Energy-Efficient Resource Allocation in Macrocell-Smallcell Heterogeneous Networks

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1 Energy-Efficient Resource Allocation in acrocell-mallcell Heterogeneous etwors Lingyun Feng, Yueyun Chen, and Xinzhe Wang University of cience and Technology Beijing, China { , Abstract Cellular users in indoor environments have difficulty to enjoy high rate services from acro Base tation (B) due to the penetration loss. mallcell, as a complement to acrocell, can enhance the coverage by constituting heterogeneous networ (Hetet). Hetet has been investigated as a promising technique and is considered as a candidate for green communications. However, interference in Hetet is an emergency issue. In this paper, an energy-efficient subchannel and power allocation scheme for a downlin of acrocell-mallcell Hetet is proposed. The resource allocation problem to maximize the Energy Efficiency (EE) for all mallcell Base tations (Bs) is formulated as a non-convex optimization problem with the condition of the guaranteed data rate and the cross-tier interference constraint. The problem is transformed into an equivalent form which can be solved by an iterative algorithm. The dual decomposition method is utilized in each iteration to obtain the closed-form solution for the optimal power and resource bloc allocation. imulation results show that the proposed EEmax algorithm outperforms the resource allocation algorithm of total capacity maximization in the performance of energy-efficient with a bit of little cost of spectrum efficiency. Index Terms Convex optimization, energy efficiency, resource allocation, smallcell I. ITRODUCTIO In a cellular networ, more than 60% of voice services and more than 90% of data traffic tae place indoor []. Therefore, it is increasingly important to provide better indoor coverage for voice, video and other high-speed data services for cellular networ operator. Therefore, mallcell, which can be used to provide indoor wireless networ coverage, is becoming more and more widely used in daily life. mallcell has a low coverage, which can greatly decrease the distance between user and base station. Therefore, the transmission power of user can be greatly reduced and the service life of mobile terminal can be increased. mallcells act as a complement to the traditional base stations (called arcocell) in cellular systems are becoming a hot research issue in the operator and academic field by constituting heterogeneous networ (Hetet). anuscript received arch, 206; revised June 22, 206. This wor is supported by the ational atural cience Foundation of China under Grant o and the Foundation of Beijing Engineering and Technology Center for Convergence etwors and Ubiquitous ervices. doi:0.2720/jcm Journal of Communications 609 Due to the scarcity of spectrum and the difficulty of actualize, spectrum sharing between mallcell and acrocell is more reasonable than spectrum division [2]. In a spectrum sharing networ, cross-tier interference between the mallcell and the acrocell is an emergency and open issue, and it will seriously affect energy efficiency. Therefore, improving the energy efficiency through resource allocation algorithm in the two-tier networ is a meaningful and challenging research issue. ower allocation has been widely used to maximize user s capacity while alleviating cross-tier interference in two-tier networs. In [3] power control is utilized to ensure adequate IR for indoor cell edge user. In [4] a tacelberg game based power control is formulated to maximize mallcells capacity. A distributed resource allocation scheme based on a potential game and convex optimization is proposed in [5] to increase the total capacity of macrocells and femtocells. Reference [6] applies the dual decomposition method to solve the sum-data-rate maximization problem in multi-user Orthogonal Frequency Division ultiple Access (OFDA) system. An energy-efficient resource assignment and power allocation in heterogeneous cloud radio access networs with Lagrange dual decomposition method is proposed in [7]. Authors in [8] propose the energy-efficient resource allocation with the consideration on Qo and bachaul lin constraints in multi-cell scenario. In [9] a Lagrangian dual decomposition based on power allocation scheme is proposed with cross-tier interference mitigation. On the other hand, channel allocation is applied to suppress the cross-tier interference. However, few wors on the energy-efficient resource allocation in Hetet with the consideration on the cross-tier interference have been studied. In this paper, we focus on an energy-efficient subchannel and power allocation scheme for a downlin of Hetet. It shows that the proposed algorithm outperforms the other algorithms in terms of the energy efficiency. The main contributions of the paper are summarized as follows: ) In the scenario of Hetet, an energy efficiency model for all mallcell Base tations (Bs) is formulated as a non-convex optimization EEmax problem with the condition of the guaranteed data rate and the cross-tier interference constraint. 2) To solve the proposed non-convex EEmax problem, the original optimized model is divided into fractional

2 where am, n, 0,, indicates whether or not the -th RB nonlinear programming and transformed into an equivalent form which can be solved by iterative algorithm. 3) The closed-form expression of the optimal power and resource bloc allocation problem is derived for each iteration with the Lagrangian dual decomposition method. 4) The efficiency of the proposed EEmax algorithm is verified by simulations, and the cost of EE improvement is a little bit of spectrum efficiency. The rest of this paper is organized as follows. ection II introduces the system model and formulates the resource allocation problem. In ection III, the non-convex problem is trans- formed into an equivalent optimization problem. By utilizing the dual decomposition method in each iteration, the transformed EE maximization problem is solved by an iterative algorithm. In ection IV, performance of the proposed algorithm is evaluated by simulations. And finally concluding remars regarding of the proposed algorithm appear in ection V. is assigned to the n-th UE in the m-th B. IR m, n, hm.2n. hm, n2, 0 B0 (3) d m,n, m,n, 2 where dm,n, hm,n, 2 hm,n, 0 B0 Therefore, we have Rm am,n, B0 Log 2 d m,n, m,n, (4) where m, n, expresses the transmit power of the m-th B allocated to the n-th UE on the -th RB; denotes the 2 transmit power of the B; hm,n, is the channel gain 2 from the m-th B to the n-th UE on the -th RB; hm,n, indicates the channel gain from the B to the n-th UE on the -th RB in the m-th B; 0 expresses the noise power spectrum density. The total power consumption a, p is mainly related II. YTE ODEL AD ROBLE FORULATIO The system model is as shown in Fig.. In this system model, we consider a single-cell downlin double layers networ, which contains a acro Base tation (B) and several macro users (UE). mallcell Base tations (Bs) are randomly distributed in the macrocell. Each smallcell base station has randomly distributed smallcell users (UE). The considered UE are located near B but far from the serving B. Thus, the cross-tier interference from B to these UE must be limited for maintaining the quality of service. As the coverage of each smallcell is usually not overlapped, transmission power is low, and the transmission loss is large. The common channel interference between smallcells is assumed to be part of the thermal noise. The bandwidth of each resource bloc is B0. The channel gain model is independent and identically distributed Rayleigh fading. to the transmit power and circuit power. The total power consumption can be obtained by a, p m (5) m where m represents the power consumption of the m-th B. m am, n, m, n, c (6) where c is circuit power consumption. Therefore, the energy-efficiency of reference smallcell is defined as the ratio of the sum of throughput to the total power consumption, of which the unit is bps/w. The optimization problem is performed under the following constraints. Total power constraint: a m,n, m,n, max m,n, 0 m (7) Fig.. ystem model of the two-tier networ. where max denotes total transmit power constraint of the B. The data rate requirement η0 should be guaranteed for mallcells whole throughput is: smallcell users to maintain their performance, which requires the following constraint C a, p Rm a () m where Rm indicates the data rate of m-th B. (2) 206 Journal of Communications B0 Log 2 d m,n, m,n, 0 n, m (8) et the interference threshold in order to control cross-tier interference from B to the UE which is nearest to B in the marcocell. Rm am, n, B0 Log 2 IR m,n, 60

3 am,n, m,n, hm,2n, 0 max C a, p a, p (9) C a, p a, p 0 Our target is to maximize the energy-efficiency of B under the cross-tier interference constraint and smallcell users data rate constraint. The corresponding problem can be formulated as the following non-convex optimization problem: max C a, p a, p a m m, n, a m uch equivalence has been proved in some wors in [7], [8]. By this theorem, for any optimization problem with an objective function in fractional form, there exists an equivalent objective function in subtractive form. F max C a, p a, p B0 Log 2 d m, n, m, n, m, n, m, n, where the Eq. (2) is equivalent to find the root of the nonlinear equation F 0. c Due to the integer variable a m, n,, the feasible domain st: C a m,n, of a is a discrete and finite set consisting of all possible RB allocation schemes. Thus, F is generally a, m n C2 a m,n, C3 continuous but non-differentiable function with respect to. Besides, it is clear that F is a convex and strictly B0 Log 2 d m,n, m,n, η0 n, m decreasing function with respect to. It is obvious that 2 am,n, m,n,hm,n, δ0 yields F 0 and F 0 with C4 m,n, m,n, max number of iteration is large enough. m,n, 0 m B. Lagrange-Dual-ethod-Based Resource Allocation olve the non-convex problem by Lagrange dual decomposition method. The dual optimization problem is as follows: The constraint condition C indicates the RB allocation limit, which can only be assigned to at most one smallcell user at a time. C2 indicates the minimum data rate requirements for each UE. C3 sets the interference threshold in order to control cross-tier interference from macro users close enough to the smallcell. 0 represents a min um,n,, vm vm 0 m where u m, n, and v m are the dual variables for the constraints C2, C3 and C4, respectively. Assuming the -th RB in the m-th B is assigned to n-th user, then a m, n,. Right now: g um.n vm max L m, n, um, n vm where L m, n, um, n vm expresses the Lagrange function of the original problem with constraint conditions C2, C3 and C4. In addition, through literature [2] the dual optimization problem often is convex, and the dual gap is almost 0 when the number of resources is sufficient for the primal problem and dual problem. Therefore, the dual function is decomposed into independent optimization problems, which can be given by () s.t: C,C2,C3,C4 where is defined as a positive variable indicating the EE. The optimal value of EE, defined as C a, p a, p (5) { m,n, } A. roblem Equivalence The original problem in Eq. (0) can be transformed into the following equivalent form: a, p (4) 0 III. UBCHAEL AD OWER ALLOCATIO ALGORITH EEAX max C a, p - a, p g um, n,, vm s.t um, n 0 n m cross-tier interference threshold, which is derived from the distance between B and UE and the requirements of the IR. C4 represents the total transmission power constraint of the B. By the definition of energy efficiency, the optimization problem (0) is non-convex, and cannot be solved by an effective algorithm. But the main function can be divided into fractional nonlinear programming [0]. Implied by [], we transform the primal problem into an equivalent problem to solve the problem (0) in ection III. g um, n vm max[ um,n B0 Log 2 d m,n, m,n, { m,n, } - m, n, vm m, n,, is n - achieved if and only if 206 Journal of Communications. It can be shown that F will converge to zero when the a (3) ( a, p ) (0) (2) (a, p) 6 2 m,n, m,n, h ] (6)

4 It is obvious that the above function is convex in m, n,. With using the T condition, the optimal power allocation is derived by u mn, 0 m, n, 2 Ln2 vm d hm, n, m, n, where 2 Therefore, we have bring B u B Ln v h y (7) 2 m, n 0 m m, n, m, n, y m, n, m, n, d mn,, (8) We compare all the UE allocations of the -th RB, m, n, in g um, n vm, the optimal RB allocation indicator for the given dual variables can be obtained by where a n arg max H 0 otherwise n m, n, H u Log y d m, n, (9) mn, m, n,, 2,,,, m n m n m n Ln2 ym, n, dm, n, u In this paper, an iterative algorithm for energy-efficient resource allocation is proposed to solve the transformed problem (). C. Iterative rocess Based on Lagrange Dual ethod Algorithm Energy-Efficient Resource Allocation ) et the maximum number of iterations I max, convergence condition r and the initial value. 2) et the iteration index i and begin the iteration. 3) for i I max 4) olve the resource allocation with i 5) Obtain a i, 6) if C a i, p i i a i, p i 7) et, a p a, p and 8) brea ; 9) else i ; p, C a, p, a, p ; r then ( i) ; C a, p i 0) et and i i ; i i a, p ) end if 2) end for At the time of the iterative algorithm, the update equation of the Lagrange factor at the l th iteration is as follows: l l l l um, n um, n u u m, n m, n l l l l (20) [ ] (2) l l l l vm vm v v m m (22) where u, and v denote the gradient utilized l m, n l in the l th iteration. l m l u, l l v and are the positive step sizes. Among them, the expression of the Lagrange factor gradient is as follows: l l l um, n am, n, B0 Log2 dm, n, m, n, 0 m, n (23) l l l 2 0 am, n, m, n, hm, n, m n l l l m max m, n, m, n, n (24) v a m (25) l where a m, n, and l m n,, represent the RB allocation and power allocation derived by the dual variables of the l -th iteration. Therefore, the power and resource bloc for maximize EE can be obtained by the above algorithm, called EEmax. IV. IULATIO REULT AD DICUIO imulation results are given in this section to evaluate the performance of the proposed energy-efficient resource allocation algorithm. In the simulations, spectrum-sharing mall- cells are randomly distributed in the macrocell coverage area, and smallcell users are randomly distributed in the coverage area of their serving smallcells. The simulation parameters are shown in Table I. TABLE I: THE IULATIO ARAETER arameter Value acro cell radius 500m acro user number 20 Distance between B and UE mall cell radius Rand(0,500) 50m UE number in each small cell 5 Distance between B and UE Distance between B and UE Distance between B and UE oise power spectral density 0 B transmission power ystem bandwidth B 0 Rand(0,50) Rand(60,20) Rand(350,420) -74dBm/Hz 45dBm 4Hz Resource bloc number 20 Circuit power consumption C UE data probability requirement 0 20dBm 60bps ath loss model B-to-UE log d 0 ath loss model B-to-UE log d 0 Fig. 2 shows that the energy efficiency in different algorithms with different number of smallcell users per smallcell. We see that the energy efficiency based on our proposed EEmax algorithm always outperforms the performance of Dmax algorithm. We can also find that, the more the number of users in a smallcell, the better the 206 Journal of Communications 62

5 performance can be obtained. This is because, as the number of the total subchannels in each smallcell is fixed, with the increase of the number of smallcell users in each smallcell, each subchannel has more candidate smallcell users to select. Therefore, higher energy efficiency can be obtained. 3 x EEmax Dmax umber of mallcell Users per mallcell Fig. 2. The energy efficiency in different algorithm with different number of smallcell users per smallcell. Fig. 3 shows the energy efficiency in different algorithms with different UE-IR thresholds. We can see that algorithm EEmax outperforms algorithm Dmax in terms of energy efficiency. It can also be seen from the figure that energy efficiency decreases with increase in UE-IR threshold. This is because the interference constraints restrict the transmit power of B in order to maintain the UE s required IR..35 x EEmax Dmax UE-IR threshold Fig. 3. The energy efficiency in different algorithm with different UE-IR threshold. From Fig. 4 we can see that the iterative algorithm can converge to the optimal energy efficiency after 5 iterations. We can also see that when the maximum transmission power is low, the energy efficiency we can achieve after several iterations is relatively low. At this moment the power consumption is mainly consumed in the circuit. With increase of the transmission power, energy efficiency is improved. From Fig. 5 we can see that when UE s IR threshold is low, B can have larger transmission power. The energy efficiency can reach its pea value after several iterations. When UE s required IR is higher, the interference constraints will restrict the transmit power of B in order to maintain the UE s required IR. At present, the energy efficiency of smallcells is shown in the picture below..4 x UE-IR-th=-0dB UE-IR-th=0dB UE-IR-th=0dB umber of Iterations Fig. 5. Energy efficiency (bps/w) versus number of iterations with different cross-tier interference constraints. Fig. 6 shows that the energy efficiency of the total throughput for D maximum resource allocation algorithm improves with the increase of the transmission power, but lower than the energy efficiency of the maximum resource allocation algorithm. On the other hand, the energy efficiency of the maximum resource allocation algorithm can reach its pea value with the increase of transmission power..3 x x max =0dBm 0.9 max =20dBm max =30dBm umber of Iterations Fig. 4. Energy efficiency (bps/w) versus number of iterations with different maximum transmit power of each B. EEmax and -0dB Dmax and -0dB ax Transmit ower of B(dBm) Fig. 6. Energy efficiency (bps/w) versus transmit power of B and cross-tier interference constraints. From Fig. 7 we see that the spectrum efficiency based on Dmax algorithm always outperforms the performance of EEmax algorithm. That is because the EEmax algorithm 206 Journal of Communications 63

6 pectrum Efficiency(bps/Hz) mainly considers maximum energy efficiency through reasonably allocating the resource and power. Therefore, the EEmax algorithm has some loss in the spectrum efficiency. However, it is acceptable when considering the enhancement in energy efficiency EEmax Dmax umber of mallcell Users per mallcell Fig. 7. The spectrum efficiency in different algorithm with different number of smallcell users per smallcell. V. COCLUIO In a spectrum sharing networ, cross-tier interference between the smallcell and the macrocell is an emergency issue and it will seriously affect energy efficiency. Improving the energy efficiency through resource allocation algorithm in the two-tier networ is meaningful. In this paper, we focus on subchannel and power allocation scheme for a downlin of macrocell-smallcell Heterogeneous etwor to maximize the energy efficiency. With the condition of the guaranteed data rate and the cross-tier interference constraint, the subchannel and power allocation problem to maximize the energy efficiency for all Bs is formulated as a non-convex optimization problem. In order to solve the proposed non-convex problem, we transformed it into an equivalent form of fractional nonlinear programming which can be solved by an iterative algorithm. imulation results show that the proposed EEmax algorithm outperforms the other algorithms in terms of the energy efficiency. The energy efficiency resource allocation with advanced cross-tier interference management in Hetet will be a hot research direction in the future. ACOWLEDGET This wor was supported by the ational atural cience Foundation of China under Grant o and the Foundation of Beijing Engineering and Technology Center for Convergence etwors and Ubiquitous ervices. REFERECE [] V. Chandrasehar, J. G. Andrews, and A. Gatherer, Femtocell networs: A survey, Communications agazine, vol. 46, no. 9, pp , [2] J. Cullen, Radio-frame presentation, Femtocell Europe, London, U, June [3] J. Zhang and G. Roche, Femtocells: Technologies and Deployment, ew Yor: Wiley, 200. [4] D. López-érez, et al., OFDA femtocells: A roadmap on interference avoidance, Communications agazine, vol. 47, no. 9, pp. 4-48, [5] D. Lopez-erez, et al., Enhanced intercell interference coordination challenges in heterogeneous networs, Wireless Communications, vol. 8, no. 3, pp , 20. [6] H.. Jo, et al., Interference mitigation using uplin power control for two-tier femtocell networs, IEEE Transactions on Wireless Communications, vol. 8, no. 0, pp , [7] D. C. Oh, H. C. Lee, and Y. H. Lee, ower control and beamforming for femtocells in the presence of channel uncertainty, IEEE Transactions on Vehicular Technology, vol. 60, no. 6, pp , 20. [8] X. ang, R. Zhang, and. otani, rice-based resource allocation for spectrum-sharing femtocell networs: A stacelberg game approach, IEEE Journal on elected Areas in Communications, vol. 30, no. 3, pp , 202. [9] J. Zhang, Z. Zhang,. Wu, and A. Huang, Optimal distributed subchannel, rate and power allocation algorithm in OFD-based two-tier femtocell networs, Vehicular Technology, 200, pp. 5. [0] J. im and D. H. Cho, A joint power and subchannel allocation scheme maximizing system capacity in indoor dense mobile communication systems, IEEE Transactions on Vehicular Technology, vol. 59, no. 9, pp , 200. [] L. Giupponi and C. Ibars, Distributed interference control in OFDA-based femtocells, in roc. IEEE 2st International ymposium on ersonal Indoor and obile Radio Communications, 200, pp [2]. Tao, Y. C. Liang, and F. Zhang, Resource allocation for delay differentiated traffic in multiuser OFD systems, IEEE Transactions on Wireless Communications, vol. 7, no. 6, pp , Lingyun Feng is a graduate student in the chool of Computer & Communication Engineering, University of cience and Technology Beijing, China. he received a bachelor degree from Tangshan College. Her research areas are wireless communications and heterogeneous networ. Yueyun Chen is a professor in the chool of Computer & Communication Engineering, University of cience and Technology Beijing, China. he received a bachelor degree from outh China University of Technology, and a master degree and a h.d. from Beijing Jiaotong University. Her current research interests include wireless and mobile communications, massive IO, signal processing, radio resource management, cognitive radio, millimeter wave communications, optimization theory on communications. Xinzhe Wang is a graduate student in the chool of Computer & Communication Engineering, University of cience and Technology Beijing, China. he received a bachelor degree from orth China University of cience and Technology. Her research areas are wireless communications and Co. 206 Journal of Communications 64