Cross-Entropy-Based Energy-Efficient Radio Resource Management in HetNets with Coordinated Multiple Points

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1 Article Cross-Entropy-Based Energy-Efficient Radio Resource Manageent in HetNets with Coordinated Multiple Points Jia Yu 1,2, Shinsuke onaka 1, Masatake Akutagawa 1 and Qinyu Zhang 2, * 1 Graduate School of Advanced Technology and Science, Tokushia University, Tokushia , Japan; yujia_hitsz@hotail.co (J.Y.; konaka@ee.tokushia-u.ac.jp (S..; akutaga@ee.tokushia-u.ac.jp (M.A. 2 Counication Engineering Research Center (CERC, Shenzhen Graduate School, Harbin Institute of Technology, Shenzhen , China * Correspondence: zqy@hit.edu.cn; Tel.: Acadeic Editor: Willy Susilo Received: 1 Noveber 2015; Accepted: 26 January 2016; Published: 2 February 2016 Abstract: Energy efficiency and spectru efficiency are the ost iportant issues for future obile systes. Heterogeneous networks (HetNets with coordinated ultiple points (CoMP are wildly approved as a proising solution to eet increasing deands of obile data traffic and to reduce energy consuptions. However, hyper-dense deployents and coplex coordination echaniss introduce several challenges in radio resource anageent (RRM of obile counication systes. To address this issue, we present an RRM approach for CoMP-based HetNets, which ais to axiize weighted energy efficiency while guaranteeing the data rate of each transission. The proposed RRM approach is based on a cross-entropy (CE optiization ethod that is an effective and low-coplexity heuristic algorith. Furtherore, we also give the ipleentations of the proposed RRM approach in centralized and decentralized ode, respectively. At last, extensive siulations are conducted to validate the effectiveness of the proposed schees. eywords: cross-entropy (CE ethod; heterogeneous network (HetNet; coordinated ultipoint (CoMP; energy efficiency (EE 1. Introduction Heterogeneous networks (HetNets [1,2] are proposed in long-ter evolution-advanced (LTE-A systes by the 3rd Generation Partnership Project (3GPP to not only eet the rapidly increasing deands of obile data traffic, but also to reduce the huge energy consuptions caused by data transissions. A HetNet is a hierarchical network where low-power access points (APs, also naed sall cell sites [3,4] are included in a acro-cell, in order to provide highly qualified services. Typical sall cell sites include pico, feto, relay and so forth. Feto [5] is ainly for indoor transissions, while pico [6] is used outdoors in a crowded place, such as a university. Relay [7] is usually built in a reote area far fro the acro-cell site (naed the Evolved Node B, or enodeb, in LTE-A HetNet to extend the coverage of the acro-cell. Figure 1 presents a siple exaple of a HetNet. Inforation 2016, 7, 3; doi: /info

2 Inforation 2016, 7, 3 2 of 17 Figure 1. Illustration of a HetNet. Although HetNets are widely considered as the ain trend in the developent of obile counication systes [3], several challenges should be dealt with before ipleentation in the real world. One of the ajor challenges is severe intercell interference aggravated by the dense deployent, which crucially affects the perforance of HetNets. As a proising easureent to deal with intercell interference, coordinated ultiple point (CoMP [8] techniques are considered to be helpful for HetNets. The basic idea of CoMP techniques is to coordinate coordinated neighboring cells, so that intercell interference can be reduced to a large extent. According to the different ways to cooperate, CoMP techniques are classified into two categories, coordinated scheduling/coordinated beaforing (CS/CB and joint processing (JP [9]. CS/CB CoMP akes neighboring cells jointly pre-code according to global channel state inforation (CSI to avoid potential interference, while JP CoMP allows neighboring cells to jointly process signals intended for a specific user in the overlapping area. Joint transission (JT is a typical JP CoMP technique that requests of cooperating cells to transit the sae data packets to a user independently and siultaneously. In this paper, we take JT CoMP as an exaple to discuss the perforance of CoMP-based HetNet, and the study can also be extended to other CoMP techniques. To fulfill the requireents of the future obile networks, CoMP-based HetNets need to provide qualified services as uch as possible while aintaining acceptable energy consuption. According to report [10], energy consuption caused by inforation and counications technology (ICT has contributed up to 5% of the world-wild power supply at present. To avoid the further increase of energy consuption, obile networks are required to significantly iprove the utility efficiency of power resources. Radio resource anageent (RRM, which adaptively allocates radio resources, such as frequency and power, according to CSIs, is beneficial for CoMP-based HetNets to enhance the energy efficiency. In this paper, we focus on RRM in a CoMP-based HetNet for the purpose of iproving the energy efficiency while guaranteeing high data rates, as well as user fairness. An optiization proble aiing at axiizing weighted energy efficiency is forulated, where the weights are eployed for aintaining the fairness of users s data rates. Several crucial constraints in practice are taken into consideration in the forulated proble. Besides the liitation on total power at each transitter, backhaul links, which connect sall cells to the enodeb for exchanging data and control inforation, are considered to have restricted capacity. Additionally, the lowest data rate of each transission is defined, in order to guarantee the quality of transissions and avoid wasting of energy. Since the forulated proble is unsolvable ixed integer prograing (MIP, we separate the whole proble into a scheduling subproble under the assuption of equal power allocation and a power allocation subproble with known scheduling results. We first proposed a centralized scheduling algorith based on cross-entropy (CE and a corresponding power allocation algorith. Since centralized algoriths involve nuerous calculations, the tie delay could be intolerable in a large-scale network. An alternative ethod to decrease the tie delay is to conduct resource allocation in a decentralized way, where calculations are distributed to sall cells. For this reason, we also propose odified algoriths that can be used in a decentralized ode. The rest of this paper is organized as follows. In Section 2, we present the considered syste odel. Then, the atheatical forulation of the discussed proble is described in Section 3. Section 4 proposes a centralized strategy of resource allocation, which includes a CE-based scheduling

3 Inforation 2016, 7, 3 3 of 17 algorith and a power allocation algorith. Section 5 odifies the proposed algoriths, so that they can be utilized in a decentralized syste. Siulation results and relevant analysis are shown in Section 6. At last, we conclude our work in Section Syste Model For the sake of siplicity, each independent transitter, including the acro-cell site and icro-cell sites, is hereby designated as a transit point (TP in this paper. We consider a downlink syste in a CoMP-based HetNet with M TPs and user eleents (UEs, as shown in Figure 2. N T and N R represent the nuber of antennas on each TP and each UE, respectively. A control unit (CU is assued to be located at the center of the network, which is responsible for anaging data inforation, as well as collecting all CSI in this network. TPs are connected to the CU by backhaul links, whereby control inforation and data packets are delivered to TPs fro the CU. Since JT CoMP is eployed in our work, there are a large nuber of data packets that need to be transitted via backhaul links. TP Backhaul Link TP Backhaul Link CU TP RB RS TP TP Frequency Tie Figure 2. Syste odel. The unit of the radio resource in both tie and frequency diensions is referred to as the resource block (RB. As defined in the LTE standard, an RB consists of 12 consecutive subcarriers for a duration of a transit tie interval ( [12]. In this paper, we assue all TPs share the sae spectru bandwidth, which is divided into N RB RBs in total. Major notations used in this paper are listed in Table 1. Several other iportant assuptions are considered in our work: channel fading is considered to be quasi-static, so that channel coefficients reain constant per ; perfect CSI acknowledgent is assued at both receivers and transitters; TPs are synchronized in ters of tie, frequency and phase, which is reasonable in the considered syste thanks to backhaul connections. Table 1. Major notations. TP, transit point; UE, user eleent; RB, resource block. Nae Meaning Nae Meaning N / nuber of TPs/UEs U set of UEs that attaching to TP N T / N R nuber of antennas at a TP/UE R n k data rate of UE k on RB n M set of all of the TPs R k accuulated average data rate of UE k M k CoMP set of UE k p n transit power used at TP on RB n β n,k index iplying the scheduling result N RB nuber of RBs

4 Inforation 2016, 7, 3 4 of CoMP Set Selection Ideally, a UE can achieve the optial data rate if all TPs cooperatively transit to it. However, the corresponding power consuption and coputational coplexity are unaffordable. An alternative is to select a CoMP set for the UE according to channel conditions. TPs in the CoMP set can provide the UE a favorable data rate at a uch lower cost. A UE-specific selection of the CoMP set includes three steps: 1. TPs broadcast reference signals (RSs periodically. 2. A UE hears the channels and easures the according to the strength of the received RSs. Based on the easureents and a given selection rule, the UE can decide its own CoMP set. 3. The UE acknowledges its decision to the CU. Denote M k as the CoMP set of UE k and M as the set including all TPs in the network. UE k decides its M k following the rule below: M k / M k = arg M RS (the strongest or RS (the strongest RS (TP otherwise where RS indicates the strength of the reference signal and is a threshold in db. UE k distinguishes the strongest RS in the first place and adds the corresponding TP to the CoMP set M k. Other TPs will be added to M k only if the strengths of their RSs are no less than (RS(the strongest db. As suggested in LTE releases, a rational is in the range of 5 6 db [11]. In the case where M k includes only the strongest TP, UE k is referred to as a non-comp UE in this paper, since no cooperation occurs during downlink transissions towards it. On the contrary, UE k is referred to as a CoMP UE if its CoMP set M k includes ore than one TPs. A CoMP UE is possibly is located at an overlapping area of neighboring cells where intercell interference seriously daages transissions. To cobat interference, TPs in M k are asked to conduct JT CoMP transissions to UE k for strengthening transit signals and reducing inter-cell interference Dynaic JT CoMP Transission JT CoMP allows TPs in UE s CoMP set to siultaneously transit the desired data signal to it. Owing to the spatial separation of the transit antennas, ultiple versions of the desired signal will be received by the UE, which generates extra spatial diversity gain and strengthens the signal. According to inforation theory [18], the obtained data rate of a JT CoMP transission to UE k on RB n is given as: H 2,k wn 2 p n R n k = b log 1 + M k H n 2 (2,k w2 p n + σ 2 M\M k where H n,k is an N R N T channel atrix between TP and UE k on the n-th RB. M \ M k is the copleentary of M k in M, which includes all of the interfering TPs. w n is the precoding vector with diensions of N T 1, which aps data strea s n onto the transit antennas of TP, and (w n H w n = 1, E s n = 1,, n. p n is the power used by TP for transitting on RB n, and n n k CN (0, σ2 I NR is the corresponding coplex Gaussian noise vector. b represents the bandwidth of an RB, which is standardized to be 180 khz in LTE-A systes [12]. Equation (2 iplies a static coordinated strategy where TPs in M k are all required to serve UE k all of the tie. However, static strategies are not always optial due to the tie variation of wireless channels. To further iprove the network perforance, we use a dynaic JT CoMP strategy where a subset of each M k rather than M k is adaptively deterined to perfor JT CoMP transission. Define a scheduling index β n,k {0, 1} to indicate scheduling results, where βn,k = 1 eans that TP (1

5 Inforation 2016, 7, 3 5 of 17 is chosen to transit to UE k on the n-th RB. Then, the data rate of a dynaic JT transission can be given as: M β n R n k = b log 1 +,k H 2,k wn 2 p n =1 M ( (3 1 β n H n 2,k,k w2 p n + σ 2 =1 where M =1 βn,k Proble Forulation In this work, we consider a practical RRM proble in ters of both spectru and power in a CoMP-based HetNet odeled in the last section. To iprove the synthesis perforance, the objective involves data rates, power consuption and fairness aong UEs at the sae tie. The optial data rate of the network can be achieved if resources are allocated to UEs with better channel conditions, regardless of those in poor condition. A side-effect of this schee is unfavorable fairness of UEs data rates. In order to enhance the fairness, we introduce the concept of proportional fairness into the objective of the RRM proble. As in [13], we weighted UE s data rate by its average data rate deterined by: R k = α R before k + (1 α R k (4 where 0 < α < 1 is the forgetting factor. The introduced weights bring UEs with worse channel conditions ore of a possibility to occupy resources and, therefore, increase the UEs data rates. The fairness of UEs data rates in the network will be iproved in this way. To quantify the degree of this fairness, [14] introduces a fairness factor, defined as: F = ( R k 2 / R 2 k. (5 Additionally, for the purpose of conserving energy, energy efficiency should be thoughtfully considered. The energy efficiency is defined by the ratio of the obtained data rate to the total power consued correspondingly. Cobining with proportional fairness principle, the objective of the RRM proble is forulated as, ax β n,k,pn N RB n=1 R n k R k / M =1 N RB β n,k pn (6 Equation (6 can be considered to axiize the weighted energy efficiency of the network. In a practical network, syste perforance is restricted by several factors. In addition to liited transit power at each TP, the finite capacity of backhaul links defines the upper liit of throughput achieved by a TP during a. Furtherore, to guarantee the quality of transissions, we ipose a threshold to the data rate of each transission. In suary, the RRM proble of the considered syste can be forulated as:

6 Inforation 2016, 7, 3 6 of 17 ax β n,k,pn N RB n=1 R n k R k / M =1 s.t. C1: 0 p n S,, n N RB β n,k pn C2: β n,k {0, 1}, β n,k 1,, n, k (7 C3: N RB β n,k Rn k C, C4: R n k R thres, k, n In Equation (7, C1 shows the power constraint at each transission where S is the largest transit power allowed by the syste; C2 ensures each index β n,k to be a bit nuber, so that a TP can serve no ore than one UE on each RB; C3 deonstrates the constrained throughput of a TP caused by the liited capacity of backhaul connections to the CU, where C represents the capacity of the backhaul link connecting TP and the CU; and C4 guarantees the data rate of each ongoing transission, where R thres is the given threshold of the data rate. 4. Centralized Algorith Since the proble in Equation (7 is NP-hard, it is unpractical to achieve the optial solution. An alternative ethod is to consider the proble as a cobination of a scheduling proble under the consuption of equal power allocation and a power allocation proble with a given scheduling result. In this way, an approxiated solution of the proble can be obtained in polynoial tie. In the rest of this section, we propose a heuristic algorith based on CE for RB scheduling with equal transit power at the first place. Then, a arush-uhn-tucker-ethod to solve the power allocation proble is presented. The algorith involving both RB scheduling and power allocation proposed in this section is centralized, which eans that the resource allocation is operated at the CU with global CSI. The centralized algorith is capable of achieving a favorable syste perforance, but it requires significant coputational effort of the CU. In the next section, we also propose a decentralized algorith of resource allocation with lower coplexity and delay of coputation, which leads to decreased perforance unavoidably CE-Based Scheduling Algorith The objective of the considered RB scheduling proble becoes: ax β n,k,pn N RB n=1 R n k R k / M =1 N RB β n,k S (8 where S is the fixed transit power. The objective is constrained by C2, C3 and C4 in Equation (7. We first propose a CE-based algorith to solve the RB scheduling proble described above. The CE ethod is a typical heuristic algorith to estiate the probabilities of rare events in coplex stochastic networks [15] and to deal with linear prograing. The basic idea of the CE ethod is to generate sufficient saples under a given strategy and then update the generating strategy according to saples. After iteratively repeating this procedure, generated saples will converge to the optial solution. The proposed CE-based scheduling algorith follows three ajor stages, including initialization, iteration and a copleentary stage to close unfavorable transissions, as shown in Figure 3.

7 Inforation 2016, 7, 3 7 of 17 Initialize the generation probability Generate surficial saples Filter saples Update generation probability Stage One NO Convergent? Stage Two YES Stage Three Output RB scheduling result Reoving unqualified transissions Output Figure 3. The ajor principle of the CE ethod Initialization Let X = [x(1,..., x (n,..., x (N RB ] (x (n [0, U ] denote a saple generated according to a given probability, which presents a possible scheduling result of TP. x(n = 0 eans that no transission is scheduled on RB n of TP. Otherwise, x(n is the ID of the scheduled UE. In the CE ethod, the scheduling proble is regarded as a stochastic procedure. The distribution of x(n is denoted by q,n = [q,n 0, q,n 1,..., q,n u,..., q,n ], where q,n U u = P{x(n = u}, u [0, U ]. Obviously, q,n u has the attributes of 0 q,n u 1 ( u,, n and u [0,U ] q,n u = 1 (, n. For the sake of accelerating convergence, we design the initial probability distribution according to estiated data rates. We first defined P{x(n = 0} = Pr 0 where Pr 0 is a given value. This probability gives an opportunity to TP for scheduling no transission on RB n. For each u U, the data rate R n u is estiated based on the fixed JT CoMP transission, as given by (2, at the initialization stage. As suggested by C4 in (7, the transission is considered to be unqualified if R n u < R thres. To save energy, the proposed algorith sets the corresponding probability to be zero, i.e., q,n u = 0. For the rest of the optional UEs, the probability is defined as q,n u = (R n u/ R tot (1 Pr 0, where R tot indicates the su data rate of all possible qualified transissions, defined as: R tot = Suarily, the initial distribution of x (n is: Iteration R n k (9 k U, R n k R thres Pr 0, u = 0 qu,n = (1 Pr 0 R n u/ R tot, u U, and R n u R thres (10 0, u U, and R n u < R thres Each iteration of the proposed algorith includes three steps. First, the algorith generates adequate saples according to a given strategy. Then, it is necessary to exclude those saples that do not satisfy the constraints and to select good saples for the next stage. At last, the probability distribution needs to be updated according to the selected saples, so that better saples will be generated in the next iteration. After sufficient iterations, the algorith gradually approaches the optial solution. Let N SAM denote the nuber of saples generated in each iteration for each TP and X1,, Xi,, X N SAM denote the corresponding saples, where Xi = [xi(1,, x i(n,, x ]. Each i(n RB

8 Inforation 2016, 7, 3 8 of 17 saple can ap into a scheduling index set {β n,k, k, n}, and leads to a weighted energy efficiency of TP given as: f (X i = N RB n=1 R n x i(n R x i(n / NRB S (11 n=1,xi (n =0 where N RB n=1,x i (n =0 S represents the total power consuption at TP according to saple X i. The ( su data rate of TP can be estiated as R X i = N RB n=1 Rn x i(n. n A qualified saple should satisfy two requireents. First, the su data rate R cannot exceed the backhaul capacity of TP. Therefore, those saples lead to overlarge su data rates, i.e., ( ( R X i > C, will be reoved. Second, the value of f X i should be high enough. Saples ( whose weighted energy efficiency f X (t (t i < f thres will also be reoved, where f thres is a threshold that increases after each iteration until it converges. Consequently, N IM (N IM N SAM qualified saples are left for updating the generation probability. Without loss of generality, qualified saples are denoted as X j (1 j N IM. At the last stage of an iteration, probability distributions are updated on the basis of qualified saples in order to generate better saples in the next iteration. The updated possibility P{x(n = u} is: q,n u = N (x j(n = u /N IM (12 where N (x j(n = u represents the nuber of ties that UE u appears in N IM saples on the n-th RB. The proposed iteration algorith is suarized as Algorith 1. Algorith 1 Iteration in the CE-based scheduling algorith. 1: f ax = f ax_pre = 0; counter = 1; 2: while counter N SAM do 3: Generate saples X according to the distribution q,n. 4: Calculate utility function of Xi, i.e., f ( Xi, according to (11. 5: Calculate the su data rate of X, i.e., R (X = k U R n k. 6: if f (X < f (t thres then 7: CONTINUE; 8: end if 9: if R (X > C then 10: CONTINUE; 11: end if 12: X counter = X 13: counter = counter : end while 15: for i = 1 to N SAM do 16: Calculate f ( Xi according to (11. 17: end for 18: Sort saples in a descending order in ters of f ( X i 19: Calculate N IM = (1 ρn SAM, and let f (t+1 ( thres = f ˆX N IM 20: if f ( ˆX 1 > fax then 21: Xout = ˆX 1, f ax_pre = f ax, f ax = f ( ˆX 1 22: end if 23: Update q,n according to (12 24: Map Xout into βn,k, and recalculate Rn k according to (3. Denote the consequence by ˆX 1, ˆX 2,, ˆX SAM

9 Inforation 2016, 7, 3 9 of Reoving Unqualified Transissions The algorith proposed above cannot ensure that the data rate of each transission is as high as the given threshold R thres. Since we put our purpose on iproving energy efficiency, it is reasonable to close those transissions that are estiated to be unqualified. Algorith 2 suaries the entire RB scheduling algorith proposed above. Algorith 2 Centralized RB scheduling algorith. 1: Calculate R n k according to Equation (2. 2: Initialize probability distribution q ( = 1,, M according to Equation (10. 3: for t = 1 : t ax do 4: for = 1 : M do 5: Process Algorith 1, and output Xout, ( = 1,, M 6: end for 7: Map obtained Xout into {βn,k }. 8: Update R n k according to Equation (3, and obtain {βn,k }. 9: if All of the eleents in q ( = 1,,,, M converge then 10: Output X out 11: BREA 12: end if 13: end for 14: Map obtained X out into {βn,k }. 15: for n = 1 : N RB do 16: for u = 1 : do 17: if R n k < R thres then 18: Let the corresponding β n,u = 0. 19: end if 20: end for 21: end for 4.2. Power Allocation Algorith With the obtained RB scheduling result, the power allocation proble can be given as: ax β n,k,pn N RB n=1 R n k R k / M =1 s.t. C1: 0 p n S,, n C3: N RB N RB β n,k pn β n,k Rn k C, C4: R n k R thres, k, n (13 The objective function in (13 is a well-known non-convex function for which the optial solution does not exist. In this work, we use an analytical ethod on the base of the T-condition to approach a local optial solution of power allocation. A solution of Equation (13 can be achieved by solving its dual function in ters of backhaul and data rate constraints given as: ax p n s.t. ( N RB / R n k M p n=1 R n k =1 0 p n S,, n M =1 λ ( NRB β n,k Rn k C + N RB µ n,k (R n k R thres (14

10 Inforation 2016, 7, 3 10 of 17 where {λ, } and {µ n,k, n, k} are non-negative Lagrangian ultipliers. However, the dual function given above is still hard to solve, since it involves too any variables (MN RB variables and Lagrangian ultipliers. To further siplify the proble, we intend to decopose Equation (14 into independent subprobles with fewer variables. Let β = N RB n=1 βn,k. β = 0 indicate the situation where no transission is scheduled for TP. This is unreasonable in the high-loading network we considered. Thus, we suppose that β = 0; then C can be rewritten as: C = N RB β n,k C N RB β n,k = N RB n=1 β n C,k (15 β After substituting (15 into (14, the proble can be decoposed into N RB independent subprobles, where each subproble is given as: ax p n / R n k M R k =1 s.t. 0 p n S, p n M =1 λ β n,k ( R n k C β + µ n,k (R n k R thres Each subproble in Equation (16 involves M variables with Lagrangian ultipliers only and can be solved independently on each RB. The coputational coplexity is significantly cut in this way. In the rest of this subsection, we propose an iterative ethod to address each subproble. Let f n (p n, λ, µ n,k denote the objective function of Equation (16. Take the first order derivative in ters of p n, and ake it equal to zero; then, a possible value of power allocation, denoted by p n, can be obtained as follows, ( ˆp n = 1 R k p n tot M λ β n,k + µ n,k =1 1 R (ptot n 2 n k R k ;k =k ( b β n,k M H n,k w n 2 1 M R k ptot n λ β n,k + µ n,k =1 Rn k p n A n (16 1 H n,k w n 2 (17 where p n tot = M =1 pn and k is the UE scheduled on RB n of TP, i.e., β n,k = 1. The derivative R n / k p n and A n are given by: and: R n k p n 2 = b( γk n 1 + γk n A n = M H n,k wn 2 β n,k, k = k (18 H n 2,k wn p n H n,k w n 2 p 2 + σ2 (19 M\{} respectively. The obtained ˆp n above ay not be in the range of [0, S]. Therefore, the real power allocation needs to be adjusted following the rule given by: where t indicates the ties of the iteration. p n(t = ax {in { ˆp n, S}, 0} (20

11 Inforation 2016, 7, 3 11 of 17 Lagrangian ultipliers can be updated in each iteration by the sub-gradient ethod [16] as follows, where v (t λ λ (t+1 µ (t+1 n,k = ax { λ (t ( NRB v (t λ β n,k Rn k C { = ax µ (t } n,k v(t µ (R thres R n k, 0 and v(t µ are the step sizes used in the current iteration for updating λ and µ n,k. 5. Decentralized Algorith The centralized strategy of resource allocation proposed above is processed on the CU with the global CSI at the beginning of each. It is possible that the tie delay caused by processing is too long to guarantee the effectiveness of a large-scale syste involving nuerous TPs and UEs. An alternative ethod for shortening the tie delay is a decentralized strategy that distributes calculations to each TP instead of the CU. Under a decentralized strategy, global CSIs are shared between TPs at the first place. Then, the resource allocation is processed at each TP independently and siultaneously, according to the known CSIs and a given strategy. In this way, the tie delay of processing can be significantly decreased, even in a large-scale network. However, due to the lack of knowledge about the scheduling results of other TPs, the accuracy of the decentralized one is unavoidably worse than the centralized one. In this section, we propose a decentralized strategy with the siilar CE-based scheduling and T-based power allocation to the centralized proposed above. Siulation results presented in Section 6 will prove that the decline of syste perforance under the proposed decentralized strategy is acceptable Decentralized RB Scheduling Algorith A decentralized RB scheduling algorith based on the CE ethod is proposed in this subsection. The sae as the centralized one proposed in Subsection 4.1, the decentralized scheduling algorith initializes the probability distribution q at the first place. Then, the iteration procedure is processed to obtain RB scheduling results. It should be noticed that the decentralized strategy cannot accurately estiate data rates of ongoing transissions due to the lack of inforation about the scheduling results of other TPs. Therefore, the decentralized scheduling algorith deletes the procedure of reoving unqualified transissions (as described in Section In the siulation, we consider unqualified transissions as failures, which waste energy and contribute nothing to the data rates of the syste. Algorith 3 suarizes the decentralized RB scheduling based on the CE ethod. Algorith 3 Decentralized RB scheduling algorith. 1: Calculate R n k according to Equation (2. 2: Initialize probability distribution q ( = 1,, M according to Equation (10. 3: for t = 1 : t ax do 4: Process Algorith 1, and output Xout, ( = 1,, M 5: if All of the eleents in q = [q,n, n] converge then 6: Output X out 7: BREA 8: end if 9: end for 10: Map the obtained X out into {βn,k }., 0 } (21

12 Inforation 2016, 7, 3 12 of Power Allocation Algorith In this subsection, we odify the power allocation algorith proposed in Subsection 4.2 to be decentralized, so that it can be processed at each TP independently and siultaneously. The individual power allocation proble of each TP is given by: ax N RB n=1 β n,k R n k R k / s.t. C1: 0 p n S, n C3: N RB β n,k Rn k C C4: R n k R thres, n, k U N RB β n,k pn n=1 As in Subsection 4.2, we constitute and solve the dual function of Equation (22, instead of solving it directly. The dual function in ters of constraints C3 and C4 is given as: ax p n s.t. ( N RB / β n R n k,k β n=1 R n,k pn k + N RB 0 p n S, n µ n,k β n,k (Rn k R thres λ ( NRB β n,k Rn k C Substituting Equation (15 into Equation (23, we can decopose the power allocation proble into N RB independent subprobles. Let f,n denote the objective of the subproble on RB n of TP, which is given as: f,n = / β n R n k,k R k β n,k pn λ β n,k ( R n k C β + (22 (23 µ n,k β n,k (Rn k R thres (24 β n,k = 0 eans that TP does not schedule any transissions on RB n. In this case, power allocation is not required, i.e., p n = 0. In the case where β n,k = 1, transit power pn can be obtained by an iterative ethod proposed in the rest of this subsection. Let k denote the UE of TP scheduled on RB n (i.e., βn,k = βn,k = 1. Taking the first order derivative of f,n with respect to p n, we obtain: f,n p n ( 1 R n = R k p n λ + µ k n,k p n R n k R k (p n 2 (25 where: R n k p n b = H n,k w n 2 p n + M β n H n,k,k w n 2 (26 H n,k w n 2 p n + σ 2 M\{}

13 Inforation 2016, 7, 3 13 of 17 / Let f n p n = 0. An expression of p n in the t-th iteration can be obtained by solving the equation, which is given as: p n(t = R n k R k H n,k w n 2 p n(t + b H n,k w n ( 2 1 M = R k p n(t H n,k w n 2 n(t p + σ 2 (27 (λ µ n,k where ultipliers λ and µ n,k should be updated according to Equation (21. A suboptial p n can be approached after sufficient iterations. 6. Siulation Results We consider a HetNet downlink syste with 37 TPs, where only 19 TPs of these conduct actual counications to UEs, and the others wrap the around to produce virtual interference. The radius of each sall cell is 250, since a dense deployent is considered. The syste includes 100 RBs, each of which is under a bandwidth of 180 khz. Therefore, the overall bandwidth of the syste is 18 MHz. Additionally, 2 2 MIMO links are created using the space channel odel (SCM [17]. Each siulation lasts 20 s, where a is 1 s. Iportant paraeters used in the siulation are listed in Table 2. Table 2. Paraeters in the siulation. Paraeters Value Layout of cells 37 hexagon cells; wrap-around used Radius of cells 250 Central frequency 2 GHz N RB, nuber of RBs 100 S, liit of transit power 20 Watt N T N R 2 2 nuber of / 20 /1 s α 0.1 Channel odel SCM (path loss + shadowing + MIMO fading Minial distance (TP and UE 35 Height of transit/receive antenna 35 /1.5 Penetration loss 20 db Traffic odel full buffer Speed of UE 10 /s The siulation is carried out to prove the proposed algoriths effectiveness. A greedy algorith, naed ax capacity, is also siulated as a benchark. The ax capacity algorith tends to allocate resources to UEs with good channel conditions, in order to reach the optial throughput of the network. In this way, UEs with worse channel conditions ay no chance to counicate. Therefore, the fairness of the ax capacity algorith is unfavorable. Figures 4 and 5 copare the perforances of the ax capacity algorith to that of the proposed one. Figure 4 deonstrates the average throughput per TP and fairness factor (as defined by Equation (5 of the syste under different resource allocation algoriths, when the transit power of each TP is 20 Watts. It is obvious that ax capacity algorith achieves an outstanding throughput and a uch worse fairness factor than the proposed one. The future obile counication syste targets to provide not only high throughput of the network, but also quality service to every UE. Therefore, the ax capacity is no longer appropriate. The proposed algoriths have uch better fairness factors. More iportantly, as shown in Figure 5, the proposed centralized algorith can also achieve an energy efficiency as good as that of ax capacity.

14 Inforation 2016, 7, 3 14 of Throughput per TP (Mbps Centralized scheduling and PA Centralized scheduling Decentralized scheduling and PA Decentralized scheduling Max capacity scheduling Fairness factor Centralized scheduling and PA Centralized scheduling Decentralized scheduling and PA Decentralized scheduling Max capacity scheduling 20 (a Throughput per TP 0.1 (b Fairness factor of UEs data rates Figure 4. Syste perforances under different resource allocation algoriths (20 Watts, infinite C, R thres = 180 kbps. Energy efficiency (Mbps/Watt Centralized scheduling and PA Centralized scheduling Decentralized scheduling and PA Decentralized scheduling and PA Max capacity scheduling 0 Figure 5. Energy efficiencies under different resource allocation algoriths (20 Watts, infinite C, R thres = 180 kbps. Results in Figures 4 and 5 also copare the perforance of the centralized algorith proposed in Section 4 and that of the decentralized algorith in Section 5. The results show that both energy efficiency and throughput are decreased when the decentralized algorith is used. Figure 6 shows the syste perforances of the proposed algoriths when the transit power of each TP is 40 Watts. Coparing the results to Figures 4 and 5, it can be seen that the energy efficiency of the centralized algorith significantly decreases when the transit power of each TP is up to 40 Watts, while the throughput does not increase. This proves that high-level transit power is not appropriate in a dense network. Additionally, the results deonstrate that the decentralized algorith is ore robust, since both energy efficiency and throughput are changed a little when different transit powers are used.

15 Inforation 2016, 7, 3 15 of 17 Energy efficiency (Mbps/Watt Centralized scheduling and PA Centralized scheduling Decentralized scheduling and PA Decentralized scheduling Througput per TP (Mbps Centralized scheduling and PA Centralized scheduling Decentralized scheduling and PA Decentralized scheduling Max capacity scheduling 0 (a Energy efficiency 20 (b Throughput per TP Figure 6. Syste perforance under different strategies (40 Watts, infinite C, R thres = 180 kbps. Siulations are also conducted under infinite, 100-Mbps and 80-Mbps backhaul liits, respectively, with a fixed R thres of 360 kbps, to clearly illustrate the effect on syste perforance caused by backhaul constraints. Restricted backhaul capacity leads to a low throughput per TP, as shown in Figure 7a, since fewer transissions are scheduled in this case. However, the tendency is different in ters of energy efficiency. Figure 7b shows that the energy efficiencies of the proposed algoriths under different backhaul liits are alost the sae. This is explained by the fact that the power consued by transissions is also reduced when backhaul capacity is restricted. Energy efficiency (Mbps/Watt Centralized, infinite C Decentralized, infinite C Centralized, C=100 Mbps Decentralized, C=100 Mbps Centralized, C=80 Mbps Decentralized, C=80 Mbps Throughput per TP (Mbps Centralized, infinite C Decentralized, infinite C Centralized, C=100 Mbps Decentralized, C=100 Mbps Centralized, C=80 Mbps Decentralized, C=80 Mbps (a Energy efficiency 30 (b Throughput per TP Figure 7. Syste perforance under different backhaul capacity (20 Watts, R thres = 360 kbps. At last, we conduct siulations when R thres is 180 kbps, 360 kbps and 540 kbps, respectively, with the fixed backhaul capacity of 100 Mbps. This shows that the throughput of our proposals grows as the increase in R thres, as shown in Figure 8a. This is because ore resources are assigned to the UEs with better channel conditions, which are possible to achieve for quality transissions. Figure 8b illustrates that the value of R thres hardly affects the energy efficiency of the syste. Since those transissions estiated to be inferior to the given R thres are closed, no (or little power is wasted. Therefore, that energy efficiency of the syste can be aintained at a high level.

16 Inforation 2016, 7, 3 16 of 17 Throughput per TP (Mbps Centralized, R thres =180 bps Centralized, R thres =360 bps Centralized, R thres =540 bps Decentralized, R thres =180 bps 10 Decentralized, R thres =360 bps Decentralized, R =540 bps thres 0 (a Throughput per TP Energy efficiency (Mbps/Watt Energy efficiency (Mbps/Watt Centralized, R thres =180 bps Centralized, R thres =360 bps Centralized, R thres =540 bps Decentralized, R thres =180 bps Decentralized, R thres =360 bps Decentralized, R thres =540 bps 0 (b Energy efficiency Figure 8. Syste perforance under different R thres (20 Watts, C = 100Mbps. 7. Conclusions In this paper, we have studied a constrained RRM proble aiing at iproving energy efficiency in a CoMP-based HetNet. To solve the proble, we first propose a CE-based RB scheduling algorith under the assuption of equal power allocation. Then, a T-based algorith for power allocation is presented. The proposed algoriths are considered to be used in a centralized way at the first place. Since the centralized strategy for RRM takes a long tie delay in large-scale networks, we odified the proposed one in order to adapt to a decentralized syste in order to shorten the tie delay for processing. Siulation results copare perforances of both the centralized and the decentralized and discuss the influence on syste perforance caused by the considered constraints. Acknowledgents: We acknowledge Yonsuke inouchi, Takahiro Eote and Ye Wang for useful coents for this work and the odification of this paper. Author Contributions: Jia Yu was responsible for the conception of the paper and the ain writing. Shinsuke onaka, Masatake Akutagawa and Qinyu Zhang were all responsible for the concept of the paper, supervising the work and reviewing. Conflicts of Interest: The authors declare no conflict of interest. References 1. Danjanovic, A.; Montojo, J.; Wei, Y.; Ji, T.; Lou, T.; Vajapeya, M.; Yoo, T.; Song, O.; Malladi, D. A survey on 3GPP heterogeneous networks. Wirel. Coun. 2011, 3, Zhang, N.; Cheng, N.; Gaage, A.; Zheng,.; Mark, J.W.; Shen, X. Cloud Assisted HetNets Toward 5G Wireless Networks. IEEE Coun. 2015, 53, Bottai, C.; Cicconetti, C.; Morelli, A.; Resellini, M.; Vitale, C. Energy-efficient user association in extreely dense sall cell networks. In Proceedings of the 2014 European Conference on Networks and Counications (EuCNC, Bologna, Italy, June 2014; pp Hoydis, J.; obayashi, M.; Debbah, M. Green Sall-Cell Networks. Veh. Technol. Mag. 2011, 1, Rangan, S. Feto-acro cellular interference control with subband scheduling and interference cancelation. In Proceedings of the 2010 IEEE GLOBECOM Workshops (GC Wkshps, Miai, FL, USA, 6 10 Deceber 2010; pp Wang, Y.; Pedersen,.-I. Perforance analysis of enhanced inter-cell interference coordination in LTE-Advanced heterogeneous networks. In Proceedings of the 2012 IEEE 75th Vehicular Technology Conference (VTC Spring, Yokohaa, Japan, 6 9 May 2012; pp Peng, M.; Liu, Y.; Wei, D.; Wang, W.; Chen, H. Hierarchical cooperative relay based heterogeneous networks. Wirel. Coun. 2011, 3,

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