Dynamic Resource Allocation for Downlink Multi-User MIMO-OFDMA

1 downloads 0 Views 317KB Size Report
Abstract—In this paper, new dynamic resource allocation algorithms are presented for the downlink of multi-user MIMO-. OFDMA/SDMA systems. Since it is ...
This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE ICC 2009 proceedings

Dynamic Resource Allocation for Downlink Multi-user MIMO-OFDMA/SDMA Systems Chongxian Zhong, Chunguo Li, Rui Zhao, Luxi Yang

Xiqi Gao

School of Information Science and Engineering Southeast University Nanjing, China

National Mobile Communications Research Lab. Southeast University Nanjing, China

Abstract—In this paper, new dynamic resource allocation algorithms are presented for the downlink of multi-user MIMOOFDMA/SDMA systems. Since it is difficult to obtain the optimal solution to the joint optimization problem, the whole procedure is divided into two steps, namely, the subcarrier-user scheduling and the resource allocation. In the first step, a new metric is proposed to measure the spatial compatibility of multiple users each with multiple receive antennas, based on which a new subcarrier-user scheduling algorithm is designed. In the second step, two dynamic resource allocation algorithms are developed to assign radio resources to the scheduled users accordingly. Simulation results demonstrate the superiority of the proposed algorithms in terms of the system throughput. Keywords-dynamic resource allocation (DRA); multiple-input multiple-output (MIMO); orthogonal frequency division multiple access (OFDMA); space division multiple access (SDMA)

I.

INTRODUCTION

Orthogonal frequency division multiple access (OFDMA) technique, which arises from orthogonal frequency division multiplexing (OFDM) and inherits its superiority of mitigating multipath fading, is capable of providing higher spectral efficiency by exploiting multi-user diversity [1]. Meanwhile, multiple-input multiple-output (MIMO) systems have attracted extensive attentions due to their promising gain in channel capacity without additional spectrum and transmit power. Particularly, space division multiple access (SDMA) technique provides substantial throughput gain by multiplexing multiple spatially separable users in the same time slot and frequency channel via beamforming or precoding techniques [2]. Moreover, dynamic resource allocation (DRA) technique has been identified as one of the most promising techniques which can achieve both higher spectral efficiency and better quality of service (QoS) [3]. However, the use of SDMA strategies complicates the resource allocation problem of OFDMA systems to a nondeterministic polynomial time complete (NP-complete) one. Although the DRA schemes proposed for OFDMA/SDMA systems in [4-7] achieved suboptimal solutions to their corresponding optimization problems, all of them were designed for single antenna terminals. When each user is equipped with multiple antennas, however, the optimization problem becomes much more complicated since the signal

space of each user has multiple dimensions. With respect to this issue, Chan et al. investigated the user scheduling and resource allocation in [8] using a zero-forcing (ZF) SDMA scheme from the viewpoint of maximizing the total system capacity without considering the constraints of the QoS requirement of each user and the modulation orders on each spatial subchannels. In this paper, we investigate the dynamic resource allocation problem for multi-user MIMO-OFDMA/SDMA downlink systems in a more realistic scenario. The objective is to maximize the total system throughput under the constraints of the transmit power available at the base station (BS), the QoS requirement of each user and the integer modulation orders available on each spatial subchannel. In order to solve such an NP-complete problem, we divide the whole optimization procedure into two steps, namely, the subcarrieruser scheduling and the resource allocation. The former identifies the optimal sets of selected users over all subcarriers, while the latter allocates radio resources to each scheduled user accordingly. II.

SYSTEM MODEL AND PROBLEM FORMULATION

We consider the downlink of a multi-user MIMO-OFDMA/ SDMA system with one BS and U mobile users, where the BS is equipped with NT transmit antennas and the uth user is equipped with N R receive antennas. The simplified system u

block diagram is depicted in Fig. 1. It is assumed that the perfect channel state information (CSI) is available at each receiver by appropriate channel estimation and can be fed back to the BS without error and delay. Suppose that there are N OFDM subcarriers in the system and the MIMO channel between BS and user u at subcarrier n is characterized by a N R × NT matrix H u , n . The channel u

matrix and the precoding matrix at subcarrier n are defined as H n = [H1,T n ... HTK , n ]T and M n = [M1 ... M K ] , respectively, where (⋅)T denotes the transpose and K denotes the number of selected users at subcarrier n . The received signal at subcarrier n is given by

This work was jointly supported by National Basic Research Program of China (2007CB310603); National Natural Science Foundation of China (60672093, 60496310); National High Technology Research and Development Program of China (2007AA01Z262).

978-1-4244-3435-0/09/$25.00 ©2009 IEEE

X n = H n M nd n + Wn

(1)

This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE ICC 2009 proceedings

User 1 dat a st r eam User 2 dat a st r eam

Subcar r i er - user scheduling

User U dat a st r eam

U user s’ Qos requirements

Pr ecoding on each subcar r i er

Ant enna 1

Power adaptations on each spatial subchannel

Adapt i ve modulators

Ant enna 2

OFDM transmitters

Ant enna NT

U user s’ CSI

Dynamic resource allocation algorithm

Figure 1. Simplified block diagram of downlink MIMO-OFDMA/SDMA system with dynamic resource allocation.

where d n and Wn denote the transmitted signal and the white Gaussian noise at subcarrier n , respectively. The received signal of user k at subcarrier n can be written as K

 d + W Xk ,n = H k ,n ∑ M l ,ndl ,n + Wk ,n = H k ,n M k ,nd k ,n + Η k ,n M k , n k ,n k ,n

(2)

l=1

where M k , n , d k , n and Wk , n denote the precoding matrix, the transmitted signal and the white Gaussian noise of user k at  subcarrier n , while M k , n = [M1, n ,... M k −1, n , M k +1, n ,..., M K ] and d k , n = [d1,T n ,..., dTk −1, n , dTk +1, n ,..., dTK , n ]T , respectively.

order to eliminate the interferences among multiple users. To satisfy this constraint, M k , n should lie in the null space of  = [H ,..., H H k ,n

T k −1, n

,H

T k +1, n

,..., H

T T K ,n

]

. Using singular value

decomposition (SVD) with the singular values arranged in descending order, H k , n can be decomposed as  =U  Σ   (1)  (0) H H k ,n k , n k , n [ Vk , n Vk , n ]

where pk , n,l and σ

2 k , n,l

(3)

where (⋅) H is the conjugate transpose, V k(1),n holds the first Lk , n

power on the lth spatial subchannel of user k at subcarrier n , respectively. The optimal value of pk , n,l can be obtained by spatial water-filling. If a square M-QAM modulation scheme with unitary mean energy is employed, the following equation holds approximately [9]. 1.5γ k , n,l ⎤ ⎡ bk , n,l = log 2 ⎢1 − (6) ⎥

holds the last NT − Lk , n RSVs. Since V

forms an orthogonal

basis for the null space of H k , n , its columns are candidates of

lth spatial subchannel of user k at subcarrier n . Considering the modulation orders available on each spatial subchannel, bk , n,l should be truncated as bk , n,l = trunc(bk , n,l ) ∈ {0, 2, 4,6,8}

corresponding to no bit transmission, QPSK, 16QAM, 64QAM, 256QAM, respectively. Therefore, letting BERkt arg et denote the target BER of user k , the optimization problem can be formulated as N

N

n =1 k =1 l =1

III.

After the above processing, the downlink system reduces to K parallel non-interfering single user MIMO channels at

each subcarrier, where the equivalent independent channel for user k at subcarrier n is H 'k , n = H k , n V k(0), n . Thus, the channel at subcarrier n is written as  (0) ⎡ H1, n V ⎤ 0 1, n ⎢ ⎥ ' % Hn = ⎢ ⎥  (0) ⎥ ⎢ 0 H V K ,n K ,n ⎦ ⎣

(4)

Using SVD, H 'k , n can be decomposed as H k' , n = U 'k , n Σ 'k , n Vk' H, n . The signal-to-noise ratio (SNR) of the lth spatial subchannel for user k at subcarrier n can be written as

K Lk ,n

R = max ∑∑∑ bk , n ,l

the precoding matrix M k , n , i.e., M k , n can be generally expressed as M k , n = V k(0), n .

ln(5 BERk ) ⎦

where BERk denotes the bit error rate (BER) of user k , bk , n,l denotes the number of bits per symbol allocated to the

 ) ) right singular vectors (RSVs) and V  (0) ( Lk , n = rank (H k ,n k ,n (0) k ,n

(5)

denote the transmit power and the noise



The ZF-based method requires H k , nM l , n = 0 for k ≠ l in

T 1, n

γ k , n,l = pk , n,l Σ 'k2, n,l σ k2, n ,l

⎧ ⎪ ⎪ s.t. ⎨ ⎪ ⎪⎩

K Lk ,n

∑∑∑ p

k , n,l

≤ PTotal

n =1 k =1 l =1

BERk ≤ BERkt arg et

(7)

bk , n,l ∈ {0, 2, 4,6,8}

DYNAMIC RESOURCE ALLOCATION FOR DOWNLINK MULTI-USER MIMO-OFDMA/SDMA SYSTEMS

Obviously, the optimization problem in (7) requires to address several issues, including user scheduling, precoding, power control and bit loading. In order to simplify it, we divide the whole optimization procedure into two steps, namely, the subcarrier-user scheduling and the resource allocation. A. Best-User-First Subcarrier-User Scheduling (BUF-SUS) Based on Distance between Truncated Signal Subspaces The critical task of developing an SDMA algorithm for OFDMA systems is to explore an effective metric to measure the spatial compatibility of multiple users at each subcarrier. Several metrics have been designed when each mobile terminal was equipped with single receive antenna [4-7].

This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE ICC 2009 proceedings

However, these metrics can not be applied directly in MIMOOFDMA/SDMA systems where each terminal is equipped multiple receive antennas. Here, we design a new effective metric according to the distance between two signal subspaces based on the idea that a good scheduler aims to schedule a user such that its row spaces are as close as possible to other users’ common nullspace. Hk ,n can be decomposed as Using SVD, (1) k ,n

H k , n = U k , n Σ k , n [V

(0) H k ,n

V ]

,

where

Lk , n ( Lk , n = rank (H k , n ) ) RSVs and V

(0) k ,n

(1) k ,n

V

holds the first

holds the last NT − Lk , n

RSVs. Similarly, H k , n is decomposed as (3). Let row(H k , n ) and null (H k , n ) denote the row space of H k , n and the nullspace of H k , n , respectively. Then, Vk(1),n forms an orthogonal basis of  (0) forms an orthogonal basis of null (H  ). row(H k , n ) and V k ,n k ,n

The distance between row(H k , n ) and null (H k , n ) is expected to be as small as possible to maximize the total throughput while suppressing interferences at subcarrier n . Since the distance between two subspaces can be measured by their orthogonal projection and moreover, Vk(1), n Vk(1), n H and V k(0), n V k(0), n H are the orthogonal

projection

onto

row(H k , n )

and

until ∑ k =1 Lk , n ≥ NT or D > ε , where ε is a threshold predetermined experimentally. The first inequality means that NT spatial subchannels have been filled completely and the second one means that all of the users to be inserted into subcarrier n are not spatial compatible with the selected users at this subcarrier. K

B. Dynamic resource allocation based on BUF-SUS scheme Even though the sets of users are fixed over all subcarriers, the complexity is prohibitively high to obtain the global solution of (7). Therefore, two fairly simple dynamic resource allocation algorithms are proposed based on the proposed BUF-SUS scheme. The first dynamic resource allocation algorithm (BUF-SUS DRA) solves (7) by allocating the total transmit power equally among N subcarriers and maximizing the throughput of each subcarrier independently. In this algorithm, three constraint conditions are considered including the maximum transmit power, the QoS requirement of each user and the modulation orders available on each spatial subchannel. For subcarrier n , the optimization problem can be formulated as Lk ,n

 ) null (H k ,n

Lk ,n

Rn = max ∑ ∑ bk , n,l

respectively, we define the distance between row(H k , n ) and

k ∈Sn l =1

 ) as null (H k ,n  )) = (V (1) ) (V (1) ) H − (V  (0) ) (V  (0) ) H D(row(H k , n ), null (H k ,n k ,n L k ,n L k ,n L k ,n L

F

(8)

where ⋅ F is the Frobenius norm operator, L = min( Lk , n , Lk , n ) ,  (0) ) select the first L singular vectors from V (1) (Vk(1),n ) L and (V k ,n L k ,n

and V k(0),n , respectively. If Lk , n = Lk , n , the definition in (8) is precise; otherwise, some error will be incurred from the truncation of signal subspace. However, the main information of signal subspaces is not lost since (Vk(1),n ) L and (V k(0),n ) L contain  ) , L largest singular values of row(H k , n ) and null (H k ,n

respectively. Therefore, the parameter D in (8) can be used as an effective metric to measure the spatial compatibility between multiple users scheduled at each subcarrier where each user is equipped with multiple receive antennas. Based on the proposed metric, we design a suboptimal subcarrier-user scheduling algorithm with low complexity. Generally speaking, in conventional multi-user single-input single-output (SISO)-OFDM systems, most of the resource allocation methods based on the criterion of maximizing total system throughput are inclined to schedule the user with the best channel state (called best user) at each subcarrier. Here, we extend this result to multi-user MIMO-OFDMA/SDMA systems and select the best user for each subcarrier during the initialization procedure, then schedule user k * sequentially which satisfies  )) k * = arg min D(row(H k , n ), null (H (9) k ,n k

⎧ ⎪ ⎪ s.t. ⎨ ⎪ ⎪⎩

∑∑p

k , n ,l

≤ Pn

k ∈S n l =1

BERk ≤ BERkt arg et

(10)

bk , n,l ∈ {0, 2, 4,6,8}

where Rn is the throughput at subcarrier n , S n is the set of the scheduled users at subcarrier n , and Pn = PTotal N . This optimization problem can be solved using the precoding strategy proposed in Section Ⅱ followed by corresponding power allocation and bit loading strategies. Solving the problem in (10) sequentially at each subcarrier, the total throughput can be obtained as R = ∑ n =1 Rn . N

In the second dynamic resource allocation algorithm (BUFSUS DRA with PR), the unused power caused by the truncation of bk , n,l at subcarrier n is accumulated and allocated to other subcarriers to be optimized [4]. Using (5) and (6), the needed power to transmit bk , n,l bits on spatial subchannel l for user k at subcarrier n is calculated as b

pk , n ,l =

(1 − 2 k ,n ,l ) ln(5 BERkt arg et ) . Thus, the unused power due to 1.5Σ 'k2, n ,l

the truncation of bk , n,l is Δpk , n ,l = pk , n,l − pk , n ,l . For subcarrier n , the optimization problem can be formulated as Lk ,n

Lk ,n

Rn = max ∑ ∑ bk , n ,l k ∈Sn l =1

⎧ ⎪ ⎪ s.t. ⎨ ⎪ ⎪⎩

∑∑p

k , n,l

≤ Pn + Pa

k ∈S n l =1

BERk ≤ BERkt arg et

(11)

bk , n,l ∈ {0, 2, 4,6,8}

where the new defined variable Pa is used to gather the accumulated unused power for the subcarriers computed

This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE ICC 2009 proceedings

previously to subcarrier n . Utilizing the power reuse strategy, the total throughput can be further improved with low complexity. IV.

SIMULATION RESULTS AND ANALYSIS

In this section, a simulation study of the proposed algorithms is undertaken, showing its superior performance in terms of the system throughput as compared to some of the existing methods. In our similations, we assume that all user terminals have the same number of receive antennas, i.e., N R = N R for ∀ u ∈ {1,2,...,U } and N R is a factor of NT . u

We also assume that the target BER of each user is 10−3 . Moreover, it is assumed that the number of OFDM subcarriers is N = 64 and all the 64 subcarriers contain useful information. The channel used in our simulations is a 7-tap channel with exponential power delay profile, 20MHz sampling frequency and 50ns rms delay spread. For comparison, the performances of the DRA methods based on random scheduling scheme (Random DRA) and the capacity maximization DRA method based on user selection (CM-US DRA) [8] are also included.

In Fig. 2, we investigate how the threshold ε affects the system throughput when two users are scheduled at each subcarrier. As shown in Fig. 2, the average throughput increases with the increase of ε , however, when ε exceeds a certain value, the throughput does not increase any more. The threshold ε is a measurement of spatial compatibility which is an important factor affects the throughput of each subcarrier. In order to select a suitable threshold ε , the tradeoff between the performance and the computational complexity should be considered. With a small threshold, more users are treated as highly correlated. Hence, fewer users can share the same subcarriers and the performance in terms of throughput is deteriorated, while the complexity is also decreased when joint ZF precoding, power adaptation and adptive bit loading are implemented since the number of scheduled users at each subcarrier is comparatively small. Likewise, with a large threshold, the throughput increases, while the computation complexity also increases correspondingly. Therefore, we set ε to be 0.5 in the following simulations according to the numerical results shown in Fig. 2. 16 Average throughput (bits/symbol/subcarrier)

Average throughput(bits/symbol/subcarrier)

2.8

2.6 NT=12,NR=6

2.4

2.2

NT=8,NR=4

2 NT=6,NR=3 1.8 NT=4,NR=2

1.6

1.4

12 10 8 6 4 2 0

0

0.2

0.4

0.6

0.8

CM-US DRA BUF-SUS DRA with QoS BUF-SUS DRA with AM BUF-SUS DRA with QoS and AM Random DRA with AM Random DRA with QoS Random DRA with QoS and AM

14

1

0

5

Threshold

20

15

20

25 Average throughput (bits/symbol/subcarrier)

12 Average throughput(bits/symbol/subcarrier)

15

(a) NT = 2

(a) SNR = 0 dB

11 NT=12,NR=6 10 9 NT=8,NR=4 8 NT=6,NR=3

7 6

NT=4,NR=2 5 4

10 Average SNR (dB)

20

15

10

5

0 0

0.2

0.4

0.6

0.8

1

Threshold

(b) SNR = 10 dB Figure 2. Average throughput vs. threshold ε when two users are scheduled at each subcarrier.

CM-US DRA BUF-SUS DRA with QoS BUF-SUS DRA with AM BUF-SUS DRA with QoS and AM Random DRA with AM Random DRA with QoS Random DRA with QoS and AM

0

5

10 Average SNR (dB)

(b) NT = 4 Figure 3. Average throughput vs. average SNR with N R = 2 , U = 20 and different NT .

This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE ICC 2009 proceedings

[4]

[5]

[6]

[7]

[8]

[9]

K. B. Letaief, Y. J. Zhang, “Dynamic multi-user resource allocation and adaptation for wireless systems,” IEEE Wireless Communications, vol.13, no.4, pp. 38-47, Aug. 2006. D. Bartolome, A. I. Perez-Neira, “Practical implementation of bit loading schemes for multiantenna multi-user wireless OFDM systems,” IEEE Trans on Commun., vol.55, no.8, pp. 1577-1587, Aug. 2007. I. Koutsopoulos, L. Tassiulas, “Adaptive resource allocation in SDMAbased wireless broadband networking with OFDM signaling,” Proceeding of IEEE INFOCOM, vol.3, pp.1376-1385, Jun. 2002. S. Thoen, L. V. Perre, M. Engels, H. D. Man, “Adaptive loading for OFDM/SDMA based wireless networks,” IEEE Trans. on Commun, vol.50. no.11, pp. 1798-1810, Nov.2002. C. F. Tsai, C. J. Chang, F. C. Ren, C. M. Yen, “Adaptive radio resource allocation for downlink OFDMA/SDMA systems,” In Proc. ICC, pp. 5683-5688, Jun. 24-28, 2007. P. W. C. Chan, R. S. Cheng, “Capacity maximization for zero-forcing MIMO-OFDMA downlink systems with multi-user diversity,” IEEE Trans. Wireless Commun., vol.6, no.5, pp. 1880-1889, May 2007. A. J. Goldsmith, S. G. Chua, “Variable-rate variable-power MQAM for fading channels,” IEEE Trans. Commun., vol.45, no.10, pp.12181230,Oct.1997. 25

15

REFERENCES

10

5

0

5

10 Average SNR (dB)

C. Y. Wong, R. S. Cheng, K. B. Letaief, R. D. Murch, “Multi-user OFDM with adaptive subcarrier, bit, and power allocation,” IEEE Journal on Selected Areas in Communications, vol.17, pp. 1747-1758, Oct. 1999. Q. H. Spencer, A.L. Swindlehurst, M. Haardt, “Zero-forcing methods for downlink spatial multiplexing in multi-user MIMO channels,” IEEE Trans. Sig. Proces. vol.52, no.2, pp. 461-471, Feb. 2004.

15

20

15

20

(a) NT = 4 40 CM-US DRA BUF-SUS DRA BUF-SUS DRA BUF-SUS DRA BUF-SUS DRA BUF-SUS DRA BUF-SUS DRA

35 30 25

with QoS with AM with QoS and AM with QoS+PR with AM+PR with QoS and AM+PR

20 15 10 5 0

[2]

with QoS with AM with QoS and AM with QoS+PR with AM+PR with QoS and AM+PR

CONCLUSIONS

In this paper, we have proposed a new metric to measure the spatial compatibility of multiple users each with multiple receive antennas, based on which the BUF-SUS algorithm is developed. Then, we have presented two fairly simple dynamic resource allocation algorithms to assign radio resources to the scheduled users accordingly. Simulation results have shown that the proposed algorithms outperform conventional methods. Particularly, the performance of the algorithm combined with power reuse strategy approaches closely to that of the optimal method based on user selection.

[1]

CM-US DRA BUF-SUS DRA BUF-SUS DRA BUF-SUS DRA BUF-SUS DRA BUF-SUS DRA BUF-SUS DRA

20

0

Average throughput (bits/symbol/subcarrier)

V.

[3]

Average throughput (bits/symbol/subcarrier)

Fig. 3 shows the average throughput achieved by different DRA algorithms without considering power reuse. It can be observed that the CM-US DRA algorithm outperforms its counterparts. This is because this algorithm selects the optimal sets of users over all subcarriers using convex optimization methods. Furthermore, it does not consider the QoS requirement of each user and the modulation orders available on each spatial subchannel. It also can be seen that our proposed BUF-SUS DRA algorithm outperforms Random DRA in all cases. This is because BUF-SUS DRA can exploit channel subspace information of each user. Utilizing the proposed metric in (8), this algorithm increases the spatial compatibility between scheduled users at each subcarrier and reduces the co-channel interference (CCI). While Random DRA algorithm schedules K users from U system users at each subcarrier randomly without considering the spatial compatibility, and thus it might lead to high CCI among scheduled users and deteriorate the throughput performance correspondingly. In Fig. 4, we investigate the effect of power reuse strategy on the performance of our proposed BUF-SUS DRA algorithm. It can be observed that, due to the utilization of power reuse strategy, the average throughput is improved in all cases. Especially, when adaptive modulation is considered only, the performance of our proposed BUF-SUS DRA with power reuse approaches closely to the CM-US DRA algorithm proposed in [8]. Fig. 4 also shows that more performance enhancement can be obtained with increasing NT . This is because an increasing number of transmit antennas provide a larger number of independent spatial subchannels, and thus more transmit power can be accumulated at each subcarrier and allocated to other subcarriers to be optimized.

0

5

10 Average SNR (dB)

(b) NT = 8 Figure 4. Average throughput vs. average SNR with N R = 2 , U = 20 and different NT considering power reuse strategy.