Cross-layer Scheduling and Dynamic Resource Allocation for Downlink Multiuser MIMO Systems with Limited Feedback Chong-xian Zhong*, Lu-xi Yang† *School †
of Information Science & Engineering, Southeast University, Nanjing, China, email:
[email protected] School of Information Science & Engineering, Southeast University, Nanjing, China, email:
[email protected]
Abstract—In this paper, we present a cross-layer scheduling and dynamic resource allocation (CLSDRA) strategy for downlink multiuser multiple-input multipleoutput (MIMO) systems with limited feedback. Based on the instantaneous partial channel state information (CSI) from physical (PHY) layer and the queue state information (QSI) from media access control (MAC) layer, the proposed scheme schedules packets and allocates resources such as channel, bit and power to the scheduled users to maximize the utility function which sums the product of each scheduled user’s delay requirement, head of line (HOL) packet waiting time, queue length and data rate. Simulation results demonstrate that our scheme outperforms the existing single-layer resource allocation or scheduling algorithms in balancing the total system throughput and the packet drop rate because the proposed strategy could utilize the QSI and the partial CSI simultaneously. Keywords—cross-layer scheduling, dynamic resource allocation, downlink multiuser MIMO systems, limited feedback.
I. INTRODUCTION With the rapid development of wireless communication techniques and the increasing popularity of wireless broadband services, it is becoming a very challenging task that how to exploit limited radio resources efficiently to obtain high spectral efficiency for future wireless communication systems due to the scarcity of radio resources and the harshness of wireless channel conditions [1]. MIMO wireless system is known of providing considerable capacity without additional spectrum or power [2]. The use of space division multiple access (SDMA) can provide substantial throughput gain in the downlink of multiuser MIMO wireless communications network [3]. Moreover, dynamic resource allocation techniques have attracted enormous research interests and have been identified as one of the most promising techniques, which can achieve both higher system spectral efficiency and better quality of service (QoS) [4]. However, most of the existing articles focus on studying the dynamic resource allocation problem from the view of PHY layer without considering the packet access characteristic, such as the randomness of the This work was supported in part by NSFC (60496310, 60672093) and NSFJS (BK2005061), and Huawei Technologies Co., Ltd.
1-4244-1284-6/07/$25.00 ©2007 IEEE
queuing behavior and the traffic arrival. Although independent consideration of PHY layer simplifies wireless system design, it is inadequate because it attempts to optimize performance at PHY layer while keeping parameters of other layers fixed without considering the effect of co-channel user interference on higher layers and the impact of local adaptation actions on overall performance [5]. Thus, cross-layer designs have gained considerable attention recently, which allow adaptation and optimization across multiple layers [6][7][8]. [5]~[8] optimize system design combining both resource allocation in PHY layer and scheduling in MAC layer, but most of these algorithms are based on the following two implicit assumptions: the first is that there is no constraint on the maximum size of every user’s transmission buffer, i.e. all the users have infinite queue size and are delay-insensitive; the second is that every scheduled user always has sufficient source packets in queue to transmit. However, in practice, we should not only consider limit queue sizes, but also ensure that users with empty transmission buffers are not scheduled despite favorable channel conditions. Moreover, most of the existing literatures about resource allocation and scheduling are based on the perfect CSI at the transmitter, which is impractical in the realistic wireless communication systems. Considering the above issues, we propose a cross-layer scheduling and dynamic resource allocation (CLSDRA) scheme for downlink multiuser MIMO Systems with limited feedback utilizing both information theory and queuing theory. The proposed scheme schedules users and allocates resources, such as channel, bit and power, to the scheduled users to maximize the utility function which sums the product of each scheduled user’s delay requirement, HOL packet waiting time [9], queue length and data rate with the partial CSI from PHY layer and the QSI from MAC layer,. Simulation results demonstrate that our scheme provides better performance which balances system throughput and packet drop rate compared to conventional single-layer scheduling schemes and existing single-layer resource allocation strategies. The remainder of this paper is organized as follows. In the next section, we introduce the system model. In section Ⅲ, we propose the CLSDRA scheme for
downlink multiuser MIMO systems. Simulation results are provided in section Ⅳ. Finally, conclusions are drawn in section Ⅴ. II. SYSTEM MODEL We consider a single-cell downlink multiuser MIMO wireless system where each of U geographically dispersed users equipped with N R antennas and the BS with NT antennas. Generally speaking, it is satisfied that U ≥ N T , N T ≥ N R in a typical cellular system. The simplified block diagram of the system model is shown in Fig.1. Input packets of each user are buffered in individual first in first out (FIFO) queues at the BS. For simplicity, the packet arrival processes are assumed to be mutually independent and modeled as Poisson processes, moreover, the inter-arrival times of each user are assumed to be independent and identically distributed (i.i.d). The system time is organized as frames and each frame can only serve integer number of packets. We assume that the wireless channels are quasi-static for each frame, i.e. the channel of each user remains unchanged within the frame duration, but varies independently and identically from frame to frame. At the beginning of each frame, the CLSDRA module schedules packets and allocates resource for scheduled users making full use of the QSI and the partial CSI simultaneously. Since the BS schedules transmission at the beginning of each frame, the packets arriving during the current frame will not be scheduled for transmission until the next frame.
the receive antenna nR of user u at frame f , and pk represents the power attenuation due to the path loss and shadow fading. Moreover, it is assumed that perfect knowledge of CSI is available at the receiver by appropriate channel estimation, whereas only partial CSI, i.e., the SINRs are available at the transmitter with limited feedback. In order to exploit multiple antennas at the transmitter with partial CSI, we borrow the idea of opportunistic multiple beamforming (OMBF) from [10]. The transmitted signal at frame f can be written as X(f ) =
NT
∑φ
nT =1
nT
(2)
( f ) snT ( f )
where φn ( f ) denotes the nT th beamforming vector T
constructed at frame f , sn ( f ) denotes the nT th T
transmitted signal at frame f . Substitute (2) into (1) and, for simplicity, drop the frame index, the received signal of user u at the nRth receive antenna is Yu , nR =
NT
∑
nT =1
Pu , nT H u , nR φnT snT + Wu , nR
(3)
We assume that the nRth receive antenna of user u knows H u , n φn ( nT = 1,..., NT ) and regard sn as the desired R
signal
T
while
T
the
other
sn' (nT' = 1,..., NT , nT' ≠ nT ) T
as
interference，the SINR at nRth receive antenna of user u corresponds to NT random beams can be computed as follows: SINRu , nR , nT =
2
PnT H u , nR φnT 1
γ
NT
+
∑
nT' =1 nT' ≠ nT
Pn' H u , nR φn' T
2
(4)
T
where γ denotes the average signal-to-noise ratio (SNR) of user u , Pn denotes the power allocated to the nT th T
transmit
antenna
and
NT
∑
nT' =1 nT' ≠ nT
Pn ' H u , nR φn' T
T
2
denotes
the
interference caused by other signals to the received signal of user u at the nRth antenna corresponds to the nT th beam. Fig.1. Simplified block diagram of a downlink multiuser MIMO system with CLSDRA
Assume that u is one of the active users at frame f , the received signal of user u at this frame can be expressed as Yu ( f ) = pu H u ( f ) X ( f ) + Wu ( f ) (1) where Yu ( f ) is N R × 1 vector which denotes the received signal of user u at frame f , X ( f ) is NT × 1 vector which denotes the transmitted signal at frame f , Wu ( f ) is N R × 1 vector which denotes additive Gaussian noise whose entries are independent identically distributed (i.i.d) complex with zero mean and variance N 0 , H u ( f ) is N R × NT matrix which denotes the channel matrix, where the entry hu ( f )( nR , nT ) ~ CN (0,1) represents the complex channel gain from transmit antenna nT to
III. CROSS-LAYER SCHEDULING AND DYNAMIC RESOURCE ALLOCATION SCHEME Considering the issues of scheduling and resource allocation outlined in section 1, we propose a cross-layer scheduling and dynamic resource allocation (CLSDRA) scheme for downlink multiuser MIMO System with limited feedback described in section 2. The objective of this scheme is to maximize the defined utility function under the constraint of total transmit power available at the BS based on the observation of the instantaneous partial CSI from PHY layer and the QSI from MAC layer, where the utility function is defined as the sum of the product of each scheduled user’s relative delay requirement, HOL packet waiting time, queue length and data rate.
For simplicity, we assume that N R = 1 and user u knows H uφn (nT = 1,..., NT ) . Based on this assumption, each T
user can calculate its SINRs corresponding to NT beams according to the equation (5) which is simplified from (4). SINRu , nT =
PnT H uφnT 1
γ
NT
∑
+
nT' =1 nT' ≠ nT
2
Pn' H uφn ' T
2
(5)
T
T
According to (5), and as far as the bit error rate (BER) requirement of each user and the realistic integer modulation scheme are considered, the transmission rate for user u on the nT th transmit antenna should be calculated by the following equation SINRu , nT ) Ru , nT = log 2 (1 + Γ
(6)
where • denotes the largest integer that is smaller than or equal to the value of the input parameter. When M-ary quadrature amplitude modulation (MQAM) is employed, Γ = − ln(5 × BERu ) /1.5 , where BERu denotes the BER requirement of user u . The utility function of our proposed CLSDRA scheme can be expressed as follows: NT
=∑
NT
k
k =1
= ∑α k ωk qk Rk
(7)
k =1
The purposes of parameters in (7) can be explained as follows. Assume user k is one of the NT users scheduled by the BS at the beginning of each frame. α k is a constant positive weight which represents the relative delay requirement of user k . Bigger value of α k implies higher delay requirement of user k and higher possibility being scheduled for this user. ω k represents the HOL packet waiting time of queue of user k . Bigger value of ω k implies longer waiting time and higher possibility being scheduled for this user. qk denotes the queue length of user k . Bigger value of qk implies larger number of data packets of user k waiting for service and higher possibility being scheduled for this user. Rk represents the transmission rate of user k . Bigger value of Rk implies better channel state of user k and higher possibility being scheduled for this user for the point of view that maximizes system throughput. Obviously, α k , ω k , qk can be obtained by QSI and Rk can be obtained by partial CSI. It can clearly be seen that this utility function can make full use of QSI and partial CSI simultaneously, which makes it possible for the proposed scheme to obtain higher system throughput while guarantees better QoS requirement of every user. Consequently, the proposed cross-layer scheduling and resource allocation scheme can be formulated as follows: max
NT
= max ∑α k ωk qk Rk k =1
subject to :
NT
∑ Pk ≤ Ptotal k =1
where Ptotal is the total transmit power available at the BS. Obviously, the optimization problem in (8) is a combinatorial optimization problem. Although we can obtain optimal solution by exhaustive search, the computational complexity required is prohibitively high. Here, we propose a suboptimal scheme to this optimization problem by assuming the total available transmit power is allocated to NT antennas equally, i.e. Pn = Ptotal / NT ,( nT = 1,..., NT ) . Based on this assumption, u can calculate its own each user u = α uωu qu Ru ,(u = 1,...,U ) according to partial CSI and QSI. Then, the CLSDRA module schedules packets of NT users out of U system users and allocates resource for the NT scheduled users correspondingly. The proposed algorithm is represented as follows: Step1. Obtain QSI from MAC layer according to queue state of each user; Step2. Obtain partial CSI from PHY layer according to limited feedback; Step3. Calculate u = α uωu qu Ru ,(u = 1,...,U ) of user u according to its QSI and partial CSI; Step4. Schedule NT users from U users to maximize
(8)
NT
= ∑α k ωk qk Rk ;
system utility function
k =1
Step5. Allocate spatial subchannel and transmit power for NT scheduled users and select corresponding modulation scheme to load bits. IV. SIMULATION RESULTS In this section, we present simulation results of the proposed CLSDRA scheme for downlink multiuser MIMO systems with limited feedback and evaluate its performance in comparison with two conventional approaches: the sum data rate maximization resource allocation method utilizing CSI only and the sum queue size maximization scheduling algorithm utilizing QSI only. The objective of the former is to maximize the utility function of
NT
∑α R k
k
, while the objective of the
k =1
latter is to maximize the utility function of
NT
∑α q k
k
. For
k =1
simplicity, we denote these three schemes as: Proposed CLSDRA, SDR MAX and SQS MAX respectively. In our simulation, we assume that the system is operating in a flat fading environment. There are 4 transmit antennas at the BS and only one receive antenna for each user. The channels between the BS and system users are i.i.d. Moreover, we assume that the traffic is non-uniform and the packet arrival processes are mutually independent. Here, we model the packet arrivals for each user as Poisson processes. The source of each user generates packets at an average rate of 100 kbps and the size of each packet is set to 256 bits. It is constrained that only integer number of packets is transmitted in each frame. The relative delay requirement of each user is set to 1, which means that the delay requirements of all users’ are identical.
0.7
considering the channel state of each user. The proposed CLSDRA scheme obtains large total throughput near to the performance of the SDR MAX. It can be seen from the above numerical results that our proposed scheme is capable of providing better performance which balances the total system throughput and the packet drop rate. This is because the proposed CLSDRA algorithm makes full use of the QSI from MAC layer and the partial CSI from PHY simultaneously to maximize the utility function defined as the sum of the product of each scheduled user’s relative delay requirement, HOL packet waiting time, queue length and data rate.
Proposed CLSDRA SDR MAX SQS MAX
0.6
Packet drop rate
0.5 0.4 0.3 0.2 0.1 0
1
1.5 2 2.5 3 3.5 Average arrival rate (packets/frame)
4
Fig.2. Packet drop rate vs. arrival rate
Fig.2 compares the packet drop rates of the three algorithms with different average arrival rates. We can see that, with the same arrival rate, the packet drop rate of SQS MAX is the smallest one among three algorithms. This is because this algorithm prevents the queue size of system users from becoming too large by scheduling NT users with the largest sum queue size utilizing QSI sufficiently. Thereby, it reduces the packet drop rate significantly. While the packet drop rate of SDR MAX is much larger than the other two schemes. This is because this scheme schedules NT users with the largest sum data rate utilizing only partial CSI from PHY layer without considering the queue size of each user. The proposed CLSDRA scheme obtains small packet drop rate approaching the performance of SQS MAX, which is necessary in practical wireless systems. 8
Total throughput
7 6 5 4 SQS MAX SDR MAX Proposed CLSDRA
3 2
0
100
200 300 400 Number of users
500
600
Fig.3. Total throughput vs. number of users when SNR=0 dB
Fig.3 depicts the total system throughput of the three algorithms with different numbers of system users when SNR=0 dB. It can be seen clearly from this figure that, with the same number of users, the total throughput of SDR MAX is the largest one among three algorithms. The enhancement in the total system throughput of this scheme is due to the fact that it scheduling NT users with the largest sum data rate utilizing partial CSI sufficiently, therefore, it increases the total throughput dramatically. Meanwhile, it is clear that the total throughput of SQS MAX is much smaller than the other two schemes. This is because the SQS MAX scheme schedules NT users with the largest sum queue size utilizing only QSI without
V. CONCLUSIONS In this paper, we propose a cross-layer scheduling and dynamic resource allocation (CLSDRA) scheme for downlink multiuser MIMO System with limited feedback. The objective of this scheme is to maximize the defined utility function under the constraint of total transmit power available at the BS based on the instantaneous partial CSI from PHY layer and the QSI from MAC layer. Our numerical results show that the proposed algorithm outperforms the conventional SDR Max scheme in the performance of packet drop rate and outperforms the existing SQS MAX scheme in the performance of total system throughput. In a word, the proposed CLSDRA scheme is capable of providing better performance which balances the total throughput and the packet drop rate. REFERENCES [1]
R. Berezdivin, R. Breinig et al., “ Next-generation wireless communications concepts and technologies”, IEEE Communication Magazine, No.3, pp.108-116, 2002. [2] E. Telatar, “Capacity of multi-antenna Gaussian channels,” European Transactions on Telecommunication, Vol. 10, No. 6, pp. 585-595, 1999. [3] Q. H. Spencer, A.L. Swindlehurst, M. Haardt, “Zero-Forcing Methods for Downlink Spatial Multiplexing in Multiuser MIMO Channels,” IEEE Transactions on Signal Processing, Vol.52, No.2, February 2006, pp. 461-471. [4] K. B. Letaief, Y. J. Zhang, “Dynamic Multiuser Resource Allocation and Adaptation for Wireless Systems,” IEEE Wireless Communications, Vol.13, No.4, August 2006, pp. 38-47. [5] I. Koutsopoulos, L. Tassiulas, “Cross-layer Adaptive Techniques for Throughput Enhancement in Wireless OFDM-based Networks,” IEEE/ACM Transaction on networking, Vol.14, October 2006, pp. 1056-1066. [6] C. Antón-Haro, P. Svedman, M. Bengtsson, A. Alexiou, A. Gameiro, “Cross-Layer Scheduling for Multi-User MIMO Systems,” IEEE Communications Magazine, Vol.44, September 2006, pp.39-45. [7] V. K. N. Lau, “Optimal Downlink Space-Time Scheduling Design with Convex Utility Functions—Multiple-Antenna Systems With Orthogonal Spatial Multiplexing,” IEEE TRansactions on Vehicular Technology, Vol.54, No.4, July 2005, pp.1322-1333. [8] N. Riato, G. Primolevo, U. Spagnolini, T. Baudone, “A Crosslayer architecture for SDMA,” 15th IST Mobile & Wireless Communication Summit, June 2006, pp. 1-5. [9] M. Andrews, K. Kumaran, K. Ramanan, A. Stolyar, P. Whiting and R. Vijayakumar, “Providing quality of service over a shared wireless link,” IEEE Communications Magazine, Vol. 39, No. 2, February 2001, pp. 150-154. [10] M. Sharif and B. Hassibi, “On the capacity of MIMO broadcast channels with partial side information,” IEEE Transactions on Information Theory, Vol. 51, No. 2, pp. 506-522, Feb. 2005.
