2014 International Conference on Computing, Networking and Communications, Wireless Communications Symposium
Distributed Framework of Downlink CoMP MU-MIMO Transmission with Adaptive Mode Switch and Power Allocation Zhiyuan Zong, Hui Feng, Tao Yang, and Bo Hu Department of Electronics Engineering Fudan University Shanghai, China, 200433 Email:
[email protected], {hfeng, taoyang, bohu}@fudan.edu.cn Abstract—The multiuser multiple input multiple output (MUMIMO) technique has been under active consideration in recent years to increase the capacity of modern wireless system. Meanwhile, the coordinated multipoint (CoMP) transmission/reception technique is adopted to mitigate the inter-cell interference (ICI) and enhance the performance of cell edge users. Hence, the CoMP technique can be applied jointly with the MU-MIMO technique (called CoMP MU-MIMO). However, in previous works, only edge users are concerned in precoding design, which causes the severe interference between edge users and center users. In this paper, a novel framework of downlink CoMP MU-MIMO transmission is proposed, which considers the joint optimization for the performance of edge users and center users in a distributed manner. In this framework, to decouple this joint optimization problem, the signal-to-leakage-plus-noise ratio (SLNR) criterion is employed. Then a channel-adaptive CoMP mode switching mechanism is established for the edge user to provide the Quality of Service (QoS). Moreover, to balance the effects of Rayleigh fading on different users, a channel-adaptive power allocation mechanism is also framed. With the total transmission power restrained, this framework can achieve a better tradeoff between edge users and center users than conventional joint transmission (JT) and coordinated beamforming (CB) methods, and result in the higher channel capacity with less inter-cell interactions. Keywords—Coordinated multipoint (CoMP); MU-MIMO; signal-to-leakage-plus-noise ratio (SLNR); mode switch; power allocation.
I.
I NTRODUCTION
In the standardizations of 3rd Generation Partnership Project (3GPP) Long-Term Evolution (LTE), multiuser multiple input multiple output (MU-MIMO) is considered as a key technique for the increase of system capacity and spectrum efficiency. In cellular MU-MIMO systems, multiple users in the same cell can communicate with their eNodeB simultaneously at the same time-frequency resource block (RB) [1]. However, without the coordination among adjacent cells, the performance of cell edge users is degenerated by the inter-cell interference (ICI). To mitigate the effects of ICI, coordinated multipoint (CoMP) transmission/reception has been adopted in 3GPP LTE-Advanced specifications, which can further increase the system capacity and improve the edge users’ performance [2]. The benefits of CoMP stem from the coordinations among several distributed macro eNodeBs [3] or in the single eNodeB
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with several remote radio equipments (RREs) [2]. Obviously, if multiple endusers equipped with multiple antennas are served in the CoMP system, the MU-MIMO technique can be applied simultaneously, which is called CoMP MU-MIMO [4]. Furthermore, the CoMP MU-MIMO transmission prefers to be implemented in a distributed manner. That is, each eNodeB can design precoding matrices for all users independently, and no channel state information (CSI) is exchanged among these eNodeBs. Hence, the whole CoMP MU-MIMO system can be decomposed into several conventional MU-MIMO sub-systems managed by corresponding eNodeBs independently. Many precoding schemes have been designed for this distributed CoMP MU-MIMO transmission system [5]–[7]. However, to the best of our knowledge, only edge users are concerned in the literature about CoMP MU-MIMO transmission (distributed or centralized) [2], [4]–[7]. Actually, in practical cellular communication scenarios, edge users and center users usually co-exist, and thus their performance should be considered jointly. Otherwise, even though the inter-user interference (IUI) among all edge users has been suppressed, the IUI still exists between edge users and center users. This leads to the performance degradation of all users. For this reason, a novel distributed framework of downlink CoMP MU-MIMO transmission is proposed in this paper, whose crucial characteristics are listed as follows. •
The CoMP MU-MIMO transmission is implemented in a distributed manner as [5]–[7]. And the edge user, whose Quality of Service (QoS) is not satisfied, can ask for the CoMP transmission from its adjacent eNodeBs; while the center user can only be served by its corresponding (serving) eNodeB.
•
In a certain MU-MIMO sub-system, the performance of edge users and center users are jointly optimized by the signal-to-leakage-plus-noise ratio (SLNR) criterion, which has the decoupled and simple nature with closed form solutions.
•
A channel-adaptive CoMP mode switching mechanism is established in this framework. There are mainly two modes for downlink CoMP transmission in previous works, which are joint transmission (JT) and coordinated beamforming (CB) [2], [3]. Compared
2014 International Conference on Computing, Networking and Communications, Wireless Communications Symposium
with the CB mode, the JT mode can obtain higher performance gain at the cost of more feedback and coordination overhead among cooperating eNodeBs. Therefore, according to different channel conditions of different edge users (with the poor QoS) at the different time, SLNR based JT and CB modes should be switched adaptively. •
A channel-adaptive power allocation mechanism for edge users and center users is established. Due to their different distances away from the base station, this mechanism is required to balance the effects of Rayleigh fading on their performance.
Simulation results show that this framework can outperform other CoMP methods in terms of average system channel capacity and symbol error rate (SER) performance. The rest of this paper is organized as follows. Section II describes the proposed framework of downlink CoMP MUMIMO transmission, which optimizes the performance of edge users and center users jointly in a distributed manner. To decouple this joint optimization problem, Section III will review the SLNR criterion briefly, and then extend it to two conventional CoMP transmission modes (JT and CB). In Section IV, adaptive mode switch and power allocation mechanisms are established to improve the performance. Section V presents simulation results and the last section draws some conclusions. II.
Different from other distributed implementations of CoMP MU-MIMO transmission [5]–[7], which only concern the performance of edge users, a novel distributed framework is proposed here. In this framework, the performance of edge users and center users is considered jointly, from a practical point of view. In such a way, each adjacent cell in Fig. 1 is equivalent to a two-user MIMO sub-system (in the circle marked with yellow-dashed lines), with its corresponding center user and the edge user. In each sub-system, the performance of these two users is optimized jointly. For convenience, we assume that all base stations employ L transmit antennas and all users are equipped with K receive antennas. To mitigate the IUI, the precoding technique from conventional MU-MIMO systems can be utilized within these local two-user MIMO sub-systems. Fig. 2 depicts the block diagram of this proposed framework, where the leaking interference from eNodeB0 to all center users is ignorable because their distances are far enough. In addition, both JT mode and CB mode are involved in this block diagram, which will be further discussed in the next section.
D ISTRIBUTED F RAMEWORK OF D OWNLINK C O MP MU-MIMO T RANSMISSION
Consider a downlink CoMP MU-MIMO transmission instance for an edge user, there are one main cell (eNodeB0 ) and multiple coordinated cells (CeNodeBj , j=1,2,...,M, M is the total number of these adjacent cells). Without loss of generality, we assume that eNodeB0 serves the edge user equipment UE0 and each CeNodeBj serves its corresponding center user equipment UEj , at the current RB (frequency reuse factor is 1). As shown in Fig. 1, the edge user (whose QoS is not satisfied) is under CoMP transmission (JT or CB) from its adjacent cells connected by X2 interface [2] or optical fiber without significant delay.
Fig. 1.
The performance gain comes from the signal combining and ICI nulling. In CB mode, the data is transmitted by only one eNodeB, while the ICI is reduced through coordinated beamforming. Therefore, JT mode makes use of the ICI while CB mode avoids it.
Distributed framework of downlink CoMP MU-MIMO transmission
These two CoMP transmission modes have their own features. In JT mode, the transmitted data of the CoMP user is shared among multiple eNodeBs for joint transmission.
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Fig. 2. Block diagram of general downlink CoMP MU-MIMO transmission
In Fig. 2, Hjj ∈ CK×L (j = 0, 1, ..., M ) denotes the channel from each base station to its corresponding user, and Hj0 ∈ CK×L (j = 1, 2, ..., M ) is the channel from each adjacent CeNodeBj to the edge user. All these channels are spatially uncorrelated flat Rayleigh fading (full rank). Each element hmn (m = 1, 2, ..., K, n = 1, 2, ..., L) of these channel matrices represents the channel coefficient from the nth transmit antenna to the mth receive antenna. Besides, these elements are independent and identically distributed (i.i.d), modeled as zero-mean complex Gaussian variables with unitvariance (or αj2 -variance) for Hjj (or Hj0 ). Here, due to the longer distance from CeNodeBj to UE0 than to UEj , αj is defined as the attenuation factor in the jth adjacent cell. Assume that these CSI are available at the local base station, correspondingly, but are not shared globally [8]–[10]. Furthermore, sj ∈ Cs×1 (s K, j = 0, 1, ..., M ) is the transmitted symbol vector of UEj , where s is the number of data streams equal for all users. The symbol vector has its constraint: E(sj sH j ) = Is , where Is is the s × s identity matrix. Before being broadcasted over the channel, each symbol vector sj should be multiplied by a precoding matrix. Let
2014 International Conference on Computing, Networking and Communications, Wireless Communications Symposium
Wjj ∈ CL×s (j = 1, 2, ..., M ) and Wj0 ∈ CL×s (j = 0, 1, ..., M ) be the precoding matrices for center users and the edge user UE0 , respectively. Thus, from Fig. 2, the received signal of size K × 1 at the edge user is obtained as r0 = H00 W00 s0 +
M j=1
Hj0 Wj0 s0 +
M
Hj0 Wjj sj +n0 , (1)
j=1
where the first two terms are intended signals for UE0 , the third term is the IUI, and n0 is the additive white Gaussian 2 noise (AWGN) with E(n0 nH 0 ) = σ IK . And similarly, the received signal at the center user UEj is rj = Hjj Wjj sj + Hjj Wj0 s0 + nj , j = 1, 2, ..., M.
(2)
where the first term is its intended signal, the second term is 2 the IUI, and the last is AWGN with E(nj nH j ) = σ IK . Note that for notational simplicity, the time index is dropped. III.
SLNR BASED J OINT O PTIMIZATION
The objective of our framework is to optimize the performance of edge users and center users jointly. From Fig. 1 and Fig. 2, we can see that if JT mode is chosen, the CoMP MU-MIMO transmission is decomposed into several two-user MIMO sub-systems, constituted by its corresponding center user and the edge user. Therefore, this global objective can be approximatively realized by the local objective of each sub-system, which only optimizes the performance of its own center user and the edge user jointly. Within each two-user sub-system, the precoding technique from conventional MU-MIMO systems can be utilized to mitigate the IUI. Generally, the signal-to-interference-plusnoise ratio (SINR) is the optimization criterion to design precoding matrices for all users. However, this SINR criterion has its coupled and complex nature, resulting in no closed form solutions. To avoid this problem, zero-forcing (ZF) based precoding methods are widely used. But they require the number of antennas at the base station to be larger than the sum of antennas of all users, which is of no practical use. For these reasons, the SLNR criterion was proposed [9], which is defined as the ratio of the received signal power at the intended user to the received (leaking) signal power at other users plus the noise power. It can decouple the joint optimization problem of the SINR criterion and has closed-form solutions. Moreover, the antenna configuration problem imposed on ZF is solved. Accordingly, we apply the SLNR criterion to design precoding matrices in each sub-system. Taking the sub-system with CeNodeBj for example, there are two SLNR metrics to be optimized, for UEj and UE0 , respectively: H H Tr Wjj Hjj Hjj Wjj , (3) SLNRjj = H Tr Wjj Kσ 2 IL /Pjj + HH j0 Hj0 Wjj H H Hj0 Hj0 Wj0 Tr Wj0 , (4) SLNRj0 = H Tr Wj0 Kσ 2 IL /Pj0 + HH jj Hjj Wj0 where Tr(·) is the trace of a matrix, Pjj and Pj0 are the transmitted signal power of UEj and UE0 , respectively. They are allocated by CeNodeBj with the constraint condition: Pjj +Pj0 = Pj , where Pj is the maximum transmission power
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of CeNodeBj . Thus, the decoupled joint optimization problem for SLNR based JT mode is opt opt {SLNRjj , SLNRj0 } , = arg max Wjj , Wj0 Wjj ,Wj0 ∈CL×s ⎧ H ⎪ ⎨ Tr Wjj Wjj = Pjj , H s.t. Tr Wj0 Wj0 = Pj0 , ⎪ ⎩ Pjj + Pj0 = Pj . (5) H 2 Since HH jj Hjj and Hj0 Hj0 are Hermitian, (Kσ IL /Pjj + 2 H and (Kσ IL /Pj0 + Hjj Hjj ) are Hermitian and positive definite, the generalized eigenvalue decomposition (GED) method is enforced to solve this problem, detailed in [9]. In cellular MU-MIMO scenarios [8]–[10], the power is equally allocated among users in the same cell. However, in this multicell CoMP scenario, this equal power allocation is not efficient. A simple but efficient power allocation mechanism, based on these SLNR metrics, is established in next section.
HH j0 Hj0 )
From (5), if the power Pj0 is zero, it implies that no symbol of UE0 is jointly transmitted. Then, we can derive the joint optimization problem for SLNR based CB mode, which is simplified from JT mode in (5), as opt = arg max SLNRjj , Wjj Wjj ∈CL×s H s.t. Tr Wjj Wjj = Pj .
(6)
Furthermore, when neither JT mode nor CB mode CoMP transmission is implemented, the SNR metrics for UEj can be defined in (7) and the optimization problem for SNR based no CoMP transmission is represented in (8), which is also the conventional single-user beamforming problem [8]: H H Hjj Hjj Wjj Tr Wjj , (7) SNRjj = H Tr Wjj (Kσ 2 IL /Pjj ) Wjj opt SNRjj , Wjj = arg max Wjj ∈CL×s (8) H s.t. Tr Wjj Wjj = Pj . IV.
A DAPTIVE M ODE S WITCH AND P OWER A LLOCATION
In Section III, SLNR based JT and CB CoMP transmission modes are set up for each two-user MIMO sub-system in our distributed framework. Nevertheless, there are still two practical problems to be solved, which are derived from the multicell coordinating nature of CoMP transmission. In general, compared with CB mode, JT mode can achieve a more remarkable performance gain at the cost of more interaction overhead among coordinated cells. So, to make a tradeoff between performance and overhead, a mode switching mechanism is required. Besides, due to their (center user and edge user) different distances away from the base station, the Rayleigh fading channel can have different effects on them. Thus, a channel-adaptive power allocation mechanism is also needed. Both these problems are crucial for further improving the performance of the joint optimization in Section III. With these mechanisms, the whole flow of our proposed CoMP MU-MIMO framework is described in Fig. 3. At the beginning, if the edge user is not satisfied with its QoS, it will
2014 International Conference on Computing, Networking and Communications, Wireless Communications Symposium
ask for the CoMP transmission from its adjacent cells and feed back its CSI. Then, in each two-user sub-system, with the perfect local CSI, the mode switch is executed. Reconsider the CeNodeBj , from (3) to (5), we can see that its maximum SLNRjj and SLNRj0 vary with different power allocating results. And in principle, the more power an user is allocated, the larger its SLNR will be. Therefore, the upper bounds of them can be defined in (9) and (10), respectively, where the total power of CeNodeBj is allocated to its center user or the edge user. And these definitions can loose the power allocation problem from this mode switch problem. sup {max SLNRjj } max SLNRjj Pjj =Pj Pjj ∈[0,Pj ]
H H Hjj Hjj Wjj Tr Wjj , = max H Kσ 2 I /P + HH H Tr Wjj L j j0 j0 Wjj sup {max SLNRj0 } max SLNRj0 Pj0 =Pj
(9)
Pj0 ∈[0,Pj ]
H H Hj0 Hj0 Wj0 Tr Wj0 H . = max Tr Wj0 Kσ 2 IL /Pj + HH jj Hjj Wj0
(10)
From the beamforming viewpoint, the SLNR metrics measures the directionality of the transmitted signal of the intended user, which also weighs the IUI degree this user will lead to. Thus, with this metrics, CeNodeBj can consider the IUI degree increased by JT mode transmission. If JT mode causes the severe IUI, CeNodeBj should be switched to CB mode, which can also reduce the inter-cell overhead. For this reason, under the best power circumstances, the relationship of these SLNR upper bounds in (9) and (10) can reflect the ability of CeNodeBj to participate in JT mode CoMP transmission. That is, then if sup {max SLNRj0 }/sup {max SLNRjj } φj , CeNodeBj executes the SLNR based JT mode in (5); otherwise, execute the SLNR based CB mode in (6). Here, φj is the switching ratio threshold of CeNodeBj , and restricts the relative size of these upper bounds for different CoMP modes. Besides, it can be verified that this ratio threshold is robust to systems with different antenna configurations (experiment results will be given in our another paper). From Fig. 3, if CB mode is chosen, the optimization problem in (6) will be solved by the GED method [9] to obtain the optimal precoding matrix for its center user; if not, the optimization problem in (5) should be solved to obtain two optimal precoding matrices for its center user and the edge user, respectively. However, in this JT mode, prior to utilizing the GED method to solve (5), the power allocation between these two users should be accomplished. Again, the upper bounds defined in (9) and (10) can be employed to make a channel-adaptive power allocation: H H ) + Tr(Wjj Wjj ) = Pj Tr(Wj0 Wj0 , (11) H H Tr(Wj0 Wj0 ) = γj Tr(Wjj Wjj ) where γj = min {sup {max SLNRjj }/sup {max SLNRj0 }, 1} denotes the willingness factor of CeNodeBj to share its power for JT transmission. Obviously, γj 1 means the willingness of CeNodeBj to serve this edge user is not greater than to serve
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Fig. 3. Framework of the downlink CoMP MU-MIMO transmission with adaptive mode switch and power allocation
its own center user. Note that if the leaking interference is ignorable after precoding, this simple mechanism can efficiently balance the effects of channel fading on these users. Therefore, the optimization problem for JT mode in (5) can be divided into two sub-problems: adaptive power allocation and obtaining optimal precoding matrices by the GED method. The last step of JT mode CoMP transmission is to request the transmitted data of the edge user from its service eNodeB0 . V.
S IMULATION R ESULTS
In this section, the performance of the proposed CoMP MU-MIMO transmission framework with adaptive mode switch and power allocation (called MS-PA) is evaluated. We compare this scheme with the SLNR based JT mode with equal power allocation (called JT) in (5), the SLNR based CB mode (CB) in (6), and no CoMP transmission (NC) in (8). The MIMO channel is with L = 4, 6 transmit antennas and K = 1 receive antenna, as described in Section II. For M = 3 adjacent cells, the attenuation factor αj (j = 1, 2, 3) of the channel to the edge user is uniformly distributed on the interval (0,1). For the main cell, the attenuation factor is set to be 0.3 for asking for the CoMP transmission by this edge user (due to its poor QoS). The switching threshold is 0.5 for all adjacent cells. All these simulations are conducted by employing a QPSK modulation with Gray mapping and the results are averaged over 105 channel realizations. Moreover, ZF receivers are utilized.
2014 International Conference on Computing, Networking and Communications, Wireless Communications Symposium
Fig. 4 plots the average system capacity versus P/σ 2 curves in different distributed CoMP transmission systems with different number of transmit antennas, where P is the maximum transmission power equal for all base stations, and the Shannon channel capacity is calculated and accumulated for the whole system. To better understand the behavior of this framework, the SER curves of the center user and the edge user are depicted in Fig. 5 (a) and (b), respectively.
Cave/B [bit/s/Hz]
L=6
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NC(L=4) JT(L=4) CB(L=4) MS−PA(L=4) NC(L=6) JT(L=6) CB(L=6) MS−PA(L=6)
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Average channel capacity in different CoMP transmission systems
It can be seen from Fig. 4 that, for both cases (L = 4, 6), the average system channel capacity of MS-PA exceeds those of other CoMP transmission systems, especially when P/σ 2 is high. Specifically, CB can hold almost the same channel capacity with NC when L = 4, but outperform it when L = 6. In addition, in the low SNR region, JT markedly decreases the channel capacity, which is mainly due to its severe IUI. 0
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(a) SER of Center User Fig. 5.
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VI.
C ONCLUSION
In this paper, we have investigated the problem of downlink CoMP MU-MIMO transmission, which combines the CoMP technique with the MU-MIMO technique. In view of the joint optimization of the performance of edge users and center users, a distributed framework of downlink CoMP MU-MIMO transmission is proposed. In this framework, the SLNR criterion is applied to decouple this joint optimization problem. To reduce the overhead of inter-cell interactions and balance the effects of Rayleigh fading, a channel-adaptive CoMP mode switching mechanism and a power allocation mechanism are established, respectively. Simulation results verify that this framework outperforms other CoMP methods in terms of the channel capacity, the demand of inter-cell interactions and the performance tradeoff between the edge user and the center user. It is clear that this framework can be extended to the scenario with multiple edge users and center users easily. In our future works, following this framework, the resource allocation and scheduling strategies will be researched. ACKNOWLEDGMENT
P/σ2 [dB]
Fig. 4.
when the total transmission power is restrained. Clearly, more transmit antennas provide more transmit diversity gains.
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(b) SER of Edge User
SER curves in different CoMP transmission systems
From Fig. 5, MS-PA is still efficient. Compared with NC, although MS-PA degenerates the SER performance of the center user, its improvement in that of the edge user is remarkable. Furthermore, this degeneration mainly results from the fact that if JT mode is chosen, the transmission power of the center user will be nearly halved. The degeneration caused by the IUI is much less in this MS-PA than JT. Besides, MS-PA demands less inter-cell interaction than JT, and makes a better performance tradeoff between these two users than JT and CB,
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This work was supported in part by the NSTMP of China (Grant Nos. 2012ZX03001007-003 and 2013ZX03003006003) and the Ph.D. Programs Foundation of Ministry of Education of China (Grant No. 20120071110028). R EFERENCES [1] K. Zu and R. de Lamare, “Low-complexity lattice reduction-aided regularized block diagonalization for MU-MIMO systems,” IEEE Commun. Lett., vol. 16, no. 6, pp. 925–928, Jun. 2012. [2] M. Sawahashi, Y. Kishiyama, A. Morimoto, D. Nishikawa, and M. Tanno, “Coordinated multipoint transmission/reception techniques for LTEadvanced [Coordinated and Distributed MIMO],” IEEE Wireless Commun., vol. 17, no. 3, pp. 26–34, Jun. 2010. [3] C. Mueller, “When CoMP is beneficial- And when it is not. Selective coordination from a spectral efficiency and a users’ throughput perspective,” in Proc. IEEE WCNC’12, Apr. 2012, pp. 1578–1583. [4] C. Wang, Q. Cui, S. Li, X. Tao, and X. Xu, “Multiuser pairing in uplink CoMP MU-MIMO systems using particle swarm optimization,” in Proc. IEEE VTC’11, Sept. 2011, pp. 1–5. [5] D. Xu and P. Ren, “Inter-user interference suppression precoding based on SLNR for multi-user joint transmission in coordinated multi-point system,” in Proc. IEEE PIMRC’12, Sept. 2012, pp. 1829–1834. [6] E. Bjornson, R. Zakhour, D. Gesbert, and B. Ottersten, “Cooperative multicell precoding: Rate region characterization and distributed strategies with instantaneous and statistical CSI,” IEEE Trans. Signal Proces., vol. 58, no. 8, pp. 4298–4310, Aug. 2010. [7] C. Shen, T.-H. Chang, K.-Y. Wang, Z. Qiu, and C.-Y. Chi, “Distributed robust multicell coordinated beamforming with imperfect CSI: An ADMM approach,” IEEE Trans. Signal Proces., vol. 60, no. 6, pp. 2988–3003, Jun. 2012. [8] A. Tarighat, M. Sadek, and A. Sayed, “A multi-user beamforming scheme for downlink MIMO channels based on maximizing signalto-leakage ratios,” in Proc. IEEE ICASSP’05, vol. 3, Mar. 2005, pp. iii/1129–iii/1132. [9] M. Sadek, A. Tarighat, and A. Sayed, “A leakage-based precoding scheme for downlink multi-user MIMO channels,” IEEE Trans. Wireless Commun., vol. 6, no. 5, pp. 1711–1721, May 2007. [10] M. Sadek and S. Aissa, “Leakage based precoding for multi-user MIMO-OFDM systems,” IEEE Trans. Wireless Commun., vol. 10, no. 8, pp. 2428–2433, Aug. 2011.
