Communications and Network, 2013, 5, 211216 http://dx.doi.org/10.4236/cn.2013.53B2040 Published Online September 2013 (http://www.scirp.org/journal/cn) Component Carrier Selection and Beamforming on Carrier Aggregated Channels in Hetero geneous Networks Changyin Sun1, Hongfeng Qing2, Shaopeng Wang2, Guangyue Lu1 1Department of Communication and Information Engineering, University of Xi’an Posts and Telecommunications, Xi’an, China 2ZTE Cooperation, Xi’an, China Email: changyin_sun@163.com Received June, 2013 ABSTRACT In this paper, component carrier selection and beamforming on carrier aggregated channels in Heterogeneous Networks are proposed. The scheme jointly selects the component carrier and precoding (i.e. beamforming) vectors with the co operation of the other cells to deal with the interference between Macro cell and Pico cell. The component carrier selec tion and beamforming is achieved by optimizing the multicell downlink throughput. This optimization results in shut ting down a subset of the component carrier in order to allow for a perfect interference removal at the receive side in the dense low power node deployment scenario. Additionally, algorithm based on Branch and Bound Method is used to reduce the search complexity of the algorithm. Simulation results show that the proposed scheme can achieve high cellaverage and celledge throughput for the Pico cell in the Heterogeneous Networks. Keywords: Heterogeneous Network; Intercell Interference Coordination; Beamforming; Carrier Aggregation 1. Introduction The concept of Heterogeneous networks has attracted a lot of interests recently to optimize the performance of the network[1]. In Heterogeneous networks(HetNet), the network topology is improved by overlaying the planned network of high power Macro base stations with smaller low power Pico base stations that are distributed in an unplanned manner or simply in hotspots where a lot of traffic is generated. These deployments can improve the overall capacity and the cell edge user performance [2]. With HetNet deployment in same spectrum, users can experience severe interference. This effect is due to the often geographically random low power node deploy ment as well as the nearfar problem arising from the imbalance in pathgains and transmission powers be tween the macro cell and low power nodes. 3GPPLTE has devoted significant standardization effort towards devising intercell interference coordination (ICIC) schemes for minimizing interference, culminating in the socalled “enhanced” ICIC (eICIC) in LTEAdvanced. The eICIC is one of the most important features of LTE Advanced, without it the range extension concept [3] loses its advantage and efficiency. The eICIC solutions are mainly divided into frequency domain solutions such as carrier aggregation and time domain solutions such as almost blank subframes (ABS) [2]. The main frequency domain multiplexing intercell interference coordination scheme used in LTEAdvanced is carrier aggregation, which basically enables a LTEAdvanced user equipment (UE) to be connected to several carriers simultane ously[2]. Carrier aggregation (CA) not only allows resource al location across carriers but also allows scheduler based fast switching between carriers without time consuming handovers, which means that a node can schedule its control information on a carrier and its data information on another carrier. So by scheduling control and data information for both Macro and Pico layers on different component carriers, interference on control and data can be avoided. It is also possible to schedule center PicoeNodeB(eNB) user data information on the same carrier that the Macro layer schedules its users, as the interference from the Macro layer on center PicoeNB users can be tolerated, while PicoeNB users in the range extension areas are still scheduled in the other carrier where the MacroeNB users are not scheduled[46] . In case of eICIC, only loose coordination among mac ros and picos is needed, which is advantageous from a deployment perspective. Coordinated multipoint trans mission (CoMP) aims to achieve additional gains on top of eICIC by tightening the coordination among cells. For example, considering the practical constraints for joint transmission, paper [7] focuses on Coordinated schedul ing/beamforming (CS/CB) based CoMP schemes in C opyright © 2013 SciRes. CN
C. Y. SUN ET AL. 212 which the concept of resource partitioning and almost blank subframes is used firstly as an effective way of mitigating the interference between the pico cell and macro cell, and then on shared subframes, CS/CB is ap plied for improved interference coordination. As a result, scheduling and beam selection gains can be achieved. However, as the number of picos grows, it becomes much harder to choose a beam good for every pico, if possible at all, so the beam selection gain will vanish. Paper [8] also employ multiple antennas in twotier fem tocell networks to provide additional degrees of freedom that can be used to help coordinate the crosstier inter ference, it propose a beamforming codebook restriction strategy. Although restricting the beamforming codebook increases the quantization error for the macrocell users, proportional fair scheduler compensate for the increased quantization error by exploiting the channel selection diversity gain and the multiuser diversity gain. As the number of femtocell grows, the opportunistic channel selection strategy will loose the limited additional de grees of freedom. In this paper, component carrier selection and Beam forming on carrier aggregated channels in Heterogeneous Networks is addressed. The Heterogeneous Networks consists of complementing the Macro layer with low power nodes such as Pico base stations, and solution such as Range Extension is assumed to extend the cov erage area of the Pico nodes. The scheme jointly selects the component carrier and precoding (i.e. beamforming) vectors with the cooperation of the other cells to deal with the interference between Macro cell and Pico cell. The component carrier and beamforming selection is optimized not only to exploit additional degrees of free dom provided by multiple antennas and component car riers, but also to restore the feasibility of the CS/CB when the number of low power nodes grows. As a result, the design will shut down a subset of the component car rier in order to allow for a perfect interference removal at the receive side in the large dense low power node de ployment scenario. Additionally, algorithm based on Branch and Bound Method is used to reduce the search complexity of the algorithm. The proposed approach is confirmed by simulation results compared with the per formance of the baseline approach. 2. System Model We consider Hetnet network with the following features: 1) a certain number of PicoeNBs are deployed through out one Macro cell layout; 2) The PicoeNBs are ran domly distributed; 3) The users are randomly distributed throughout the cell area. Now consider the downlink transmission with M users and K carriers in the network. The BSs and the users are assumed to have N transmit antenna and one receive an tenna, respectively. For simplicity, the transmit power is kept the same in each carrier per cell q, i.e. q. Let the binary matrix ,, P {a a{0,1}} kmkmK M A describes the carrier selection among the users, where ,1 km a de notes that carrier k is assigned to user m, otherwise, ,0 km a . Now, denote by ,,,, ,kmikmiki S hb the channel power gain to the selected mobile user m in cell q from the cell i base station, in resource slot t, where 12 ,,,, ,,,, [,, N kmikmikmikmi hh hh] denotes the channel vector of the user m in cell q from the cell i base station, 1 , ki bC is the beamforming vectors used to map the user in cell i data symbols to the transmit signals. The channel gains are assumed to be constant over each such resource slot, i.e., we have a block fading scenario. Note that the gain ,,kmq corre sponds to the desired communication link, whereas the gains ,,kmi for i S Sq correspond to the unwanted in terference links. Assuming the transmitted symbols to be independent random variables with zero mean and a variance q, the signal to noiseplusinterference ratio (SINR) for each user is given by: P 2 ,,, ,, 22 ,,,, 1,   qkmqkq kmq N ki ikmikiq iiq P SINR aP hb hb (1) where is the variance of the independent zeromean AWGN. Then the achievable rate for user m is given by: ,2,, 11 log (1) KK mqkmq kmq kk RSINR ,, R (2) Assume at time slot t, only one user ()mSq is scheduled at each basestation q, so we will not distin guish cell q and the user served by cell q for simplicity, then from (1) and (2) the total achievable throughput (sum rate) is then found as , 1 Q mq q RR 2 ,,,, 2 11 22 ,,,, 1,  log (1)  QK kq qkqqkq N qk ki ikqikiq iiq aP RaP hb hb (3) The component carrier selection and interference coor dination problems are to find the matrix A and ,kq such that the objective function is optimized. Assuming the goal is to achieve the highest system throughput while ensuring proportional fairness among different users, the following utility function needs to be maximized: b , 11 , 1 , ..1) 2) 1 QK qkq qk K kq q k kq RR ta b C (4) Copyright © 2013 SciRes. CN
C. Y. SUN ET AL. 213 The constrained problem (4) is a mixed binarynon convex problem. To find the global optimum, one has to exhaustively search through all possible ,ki (real val ues) and ,kq (binary values). Here, we shall first de compose it into the K independent percarrier objective function, then adopt the method of alternatingly optimiz ing antenna vectors and the component carrier selection. b a The Lagrangian of problem (4), dualized with respect to the constraint 1) is defined as: ,, 11 {} K qkq qkqqq kqq q Ra C (5) This Lagrangian can be decomposed into the K inde pendent percarrier objective function. For a particularq the optimization problem (5) can be solved in a percar rier fashion: , , {,}argmin{ } ..1) 1 2) 0 3) {0,1} opt kk k kq q kq st a Ba b (6) where ,,kqkqqkq Ra . To solve (4) by (6), q should be tuned to enforce the constraints as in [9], where an efficient Lagrange multi plier search procedure is presented. This procedure for the Lagrange multipliers is assumed in the following update formula: 1 , 1 ( K tt qq qkq k Ca ) (7) 1, 2,,qQ where () means max(0, x), t is the iteration number, is a step size parameter and q is the number of carrier selected corresponding to the Lagrange multipli ers at hand. C Assume q is fixed and ,kq is selected on carrier k, the transmit beamforming vector q of cell q in carrier k which maximizes the sum rate in (6) is given by the following dominant eigenvector problem [10]: ab , 1, () Q iq b iiq qi,qq EAb q b q (8) where , and the real values H qq,qq, Ehh H i,qi,q i,q Ahh ,iq is defined as following: 22 2 ,22 2    qq i iq iq q PP P qq,qq i,i i ii,ii i Ihb hb IhbI (9) And is the received interference power of user q: q I 2 1,  Q i iiq P qq,i Ihb i With fixed we denote (10) The optimum point are the eigenvector corre sponding to the largest (resp. smallest) eigenvalue of (8). * q b * ,ki q bb 2 ,,,, ,  kqqkqqkq hhb, 2 ,,,, ,  qikqi qi hbne can get a k h Thus, ofrom (6) with : ,kq 2 , ,,,  qq kqi ,,  (1) kq q k aPh 2, 11 22 1, log QK kqkq N qk ki iq iiq a aP N (11) 2.1. Linear Convex Relaxation Approach hese de h Unfortunately, for given Lagrange multipliers, t coupled optimization problems (11) are themselves dif ficult nonconvex problems. So a novel lowcomplexity optimization algorithm is presented. The algorithm is based on a relaxation of the nonconvex percarrier opti mization problem (11) leading to a more direct and con ceptually simple procedure. The convex relaxation starts with rewriting the objec tive function of (11) in the following form: 22 2,,, 1 {log () Q kkiikqiq qi JaPh , 22 2, 1, } log() qkq Q ki ikqq qiiq a aPh (12) which consists of a convex part A (trst part ) and a ,,  i he fi concave part B. This objective function is a difference of convex (d.c.) functions which is known to correspond to a hard optimization problem [9]. The crucial step is now to relax the nonconvex part B by hyperplane overestima tors, leading to the following relaxed objective: ,, , 1, () Q rel kkikiki qiiq Auav (13) where ,, , 1, () Q ki kiki iiq ua v 22 2,, 1, log ( ki h) Q ki iq iiq aP (14) This is tight with equality at approximtion apoint ,ki a. The obtained relaxed objective function is a convex fu solved by the Branch and bound. Branch and bo11] is a general nction. The constraints are also convex leading to a convex optimization problem which can be solved effi ciently. The solution of this convex relaxation forms an upper bound for the global minimum. Using the obtained upper bound as a new point of approximation (see algorithm 1) it can be proven that the sequence of relaxations pro duces a monotonically decreasing objective value and will always converge. The proof is trivial and omitted due to space limitations. Upon convergence it can be proven that the obtained solution is a local optimum. Although there is no theoretical proof for global optimal ity, simulation results are very promising showing global optimality for very different scenarios. 2.2. Branch and Bound Method The binary convex problems (11) are und [ Copyright © 2013 SciRes. CN
C. Y. SUN ET AL. 214 Table 2. Algorithm 2. m 2 Branch and bound method technique for finding optimal solutions of various opti mization problems. A branch and bound procedure has two ingredients. The first ingredient is a smart way of covering the feasible region by several smaller subre gions. This leads to a branching operation. The second ingredient is bounding, which is a way of finding upper and lower bounds for the optimal solution within a feasi ble subregion. The core of the approach is the simple observation that (for a maximization task) if the upper bound of a subregion A is smaller than the lower bound for some other subregion B, then subregion A may be safely discarded from the search. To efficiently solve this problem by branch and bound method, the problem is convex relaxed as: S ubject to: {} argmin{} opt relk J k a (15) 0 q ,ki a Which is convex with c [0,1] ontvariable , if we denote as its optimal value, and the optimue of th nan thod: round each bi inues k a al val is 1 e original problem is denoted * p, then 1 L a lower bound ohe optimal value of (11). An upper bound (denoted 1 U) o * p c be fund by several ways, one more sophisticated L n t me isnary variable k a then we'ltain th upper bound. If 11 UL l ob , we can quit. In the branchinoperation, we pick any index {q}, and ubproblems: th g form two se first problem and the second problem. The first and the second problem is the relaxed problems with ,0 kq a and ,1 kq a respectively. Solving the first and the second problem, we obtain the {lower, upper} bounds } an{L , U d{L,U} for ,0 mk a and ,1 mk a respectively, thus the new bounds on * p: * 22 min{ ,}min{,)LLLpUUU (16) } The Branch and bound algorithm continue to nary tree by splitting, relaxing, calculating bo su Algorithm 1 Successive linear CC k form bi unds on bproblems. The common strategy to select the leaf node for further split operation is to pick a node with smallest L, while that to select the variable for further split operation is either the‘least ambivalent’ or the‘most ambivalent’ way. The ‘least ambivalent’ way will choose {q} for which *{0,1}q, with largest Lagrange multi plier, while the ‘most ambivalent’ way will choose {q} for which * q− 1imum. Table 1. Algotithm1. /2 is min convex relaxation for 1: Repeat l 2: Fo 3: ti 4: End For. 5: minimize: solve problem (12) with Relaxed ( r i=1 to Q. ghten: compute ,() ki ul ,() ki vl rel k ) Algorith Branching: 1: choose one of the carrier selection index{q}; 2: solve two convex relaxed problems (11): set ,0 kq a and ,1 kq a respectively Bounding: 3: take the optimal value of the two convex relaxed problems as the = . lower bounds{ L ,L}; 4: take the solution of the two convex relaxed p = { roblems as the upper bounds,UU }when round all the relaxed binary variables to 0 or 1; 5: take minimum of the lower bounds as the current lower bound 2min{ ,}LLL on the optimal value of the optimization problem; 6: take minimum othe f upper bounds as the current upper bound 2min{ ,)UUUon the optimal value of the optimization problem; Pruning: 7: If 22 UL then quit the algorithm. subtree (subpr h the‘ment; to step 2. 8:else select the leaf node for further split operation :select the oblem) with the smallest lower bound to be split; 9: end if 10: select te variable for further split operation :select another as not been so far used while meet the ‘most amindex{q} which h bivalent’ orost ambivalent’ requirem 11: go 3 I a astem. For comparison purpose, the per formances of the network with all the carriers fully re o station are also given. For . Simulation Results n this section, simulation results are presented to evalu te the performances of the proposed scheme in a carrier ggregation sy used between macro and pic simplicity, we only consider one cell network which contains 1 MacroeNB and 2 PicoeNBs. The radius of Macro cell is 1000m. And the total number of users is 40. The range extension threshold is 10dB. Detailed simula tion parameters including channel model and system as sumptions are summarized in Table 3. Most of them are set according to the LTEA simulation assumptions. First , equal cell specific weight in the system sum rate is used, and none uniform user distribution across the macro cell is assumed, in this case, the users are dropped at the dense area which overlay both the pico cells and is about 12% of the Macro cell area. The cumulative dis tribution function (CDF) performances of the networks with the new joint carrier selection and beamforming scheme and frequency reuse 1 with beamforming scheme are compared in Figure 1. Compared to the networks where carriers are fully reused (‘Reuse 1’) between Macro cell and pico cell, the throughput performance of the macro cell with the proposed interference coordina tion scheme is significantly improved when equal cell specific weight is applied. On the contrary, the through put performance of the Pico cell with the proposed scheme is a little improved compared with that of the 6:End Loop until convergence Copyright © 2013 SciRes. CN
C. Y. SUN ET AL. 215 baseline scheme. Moreover, in order to clearly verify the effects of the proposed scheme, we also present the per formance of the network throughput. Compared to the baseline scheme where carriers are fully reused (‘Reuse 1’) between Macro cell and pico cell, the system through put performance with the proposed interference coordi nation scheme is significantly improved. In this case, we see gains beyond simple beamforming coordination gain. Table 3. Simulation Assumption. Parameters Value Carrier bandwidth 10MHz Number of Carriers 2 Path loss model Pico (R), R in km Path loss model Macro (dB) 128.1+37.6log10(R), R in km Shadowingition (dB) cro (dBm) (dBm) dB) 140.7+36.7log10( standard dev8 Transmit power Ma43 Transmit power Pico 20 Number of Tx Antenna 2 Number of Re Antenna 1 0100 200 300 0 0.2 0.4 0.6 0.8 1 Cell throughput(Mbit/s) on with beamforming CDF CC seleti Macro Pico1 Pico2 System 0100 200 300 0 0.2 0.4 0.6 0.8 1 Cell throughput(Mbit/s) CDF Reuse 1 with beamforming Macro Pico1 Pico2 System Figure 1. Performances with equal weight. Next, the CDF performances of the networks with none uniform user distribution and with cell specific weight 12 {,,}{1/5,2/5,2/5} MPP 2. Compared with the uniform are compared in Figure cells weight {1,1,1} in the Pico cen sc e of the Macro cell is a little im m provided by m for mitigating the interference ell and macro cell, then component o restore the feasibility of CB in the Figure 1, the throughput performance of ll with the proposed interference coordinatio heme is significantly improved when cell specific weight is applied. On the contrary, the throughput per formancprovment com pared with that of the reuse one scheme. In general we see there is both cell and system per formance improvement in throughput in using joint car rier selection and beamforming for interference coordi nation over the baseline scheme in both the scenarios. The results suggest that the interference coordination not only exploit additional degrees of freedo ultiple antennas and component carriers, but also to restore the feasibility of the CS/CB when the number of low power nodes grows, which is achieved by shutting down a subset of the component carrier in order to allow for a perfect interference removal at the receive side in the large dense low power node deployment scenario. More over, with different cell specific weight in sum rate, further load offset effect is observed beyond simple range extension scheme. 4. Conclusions In this paper, we consider joint component carrier selec tion and beamforming for carrier aggregation system in Heterogeneous Networks. In the proposed scheme, CS/CB is firstly applied between the pico c carrier is selected t 0100 200 300 0 0.2 0.4 0.6 0.8 1 CDF CC seletion with beamforming Macro Pico1 Pico2 System Cell throughput(Mbit/s) 0100 200300 0 0.2 0.4 0.6 0.8 1 Cell throughput(Mbit/s) CDF Reuse 1 with beamforming Macro Pico1 Pico2 System Figure 2. Performances with unequal weight. dense low power node scenario. The component carrier and beamforming selection is optimized not only to ex ploit additional degrees of freedom provided by multiple antennas and component carriers, but also t restore the feasibi ower nodes wn a o lity of the CS/CB when the number of low p grows. As a result, the design will shut do subset of the component carrier in order to allow for a perfect interference removal at the receive side in the Copyright © 2013 SciRes. CN
C. Y. SUN ET AL. Copyright © 2013 SciRes. CN 216 undation of Education department of Shaanxi dation of ZTE Forum. large dense low power node deployment scenario. Addi tionally, algorithm based on Branch and Bound Method is used to reduce the search complexity of the algorithm. The proposed approach is confirmed by simulation re sults compared with the performance of the baseline ap proach. 5. Acknowledgements This work was supported in part by National Natural Science Foundation of China (61102047, 61271276); Key project (2012ZX03001025) of China, Natural Sci ence Fo Province(2013JK1045); Foun REFERENCES [1] Qualcomm Incorporated, LTE advanced: heterogeneous networks, Feb. 2010. Availalbe: http://www.qualcomm.co.kr/documents/lteadvancedheter ogeneousnetworks. [2] E. Dahlman, S. Parkvallold, “4G: LTE/LTEadvdband,” Academ and J. Sk anced for Mobile Broaic Press, 2011. [3] 3GPP Tdoc R4083018, Qualcomm Europe, Range Ex pansion for Efficient Support of Heterogeneous Networks, Aug., 2008. [4] Y. Wang, K. I. Pedersen, T. B. Sorensen and P. E. Mo gensen, “Carrier Load Balancing and Packet Scheduling for Multicarrier Systems,” IEEE Transactions Wireless Communications, Vol. 9, 2010, pp. 17801789. doi:10.1109/TWC.2010.05.091310 [5] Y. Yan, A. X. Li and X. Y. Gao, “Hidetoshi Kayama, A New Autonomous Component Carrier Selection Scheme for Home eNB in LTEA System,” in Proceeding IEEE mmunications Magazine, VTC, 2011 Spring, May 2011. [6] K. I. Pedersen, F. Frederiksen, C. Rosa and H. Nguyen, Carrier Aggregation for LTEadvanced: Functionality and Performance Aspects, IEEE Co Vol. 49, No. 6, 2011, pp. 8995. doi:10.1109/MCOM.2011.5783991 [7] A. Barbieri, P. Gaal, S. Geirhofer, T. Ji, D. Malladi, Y. Wei and F. Xue, “Coordinated Downlink M Communications in Heterogeneous ultipoint Cellular Networks,” tocell Networks,” IEEE Transactions on pp. Information Theory and Applications Workshop (ITA), 2012, pp. 716. [8] W. Seo, S. Choi and D. Hong, “A Beamforming Code book Restriction for CrossTier Interference Coordination in TwoTier Fem Vehicular Technology, Vol. 60, No. 4, pp. 1651166. [9] W. Yu and R. Lui, “Dual Methods for Nonconvex Spec trum Optimization of Multicarrier Systems, IEEE Trans actions Communications, Vol. 54, No. 7, 2006, 13101322. doi:10.1109/TCOMM.2006.877962 [10] K. M. Ho Zuleita, M. Kaynia and D. Gesbert, Distributed Power Control and Beamforming on MIMO Interference Channels, Wireless Conference (EW), European, April tion, Springer, 2002. 2010, pp. 654660. [11] P. M. Pardalos and H. E. Romeijn, Handbook of Global Optimization Volume 2 (Nonconvex Optimization and Its Applications), 1 Edi
