Communications and Network, 2013, 5, 1519 doi:10.4236/cn.2013.52B003 Published Online May 2013 (http://www.scirp.org/journal/cn) Optimal Power Allocation Scheme for Downlink CoMP Systems Jun Li1, Han Hai1, Ying Guo2, Moon Ho Lee1 1Department of Electronic and Information Engineering, Chonbuk National University, Jeonju, Korea 2School of Information Science & Engineering Central South University, Changsha, China Email: lijun52018@jbnu.ac.kr, hhhtgy@jbnu.ac.kr, yingguo@mail.csu.edu.cn, moonho@jbnu.ac.kr Received 2013 ABSTRACT Coordinated multipoint transmission and reception (CoMP) scheme enable LTEAdvanced systems to achieve their higher spectral efficiency. Allowing base stations to cooperate one another is one of the solutions to mitigate the inter cell interference (ICI). In this paper, we propose an iterative power allocation scheme with MMSE procoding based on a modified waterfilling for downlink CoMP systems, which achieves the optimal performance. The simulation results show that our proposed system can achieve its optimal rate according to its antenna configuration. Comparing them with a block diagonalization (BD) shows the advantages of MMSE precoding, in particular at a low SNR region. Keywords: CoMP; Precoding; Power Allocation; Waterfilling 1. Introduction Coordinated multipoint transmission and reception (CoMP) scheme has been widely used for LTEAdvanced system to enhance cell average and cell edge throughput. Accord ing to a coordinating fashion, CoMP scheme is classified into two strategies [1]: Joint processing (JP) and coordi nated scheduing/beamforming (CS/CB). In the JP strategy as shown in Figure 1, each user equipment (UE) simul taneously receives data from multiple base stations (BSs) with joint multiuser precoding, which is required to share both user data and channel state information (CSI) between base stations (BSs) and user equipments (UEs). Stemming from that, this JP strategy could be used to contribute to not only improving the strength of the receive signal but also cancelling interference. However, it is re quired to exchange the significant amount of data among links participating in its coordination. Besides, substan tial overheads should be taken into account in the network. Compared with JP, CS/CB can avoid intercell inter ference (ICI) by applying precoding to each BS on an in dividual basis, which is required to share only CSI without holding user data in common. As depicted in Figure 2, the solid lines denote the desired signals and the dashed lines denote the interference from other BSs locating in other cells. Since sharing CSI requires much lower ca pacity than sharing data [2], CS/CB needs much lower backhaul capacity than JP. A lot of studies have been done on CS/CB [35]. However, an effective algorithm to eliminate the interference for downlink CoMP and network MIMO is still not sufficient. If the interference is known at the transmitters, cooperative encoding using dirty paper coding (DPC) could mitigate the intercell interference (ICI) [6]. Apart from DPC, a zeroforcing (ZF) scheme based on block diagonalization (BD) is proposed in [7]. In [8], BD is applied to a multicell scenario with an ICI reduction scheme. However, as pointed out in [9], per formance of BD is suboptimal at a low SNR. In this paper, we use the MMSE precoding to compensate the noise with the interference, with the goal of maximizing the weighted sum rate (WSR). BS 1BS 2 BS 3 UE 3 UE 1UE 2 Figure 1. Joint processing (JP). Copyright © 2013 SciRes. CN
J. Li ET AL. 16 BS 1BS 2 BS 3 UE 3 UE 1UE 2 Figure 2. Coordinated scheding/bea mfor ming (CS/CB A solution to maximizing the WSR is proposed in [10] on s organized as follows. In Section 2, we sh 2. System Model e cluster which is comprised of ). the condition that each UE is equipped with a single antenna and the precoding matrix is chosen in order to maximize the signalnoiseplusinterference ratios (SINR) for each user. Aside from this, a power allocation scheme is also proposed. In [11], noniterative waterfilling scheme is proposed to solve the problem occurring when applying BD. This paper i ow a proposed system model. In Section 3, we over view conventional power allocation schemes and propose a modified optimal power selection scheme. In Section 4, we show that our proposed system outperforms conven tional systems using computer simulation. In Section 5, we come to some conclusions. Consider a cooperativ both N BSs and N UEs on the condition that each BS is equipped with t antennas while each UE is equipped with a single anna. In addition, each cell has both a single BS and UE, under the situation that each UE re gards the nearest BS as its local BS. Figure 3 illustrates our system mo ten del. Each BS is de noted by each circle, which is represented by the (i), where 1 ≤ i ≤ N. Aside from this, 1 , t ji h´ Î indicates the channel vector from a coordinateEi, while N 1 [v ,,v] t ii i v= indicates a beamforming vector used to rference between BSi and UEi. In addi tion, the solid lines denote the desired signals while dashed lines denote the interference from the coordinated BSs. Our p d BSj to a U mitigate the inte roposed system is represented as follow. The re ceived signal of UEi, i y is given by BSi with power i P (2) (1) ( N ) 1 2 N 1 v 2 v N v BSs UEs 1 x 2 x N x 1,1 h 1,2 h 1,N h 2,1 h 2,2 h 2,N h ,1N h ,2N h ,NN h Figure 3. Downlink Multiuser beamforming of the CoMP. nder CoMP transmission mode where i z (1) Besides, u1,, ,iN= ,, 1, . HH ii iii jijj jji yx xhv hv =¹ =+ + å N j Sj is the intercell interference signal trans mitted by B. The desired signal i of UEi is only transmitted by BSi. u z denotes the noise at UEi, which is a white Gaussian radom variable with zero mean and variance 2 s. n 3. Power Allocation Scheme The design of the precoding matrix [ 1,,, iN Vv vv= are chosen in INR (2) where SINR is the signal to noiseplusinterference ratio and the optimization of the powers i P order to maximize a WSR: N () 2 1 log 1. ii i RSa = =+ å i at each receive antenna. The value [0,1] i aÎ indicates the priority of each user, in particular ual prior ity, case of eq 1 iNa=, for all i. In this section, the received SINR for UEi is 2 H , 2 2 , 1, , ii i i iN H ij j jji iSINR Phvs =¹ = +å (3) where Phv represents the norm, 2 , H iii hv.is the desired signal power of UEi, and 2 , 1, N H ij j jji Phv =¹ åindicates the interference signal power from the other BSs. It should satisfy the condition of power constraint max S P: 2 max 1 . N ii BS i PPv = £ å (4) Copyright © 2013 SciRes. CN
J. Li ET AL. 17 The beamforming matrix is chose MMSE criterion [12], which maximizes receiver. Therefore, the beamforming matrix is repre se V n according to the SINR at the nted as 1 1, HH N VHHH I  æö ÷ ç÷ =+ ç÷ ç (5) r÷ ç èø where , is the sign ratio (S a possibl power is an N by N identity where ). For simplicity without loss of generality, we can ap ate the equation (6) as 1 [] T iM Hhhh= NR), defined as a rat and noise power 2 s. r io of N I altonoise e maximum matrix. The general problem is to find the powers i P to sat isfy () 2 maxlog 1, N ii SINRa ìü ïï ïï + íý å (6) 1 i= ïï ïï îþ [0,1] i aÎ (11 N i ia == å proxim 2 2 log 1 H N i Phv a æö ÷ ç÷ ç÷ ç÷ ç ç+ ç å, 2 1 , 1, . ii i i N H iji jj jji Phv = =¹ ÷ ÷ ÷ ÷ ç÷ ç÷ ç÷ ç÷ ÷ ç èø å (7) Since the powers of different users are cou an optimization approach. We assume that all the powers except are set, that is . Therefore, two sub op cation of waterfilling scheme is given by pled, we set i j timum procedures are proposed to derive a closed form solution. 3.1. Waterfilling Scheme The power allo P ,Pj i¹ 22 , 2, ij ii H pK hv a¹ êú = êú (8) , H ji j j iii Ps + ù +ú êú ëû where hv é ê å + ⋅ ent. The denotes the maximum between ze argum constant K can be found in [12]. In par ticular, ro and the 1 i aN= is chosen for a standard waterfilling. um sum 3.2. Modified Waterfilling Scheme The maxim of squared weights is defined as: () 2 max . BS ik kN vW= 1, ,= Therefore, we have to find a constant value K for (9) all the power , the following equatio i Pn holds: 22 , 2. H ji jj ij i iBS H i P pK hv hv s a¹ éù + êú êú = êú W å (10) ,iii + êú ëû This corresponds to a watrefilling distribution with variable water level. In block diagonalization, the SINR is given by [13] 2 2, ii i P SINRl = (11) s w precodg matrix is chosen from [13]fore, the weighted sum rate is here i l are the diagonal elements of HV where the in. There 2 22 1 log 1. Nii i i P Rl as = æö ÷ ç÷ ç =+ ÷ ç÷ ç÷ ç èø å (12) The solution is given as [11]: 2 2, ii i PK s al + ù ú = ú ú û (13) which is also a waterfilling distribution with equal prior ity. In fact, the procedures of itera presented before are based on the fact that the powers ihould be found. There, we should re e r the proposed iterative waterfilling aterfilling (MMSE PMWF) found by exhaustive search set to 0 dB. We can see that the optimum MMSE pre co tive optimization as j P for ji¹ are known to obtain i P. For this, a joint optimzation s resul efor pe un at the aforementioned waterfilling procedures to find each i P by adjusting j P values of the preceding step til the ting rate converges after setting arbitrary initial values for j P. 4. Simulation Results In this section, wanalyze the performance in terms of achievable rates fo (MMSE PWF), modified w and the optimum solution (MMSE ES). We also compare these performances to those of blockdiagonalization using a waterfilling scheme (BD WF). For these numerical results, the channel matrix entries are assumed to be independent identically distributed zero mean complex Gaussian random variables with variance of 0.5 per dimension. The initial powers for the iterative WF and MWF have been set equal to the i P of the uni form power distribution and the final power allocations are obtained after 5 iterations in all the simulations. For a fair comparison, SNR is defined as the ratio in dB of 2 max / BS Ps. In Figure 4, we compare the different solutions in terms of mean achievable rate for each user on the condi tion that each user has the same priority and the SNR is ding found by ES outperforms BD WF for all the val ues of the number of transmit antennas t N, and MMSE PMWF also outperforms MMSE PWF. Interestingly, the simple solution of MMSE PMWF outperforms BD WF Copyright © 2013 SciRes. CN
J. Li ET AL. 18 that requires a lengthy numerical optimization, in par ticular at the low SNR. In addition, we obtain the region of achievable rates for SNR=0 dB in Figure 5, where we show the effect of the different power allocation schemes with MMSE pre coding. We can see that MMSE PMWF obtains higher ac e optimum power distribution can be ob ta hievable rates than MMSE PWF. As the number of transmit antennas increases, the difference between MMSE ES and MMSE MWF is larger. However, even if suboptimal, MMSE MWF outperforms BD WF as shown in Figure 1, without resorting to a lengthy numerical optimization. The main difference in terms of complexity between MMSE and BD approaches is coming from the power optimization procedure. From the simulation results, we can see that th ined through a lengthy exhaustive search while water filling approaches allow a highly reduced complexity at 11.5 22.5 33.5 4 0.5 1 1.5 2 2.5 3 Number of transmit antennas N t Mean Rat e per user [bits/sec / Hz] MMSE E S MMSE P MW F MMSE P W F BD WF Figure 4. Mean achievable rate for each user with equal probability, N=2 and SNR=0 dB. 00.5 11.5 22.5 3 0 0. 5 1 1. 5 2 2. 5 3 3. 5 mean Rat e us er 1 [ bi t s/sec/Hz] Mean Rat e ues r 2 [ bit s/s ec/ Hz ] MMSE ES MMSE PMWF MMSE PWF N t =3 N t =2 N t =1 Figure 5. Region of mean achievable rates with N=2 and SNR=0 dB. the expense of some performance degradation. Since waterfilling is performed over N user transmissions, it does not depend on the number of transmit antennas. Therefore, the complexity of PWF and PMWF is irre spective of the number of antennas per BS. In addition, MMSE PMWF is a good choice in terms of the balance between complexity and achievable rates. 5. Conclusions In this paper, we present feasible combinations of MMSE based beamforming and iterative waterfilling power al location schemes that can be applied to the downlink of a CBST system while they are required to take a tradeoff between complexity and achievable rates into considera ed with MMSE beamforming outperforms a R regime. ments tion. In addition, we show that the iterative MWF alloca tion combin BD scheme that requires a lengthy numerical optimiza tion in the low and moderate SNR regimes under a twobase station/twouser simplified scenario. Further more, we show that our proposed iterative MWF scheme obtains a performance close to that of MMSE by exhaus tive search at a high SNR regime as well as MMSE and BD have the same performance at a high SN 6. Acknowledge This work was supported by the National Research Foundation of Korea (NRF) grant funded by the World Class University R322012000200140, the Korean government (MEST) 2012002521, and BSRP 2010 0020942 Korea. REFERENCES [1] M. Sawahashi, Y. Kishiyama, A. Morimoto, M. Nishi kawa and D. Tanno, “Coordinated Multipoint Transmis sion/Reception Techniques for Iteadvanced,” IEEE Wire less Communications, Vol. 17, No. 3, 2010, pp. 2634. doi.org/10.1109/MWC.2010.5490976 [2] D. Samardzija and H. Huang, “Determining Backhaul Bandwidth Requirements for Network MIMO,” 17th Conference (EUSIPCO 2009, pp. 14941498. European Signal Processing 2009), Glasgow, Scotland, [3] W. Choi and J. G. Andrews, “The Capacity Gain from Intercell Scheduling in Multiantenna Systems,” IEEE Transactions on Wireless Communication, Vol. 7, No. 2, 2008, pp. 714725. doi:10.1109/TWC.2008.060615 [4] T. Ren and R. J. La, “Downlink Beamforming Algo rithms with Intercell Interference in Cellular Networks,” IEEE Transactions on Wireles Communincation, Vol. 5, No.10,2006,pp6.04580.28142823.doi:10.1109/TWC.200 [5] S. G. Kiani aal and Distributed 2008, pp. 288297. doi:10.1109/TWC.2008.060503 nd D. Gesbert, “Optim Scheduling for Multicell Capacity Maximization,” IEEE Transactions on Wireless Communication, Vol. 7, No. 1, Copyright © 2013 SciRes. CN
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