Energy-Efficient Downlink Transmission in Two-Tier Network MIMO OFDMA Networks

Transcription

1 Energy-Efficient Downlink Transmission in Two-Tier Network MIMO OFDMA Networks Ahmed Hamdi Sakr and Ekram Hossain Abstract We propose an energy-efficient resource allocation scheme for downlink transmission in two-tier Network MIMO OFDMA-based macrocell-femtocell networks where the femtocells form clusters of equal size. The proposed scheme uses a joint zero-forcing beamforming with semi-orthogonal user selection (ZFBF-SUS) transmission at each network tier to perform subcarrier and precoding coefficients allocation. Then, power allocation is optimized in order to maximize the total system energy efficiency (i.e., average number of successfully transmitted bits per energy unit [bit/joule], or equivalently the average data rate per unit power [bps/watt]). The macro base stations (MBSs) and the femto base stations (FBSs) in a cluster maximize their energy efficiency in distributed manner while considering the cross-tier interference and the capacity limitations of backhaul links. The problem of maximizing energy efficiency is formulated as a fractional program and solved by using the Dinkelbach iterative algorithm. Numerical results show that the proposed scheme outperforms the scheme that maximizes the system average capacity, in terms of energy efficiency, and also improves the total system performance in terms of energy efficiency and average system capacity when compared to a single-tier system. Keywords: Two-tier OFDMA networks, network MIMO, energy efficiency, resource allocation. I. INTRODUCTION Using femtocells can reduce the energy consumption for cellular wireless access by offloading users from the macro base stations (MBSs) to the low-power femto base stations (FBSs) and thus reducing the required energy to serve the macro user equipments (MUEs) and the femto user equipments (FUEs). In addition, it increases the system capacity and improves the cell coverage. Unfortunately, this two-tier system suffers from both cross-tier and co-tier interferences [1]. To mitigate co-tier interference, the concept of cooperative communication has been of great interest recently. Network multiple-input multiple-output (N-MIMO) is a form of cooperation in which each user is served by multiple base stations, where these base stations exchange the users data and their channel state information (CSI). Then, the base stations coordinate the transmissions with each other where the signal processing is distributed among all the cooperating transmitters. Beamforming strategy, such as zero-forcing beam-forming (ZFBF), can be used in N-MIMO to serve multiple users on the same subcarrier at the same time by choosing precoding coefficients to cancel out the interference [], [3]. With the large scale deployment of two-tier networks to meet the users requirements, both the power consumption and global greenhouse gas emissions increase []. So, resource allocation schemes that enhance the energy efficiency have The authors are with the Department of Electrical and Computer Engineering, University of Manitoba, Winnipeg, Canada ( s: Ahmed.Sakr@umanitoba.ca, Ekram.Hossain@umanitoba.ca). This work was supported by a Strategic Project Grant (STPGP 3085) from the Natural Sciences and Engineering Research Council of Canada. become as important as that maximize the system capacity. Many previous works in the literature only focused on resource allocation techniques that maximize the system capacity in two-tier networks and ignored the issue of energy consumption [5], while some other works focus on maximizing energy efficiency in the single-tier system [6], [7]. In [6], an energyefficient multicell cooperation scheme is proposed considering the total power consumption as well as the backhaul link maximum capacity. The authors in [7] proposes a resource allocation scheme to minimize the transmit power subject to given users data requirements in a single cell multiuser MIMO system. In the context of two-tier OFDMA systems, [8] considers a soft frequency reuse strategy to avoid cotier and cross-tier interference, and the system is optimized in terms of the energy efficiency. In [9], an energy-efficient subcarrier allocation scheme is proposed to minimize the downlink energy consumption under throughput constraint. Following the works in [6] and [10] on single-tier cellular systems, in this paper, we propose a distributed 1 energyefficient downlink transmission scheme based on N-MIMO for two-tier OFDMA-based cellular networks. The main idea of the proposed scheme is to maximize the energy efficiency of each tier separately to reduce the complexity of the system, while limiting the effect of cross-tier interference. We then decompose each problem into three phases to allocate subcarriers, precoding coefficients, as well as power. We consider the total circuit power consumption, capacity limitation of the backhaul network, and limited power budget. The results show that the two-tier system outperforms the single-tier system in terms of energy efficiency and average capacity. It also shows that the proposed scheme surpasses the scheme that maximizes the system average capacity in terms of energy efficiency. The rest of this paper is organized as follows. In Section II, we describe the system model and define the performance metrics. Section III formulates the optimization problem for maximizing the energy efficiency at the macro-tier and the femto-tier. The solution methodology for the proposed formulation is explained in Section IV. Finally, the numerical results and conclusion are given in Section VI and Section V, respectively. II. SYSTEM MODEL A. Two-Tier Macrocell-Femtocell Network Model We consider a two-tier wireless cellular network existing in D R, where the first tier and the second tier are macrocells and femtocells, respectively. As shown in Fig. 1, the macro-tier consists of M MBSs all connected to a central unit through a control link to acquire the resource allocation 1 This is distributed in the sense that the proposed scheme can be executed at each tier, i.e., at the macro-tier and at each cluster of femtocells in the femto-tier, separately.

2 MBS FBS Central Unit MU FU Control Link Backhaul Link Fig. 1. A two-tier cellular system with M = 3 MBSs, Z = 3 FBSs per cluster, and C = 7 clusters. policy. In addition, all MBSs are assumed to communicate with each other via a capacity-limited backhaul mesh network to exchange users data. On the other hand, the femto-tier consists of C clusters of FBSs, where all clusters have the To remove this watermark, please purchase SmartDraw at or call same size of Z FBSs. FBSs within the same cluster exchange the control signals and users data through IP core network via capacity-limited backhaul links. All FBSs have the same coverage radius R f and operate in closed-access mode. The central unit and the FBSs can exchange control signals through the IP core network. This network serves a total of U M MUEs and C c=1 U c FUEs, where U c is the number of FUEs served by the c-th cluster. All network elements (i.e., MBSs, FBSs, MUEs, and FUEs) have a single antenna configuration. B. Channel Model and Capacity The available bandwidth B is divided into N OFDMA subcarriers for downlink transmissions. We assume a frequency reuse factor of 1 where all MBSs and FBSs share the same bandwidth. Thus, the network can serve up to M MUEs and Z FUEs per cluster at the same time on each subcarrier. The global CSI is assumed to be perfectly estimated and known at the central unit. In this model, we consider both crosstier and co-tier interference while the cross-cluster interference is neglected due to the wall penetration losses. Therefore, the signal-to-interference-plus-noise ratio (SINR) at a generic MUE i on subcarrier n is given by M h i m(n)wm(n) i p i m(n) SINR i m=1 M (n) =, (1) σz + IM i (n) + C Ic(n) i c=1 IM i (n) = k S M (n) M m=1 hi m(n)wm(n) k p k m(n), () k i Ic(n) i = u S c(n) Z f=1 hi c,f (n)vu c,f p (n) u c,f (n). (3) IM i (n) and Ii c(n) are the received interference power at MUE i on subcarrier n from the macro-tier (co-tier interference) and femto cluster c (cross-tier interference), respectively, and σz is the variance of AWGN. The numerator in the expression for SINR i M (n) represents the coded signal power received at the MUE on subcarrier n from the M cooperating MBSs. h i m(n) = x i m(n) lm i is the total channel gain between The problem of clustering of the FBSs is out of the scope of this paper. MBS m and MUE i where x i m(n) and lm i represent the smallscale fading coefficient on subcarrier n and the path-loss, respectively. h i c,f (n) is the total channel gain between FBS f from cluster c and MUE i on subcarrier n. wm(n) i and vc,f u (n) are the precoding coefficient used by the macro-tier and cluster c, respectively, to perform ZFBF on subcarrier n. p i m(n) is the transmit power of MBS m to user i on subcarrier n, p u c,f (n) is the transmit power of FBS f from cluster c to user u, and S M (n) and SF c (n) are the sets of users using subcarrier n from the macro-tier and cluster c, respectively. For an FUE j served by cluster c, the SINR on subcarrier n is given by Z g j c,f (n)vj c,f (n) p j c,f (n) SINR j f=1 c(n) = σz + Ic j (n) + IM c (n), () Ic j (n) = k S c(n) Z f=1 gj c,f (n)vk c,f p (n) k c,f (n), (5) k j IM c (n) = k S M (n) M m=1 gav m,c(n)wm(n) k p k m(n). (6) IM c (n) is the received cross-tier interference power at FUE j on subcarrier n from the macro-tier, Ic j (n) is the received intra-cluster interference power, and the numerator in the expression for SINR j c(n) represents the coded signal power received at FUE j on subcarrier n from the Z cooperating FBSs within the same cluster c. g j c,f (n) is the total channel gain between FBS f from cluster c and FUE j on subcarrier n, while gm,c(n) av is the average channel gain between MBS m and FBS cluster c on subcarrier n. Using (1) and (), we express the channel capacity for MUE i and FUE j at cluster c, respectively, as c i M (n) = B N log ( 1 + SINR i M (n) ), (7) c j c(n) = B N log ( 1 + SINR j c (n) ), (8) Then, the total capacity of the macro-tier and femto-tier can be obtained, respectively, as TC M = N TC c = N n=1 i S M (n) n=1 C. Power Consumption Model c i M (n), (9) j S c F (n) c j c(n). (10) 1) Macro-Tier: The considered model for the total power consumption of the macro-tier, TP M, consists of a linear part which is proportional to the RF transmit power, a constant part that represents the signal processing power, and another constant part PBM tot that includes the power consumption in the backhaul network [11]. Hence, TP M = α M N m=1 n=1 i S M (n) w i m(n)p i m(n) + MP + P tot BM, (11) where α 1 represents the MBS s power amplifier inefficiency and P is the signal processing power per MBS.

3 ) Femto-Tier Power Consumption: Similarly, the power consumption of any cluster c can also employ the same model with a linear part and two constant parts, hence, the total power consumption of cluster c is given by TP c = β Z f=1 n=1 v j j SF c (n) c,f (n)pj c,f (n) + ZP CF + PBF tot, (1) where β 1 is the FBS power amplifier inefficiency constant and P CF is the signal processing power per FBS. D. Energy Efficiency Metric We define the energy efficiency as the average number of successfully transmitted bits per energy unit (bit/joule) which is equivalent to the average data rate per power unit (bps/watt). Using (9)-(1), we obtain the energy efficiency of the macrotier and cluster c, respectively, as III. EE M = TC M TP M, (13) EE c = TC c TP c. (1) PROBLEM FORMULATION FOR ENERGY-EFFICIENT RESOURCE ALLOCATION A. Generic Objective Function The objective of this work is to maximize the energy efficiency of the two-tier cellular network. Through this context, resource allocation means power allocation P, precoding coefficient allocation W, and subcarrier allocation S. For energy-efficient resource allocation, the macro-tier and each cluster of FBSs maximize their own energy efficiency, given by (13) and (1), in a distributed manner under cross-tier interference constraints as well as backhaul links capacity limitations. In this case, we have 1 + C different optimization problems (i.e., C problem for the femto-tier and one problem for the macro-tier) with the same structure. Thus, we define a generic objective function that can be written as EE = max EE = max TC(P, W, S) TP(P, W, S), (15) where EE, TC, and TP could be the energy efficiency, total capacity, and total power consumption of the macro-tier or any cluster of FBSs depending on which optimization problem is under consideration. B. Resource Allocation Problem 1) Macro-Tier Optimization Problem: For any MUE, we assume that the nearest MBS to this equipment is responsible for sending its data to all the other cooperating MBSs via the backhaul network. Therefore, we define A m as the set of MUEs whose data are sent by MBS m. The macro-tier optimization problem is given by max EE M (16) s.t. C1: wm(n) i Pm(n) i P T M, m, n=1 i S M (n) C: S M (n) M, n, C3:I c M (n) I th M, n, c, C: c i M (n) RM max, m, i S M (n) A m n=1 C5:p i m(n) 0, n, i, m, where C1 is the power budget constraint and P T M is the maximum allowable transmit power by any MBS. C guarantees that each subcarrier n is reused by a maximum of M MUEs for a proper cooperation between the M MBSs, where denotes the set cardinality. C3 ensures that the amount of cross-tier interference introduced by the macro-tier on the femto-tier is always below the interference threshold IM th, while C is the backhaul links capacity constraint where RM max is the backhaul link maximum capacity. ) Femto-Tier Optimization Problem: In the femto-tier, we have C different optimization problems, one problem per each cluster. For any cluster c, the optimal resource allocation can be achieved by solving max EE c (17) s.t. C1: v j c,f (n) p j c,f (n) P T F, f c, n=1 j S c(n) C: S c (n) Z, n, C3:Ic(n) i Ith F C, n, i S M (n), C: N n=1 j S c(n) c j c(n) R max F, C5:p j c,f (n) 0, n, j, f, where, similar to (16), C1 C are constraints on maximum allowable transmit power by any FBS, subcarrier reuse, crosstier interference introduced by cluster c on the macro-tier, and the capacity of backhaul links. In C, we assume that the data of all FUEs in a cluster c are sent to the Z cooperating FBSs by the IP core network via Z backhaul links, cf. Fig. 1. IV. SOLUTION METHODOLOGY In this section, we recall the generic objective function (15) and formulate a general optimization problem as follows: {P, W, S } = arg max TC(P, W, S) TP(P, W, S) s.t. C1, C, C3, C, C5. (18) We propose an algorithm to solve the general optimization problem (18) which has the same structure as the set of optimization problems (16) and (17). The problem is decomposed to three subproblems; namely, user selection, precoding, and power allocations subproblems. We use a semi-orthogonal user selection (SUS) scheme that is proposed in [10] and ZFBF to obtain S and W, respectively. In the third step, for a given S and W, we use the Dinkelbach iterative method to solve the power allocation problem [1]. A. Zero-forcing Beamforming with Semi-orthogonal User Selection (ZFBF-SUS) Scheme The main idea of the scheme is to group users who are semi-orthogonal to each other to be served simultaneously on

4 the same subcarrier. Then, ZFBF is used to cancel out the interference between the cooperating transmitters. The scheme is shown to have an asymptotically optimal performance and is summarized in [10]. Using this scheme results in canceling out the co-tier interference between the cooperating transmitters whether they are MBSs or FBSs in the same cluster. Hence, I i M (n) = Ij c (n) = 0. In addition, the algorithm satisfies C where no more than M MUEs, or Z FUEs from the same cluster, are allowed to share the same subcarrier. An additional constraint C6 is added to (18) to decouple the power allocation variables from the calculation of the precoding coefficients. This constraint forces all the cooperating transmitters, MBSs or FBSs, to transmit with the same power on subcarrier the same subcarrier, i.e, P i 1(n) = P i (n) = = P i M (n) and P j c,1 (n) = P j c, (n) = = P j c,z (n). B. Power Allocation For a given S and W, the problem in (18) reduces to P TC(P) = arg max P TP(P) s.t. C1, C3, C, C5, C6. (19) The objective function of (19) is in a fractional form and non-convex in general; however, it could be transformed into an equivalent form with the same optimal decision parameters; i.e., P, as stated in the following theorem. Theorem 1. EE TC(P) = max if, and only if, P TP(P) TC(P ) EE TP(P ) = max TC(P) P EE TP(P) = 0. Using Theorem 1, we can transform the problem in (19) into (0), then we can use Dinkelbach iterative method to obtain the optimal EE. The algorithm is summarized in [13]. For the proof of the convergence of Dinkelbach method as well as the proof of Theorem 1, refer to [1]. P = arg max TC(P) EE TP(P) P s.t. C1, C3, C, C5, C6. (0) Due to C, the problem in (0) is still non-convex. Therefore, we use the Lagrangian relaxation L(P, λ, θ, ρ) to obtain the dual problem as min max λ,θ,ρ P L(P, λ, θ, ρ), (1) where λ, θ, and ρ are the Lagrangian multipliers of C1, C3, and C, respectively. For the dual problem (1), the KKT conditions are necessary and sufficient for the optimal solution. Therefore, we can obtain a closed-form solution for the power allocation for a given S, W, and EE for the two tiers as follows p i m(n) = P : p j c,f (n)= B N ln() 1 ρ m κ i (n) σz + C + I i c (n) c=1 M, h i m (n)wi a (n) a=1 + B 1 ρ c N ln() σ ϕ j z +Ic M (n) c(n) Z g j c,f (n)vj c,f (n) f=1, () TABLE I. SIMULATION PARAMETERS Parameter Value Total bandwidth B 1.5 MHz Number of subcarriers N 3 Noise variance σz 13 dbm Power amplifier constants α, β 5, MBS power model constant MP + PBM tot 3 0 W FBS power model constant ZP CF + PBF tot 3 W Interference threshold IM th, IF th 11 dbm Backhaul link capacity RM max, R max 36, 100 Mbps where κ i (n)= M (λ a +αee M ) wa(n) i + C M θ n,c a=1 F c=1 b=1 gb,c av (n)wi b (n), ϕ j c(n)= Z (λ c,a +βee c ) vc,a(n) j + Z θ c,j,k h k c,f (n)vj c,f (n). a=1 k S M (n) f=1 The power allocation in () is obtained iteratively and the Lagrangian multipliers are updated using the subgradient method [1]. The allocated transmit power for MUEs, or FUEs, takes the form of multi-level water-filling in which a larger value of κ i (n), or ϕ j c(n), results in allocating less power to this user, i.e., lower water level, to limit the crosstier interference caused by the macro-tier, or the femto-tier, respectively. The cross-tier interference thresholds IM th and Ith M do not appear in the power equations; however, Lagrangian multipliers θ control the power levels, which in turn limits the cross-tier interference to satisfy C3 in both (16) and (17) and protecte both tiers. Note that, M a=1 hi m(n)wa(n) i and M b=1 gav b,c (n)wi b (n) represent the effective channel gains for the links to MUE and FUE, respectively. V. SIMULATION RESULTS The performance of the proposed energy-efficient resource allocation scheme for two-tier N-MIMO-based OFDMA cellular networks is evaluated based on Monte Carlo simulations. Then, some results are compared to those in [6] of the singletier network. The simulated network has M = 3 MBSs and C = 15 clusters of FBSs placed randomly over D according to a uniform distribution. Each cluster has Z = 3 FBSs. The inter- MBS distance is 500 m, while the inter-fbs distance is 0 m within the same cluster. The system serves a total of 5 MUEs and 180 FUEs which are distributed uniformly over D. 3GPP urban path-loss [15] and Rayleigh fading channel models are used. Table I summarizes the simulation parameters. In this section, we compare three schemes; namely, capacity maximization (), two-tier energy efficiency maximization (-EEM), and only-femto-tier energy efficiency maximization (F-EEM). In the scheme, as the name implies, the system maximizes the average capacity of the two tiers in the same distributed manner, while the -EEM scheme is the scheme described in Section III. The F-EEM scheme is a mixed scheme in which the macro-tier maximizes its average capacity while the femto-tier maximizes its energy efficiency. We evaluate the performance in terms of energy efficiency and average capacity. In addition, we investigate the influence of introducing FBSs to the single-tier system. Only for the latter case, to evaluate the performance of the single-tier system, we simply assume that there is no cross-tier interference.

5 7 x x 106 Energy Efficiency (bps/watt) EEM, cross-tier interference = 0 -EEM, cross-tier interference = P TM Fig.. Macro-tier energy efficiency versus MBS maximum allowable transmit power, P T F = 10 dbm. Average Energy Efficiency (bps/watt/cluster) 7 x EEM -EEM, cross-tier interference = P TM Fig. 3. Femto-tier average energy efficiency versus MBS maximum allowable transmit power, P T F = 10 dbm. A. Energy Efficiency Figs. and 3 show the energy efficiency of the macro-tier and femto-tier, respectively, as a function of the MBS available power budget P T M, for P T F = 10 dbm. From the macro-tier perspective, as seen in Fig., the coexistence of both the MBSs and FBSs deteriorates the energy efficiency in both and -EEM schemes. This loss is due to the cross-tier interference caused by the femto-tier which makes each MBS to increase its transmit powers to maintain the same capacity which, in turn, leads to a lower energy efficiency. When comparing the scheme to -EEM scheme, we can observe that the is a greedy scheme since its objective is to maximize the average capacity, not the energy efficiency. This is, the scheme is willing to consume more power when available regardless of how much is the system capacity enhancement or the energy efficiency deterioration which causes the energy efficiency to decrease. On the other hand, the -EEM scheme tends to have a constant performance to maintain a higher energy efficiency with limiting its power consumption. Fig. 3 makes the same comparison, as in Fig., but from the femto-tier perspective. It can be seen that the femto-tier achieves a very high energy efficiency compared to the macrotier which compensates for the aforementioned performance loss in the macro-tier. Thus, with the existence of the femto- Average Energy Efficiency (bps/watt/cluster) 3, P TM -EEM, P TM, P TM -EEMM, P TM F-EEM, P TM P TF Fig.. Femto-tier average energy efficiency per cluster versus FBS maximum allowable transmit power. tier, the overall system performance outperforms the single-tier system in terms of energy efficiency. It can also be seen in Fig. 3 that the average energy efficiency of the femto-tier decreases with increasing the MBS maximum transmit power. This loss is due to the increase in cross-tier interference that forces each FBS to increase its transmit power. However, the -EEM scheme limits this loss in energy efficiency by clipping the MBSs transmit power after the achieving the highest energy efficiency (Fig. ) and imposing the interference constraint C3. Fig. illustrates the relationship between the FBS maximum transmit power P T F and the average femto-tier energy efficiency for different MBS maximum transmit power P T M. For the scheme, the average energy efficiency of the femto-tier decreases with increasing P T M (e.g., from 37 dbm to 3 dbm in this case). This occurs due to the increas in crosstier interference. For the -EEM scheme, Fig. shows that, no matter how high P T M is, the femto-tier always maintains its maximum average energy efficiency. This is true when the macro-tier operates in the constant-performance regime or in the high power regime (Fig. ) because the MBSs power consumption is the same even when more power is available. In addition, the F-EEM scheme gives a better performance than the scheme (Fig. ); however, the energy efficiency loss is inevitable, compared to -EEM scheme, since the macro-tier aims at maximizing its average capacity. B. Average Capacity The results in Figs. 5-7 along with the results in Figs. - explain the behavior of the whole system. For example, Fig. 5 shows the loss in the macro-tier average capacity due to the presence of cross-tier interference caused by FBSs in both and -EEM schemes. It also shows the loss of the average capacity in the high MBS maximum power regime for -EEM scheme compared to scheme. Note that this loss is intended by the system by reducing the power consumption in order not to degrade the macro-tier energy efficiency. Fig. 6 depicts the effect of increasing the FBS maximum transmit power P T F on the macro-tier average capacity, for P T M. It can be seen that the macro-tier capacity deteriorates with with increasing P T F. The -EEM scheme provides a lower average macro-tier capacity compared to the since its objective is not maximizing the capacity.

6 Average Capacity (bps/hz/mbs) EEM, cross-tier interference = 0 -EEM, cross-tier interference = P TM Fig. 5. Macro-tier average capacity versus MBS maximum allowable transmit power, P T F = 10 dbm. Average Capacity (bps/hz/mbs) EEM, cross-tier interference = 0 -EEM, cross-tier interference = P TF Fig. 6. Macro-tier average capacity versus FBS maximum allowable transmit power, P T M. Average Capacity (bps/hz/fbs) , P TM -EEM, P TM, P TM -EEM, P TM F-EEM, P TM P TF Fig. 7. Femto-tier average capacity per FBS versus FBS maximum allowable transmit power. However, the performance approaches that of the scheme for high values of P T F because the capacity is limited by the cross-tier interference. On the other hand, Fig. 7 shows the benefits of using the -EEM scheme over the F-EEM and schemes from the femto-tier and total system point of view. The -EEM scheme achieves the highest average capacity independent of the MBS maximum transmit power when the macro-tier operates in the constant energy efficiency regime. Since the capacity of the femto-tier is much higher than that of the macro-tier, the overall performance of the system when using the -EEM scheme outperforms the F-EEM and schemes in terms of both energy efficiency and total capacity. VI. CONCLUSION We have proposed an energy-efficient distributed resource allocation scheme for downlink transmission in two-tier OFDMA femtocell networks. The results have shown that the proposed scheme has a better performance, in terms of energy efficiency, compared to the schemes that maximize the system average capacity. In addition, it improves the average system capacity and energy efficiency compared to single-tier systems. Fairness is not guaranteed in the proposed scheme since there is no constraint on the single user minimum data requirement. However, introducing the femto-tier increases the opportunity of users to experience good service and high data rates. REFERENCES [1] N. Saquib, E. Hossain, L. B. Le, and D. I. Kim, Interference management in OFDMA femtocell networks: Issues and approaches, IEEE Wireless Communications, vol. 19, no. 3, pp , 01. [] O. Somekh, O. Simeone, Y. Bar-Ness, A. M. Haimovich, and S. Shamai, Cooperative multicell zero-forcing beamforming in cellular downlink channels, IEEE Trans. Inf. Theory, vol. 55, no. 7, pp , 009. [3] S. Venkatesan, A. Lozano, and R. Valenzuela, Network MIMO: Overcoming intercell interference in indoor wireless systems, in Conf. Rec. of IEEE 1st Asilomar Conference on Signals, Systems and Computers (ACSSC), 007, pp [] G. Fettweis and E. Zimmermann, ICT energy consumption-trends and challenges, in Proc. of the 11th International Symposium on Wireless Personal Multimedia Communications (WPMC), vol., no., 008. [5] W. C. Cheung, T. Q. Quek, and M. Kountouris, Throughput optimization, spectrum allocation, and access control in two-tier femtocell networks, IEEE J. Select. Areas Commun., vol. 30, no. 3, pp , 01. [6] D. W. K. Ng, E. S. Lo, and R. Schober, Energy-efficient resource allocation in multi-cell OFDMA systems with limited backhaul capacity, in IEEE Trans. Wireless Commun., vol.11, no.10, pp , 01. [7] Y. Shin, T. S. Kang, and H. M. Kim, An efficient resource allocation for multiuser MIMO-OFDM systems with zero-forcing beamformer, in 007 IEEE 18th International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC), 007, pp [8] W. Li, W. Zheng, H. Zhang, T. Su, and X. Wen, Energy-efficient resource allocation with interference mitigation for two-tier OFDMA femtocell networks, in 01 IEEE 3rd International Symposium on Personal Indoor and Mobile Radio Communications (PIMRC), 01, pp [9] W. Cheng, H. Zhang, L. Zhao, and Y. Li, Energy efficient spectrum allocation for green radio in two-tier cellular networks, in 010 IEEE Global Telecommunications Conference (GLOBECOM), 010, pp [10] T. Yoo and A. Goldsmith, On the optimality of multiantenna broadcast scheduling using zero-forcing beamforming, IEEE J. Select. Areas Commun., vol., no. 3, pp , 006. [11] F. Richter, A. J. Fehske, and G. P. Fettweis, Energy efficiency aspects of base station deployment strategies for cellular networks, in IEEE 70th Vehicular Technology Conference Fall (VTC), 009, pp [1] W. Dinkelbach, On nonlinear fractional programming, Management Science, vol. 13, no. 7, pp. 9 98, [13] A. H. Sakr and E. Hossain, Location-aware coordinated multipoint transmission in OFDMA networks, in Proc. of IEEE International Conference on Communications 01 (ICC 1), Sydney, Australia, 01. [1] S. Boyd, L. Xiao, and A. Mutapcic, Subgradient methods, lecture notes of EE39o, Stanford University, Autumn Quarter, vol. 00, 003. [15] 3GPP, Further Advancements for E-UTRAN physical layer aspects (Release 9), 3GPP, TR 36.81, Mar. 010.