ited (RPL) power assignment, so that the fair packet loss sharing. (FPLS) scheduling can be implemented in the multi-cell resource allocation. The basic idea of ...
Resource Allocation in Multi-Cell CDMA Communication Systems Vincent Huang and Weihua Zhuang Department of Electrical & Computer Engineering, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1 Abstract— In a multimedia code division multiple access (CDMA) system, the network performance depends on the success and efficiency in allocating system resources. The system resources in terms of bandwidth and power should be efficiently distributed to each mobile to guarantee its quality of service (QoS) requirements. In this paper, we propose a received power limited (RPL) power assignment, so that the fair packet loss sharing (FPLS) scheduling can be implemented in the multi-cell resource allocation. The basic idea of FPLS is to schedule the transmission of multimedia packets in such a way that all the users have a fair share of packet loss according to their QoS requirements, which maximizes the number of the served users under the QoS constraints. The RPL minimizes the received power for each packet. With known path loss, it in turn minimizes the transmitted power as well. The intercell interference caused by the scheduled packets is also limited by the scheduling to increase the system capacity.
I. I NTRODUCTION The next generation wireless communication systems are anticipated to provide a broad range of multimedia services including voice, data, and video to mobile users (MUs). Unlike wireline communication systems, wireless systems have a very scarce bandwidth of available frequency spectrum. The limited network resources have to be used efficiently to provide satisfactory services to the MUs. Wideband code division multiple access (CDMA) has been selected as the major multiple access technique for the third-generation wireless systems. For a CDMA system, power control has to be used to combat the near-far problem. In supporting voice only services, the received signal power from each of the MUs in the cell is maintained at a constant level in the uplink at the base station (BS) [1]. However, in a multimedia CDMA system, different traffic classes require different transmission accuracies specified by bit error rate (BER). If the received power is kept at the same level for all the traffic classes, the capacity is limited by the most stringent BER requirement and cannot be used efficiently. Recently, several approaches have been proposed for optimal power control for multimedia traffic to maximize the capacity or to minimize the total transmitted power [2–4]. Packetized transmission over wireless links makes it possible to achieve a high statistical multiplexing gain. Packet flows generated by MUs can be classified to several traffic classes. Each of these classes has its unique quality-of-service (QoS) requirements and traffic characteristics. Due to heterogeneous nature of multimedia traffic flows, the traditional voice-based medium access control (MAC) protocols do not perform well in a multimedia environment. A flexible MAC protocol which can efficiently accommodate multimedia traffic is required. One important MAC issue is the packet scheduling. The order of packet transmissions for multimedia traffic has a great impact This research was supported by a research grant (RGP1N155131) from the Natural Science and Engineering Research Council (NSERC) of Canada.
on the efficiency and performance of wireless systems. However, the design of a packet scheduler involves balancing a number of conflicting requirements. In [5], a scheduled CDMA method with power control is proposed, where only the single cell case is considered. We have previously proposed a more efficient fair packet loss sharing (FPLS) scheduling algorithm [6] for a single cell system. For a practical CDMA system, intercell interference must be consider in the scheduling. Since a CDMA system is interference limited, an effective control of the intercell interference can increase the system capacity. When the interference level gets higher, the transmitted power has to be increased to maintain a desired signal-to-interference plus noise ratio (SINR), thus it causes even higher interference to other MUs. One way to control the intercell interference is to assign proper transmitted power to each packet so that a minimum power is used to guarantee the SINR requirement. The order of packet transmission also plays an important role in reducing intercell interference. Given the SINR requirement, the transmitted power is inversely proportional to the path gain. Since the channel conditions are changing constantly, the packet scheduling should be adaptive to the path loss. In [7], a truncated power control is proposed. When the propagation gain is below a cutoff level, the transmission is suspended. This can effectively reduce the interference level and increase the system capacity. However, for a variable traffic load, a fixed cutoff level is not optimal. In this paper, we combine the FPLS scheduling with a new power control scheme for packet scheduling in a multi-cell system. Based on the estimation of the dynamical intercell interference, using FPLS, fair resource allocation and QoS satisfaction to all the MUs can be achieved at the same time. If the packet transmission from an MU is suspended due to a bad channel condition, the MU is compensated with more resources for transmitting more packets at a later time when the channel condition is improved. We also use a received power limited (RPL) power assignment, where the total maximum received power (including the intercell interference) is limited at the BS. Thus, when the interference increases, the total transmitted power from the MUs in the cell decreases, which means that less packets can be scheduled. In this way, instead of letting MUs competing with each other using higher power, high interference can be avoided and the capacity can be increased. Similar to the approach of the truncated power, transmissions of packets from MUs with very bad channels have to be controlled. When the interference from all the packets scheduled for a time slot exceeds a preset threshold, no new packet can be scheduled for the slot. Thus, a packet from an MU with a bad channel condition has a higher chance to be scheduled in a low traffic load than in a high traffic load, so as to effectively control the interference level.
[
II. S YSTEM M ODEL Consider a multi-cell system with a hexagonal cell structure, the actual cell boundaries are normally irregular due to shadowing and varying traffic conditions. When an MU moves slowly relative to the carrier wavelength and symbol rate, the propaga tion path loss from an MU to the th BS is generally modeled by "!$# (1)
where is a constant that depends on the antenna gains, the signal wavelengths, etc., % is a path-loss exponent, &
" is a zero-mean Gaussian random variable with variance ')( , is the distance between the th BS and the MU. For simplicity, *
"
" we use and & instead of and & in the following. The cellular system is a hybrid time-division (TD)/CDMA system with packetized transmission [8], employing time division duplex (TDD) for better accommodating asymmetric traffic loads between the uplink and downlink. Time is partitioned into frames of a constant duration. Each frame is divided into time slots of constant length. Multiple access within each time slot is accomplished by assigning unique pseudo-random noise (PN) code sequence(s) to each MU. The source information from and to MUs is segmented into packets of equal length. The packets are transmitted at a constant bit rate, each requiring a time slot for transmission. Packet transmission from and to mobile users is synchronized in time. The decision on packet transmission in each time slot for both uplink and downlink is made at the BS and is broadcast to the MUs by a MAC protocol. Intercell Interference Modeling - In the uplink transmission, the total intercell interference is produced by all MUs in other cells. Consider an MU connected to the th ( ,+ ) BS. The interference seen at the center zeroth ( ) BS from one packet transmission of this mobile is
- /. 10 "
.:
#32
54 76 8 "!9#
(2)
where is the average received power of one packet from MU at its home BS. Also, an MU is always BS to
=assigned @ 4 7to6 the A8 "!$# is which the path loss is smallest, i.e., ; #? less than unity. The total intercell interference is given by
B
.: 0
all packets
where
E 0 & # GK& I " #
"
#32
CD4 76 8 "!$#FE 0 GH& JI " #
2
IONQP C 4 6 8 "!$#UT ML P 6SR I 2 otherwise.
(3)
Note that if an MU is not scheduled to transmit a packet in the . current time slot, the associate received power is zero. C "!9# in the path loss is to model the The component shadow effect. The shadowing process is correlated from frame to frame. Let &V;*WX? denote the mean shadowing level at time W . Assuming &V;*WX? is a constant over each frame duration (Y:Z ), the correlation can be modeled by
&V;YQ?
\[] _ ^` V& ;YaG ?bdc;eYQ?
(4)
where &V;YQ? is the &V;fWX? value in the Y th frame, is correlation between two points separated by one meter, g is the velocity of MU , and c;eY5? ’s are i.i.d. Gaussian random variable with zero
_l$` )Ch 7!! i j"j kk l$`
mean and standard deviation '
[9].
MAC Protocol - Fig. 1 shows the TDD multi-code TD/CDMA for multi-rate packet transmission [8]. For the uplink, there are several request access mini-slots of a constant duration in the beginning of the frame, followed by a number of packet transmission slots of a constant duration. The downlink transmission in each frame starts with a control slot. The control slot is a broadcast time slot which consists of a request acknowledgment (ACK) sub-slot and a transmission permission (TP) sub-slot. The ACK sub-slot is used to acknowledge the received requests from the MUs and the TP sub-slot is used to broadcast the packet scheduling for the uplink transmission in the next frame. In the following, we focus on the uplink transmission. The downlink transmission is controlled by the BS and can be done in a similar way. Guard Time
Downlink
Uplink Request Access slots slot slot 1 2
Request Update slots
...
m"p
slot
Control slot slot slot 1 2
...
mon
slot
ACK slot TP slot
Fig. 1. Time slots of uplink and downlink.
QoS Provisioning - The QoS parameters under consideration are transmission accuracy and delay requirements. The overall transmission accuracy requirement is represented by packet loss and transmission BER (over the wireless link) requirements. In real-time communications, an MU requires its packets to be delivered to the destination within a certain time period; otherwise, the packets will be worthless and the service quality will be poor. Here we consider the delay over the wireless link only. The delay requirement can be represented by the life span of each packet. The life span is a set of frames from the moment that the packet is generated to the moment that the required delay bound is reached. The residual delay bound is the difference between the required delay bound and the total accumulated queueing delay up to the time of packet scheduling and is also referred to as time-out value of the packet. Packet loss due to buffer overflow or exceeding the delay bound is referred to as packet loss probability (PLP). The BER requirements are to be guaranteed by properly arranging simultaneous packet transmissions and controlling their transmitted power levels; the delay and PLP requirements are to be guaranteed by proper packet scheduling. III. T HE M ULTI - CELL FAIR PACKET S CHEDULER The main objectives of the packet scheduler proposed here are to guarantee the QoS requirements of all MUs and to maximize the resource utilization so that the system can support as many satisfied MUs as possible. There is a trade-off between
the two objectives. High QoS requirements will cause low resource utilization. The scheduler will provide each MU with just enough resources to satisfy its QoS requirements without over-allocating resources. Since the CDMA system is interference limited, the power assigned to each MU depends on both intercell and intracell interference which in turn is the power from other MUs. Scaling down the transmitted power levels of all MUs will provide high resource utilization. To achieve the objectives, the scheduler first decides the order of the transmissions, i.e., the priorities for the MUs to transmit their packets. In a high traffic load condition when the number of packets waiting for transmission is in the neighborhood of the system capacity, the priority for transmission should be a function of the delay requirements, packet loss requirements, and traffic load characteristics. Once the priorities are determined, a packet from the user with the highest priority will be scheduled for transmission [6]. The scheduling process is illustrated in Fig. 2. Each MU has its own buffer to store the incoming packets. The buffer sizes are large enough so that no packet is lost due to buffer overflow. One packet is pulled each time from an MU decided by the FPLS algorithm. The scheduler then decides in which time slot the packet can be transmitted and assigns the proper received power to the packet. The power of previous scheduled packets for the same slot will also be updated.
L
L
.:
User 2
User I Inter-cell Interference
One time frame
Fig. 2. The packet scheduling procedure.
Review of the FPLS Algorithm - The FPLS algorithm proposed in [6] is used to decide how many packets to be dropped from each MU during a congestion period. The QoS requirements and traffic rate distribution is used in the decision making. If one packet has to be dropped, each MU has a share of it. Since a packet has to be dropped as a whole, a packet from the MU with the largest share will be dropped. However, this will be recorded and carried over to the future frames so that a fair resource allocation among all the MUs can be achieved. RPL Power Assignment - The knowledge of intercell interference in the next frame is needed in scheduling packets for transmission in that frame. In the distributed resource allocation where each BS independently schedules packet transmission in its cell, the knowledge of intercell interference is not available. Assuming the total traffic load changes slowly from frame to frame, the intercell interference can be estimated from the pre. vious frames. Let Z denote the sum of intercell interference and thermal noise, where the intercell interference is the dominant term. The received SINR after despreading for a packet from MU , , is given by
A
.Q ! c .
b
. Z
I
(5)
.
and
which leads to
.
4 ! 8 i 7i ` 4 ! 8 7i i `
#
.Q
.
.
b
b 1
$ %
&
(6)
(7)
(8)
From (8), the ratio of to is a constant depending only on processing gain and SINR requirements, but independent of the number of packets scheduled in the time slot. Also, from (8), we have
% %
Received power assignment Total received power level
A
, we have .: 4 i 8 ` 4 ! 8 F4 ! 8 .
4 Q ! 8"4 ! i 4 8 `! 8 :
Solving for
FPLS Scheduler User 1
.:
where is the processing gain, is the received power of the desired signal, c is total scheduled packets from MU in the time slot, and is the total number of active MUs in the system. For presentation clarity, consider two MUs and of two different traffic classes, class-I and class-II, respectively. MU has c packets and MU has c packets for transmission in the current time slot. The SINRs are given by
% .
.
and
(9)
Since the system capacity in a CDMA system is interference limited, we want to minimize the transmitted power and thus to reduce interference under the QoS constraints. Given a path loss, minimizing the transmitted power is equivalent to minimizing the received power. Due to the interference limited nature, the number of packets that can be scheduled in each time slot depends on the class and QoS requirements of the packets waiting for transmission, resulting in a very high complexity for an optimal solution. As a result, a sub-optimal solution is proposed, in which the total power increase for each scheduled packet is minimized. As given in (8), the received powers for packets from different classes are proportional to each other and independent of the number of packets scheduled. Traffic with different SINR requirements can be viewed as a single traffic class if each assigned power is proportionally scaled. For ex ample, a packet of class-II is equivalent to packets of classI. We use to denote the current equivalent number packets of T class-I for time slot , T , where is the number of uplink time slots in one frame. For a new packet from MU of . class-I, from (5), the received power can be calculated from
'
( *)
(
resulting in
. '
_.
Z
G '
for
0 '132 1
'
. ' . ' . b
',+-
<
% *)
'
(10)
Z and
' 4 ' 0 '
< /.
(11)
The total received power increase due to the newly scheduled packet is . . . b (12)
0 . '
where is the required received power increase of each previously scheduled packet because of the interference generated by the new packet and is given by
0 . '
.
_.
Z
Z
G ' G G ;3 '@G ? f. (13) Z ; G '? ( b ; G '? 0 . '132 1 From (11)-(13), decreases when ' gets smaller. There-
fore, the total power increase is minimum when the new packet is scheduled in the time slot with the minimum total power. Given the processing gain and SINR requirements, the received powers of the packets in the same time slot are always proportional to each other. The intracell interference caused by one class-II packet is equal to the intracell interference caused by class-I packets. Therefore, we have .: . G ;7; c G ?bdc ? Z (14)
%
%
G .
i.e.,
; c G ?b c . Z
%
(15)
This means, if we increase c by one, the increase of the inverse power for each class-I packet is given by
0
;. ? G .
Z
(16)
and, if we increase c by one, the increase of the inverse power for each class-I packet is given by
.:
+
.
0
% I ;. ? G . Z
(17)
where Z to avoid a negative power assignment. Thus, the received powers of previously scheduled packet should be updated according to (16)-(17) and the received power of a new packet can be assigned to be the updated value. When the intercell interference is increased, the assigned power to each packet has to be increased to maintain the required SINR. This, in turn, will cause more increase in the intercell interference. Therefore, the assigned power has to be limited in some way. Here, the total received power plus inter. . b Z is upper limited by a preset threshference ! c old in the scheduling. With the limit, when the intercell interference increases, the number of scheduled packets is reduced, which will in turn reduce the intercell interference. To schedule a packet, we first examine whether the total received power is below the threshold, and then check if the total intercell interference caused to other cells is below a certain level. Instead of a fixed cut-off level for each user, we use a limit on the total intercell interference. Hence, a packet with a large path loss to its BS is less likely to be scheduled during a high traffic load period than during a low traffic load period. In this way, we can have flexibility in the scheduling and keep the interference low. In the above analysis, the intercell interference is assumed to be constant in each frame. However, the exact value cannot be predicted due to the dynamics of packet flows and the path losses. Since the interference is a sum of the powers from many
0
.
2) 1
MUs in other cells, the estimation error . Z can be modeled by I a Gaussian distribution ; 'SZ ( ? . Let denote the required outage probability, i.e., the probability of received SINR being . less than the required threshold has to be not larger than , . and let Z denote the estimated intercell interference, then
.
and
0
Z
.
Zb .Q
0
.
2) 1
Z
(18)
d.
2) 1
(19)
' b ZS2 0 0 . 0 .Q . /. 2 ) 1 Z 3G ' G Z (20) 2 2 0 . 2) 1 . For a given , the value of Z that can be tolerated can be calculated numerically from the following equation 0. . 2) 1 Z (21) G erf ' Z 0. 1
.Q
.
( # YW . We can add the Z value to where erf ;V? . the estimated Z in the power assignment to guarantee the desired outage probability.
IV. P ERFORMANCE E VALUATION We consider a target cell surrounded by 6 neighboring cells in the first tier, and three traffic classes (voice, video and data). Each time frame is 10 ms in length and is partitioned into eight time slots. Each time slot has a duration of 1.25 ms. The voice traffic is simulated by the on-off model. During the on-state, one packet is generated in each frame. On average, an on-state lasts ten frames and an off-state lasts 15 frames. The video traffic has a variable rate. We use a model similar to the one in [10]. The rate is Gaussian distributed with a mean of 17 packets and &% packets. The minimum and maxstandard deviation "!$# imum video rates are zero and 34 packets/frame respectively. The rate is correlated from frame to frame. The autocorrelation coefficient between two consecutive frames is 0.6. The short message transfer protocol (SMTP) is used to simulate the data traffic. The data size of SMTP traffic can be modeled by ')(+* ( normal distribution and data burst arrival rate follows Poisson distribution [11]. Using the data from Table X in [11], we simulate the SMTP traffic with an average arrival interval of 10 frames and size of each data burst following a ')(+* -normal dis( tribution with a geometric mean of 10 packets and a geometric standard deviation # ! . The SINR requirements are 7 dB for voice and video traffic and 8.75 dB for data. The delay tolerance for voice, video and data packets is 5, 20 and 40 frames, respectively. The PLP requirements for voice, video and data 5 ( , CD-, , and 5-. , respectively. traffic classes are set to The initial MU locations are independent and uniformly distributed over the seven cells. An MU can move away from the starting in any direction which is uniformly distributed I point +0 . The in initial velocity of MUs is assumed to be a !+/ Gaussian random variable with a mean of 50 km/h and truncated between zero and 100 km/h with a probability of 1+132 . The variation of the direction of the movement from frame to 0 frame is uniformly distributed in the range of 46587 . The velocity increment of each MU from frame to frame is taken to be a
−1
10
Voice −2
10
Packet Loss Probability
uniformly distributed random variable in the range 4 2 of the current velocity. Consider a traffic load uniformly distributed in the seven cells. We schedule the packet transmission in the center cell and use the same packet scheduling for the other six cells to calculate the intercell interference level. The interference level in the previous frame is used in the current frame for power assignment. The cell radius is 2 km, path-loss exponent % is 4, and the shadowing variance ' ) is 8 dB. The shadowing correlation parameter is 0.9. We choose the maximum received power as 60 units, with the background thermal noise power being 0.1 unit. The interference level is limited at 60 percent of the maximum received power.
Video −3
10
Data
−4
10
−5
10
0
20
40
60
80 100 User Index
120
140
160
180
Fig. 4. The average PLP for 167 voice users, 5 video users and 5 data users.
20
18
−1
10
16 Voice
12 −2
10 Packet Loss Probability
Probability Density
14
10
8
6
Video
−3
10
4
2 Data
0 −0.5
−0.4
−0.3
−0.2
−0.1 0 0.1 Estimation Error in Power Units
0.2
0.3
0.4
0.5 −4
10
Fig. 3. The interference estimation error (shaded area) and Gaussian distribution (solid line).
0
Fig. 3 shows the interference estimation error in each frame can be modeled as a Gaussian random variable with a very . small variance. We can use this model to calculate Z to guarantee the outage probability. Fig. 4 shows the simulation results of packet loss rate for 167 voice mobiles, 5 video mobiles and 5 data mobiles. The PLP requirements for all the mobiles are satisfied at the same time. If we increase the number of voice mobile users by two to 169, as shown in Fig. 5, none of the users’ PLP requirements can be satisfied. The PLP is increased for all the traffic classes. The average delay for all the packets is also increased. The results demonstrate the fair sharing of system resources among all the MUs, and provide a bound on the system capacity in terms of the MU numbers with QoS satisfaction. V. C ONCLUSION In this paper, we propose a multi-cell packet scheduling scheme which combines the FPLS scheduling with RPL power assignment. The scheduling is based on the intercell interference estimation from frame to frame. Simulation demonstrates that the error can be characterized by a Gaussian distribution. The scheduling method ensures that the QoS requirements of all the users can be satisfied at the same time, which maximizes the number of users supported by the system under QoS constraints. With the RPL power assignment, the received power is kept at a low level to reduce the intercell interference while satisfying the SINR requirements of the users. Simulation re-
0
20
40
60
80 100 User Index
120
140
160
180
Fig. 5. The average PLP for 169 voice users, 5 video users and 5 data users.
sults show that efficiency of the proposed packet scheduling in supporting the three traffic classes. R EFERENCES [1] K. S. Gilhousen, I. M. Jacobs, R. Padovani, A. J. Viterbi, L. A. Weaver, Jr., and C. E. Wheatley III, “On the capacity of a cellular CDMA system,” IEEE Trans. on Veh. Technol., vol. 40, pp. 303–312, May 1991. [2] M. Soleimanipour, Modeling and Resource Management in Wireless Multimedia WCDMA Systems. PhD thesis, University of Waterloo, 1999. [3] L. C. Yun and D. G. Messerschmitt, “Variable quality of service in CDMA systems by statistical power control,” in Proc. IEEE ICC’95, vol. 2, pp. 713–719, 1995. [4] S. Yao and E. Geraniotis, “Optimal power control law for multi-media multi-rate CDMA systems,” in Proc. IEEE VTC’96, vol. 1, pp. 392–396, 1996. [5] M. A. Arad and A. Leon-Garcia, “Scheduled CDMA: A hybrid multiple access for wireless ATM networks,” in Proc. PIMRC’96, pp. 913–917, 1996. [6] V. Huang and W. Zhuang, “Fair packet loss sharing (FPLS) bandwidth allocation in wireless multimedia CDMA communications,” in Proc. Wireless’2001, (San Francisco, USA), pp. 198–203, May - June 2001. [7] S. W. Kim and A. J. Goldsmith, “Truncated power control in codedivision multiple-access communications,” IEEE Trans. on Veh. Technol., pp. 965–972, May 2000. [8] V. Huang and W. Zhuang, “Optimal resource mangement in packetswitching TDD CDMA systems,” IEEE Personal Communications, pp. 26–31, Dec. 2000. [9] G. L. St¨uber, Principles of Mobile Communication. Kluwer Academic Publishers, 2nd ed., 2001. [10] S. Manji and W. Zhuang, “Power control and capacity analysis for a packetized indoor multimedia DS-CDMA network,” IEEE Trans. on Veh. Technol., vol. 49, pp. 911–935, May 2000. [11] V. Paxson, “Empirically derived analytic models of wide-area TCP connections,” IEEE/ACM Trans. on Networking, vol. 2, pp. 316–336, Aug. 1994.
