the ith subcarrier, select the other L−1 UEs whose scheduling priorities µk are the highest. Construct the UE set Ui with this L−1 UEs and the UE j and construct spatial subchannel set Fi with the spatial subchannels of this L UEs. Use the antenna selection algorithm to select L spatial subchannels from the set Fi to construct the channel matrix Hi under the constraint that one UE can be allocated only one spatial channel. Use the channel matrix Hi to calculate the spatial subchannel gains and then allocate transmit power to each spatial subchannel using the modified water filling algorithm (MWF) and update D = D − i and wk , buf f erk , plrk (k ∈ Ui ), and if buf f erk = 0, update C = C−k. Check the set C, if |C| > 0, go to step 5, else end. Check the set D, if |D| > 0, go to step 1, else end.

In step 2 of JSFP, the UE k’s channel capacity on the ith subcarrier can be denoted as   Pn H (10) Hk,i Hk,i rk,i = log2 det IMR ×MR + MT σ 2

where IMR ×MR is the MR × MR identity matrix and det(·) where wk is the waiting time of UE k’s head of line packet, is the determinant of the matrix. rk,max is the UE k’s largest channel capacity on the idle The antenna selection algorithm (AS) in step 4 of JSFP can subcarriers, and f (plrk ) is the function of plrk which is be described as follows. defined as  plrk Algorithm 1 The antenna selection algorithm (AS) α plrthreshold plrk ≤ plrthreshold (9) Step 1: Initialize Ui = {j, k1 , k2 , . . . , kL−1 }, f (plrk ) = 2×plrthreshold −plrk plrthreshold H H H α plrk > plrthreshold k ∈ Ui , H = [hH k,1 , hk,2 , . . . , hk,M ] , R

H H H H Fi = {hH where α is a positive constant number to ensure that when j,1 , . . . hj,MR , hk1 ,1 . . . , hk2 ,1 , . . . hkL −1,MR }, i = ∅, nr = 0. H plrk ≤ plrthreshold , f (plrk ) is a monotone increasing function ˜ m) ( hk,m 2 ), where ˜ = arg max of plrk and when plrk > plrthreshold , f (plrk ) is a monotone Step 2: Select (k, k∈Ui ,1≤m≤MR decreasing function of plrk . α can adjust the weight of the  · 2 is the 2-norm of the vector. plrk in µk . i = [HH H ]H , nr = nr + 1, ˜m k, ˜ Let C be the set of the K available UEs, D be the set of N H H ˜ delete hH ˜ , hk,2 ˜ , . . . , hk,M ˜ R from Fi , delete k from Ui . k,1 available subcarriers, buf f erk be the number of the packets H H H i , hH ¯ i = [H in the BS’s buffer which are waiting to be transmitted to the Step 3: H k,m ] , hk,m ∈ Fi , nr = nr + 1, UE k, L be the number of the available spatial subchannels 

˜ m) ¯ iH ¯H) , select (k, ˜ = arg max log2 det(I + MPnσ2 H on each subcarrier, rk,i be the kth UE’s MIMO channel i k∈Ui ,1≤m≤MR T capacity on the ith subcarrier, and Fn be the set of the spatial H H H H i = [H H H , h ] , delete h , h , . . . , hH ˜m ˜ ˜ ˜ R from i k, ˜ k,1 k,2 k,M subchannels of the selected UEs on the nth subcarrier. The ˜ Fi , delete k from Ui . details of the algorithm are given below. Step 4: Repeat step3 until nr = L. Joint Space-frequency-power Scheduling Algorithm(JSFP)

Step 1: Initialize D = {1, 2, . . . , N } and C = {1, 2, . . . , K}. Step 2: Calculate the scheduling priority of the UEs, µk = wk rk,i f (plrk ) with i = arg maxn∈D rk,n

In step 4 of JSFP, after Hi has been constructed, the transmit power can be assigned to the spatial subchannels using the MWF algorithm. Define ηb = wb f (plrb ) as the spatial subchannel’s priority, where wb and plrb are queuing states of the packets for the UE corresponding to the spatial subchaennel.

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Let Ai , Bi and Ci be the set of the spatial subchannels with lower priority, the set of the spatial subchannels with higher priority and the set of the served spatial subchannels, let mui , bui , pui (u ∈ Ui ) be the modulation scheme, loading bit and transmit power of the spatial subchannel corresponding to the UE u on the ith subcarrier, and let plrt be the packet loss ratio threshold to identify the urgent and non-urgent UEs and | · | be the size of the UE set, then the MWF algorithm can be described as follows.

Initialize D and C Calculate and sort uk=wk rk,max f(plrk), where k∈C Select j= arg max uk , k∈C Allocate the ith subcarrier to the jth UE Construct the set Fi and select L spatial subchannels to construct Hi

Calculate spatial subchannel gain and allocate the power using the modified water filling algorithm

Algorithm 2 The modified water filling algorithm (MWF) 1: 2: 3: 4: 5: 6: 7: 8: 9: 10: 11: 12: 13: 14: 15: 16: 17: 18: 19: 20: 21: 22: 23: 24: 25: 26: 27: 28: 29: 30: 31:

Initialize: mui = 0, bui = 0, pui = 0 (u ∈ Ui ), Pi = for k = 1 : |Ui | do if plrUik > plrt then Uik ∈ Bi else Uik ∈ Ai end if end for while |Bi | > 0&&Pi > 0 do Calculate ηb = wb f (plrb ), b ∈ Bi l = arg max(ηb )

Pmax N

Update D=D-i and refresh bufferk, wk, plrk, k∈Ui and if bufferk=0, update C=C-k

|C|>0? Yes

No

Fig. 2.

if mli bli = bli + ∆bli , ∆pli < Pi then mli bli = bli + ∆bli , pli = pli + ∆pli , Pi = Pi − ∆pli , Ci = Ci ∪ l, refresh ηl else Bi = Bi − l end if end while while |Ai | > 0&&Pi > 0 do for t = 1 : |Ai | do At At At At At if mi i = mi i + 1, bi i = bi i + ∆bti , ∆pi i < Pi then t Ati

=

|D|>0?

end

b∈Bi = mli + 1, = mli + 1,

∆¯ pi

No

Yes

Ai

∆pi

At ∆bi i

else Ai = Ai − Ati end if end for r = arg min (∆¯ pai ) a∈Ai

Pi = Pi − ∆pri , mri = mri + 1, bri = bri + ∆bri , pri = pri + ∆pri , Ci = Ci ∪ r end while if Pi > 0 then pci = pci + |CPii| , c ∈ Ci end if

In the resource allocation process, when the UE with the highest scheduling priority has been selected by the JSFP scheduler, the free subcarrier assigned to the UE has also been determined. Then the scheduler selects the other UEs with the highest priorities on this subcarrier to construct the UE set to be served. After the channel matrix has been constructed through antenna selection, the data rate and transmit power can be assigned to the spatial subchannels through the power

The schematic drawing of the JSFP algorithm.

allocation algorithm. The process will be repeated until no free subcarrier is left or no packet waits in the buffer to be transmitted. Fig. 2 presents a diagram that describes the operation of JSFP. IV. S IMULATION R ESULTS In this section we adopt the LTE TDD system as the simulation scenario. The performances of the proposed algorithm are compared with other two scheduling approaches, namely the modified largest weighted delay first (M-LWDF) algorithm [6] and the packet loss rate (PLR) based scheduling algorithm [7]. In the simulation, an OFDM system with 600 traffic subcarriers is considered and every eight adjacent subcarriers are combined together as a subcarrier group on which the same coding and modulation scheme are applied, and the antenna configuration between the BS and the UE is 2 × 1 or 4 × 2. The ZFB strategy is adopted to convert the mutiuser MIMO channel into independent spatial subchannels between which there is no multiuser interference and on each subcarrier MT spatial subchannels can be formed which will be allocated to different UEs according to the proposed AS algorithm. The UEs are uniformly distributed in the cell and real time service is assumed to be the real time video streaming service with the average data rate 450 Kbps [8]. We define Wmax to be 0.1s, plrthreshold to be 0.03 and plrt to be 0. If the UE’s packet loss ratio is larger than plrthreshold for consecutive 300 frames the UE will drop out of the system. To mitigate the adjacent cell interference, especially for the cell-edge UEs, the soft frequency reuse scheme [9] is adopted. In this scheme the subcarrier groups are divided into two sets, the major set and the minor set. The major set can be used to cover the whole cell area and the minor set is used only

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TABLE II S IMULATION PARAMETERS

system throughput VS UE number 18 M−LWDF 2T1R M−LWDF 4T2R PLR 2T1R PLR 4T2R JSFP 2T1R JSFP 4T2R

system throughput (Mbps)

16 14

Parameter Carrier Frequency Band width Sample frequency Sub-carrier spacing CP length(µs/samples) FFT Size Occupied subcarriers number Subcarrier group number Inter-site distance Cell number Distance-dependent path loss Lognormal shadowing Shadowing standard deviation Correlation distance of shadowing Shadowing correlation between cells Channel model Total BS TX power Minimum distance between UE and cell UE data rate

12 10 8 6 4 2

5

10

15

20

25

30

35

40

UE number per cell

Fig. 3. Comparison of the system throughput between the scheduling algorithms under different antenna configurations.

MCS 1 2 3 4 5

TABLE I MCS AND THE SNR T HRESHOLD Mod Code Ratio Data bits SNR threshold QPSK 1/3 2/3 -2 dB QPSK 1/2 1 0.5 dB QPSK 3/4 3/2 3.7 dB 16 QAM 1/2 2 6.3 dB 16 QAM 3/4 3 10 dB

Assumption 2 GHz 10 MHz 15.36 MHz 15 kHz 7.29/112 1024 600 75 2 Km 27 L=128.1+37.6log10(R), R in km Similar to UMTS 30.03 (B.1.4.1.4) 8 dB 50 m (D.4 in UMTS 30.03) 1.0 Spatial Channel Model (SCM) [11] 43 dBm >= 35 meters 450 Kbps

can be calculated as in the inner part of the cell. There is no overlap between the major sets in the three neighbouring cells. In the simulation, the cell radius is R = 1000 m, and the radius of the inner area is set to be 0.8R. The ratio between the size of the minor set and that of the major set is about 2, namely the minor set has 30 subcarrier groups while the major set has 15 subcarrier groups. The bit error rate (BER) and throughput performance of OFDMA system is simulated in AWGN channel in link level, and the curve is used as the lookup table for system level simulation to find the appropriate coding and modulation scheme according to the SINR of the received singnal on the spatial subchannels. In Table I the SNR thresholds for the different modulation and code scheme (MCS) are listed. The traffic sub-frame structure for TDD mode operation of E-UTRA is proposed in [10]. Every 10ms is divided into two sub-frames, each sub-frame has 7 service slots and 3 signaling slots, the length of the service slot is 0.675ms and each slot contains 9 OFDM symbols and 6 slots can be used to transmit data. In the simulation, all the 6 service timeslots are used for the downlink transmission and the resource allocation is performed for each sub-frame during which the channel response is assumed to be invariant. The other simulation parameters are listed in Table II. In our simulation, on each subcarrier the M-LWDF scheduler and the PLR scheduler select the L UEs with the highest priority to construct the UE set Ui and select the corresponding receive antenna vectors to construct vector set Fi , and then adopt the AS algorithm and MWF algorithm to select receive antennas and allocate the transmit power. For the M-LWDF scheme on the ith subcarrier the UE k’s scheduling priority

µk,i = wk rk,i

(11)

For the PLR scheme the UE k’s scheduling priority on the ith subcarrier can be described as  plrthreshold  if plrk > plrthreshold wk rk,i plrk δ if plrk < δ  plrthreshold µk,i = wk rk,i plrthreshold  plrk w r otherwise k k,i plrthreshold (12) where δ is a non-zero constant which is less than plrthreshold . In the simulation δ is set to be 0.0001. In the following the simulation results are presented. Fig. 3, Fig. 4, and Fig. 5 investigate the system throughput, and the UE drop rate of the scheduling schemes respectively. During every scheduling period the JSFP scheduler will allocate the free subcarrier with the best quality to the most urgent UEs, and thus the UE’s QoS can be effectively guaranteed with the lest subcarriers. However, if the scheduler doesn’t consider the subcarrier allocation order, to meet the urgent UE’s requirement, more subcarriers than the amount that the UE actually needs may be assigned to the UE and there will be less free subcarrier left to be allocated to the other UEs. When the number of the UE per cell is 40, compared with MLWDF and PLR, the UE drop rate of JSFP has been decreased by 20% and 14% respectively when MT = 2, MR = 1, and when MT = 4, MR = 2, the UE drop rate has been decreased by 15% and 25% respectively. In Fig 6, the UE drop rates of the JSFP using different power allocation schemes are presneted. The objective of water filling algorithm (WF) is to maximize the channel capacity. WF will allocate more power to the spatial subchannels with higher channel gains, but may not allocate any power to the spatial

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UE drop rate VS UE number 0.35 M−LWDF 2T1R PLR 2T1R JSFP 2T1R

0.3

UE drop rate

0.25

0.2

0.15

0.1

0.05

0

5

10

15

20

25

30

35

40

UE number per cell

Fig. 4. Drop rate of real time video traffic under different UE numbers, MT = 2, MR = 1. UE drop rate VS UE number 0.08 M−LWDF 4T2R PLR 4T2R JSFP 4T2R

0.07

UE drop rate

0.06 0.05 0.04 0.03

subchannels with smaller channel gains. So although the UE with large packet loss ratio but lower spatial channel gain can be selected to the serving UE set, there is no guarantee that transmit power will be allocated to the UE’s spatial subchannel. As the MWF takes the UE’s QoS requirement into account, it ensures that the urgent UEs with smaller spatial subchannel gains can be allocated transmit power. When MT = 2, MR = 1, K = 40. compared with WF, the MWF can reduce the UE drop rate by 7% and when MT = 4, MR = 2, K = 40, the UE drop rate can be reduced by 50%. The cumulative density functions (CDF) of the UEs’ average packet delay of the different scheduling algorithms for MT = 2, MR = 1, K = 40 are given in Fig. 7. Through further analysis, we come to the conclusion that the mean value of the UEs’ average packet delay of JSFP is the largest among the algorithms, and the corresponding variance is small. This shows that as the JSFP scheduler takes the packet loss rate into account, on the one hand, it avoids to serve the UE with larger capacity but smaller packet delay, and on the other hand, it ensures that the UE with smaller capacity but larger packet delay will have more opportunities to be served.

0.02

V. C ONCLUSIONS

0.01 0

5

10

15

20

25

30

35

40

UE number per cell

Fig. 5. Drop rate of real time video traffic under different UE numbers, MT = 4, MR = 2. UE Drop Rate VS UE number RT 0.25 JSFP−WF 4T2R JSFP−WF 2T1R JSFP−MWF 2T1R JSFP−MWF 4T2R

UE Drop Rate (%)

0.2

0.15

The next generation wireless communication systems are expected to provide a stringent QoS for the wireless service under the constraint of the limited wireless resource. In this paper a cross-layer scheduling algorithm for real time service in multiuser cellular MIMO-OFDM system has been proposed. This algorithm jointly implements the scheduling in the MAC layer and the subcarrier, bit and power allocation in the PHY layer. The simulation results show that the proposed algorithm can effectively guarantee the UEs’ QoS requirements and achieves significant improvement in the system’s UE drop rate. R EFERENCES

0.1

0.05

0

5

10

15

20

25

30

35

40

UE number per cell

Fig. 6. Drop rate of the real time video traffic of the JSFP algorithm using different power allocation schemes. The CDF of average packet delay 1 M−LWDF 2T1R PLR 2T1R JSFP 2T1R

0.9 0.8 0.7

P(t