ARecent report pointed out that in 2014 the amount of data

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1 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. XX, NO. XX, JANUARY 2XX 1 QoS-Aware Energy Efficient Association and Resource Scheduling for HetNets Taewoon Ki and J. Morris Chang, Senior Meber, IEEE Abstract A heterogeneous network (HetNet) can actively utilize the spectru reuse with low power consuption, and thus is proising for the next-generation cellular networks. However, there are soe technical challenges to be overcoe in order for HetNets to be practical, and we address the following two in this paper. One is how to forulate the association and resource scheduling proble in a way that an optial solution can be found in a reasonable aount of tie, and the other is how to accoodate varying users deand. In order to iniize the power consuption and to satisfy varying users QoS (Quality of service) requireents, we propose a low-coplex, distributed association and resource allocation schee. By taking a cost-based approach, we first separate a non-convex joint association and resource allocation proble into two subprobles. The channel allocation and base station assignent proble is then relaxed so that the proble becoes tractable. For the power allocation proble, we introduce a low-coplex iterative algorith by using the decoposition theory. The evaluation results show that the proposed solution can aintain the overall power consuption iniized while satisfying the QoS requireents. Index Ters Heterogeneous networks, sallcell, association, resource scheduling, power consuption, quality of service. I. INTRODUCTION ARecent report pointed out that in 214 the aount of data traffic fro obile devices increased 69%, resulting in a onthly usage of 2.5 exabytes [1]. Such an explosive increase in obile traffic has been led by a widespread usage of obile handheld devices and bandwidth-hungry applications. The ever-increasing obile traffic is unlikely to be saturated at least for the next five years; rather, the total aount of traffic generated by obile devices is expected to be increased by tenfold between 214 and 219 [1]. On one hand, experts fro acadeia and industry are seeking for ways of boosting up the counication technology to be prepared for the sharply-increasing traffic deand. On the other hand, the increased energy consuption is a atter of concern to the environent because of the greenhouse gas eissions and the increasing OPEX 1. It is estiated that the ICT sector accounts for 2% of the total CO 2 eission, and aong those fro networks, to be specific, the obile counication infrastructures will contribute ore than 5% by 22 [2]. In particular, the power consuption fro BSs is expected to account for 6 8% of the total power usage fro cellular networks [3] due to the rapid growth in both the nuber of BSs deployed and the aggregate obile traffic. T. Ki is with the Departent of Electrical and Coputer Engineering, Iowa State University, Aes, IA 511, USA. E-ail: tki@iastate.edu. J. M. Chang is with the Departent of Electrical Engineering, University of South Florida, Tapa, FL 33647, USA. E-ail: chang5@usf.edu. 1 Abbreviations and acronys are listed in Table I. CAPEX HetNet ICT LTE MBS OFDMA OPEX QoS SBS SINR UE Table I ABBREVIATIONS AND ACRONYMS CAPital EXpenditure Heterogeneous Network Inforation and Counications Technology Long-Ter Evolution Macro Base Station Orthogonal Frequency-Division Multiple Access OPerational EXpenditure Quality of Service Sallcell Base Station Signal-to-Interference-plus-Noise Ratio User Equipent Aong those technologies taking the two aforeentioned aspects into account, the heterogeneous architecture [4] is one of the ost proising technologies, because it is not only applicable to the current 4G networking syste, but also considered as an essential coponent for the future generation (5G) networking syste [5] [6] [7]. A HetNet, in general, is fored by deploying ultiple low-power, low-cost SBS (e.g., icrocells, picocells and fetocells) on top of a highpower MBS, and it has any advantages. For exaple, due to the short coverage of SBSs, the spectru reuse can be actively exercised. Also the channel quality between an SBS and its associated UE is so good that a higher data rate can be easily achieved, while operating in low power. Being relatively copact in size as well as the ease of installation enables SBSs to be flexibly deployed so that they can effectively extend the coverage of MBSs and offload users traffic especially in crowded areas, such as shopping alls, sport stadius, concert arenas and so forth. Further, uch cheaper CAPEX and OPEX of SBSs have intrigued a great aount of attention fro both acadeia and industry. Motivated by the fact that HetNet is a cost-effective and practical solution, the use of SBSs has been widely introduced (including [5], [7] and [8]) and studied in any literatures (please refer to Section II. Related Work). In addition, the concept of HetNet is accepted by the standard body and introduced in LTE [4] [9] [1]. One coon concern in those works is either how to offload the user traffic fro an MBS to SBSs or how to schedule the network resource so as to achieve their own objectives, such as axiizing spectral efficiency, energy efficiency, a certain utility easure and so forth. As entioned in [11], however, introducing SBSs ay rather increase the overall power consuption unless they are handled carefully. In general, the careful handling includes well-designed offloading strategies (i.e., establishing associations between UEs and SBSs), preferably with a dynaic

2 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. XX, NO. XX, JANUARY 2XX 2 switching on/off schee [2] [3], and resource scheduling (i.e., transission power control and bandwidth allocation). Even after the optial decision has been ade, one cannot guarantee the optial decision will reain optial in the future because the QoS requireent of each user and/or the wireless link quality frequently changes over tie. However, a frequent anual reconfiguration of the syste is not appealing because it is hard to be responsive to the network dynaics, and also increases OPEX to a large extent especially when the BSs are densely deployed [1]. In this regard, a self-configuring or an autoated echanis that is able to respond or adapt to the network dynaics needs to be studied fro the perspective of HetNets. In addition, the centrality can cause a serious issue especially in HetNets. In a centralized syste, all decisions are ade by one or a sall group of entities. As a result, a huge volue of inforation should be either exchanged in real-tie or stored/updated at a shared storage, which incurs a significant burden to the syste. In addition, a centralized syste requires a high processing capability and power consuption to handle a large volue of data as the network grows in size. For those reasons, a centralized syste ay not be responsive and it ight even consue a large aount of power for resource scheduling; whereas a distributed algorith does not. In this paper, we study the distributed user association and resource allocation for HetNets that iniizes the overall power consuption. By considering both association and resource scheduling together, we propose a coplete anageent fraework for an energy-efficient HetNet. In order to efficiently schedule the use of BSs as well as the networking resource (i.e., transission power and spectru) we forulate a two-stage iterative optiization proble which can be solved in a distributed anner without requiring a heavy control essage exchange or a high coputational cost. To do so, we first partition the non-convex, joint association and resource allocation proble into two subprobles by using a cost-based approach that effectively estiates the power use. In addition, relaxation and decoposition techniques are applied to the association and the resource scheduling probles, respectively, so as to reduce the coputational coplexity. After the decoposition, we propose a distributed power update ethod, which converges to the optiu; we show its convergence by both siulation and analysis. An extensive aount of evaluations and coparison studies has been perfored on various network scenarios to show the effectiveness of the proposed BS/channel assignent and power allocation schee. Lastly, we show the efficiency of the proposed schee by showing its fast convergence. The rest of this paper is organized as follows. Section II introduces soe of the relevant literatures to the proposed ethod in this paper. In Section III, we describe the network odel and then introduce the proble forulation for both i) BS association and channel assignent and ii) power allocation. Section IV presents the evaluation and coparison results, and finally Section V concludes the paper. II. RELATED WORK In addition to the research on the energy-efficient channel assignent and power allocation for hoogeneous cellular networks [12] [13], a large volue of studies have been done on two-/ulti-tier HetNets aiing at optiizing the user association (referred to as access control) and/or resource scheduling (referred to as resource allocation). Zhang et al. [14] proposed a user association and interference anageent schee that axiizes the su utility of the average achievable rates. A group uting schee is also used to reduce the interference between nearby SBSs, but the proposed ethod does not consider the QoS requireents. The authors in [15] proposed a gae-theoretic approach to forulate a user association proble that axiizes the throughput. They further showed the practicality of the proposed ethod by studying its convergence behavior, yet leaving the QoS requireents unexplored. Singh et al. [16] proposed a general odel for the joint resource partitioning and offloading on a two-tier HetNet. They derived the optial strategy that iproves the rate of cell edge users. However, their work did not consider the QoS requireents. The work in [17] proposed a cell association and resource allocation schee for downlink HetNets that balances the network traffic. They also developed a distributed algorith, yet leaving the QoS requireents unexplored. Feto-atching [18] is an auction-based algorith for load balancing and fair resource sharing aong BSs and UEs, respectively, on Het- Nets. The authors also proposed a polynoial-tie solution by transforing the initial proble forulation. However, the evaluation has been done on a siple network where there is only a single MBS, and QoS requireents are not considered. Shen et al. [19] studied the joint association and power control proble with beaforing, and then proposed an iterative ethod for the corresponding proble. The proble forulation therein axiizes the network utility function considering the proportional fairness. However, the QoS constraints are left unexplored. The work in [2] considers a joint channel allocation and power control proble for fetocell networks. The proposed solution axiizes the total iniu spectral efficiency, and the corresponding distributed algorith is also developed. However, the work did not pay attention to satisfying QoS requireents in particular for the fetocell UEs. Ngo et al. [21] proposed a joint subchannel and power allocation schee for downlink HetNets. The proposed algorith axiizes the total throughput for the second-tier UEs, while causing no perforance degradation to the first-tier UEs. The liitation of the work is twofold. One is that it assues the fixed power allocation, and the other is that it does not consider the QoS requireents for the second-tier UEs. The proposed work in [22] forulated the throughput axiization proble, subject to QoS requireents for twotier fetocell networks. It also studied the effect of different fetocell access policies (i.e., open and closed) on the overall throughput perforance. However, the work in [22] ay encounter a scalability issue since it lacks a distributed echanis which is very iportant, in particular, when the

3 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. XX, NO. XX, JANUARY 2XX 3 network size becoes large. Bao et al. [23] proposed an optial resource allocation schee on HetNets that axiizes the downlink su throughput. The authors also considered both spatial and teporal diensions, i.e., rando distribution of BSs and dynaic user traffic session arrivals in tie, respectively. However, the absence of a distributed counterpart ay cause a scalability issue on a large-scale network. The authors in [24] proposed a fraework on which they studied the joint association and resource allocation proble for HetNets. By aking use of the fraework, they copared the different channel allocation strategies and different association rules with each other. The proposed work therein is centralized, which ay not be scalable with respect to the network size. Chandrasekhar et al. [25] proposed an optial spectru allocation policy for HetNets that axiizes the area spectral efficiency with the QoS requireent considered. However, their work is liited in that SBSs use a siple channel allocation policy, i.e., Round Robin, and all channels are assigned equal transission powers which ay not achieve the optial perforance. Zhuang et al. [26] proposed a trafficadaptive resource allocation algorith that schedules the spectru resource in an adaptive anner, subject to the network layer QoS, i.e., delay. A siple power allocation schee is used such that it assigns an equal power over the spectru, which ay not achieve the optial perforance. Abdelnasser et al. [27] proposed a power and channel allocation schee for a two-tier HetNet. They forulated a tier-aware resource allocation proble subject to QoS requireents, and then proposed a distributed algorith. However, their network odel is not practical in that they consider only a single MBS, and they also assue equal power allocation for MBS UEs which ay not achieve the optial perforance. Y. Li et al. [28] studied a QoS-guaranteed D2D (device-todevice) network underlying a cellular network. The proposed joint adission control and resource allocation proble in [28] is decoupled into four subprobles, i.e., ode selection, adission control, partner assignent and power allocation, to ake the proble tractable. In addition, they proposed a fast heuristic algorith to further reduce the coputational cost. The authors considered a uplink transission in a singletier D2D-enabled network, whereas we focus on two-tier downlink cellular networks in this paper. We also consider the general network configuration where there are ultiple BSs are deployed, while the work in [28] considered a single BS scenario. Son et al. [29] studied an interference anageent schee for downlink heterogeneous networks, and proposed REFIM (REFerence based Interference Manageent). The proposed user scheduling and power allocation ethod in [29] is converted to a low-coplex algorith by using the notion of reference users. REFIM is a weighted throughput axiization proble, and does not consider the QoS requireents. Also, REFIM considers only a single user with the axiu channel gain when allocating transission power for each channel, while the proposed ethod in this paper considers the actual aount of interference in order to satisfy QoS requireents and to iniize the power consuption. Li et al. [3] forulated a stochastic optiization proble for energy-efficient operations for HetNets considering both spatial and teporal traffic fluctuations. The proposed algorith, SEED (Steerable Energy ExpenDiture), decouples optiization variables to reduce the coputational coplexity of the user association and subcarrier assignent subprobles. In addition, a sequential approxiation and a greedy heuristic approach are used for power allocation and BS operation probles, respectively. Although the the proposed schee in [3] tries to stabilize the network by assuring a finite average delay, it does not take the QoS requireents of individual users into account. For other previous works that are not discussed here, please refer to [27]. Although the aforeentioned previous literatures studied two-tier HetNets fro various perspectives, the proposed work in this paper has ade the following advanceent. We consider both user association and resource allocation together, and the proposed ethod allows UEs to be dynaically offloaded to SBSs, which all together is expected to enhance the capacity of the cellular networks to a large extent. Our work directly focuses on the energy iniization which has gained ore and ore attention recently, and also we consider any practical constraints. The proposed schee considers the users QoS requireents which has been ignored in any literatures. In addition, it allocates optial power levels to different UEs instead of assigning equal powers to all channels. Thus, the proposed ethod in this paper is expected to fulfill the service requireents of users, while spending no ore than necessary aount of power. In addition, a novel lightweight, distributed echanis is provided with the proof of convergence, all of which are crucial as the network grows in size. The proposed schee is evaluated under various and practical scenarios with a realistic channel odel. Lastly, through coprehensive perforance coparison, we show that the proposed schee can effectively schedule the networking resource on HetNets. III. PROBLEM FORMULATION We begin this section by describing the network odel and assuptions. In what follows, we introduce how the optial user association and resource allocation proble are forulated. A. Network Model and Assuptions Throughout the paper, we focus on the downlink transission for a two-tier OFDMA (Orthogonal Frequency-Division Multiple Access) cellular network. On the network are M MBSs, and each of which is overlaid by S SBSs. MBSs are distributed in a planned anner (e.g., by keeping the sae inter-cell distance between the nearby MBSs) in order to provide area coverage, obility anageent and so forth; while SBSs are randoly 2 distributed [4] [14] [17] [18] [31] [32] [33]. The reason for assuing the rando deployent of SBSs is that their deployent is uch less planned [11] copared to that of MBSs. To be specific, they are likely to be installed on deand or in an ad hoc anner so as to 2 In Section IV, we have used Unifor distribution for siulation.

4 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. XX, NO. XX, JANUARY 2XX 4 fulfill a sudden or periodic increase of the QoS requireent in certain areas such as a shopping center, sports coplex, office, household and so forth. It is worth entioning that the proposed schee does not assue or rely on any specific area or region. Therefore, in order to show that the proposed schee does not depend on any certain distributions of SBS, a rando distribution is used to represent the placeent/layout of SBSs in general. All MBSs are always active in order to provide the full area coverage to all UEs [1]. On the other hand, SBSs ay or ay not be active depending on the user association status at the oent. Any non-offloaded UEs are autoatically associated with the MBS that provides the strongest signal strength by default. MBSs and SBSs are assued to operate on different frequency bands to avoid cross-tier interference [22] [23] [25] [33]. However, the sae type of base stations share the sae frequency range, and thus they always interfere with each other. In this work, the coverage of an MBS indicates the area within which all non-offloaded UEs shall associate with the MBS. However, the signal generated by each MBS propagates beyond its coverage, and thus incurs interference to the rest MBSs; this principle applies to SBSs as well. Both types of base stations can access the core network through wired counication links. Each MBS has U UEs (or users) whose average data rate requireents are known. We assue that SBSs operate fully (or in part) with an open access ode. 3 The available bandwidth is divided into ultiple channels, each of which is f-wide in Hz. We also assue the continuous power and rate control. Soe of the frequently-used notations are suarized in Table II, and other notations that are not on the table will be introduced when necessary. B. Cost-Based Proble Separation Considering that the joint association and resource allocation proble belongs to a ixed integer nonlinear progra with the decision variables coupled, the coputational cost of the joint proble is prohibitive. Thus, the approach taken in this work is to first partition the proble into two, one for the user association and channel allocation (Stage 1), and the other for the power allocation (Stage 2), and then apply relaxation and decoposition techniques, respectively, in order to ake the whole procedure tractable and suitable for online resource scheduling. To this end, we have introduced a cost function, by which the original proble will be separated into two. It is worth entioning that after the partitioning, the proposed two-staged ethod ay result in a sub-optial solution. After the proble separation, however, Stage 1 does not know how uch power will actually be used for counication. Therefore, it is crucial that the cost needs to be designed in a way that it can correctly estiate the aount of power to be used. At the beginning of Stage 1, a UE u U senses the pilot signals fro nearby BSs over the entire channels, and produces 3 If all the SBSs are deployed by the end-users, the open access ode ay not be a practical assuption to ake. However, by focusing on the scenario where all SBSs are deployed by the network operator, or considering only those SBSs operating with the open access ode (or the hybrid ode [11]), we argue that this assuption still holds. Table II SUMMARY OF NOTATIONS M Nuber of MBSs on the network S Nuber of SBSs on a acrocell U Nuber of UEs on a acrocell N ch Nuber of available channels Nch M Nuber of available channels for an MBS Nch S Nuber of available channels for an SBS N M Index set of MBS-accessible channels N S Index set of SBS-accessible channels M Index set of MBSs, {1, 2,,,, M} S Index set of SBSs overlaid on MBS, {1, 2,..., s,..., S} U Index set of UEs within the coverage of MBS, {1, 2,..., u,..., U} U Subset of U. UEs associated with MBS Us Subset of U. UEs associated with SBS s S p Transission power vector of MBS over channels p s Transission power vector of SBS s S over channels gu Channel gain vector of UE u U over channels η thr SINR threshold ru QoS (i.e., data rate) requireent of UE u U f Channel bandwidth Pax M Maxiu transission power of MBS Pax S Maxiu transission power of SBS c u Cost vector of UE u U over channels N Per-Hz noise power a channel gain vector gu R N ch +. Out of N ch entries in gu, Nch M eleents correspond to the easured channel gains between UE u U and MBS over Nch M channels that are accessible to MBSs. Therefore, all the Nch M eleents in g u are strictly positive due to the area coverage provided by the closest MBS, while the rest eleents are nonnegative. If a UE resides within the coverage of an SBS, we have gu Nch where is an eleent-wise greater than operator and Nch is an N ch -by-1 zero vector. Also, in such cases, a UE can recognize the identifier of the SBS by decoding the pilot signal. To be consistent throughout the paper, let us assue that the indices of the channels used by MBSs coe before the ones used by SBSs. In other words, out of N ch nuber of channels available whose index starts fro 1 to N ch, each MBS has an access to the channels indexed by 1, 2,, Nch M, while an SBS is allowed to use the ones indexed by Nch M +1,, N ch. In this regard, let N M and N S be {1, 2,, n,, Nch M } and {Nch M + 1,, n,, N ch}, respectively. Given gu and the data rate requireent ru R ++, each UE u builds its own cost vector c u R N ch ++, where its n-th entry is: { c (2 r u 1)/g u,n = u,n, if gu,n >. (1), otherwise, where r u = ru / f is a noralized data rate requireent. In fact, c u is a easure of power required to satisfy the data rate requireent of UE u U across all channels with the interference and noise ter ignored. According to the Shannon's well-known channel capacity forula, an achievable bit rate over a channel is defined as C = B log 2 (1 + gp I+N ), where C is channel capacity easured in bits per second (bps), g is channel gain, P is transission power, I is interference and N is noise. In order not to violate the QoS

5 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. XX, NO. XX, JANUARY 2XX 5 requireent for each UE, we need to satisfy the constraint rn C. Since the iniu power is achieved when the QoS requireent is satisfied with equality, we can rewrite the Shannon's capacity forula as follows after replacing B and g with f and gu,n, respectively, to be consistent in notation: ru = f log 2 (1 + g u,n P I+N ) or r u = r u f = log 2 (1 + g u,n P I+N ). After rearranging the equation, the iniu transission power that satisfies the QoS requireent can be found by P = (2 r u )(I +N)/g u,n. By assuing the su of interference and noise is not doinant in deterining the transission power, we get the following relation which leads to how we defined the cost ter in Eq. (1), i.e., P 2 r u /g u,n = c u,n. After gathering the cost vectors fro all UE ( u U ) along with their nearby SBS IDs, if applicable, an MBS runs both Stage 1 and 2 in sequence which will be discussed as follows. C. Stage 1: User Association and Channel Assignent The goal of this stage is to find the best association (i.e., an offloading strategy) and channel assignent that iniizes the overall cost, which represents the expected aount of power use as discussed before. Given the cost vectors collected, we have the following optiization proble P. 2 for each MBS that iniizes the overall cost of aking user association and channel assignent. Please note that s.t. in the proble forulation stands for subject to. in tr[x (c ) T ] (2a) X s.t. N ch Xu,n = 1, u U n=1 Xu,n 1, n N M u U Xu,n Iu,s 1, n N S, s S u U X {, 1} U N ch, (2b) (2c) (2d) (2e) where tr[ ] is the trace function that sus the diagonal eleents of a atrix, the decision variable X is a U- by-n ch atrix of which (u, n) eleent is 1 (or ) if UE u is (or is not) assigned to channel n, c is a U-by-N ch atrix whose u-th row corresponds to the cost vector of UE u and I is an U-by-S atrix whose (u, s) eleent is 1 if UE u successfully decoded the pilot signal fro SBS s. The objective function (2a) in P. 2 calculates the total cost with respect to the apping between UEs and channels (and BS as well). The objective function can also be written as u U X u (c u ) T or Nch u U n=1 X u,n c u,n. Since the cost Xu,n c u,n is eaningful only when u = u and n = n, we take the su of only the diagonal eleents fro X (c ) T, i.e., tr[x (c ) T ]. Each UE is allowed to use 1 unit of channel resource (2b), and each MBS and SBS channel cannot be used for ore than 1 unit each, (2c) and (2d), respectively. The decision variable represents a ebership relation, and thus is binary (2e). Please note that P. 2 runs on a sall tie scale; for exaple, 1 s to coply with the 3GPP E-UTRA requireent [9]. Given that 3GPP E-UTRA akes use of physical resource blocks for counication, even when the nuber of available channels is less than that of active UEs, the proposed ethod can still fulfill the service deand fro UEs by scheduling the resource blocks. As long as the deand fro a UE can be satisfied without violating the delay constraint, the proposed ethod ay schedule the UE for counication in one of the following tie slots if the nuber of available channels at the oent is not enough. That is, having failed in assigning a BS/channel to a UE for the oent does not necessarily ean a failure in satisfying the UE s QoS requireent. In addition, the densely deployed, short-range SBSs can achieve high frequency reuse, eaning that the aggregate nuber of channels seen by users can be larger than that of physical channels. However, if the aggregate service deand for a certain period exceeds the axiu attainable throughput over the network during the sae period, soe of the active users ay experience service degradation, which will be discussed in Section III-D. Due to the cobinatorial nature of P. 2, however, the proble is not tractable, and thus is not suitable for an online scheduling. By relaxing the binary constraint (2e), we get the following convex proble that can be efficiently solved by each MBS with the coplexity of O((U N ch ) 3 ) when the interior point ethod is used. in tr[x (c ) T ] (3a) X s.t. N ch Xu,n = 1, u U n=1 Xu,n 1, n N M u U Xu,n Iu,s 1, n N S, s S u U X [, 1] U N ch. (3b) (3c) (3d) (3e) Although the optial solutions fro both P. 2 and P. 3 indicate the channel assignent as well as the user association for each UE, both solutions are not the sae in practice. The binary solution fro P. 2 lets each UE use the assigned channel and BS for a unit tie, whereas the (possibly) non-binary solution fro P. 3 forces a UE to hop between channels (and possibly between BSs as well) during the sae unit tie since the optial solution indicates the fraction of tie that a UE is allowed to use one or ore BSs and channels. The nonbinary solution sees to be attractive since it yields a better (or at least the sae) optial value because of the relaxation. However, it increases the aount of control essages as well as the scheduling coplexity due to the frequent handover and channel hopping that should be ade on a very precise tiescale. In this regard, we will recover binary solutions fro the non-binary solutions fro the relaxed optiization proble P. 3 by using the one-by-one reoval algorith [27] [34] [35] [36]. This relax-and-recover approach will help the syste

6 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. XX, NO. XX, JANUARY 2XX 6 aintain a low coplexity in both coputation and operation. Algorith 1 Gradual one-by-one reoval (for MBS ) 1: repeat 2: Solve the relaxed optiization proble P. 3 3: for u U do 4: n = arg in n X u,n such that X u,n 5: Set X u,n = 6: end for 7: until all X u,n are binary The Algo. 1 iteratively solves the relaxed optiization proble (line 2), searches for the nonzero iniu value for each UE (line 4), and forces each to be zero (line 5). Each MBS concurrently runs the algorith which terinates in less than or equal to N ch nuber of iterations. Please note that the solution found by running Algo. 1 ay yield a suboptial solution to P. 2; the optiality of the solution will be investigated in Section IV. Given the recovered binary user association and channel assignent decision, the following Stage 2 allocates the iniu power to each UE. Note that the channel assignent proble also finds the best BS atch for each UE. Those SBSs with no UE associated shall change their state into the SLEEP ode in order to save energy, while the other SBSs stay in the ACTIVE ode [11]. D. Stage 2: Power Allocation This stage allocates the iniu power to each UE by taking both SINR and QoS requireents into account. In this regard, we first forulate the centralized power allocation proble where one or a sall nuber of central entities have to control the downlink power for all BSs. In what follows, the centralized proble is decoposed into ultiple low-coplex subprobles which are scalable and suitable for online scheduling. Before introducing the Stage 2 proble forulation, let us extend the notation of the channel gain so that we can coprehensively represent the gain between all the entities including that do not even belong to the sae acrocell. As a reinder, the channel gain gu represents the channel gain between UE u U and either MBS or SBS s S, where all of the are within the coverage of MBS. This is because gu is deterined by overhearing the pilot signals over channels; thus, it should be coupled with the nearest MBS and SBS (if applicable). Let G, u,n be the gain over channel n between UE u and MBS, where u does not need to be a eber of U. In the sae anner, let G s, u,n be the gain over channel n between UE u and SBS s, where u does not need to be a eber of U, but s ust be a eber of MBS, i.e., s S. Thus, for any UE u U, we have g u,n = G, u,n for any n N M. On the other hand, we have g u,n G, u,n for any n N M N S if. Given the BS association and channel assignent ade in Stage 1, we have the power allocation proble P. 4 for MBS and all SBSs therein (i.e., s S ) that iniizes the overall power consuption. in P P,n + Ps,n (4a) n N M s S n N S s.t. ηu,n η thr Xu,n, n N M, u U ηu,n η thr Xu,n, n N S, u Us, s S (4b) (4c) flog 2 (1 + η u,n) r u X u,n, n N M, u U (4d) flog 2 (1 + η u,n) r u X u,n, n N S, u U s, s S (4e) P,n Pax, M n N M (4f) P,n Pax M (4g) n N M Ps,n Pax, S n N S, s S (4h) Ps,n Pax, S s S, (4i) n N S where P,n is the power allocated by MBS over channel n N M, Ps,n is the power allocated by SBS s S over channel n N S, and ηu,n in Eq. (4b) and Eq. (4c) is the easure of SINR defined in Eq. (5a) and Eq. (5b), respectively. If a UE u U is to associate with an MBS (i.e., u U ) on a certain channel n N M, the interference that the UE u will experience is related to the transission power allocated to the sae channel by the other MBSs, which corresponds to Eq. (5a). On the other hand, if a UE is coupled with an SBS on a certain channel n N S, it will sense the interference caused by all the other SBSs on the network that have allocated transission power to the sae channel as in Eq. (5b). To be specific, in Eq. (5b) the first ter in the denoinator easures the interference fro other SBSs in the sae acrocell, whereas the second ter easures the interference fro all SBSs that do not belong to the sae acrocell. Note that the aount of interference to an SBS-associated UE is not significant ainly due to the low transission power of SBSs, and the penetration loss of walls. For each UE that is associated with an MBS or SBS, its SINR should be greater than or equal to the predefined threshold, η thr, as in Eq. (4b) and Eq. (4c), respectively. The QoS requireents of UEs that are associated with an MBS or an SBS should be satisfied according to Eq. (4d) or Eq. (4e), respectively. The transission power allocated to a certain channel cannot exceed the power budget of an MBS or an SBS as in Eq. (4f) or Eq. (4h), respectively. Finally, the aggregate transission power of an MBS or an SBS cannot be larger than its power budget as denoted by Eq. (4g) or Eq. (4i), respectively. It is worth entioning that solving P. 4 for MBS and all active SBSs therein is not independent of that of others since each MBS and all SBSs therein need to know the intertier interference fro the rest MBSs and SBSs, respectively. Therefore, a single or a set of coputing resource has to solve the network-wide power allocation proble, aking the centralized approach ipractical for an online resource

7 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. XX, NO. XX, JANUARY 2XX 7 η u,n = G, u,n P,n M G, u,n P,n + f N G s, u,n Ps,n s s S Gs, u,n P s,n + M s S Gs, u,n P s,n + f N if u U. if u U s. (5a) (5b) scheduling. In what follows, we transfor the centralized power allocation proble P. 4 into low-coplex subprobles such that each subproble can be quickly solved in a distributed anner. In order to build a distributed syste we decopose the centralized proble P. 4 by using the decoposition theory [37], and then transfor it into low-coplex subprobles that can be independently solved by each BS. The power allocation proble P. 4 which is for both MBS and all SBSs therein (i.e., s S ) already has two sets of easilyseparable coponents. The first ter in the objective function (4a) along with the following four constraints (4b), (4d), (4f) and (4g) fors the MBS power iniization proble which is independent of that for SBSs, i.e., the reaining parts of the proble. Therefore, we can for the power allocation proble only for MBS as follows. in P s.t. n N M P,n η u,n η thr X u,n, n N M, u U (6a) (6b) flog 2 (1 + η u,n) r u X u,n, n N M, u U (6c) P,n Pax, M n N M (6d) P,n Pax. M (6e) n N M What is left in P. 4 after taking P. 6 out is the power iniization proble for all SBSs s S, where its objective is to iniize the su of transission power used by all SBSs in acrocell with the following constraints, (4c), (4e), (4h) and (4i). Miniizing the total power usage is equivalent to iniizing each individually. Also, the set of constraints for each SBS s is independent of that for the rest SBSs provided the transission power of other SBSs are fixed. As a result, we have the power allocation proble for each SBS s S as follows which can be solved if the transission power and the channel gain inforation of other SBSs are assued to be known. 4 in P s s.t. n N S P s,n η u,n η thr X u,n, n N S, u U s flog 2 (1 + η u,n) r u X u,n, n N S, u U s (7a) (7b) (7c) 4 Please note that the proposed ethod does not directly solve P. 7 and thus, it does not really ake such assuptions. In fact, P. 7 is one of the steps that we ake to design the distributed power allocation ethod which will yield the global optial solution without aking the assuptions. Ps,n Pax, S n N S (7d) Ps,n Pax. S (7e) n N S Although both P. 6 and P. 7 as they are cannot be further decoposed due to the coupling constraints in (6e) and (7e), respectively, we can use the decoposability structure by foring a Lagrangian of each to ake both probles be decoposed. By relaxing (6e), the Lagrangian of P. 6 is given as below. in P P,n + λ( P,n Pax) M (8a) n N M n N M s.t. constraints in: (6b), (6c), (6d), where λ is a nonnegative Lagrangian ultiplier. As a result, we have a Lagrange dual proble as follows. ax in P λ P,n + λ( P,n Pax) M (9a) n N M n N M s.t. constraints in: (6b), (6c), (6d). We assue that each BS has ultiple processors or at least a single processor with the ultithreading capability, each of which is dedicated to each channel for power update. The dedicated processor or thread to each channel is called channel anager, which is in charge of controlling the downlink transission power of the assigned channel. At the lower level, the channel anager for channel n N M solves the following power iniization proble if there is a UE u associated with the channel (i.e., X u,n = 1). in P,n h,n(λ) = (1 + λ)p,n (1a) s.t. ηu,n η thr (1b) flog 2 (1 + ηu,n) ru (1c) P,n Pax. M (1d) Then, the higher level proble fors a axiization proble over the Lagrange ultiplier as follows. ax h (λ) = h,n(λ) λpax M (11a) λ n N M Since the dual function h (λ) is differentiable, the higher level proble can be solved with a gradient ethod of which update ethod is given below. λ t+1 = [λ t + α t (,n Pax)] M +, (12) n N M P where t is a nonnegative, integer-valued iteration count, α is a positive stepsize, and [ ] + = ax{, } is a projection operator to the nonnegative orthant. The initial λ can be set to soe

8 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. XX, NO. XX, JANUARY 2XX 8 non-negative value, e.g., zero, and α can be a sufficiently sall positive nuber; please refer to [37] for further details on the step-size. Then, the dual variable λ t will converge to the dual optial λ as t [37]. By taking a closer look at the lower-level proble P. 1, we can further siplify the power allocation procedure, and find a siple ethod to solve it by an even ore efficient way than the decoposed ones. Since λ is nonnegative and coon to all lower level probles, dropping the 1 + λ ter fro the objective function does not change the optial decision value. For a power iniization proble with an SINR constraint, the optiality is achieved when the constraint is satisfied with equality, which is also true for the sae proble with a QoS constraint. Therefore, the solution of P. 1 can siply be found by: P,n = in{ax{p (s),n, P (q),n }, P ax}, M (13) where P (s),n and P (q),n are the solutions that satisfy SINR and QoS requireents, respectively, with equality. In the sae anner, we can derive the distributed power allocation ethod for each SBS. By relaxing (7e) which is the coupling constraint in P. 7, we have the following Lagrangian. in P P s,n + λ( Ps,n Pax) S s n N S n N S s.t. constraints in: (7b), (7c), (7d), (14a) where λ is a nonnegative Lagrangian ultiplier. At the lower level, the channel anager for channel n N S solves the following power iniization proble if there is a UE associated with the channel (i.e., Xu,n = 1). in Ps,n s.t. h s,n(λ) = (1 + λ)p s,n (15a) ηu,n η thr (15b) flog 2 (1 + ηu,n) ru (15c) Ps,n Pax. S (15d) Considering the optiality condition of the given power iniization proble P. 15, its solution can be found by the following siple ethod as we did for each MBS channel anager. P s,n = in{ax{ps,n (s), Ps,n (q) }, Pax}, S (16) where Ps,n (s) and Ps,n (q) are the solutions that satisfy SINR and QoS requireents, respectively, with equality. Although each channel anager considers and guarantees the per-channel power budget constraint (i.e., the axiu transission power for the channel should not be greater than Pax M or Pax), S it does not guarantee the per-bs power budget constraint (i.e., the total power use over all channels should not be greater than Pax M or Pax) S is also satisfied. For exaple, for n, n+1 N M, having P,n = Pax M and P,n+1 = Pax M at the sae tie does not violate the power budget constraint of each channel anager. However, that is not a feasible solution because the su transission power over channels cannot exceed Pax. M Therefore, the upper level entity should check whether the su power constraint is violated or not. To this end, we use a siple policy for the upper level entity that if the aggregate power budget constraint is violated, let all active channel anagers use the sae transission power. 5 To be specific, for each MBS of which su power constraint is violated, let each channel anager with an associated UE allocate the transission power in the following anner, P,n = P M ax/ U, where is the cardinality of a set. For each active SBS s of which su power constraint is violated, let each channel anager with an associated UE use the power as P s,n = P S ax/ U s. On the other hand, as long as the su power constraint is satisfied, the upper level entity does not interrupt the power update procedures at lower-level channel anagers. E. Convergence By using the analytical fraework for convergence presented in [39], we prove that the proposed distributed power control algoriths in Eq. (13) and Eq. (16) converge to their corresponding optiu. Since both algoriths share the sae structure and do not interfere with each other, we prove the convergence for an MBS, i.e., Eq. (13). However, the following proof can be easily applied to the case for any SBS s S, i.e., Eq. (16). To begin with, if the feasible power region is epty, i.e., if the power allocation proble P. 6 is infeasible, the transission power for each channel converges (abruptly) to Pax/ U M. This is because each channel anager is forced to use the equal transission power when the su power constraint is violated. In order to show convergence of the proposed schee for the case of having a non-epty feasible power region, what follows is to transfor the proposed power control ethod to the for of interference function, which is one of the key coponents in convergence analysis proposed in [39]. Since we consider only the case that the feasible power region is nonepty, we can siplify P. 6 by ignoring both constraints (6d) and (6e). After rearranging (6c), then, we get the following proble P. 17. in (17a) P P,n n N M s.t. η u,n η thr X u,n, n N M, u U (17b) η u,n 2 r u X u,n 1, n N M, u U. (17c) Since the optiality of P. 17 is achieved when aong the two constraints, (17b) and (17c), the one that requires a higher transission power is satisfied with equality, we can rewrite the proble as follows. in (18a) P s.t. η u,n = q u,n, n N M, u U, (18b) where q u,n = ax{η thr X u,n, 2 r u X u,n 1}. The proble is always feasible by assuption, and the optial power for each active channel is given by solving the equality constraint 5 Assigning the sae power to all active channels provides close-to-optial perforance [38].

9 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. XX, NO. XX, JANUARY 2XX 9 Eq. (18b). Therefore, we can find the power update ethod directly fro P. 18 after plugging in the SINR expression, Eq. (5a), to ηu,n. Then, the distributed power update ethod for an active channel n of MBS which is associated with UE u becoes: P,n[t + 1] = q u,n G, u,n ( M G, u,n P,n[t] + f N ). It is worth entioning that this is equivalent to the power update ethod in Eq. (13) provided the feasible power region is nonepty and both the channel gain and the aount of interference are reported fro UE. According to [39], an iterative power update ethod, in general, is given by p[t + 1] = I(p[t]), where I( ) is interference function. 6 We use I,n( ) to indicate the interference function for an active channel n of MBS. The interference function is standard if it satisfies positivity, onotonicity and scalability properties for all nonnegative power vectors. Also, we use an overloaded notation P to indicate the transission power of all MBSs. The positivity property, I,n(P ) >, is always satisfied because of the strictly positive background noise even when P =, we have q u,n f N G,n >. The interference function also satisfies the onotonicity property, i.e., if u,n P + P, then I,n(P + ) I,n(P ). Let P + = (1 + ɛ)p for ɛ. Then, we have I,n(P + ) = I,n((1 + ɛ)p ) = I,n(P ) + q u,n (ɛ I,n(P ), G, u,n M G, u,n P,n) fro which we can conclude that the onotonicity property is always satisfied. Finally, the positivity property and convexity of the interference function iply scalability, i.e., for all α > 1, αi,n(p ) > I,n(αP ). Since the interference function I,n( ) satisfies the three properties, the proposed power update ethod is called standard power control algorith [39]. Due to the convexity of the proble P. 17 (or P. 6), there exists an optial power allocation vector, eaning that the proposed power update ethod has a fixed point. Then, the fixed point is unique by [39, Theore 1]. Finally, by using [39, Theore 2] we conclude that the proposed power update ethod converges to a unique fixed point for any initial power vector as long as the feasible power region is not epty. F. Overall Procedure In this section, the overall procedures of the proposed schee is given, i.e., the BS association and channel assignent in Stage 1 and the power allocation in Stage 2, as a suary of the current section. At the beginning of Stage 1, all BSs transit pilot signals over the entire channels to which they have an access. UE u senses the signal, calculates the per-channel cost, and transits the cost vector c u to MBS. Then, MBS deterines the UE-BS association and channel assignent by running Algo. 1. The decision ade by MBS is broadcasted to all SBSs ( s S ) and all UEs ( u U ). 6 Note that the notation I in Section III-E is different fro the one in Section III-C. Each active MBS channel anager with an associated UE runs Eq. (13) to deterine the downlink power, and the UE sends the easured channel gain and interference back to the channel anager. This power allocation procedure iterates until the change of the power becoes less than the given threshold.each active SBS channel anager with an associate UE runs the sae procedure except that it runs Eq. (16) to deterine the downlink transission power. While each active channel anager tries to deterine the transission power, each BS checks if the su power exceeds the power budget. If it does, the BS stops all active channel anagers and lets the use the sae power, P,n = Pax/ U M (in case of MBS) and Ps,n = Pax/ U S s (in case of SBS) for downlink counication. If it does not, the BS waits until all active channel anagers finish their power allocation procedures. IV. EVALUATION We ipleented and siulated the proposed algorith along with others for coparison on top of MATLAB [4] and CVX [41]. The following Section IV-A describes the network configurations and paraeter settings which are coon to all scenarios considered in this section. In Section IV-B we show that for Stage 1, the optiality gap between the proposed solution (i.e., Algo. 1) and the optial BS association and channel assignent (i.e., P. 2) is sall. What follows is the perforance evaluation and coparison of the proposed schee to others in ters of the power consuption on different networks, i.e., single-cell, sall-scale and large-scale networks, in Section IV-C, Section IV-D and Section IV-E, respectively. For coparison to the optial solution, we introduce a new etric, D X ( ), to easure the difference in the Stage 1 decision between a certain ethod and the optial solution, which is defined as follows: D X (<ethod>) = Xoptial Xethod 1, where Y 1 = y Y y. Here, X optial is the optial solution found by solving P. 2, whereas Xethod is the optial solution found by solving the corresponding proble for <ethod>. In other word, D X (<ethod>) counts the nuber of entries that do not atch between the two solutions. In addition, we have ipleented one ore schee, called SSSF (Strongest Signal Strength First) for coparison. In contrast to the proposed ethod which considers both the channel gain and the service deand, SSSF takes only the signal strength into account when aking BS association and channel assignent. It is easy to ipleent SSSF or any siilar variations due to the general structure of the Stage 1 proble. In contrast to the proposed ethod which iniizes the cost values, SSSF axiizes the su of the benefit which is equal to the channel gains. After replacing c with the benefit, we can siply replace the objective function P. 2 with the benefit-su axiization proble. We have directly solved SSSF by using the MATLAB (M)ILP solver which uses Branch-and-Bound algorith. A. Network Configuration There are M MBSs that are regularly deployed with keeping the inter-cell distance of 6 aong adjacent ones. Each

10 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. XX, NO. XX, JANUARY 2XX 1 MBS has 3 of coverage, and is overlaid by S indoor SBSs and U UEs. We have used a Unifor distribution for locating SBSs and UEs. A UE is located indoor if it is placed within the coverage of a SBS which is 3. The QoS requireent of each UE is randoly drawn fro a Unifor distribution. The total BS transission power of MBS and SBS is 46 db (4 W) and 2 db (1 W), respectively [33]. The channel odel fro [33] is used, which includes the distance dependent path-loss, penetration loss (when applicable), ultipath fading and lognoral shadowing. The path-loss between a BS and a UE is listed below. The unit of path-loss is db, and R is the distance between two entities in the unit of eter. MBS and an indoor UE: log(R) + L ow, MBS and an outdoor UE: log(R), SBS and its associated UE: log(R), and SBS and an outdoor UE: ax{ log(R), log(R)} + L ow, where L ow is the penetration loss of an outdoor wall, which is 2 db. In case of the path-loss between an indoor UE and an SBS located in a different building, the penetration loss gets doubled. The Rayleigh fading odel is used to capture the ultipath effect, and the standard deviation of lognoral shadowing is as follows. MBS and an indoor UE: 1 db, MBS and an outdoor UE: 1 db, SBS and its associated UE: 4 db, and SBS and an outdoor UE: 8 db. In addition, for a fair coparison to [27] we set f = 18 khz and per-hz noise power N = 1 13 W in accordance with the paraeters declared therein. B. Optiality Gap in Stage 1 As aforeentioned in Section III-C, the Algo. 1 iteratively solves P. 3 and recovers binary solutions instead of directly solving P. 2 to lower the coputational coplexity. Due to the relaxation on binary variables, Algo. 1 ay yield a suboptial solution to P. 2 which possibly affects the power consuption in the subsequent Stage 2 for power allocation. In order to check by how uch the solution of Algo. 1 is deviated fro the optial solution to P. 2, we have ipleented and solved P. 2 by using the MATLAB (M)ILP solver which uses Branchand-Bound algorith. Each data point in both Fig. 1 and Fig. 2 is an average of 2 runs of randoly-generated scenarios, where there are 4 SBSs on an MBS. The nuber of UEs in a acrocell is set to 1, 2,, 5. Also, 95% of the confidence interval is arked on each data point in Fig. 1. Fig. 1 shows the (noralized) iniu cost found by running Algo. 1 and P. 2, referred to as Proposed and Optial, respectively, in the figure. For each different nuber of UEs on a acrocell, the proposed ethod results in a close-tooptial objective value. In order to take a closer look at the difference in the two objective values, Fig. 2 shows the error ratio e = ˆp p /p, where ˆp and p are the noralized Miniu Cost Proposed Optial Nuber of UEs Figure 1. Miniu cost in Stage 1 for the optial and the proposed BS/channel assignent ethod. Error Ratio Nuber of UEs Figure 2. Error ratio of the iniu cost in Stage 1 for the proposed BS/channel assignent ethod. iniu cost found by running Algo. 1 and solving P. 2, respectively. As it can be seen in Fig. 2 the error ratio becoes stable as the nuber of UEs increases and does not exceed.8. That is, the proposed Algo. 1 yields a sub-optial solution to P. 2 with a sall optiality gap. In what follows, we show the power consuption of the proposed ethod along with others for coparison, and show the effect of the sub-optiality on the power consuption. C. Single-Cell Networks In addition to coparing to the optial solution and SSSF, we copare the perforance of the proposed ethod to [27], which is denoted by Abdelnasser in Fig. 4 and Fig. 5. In contrast to the proposed schee which assues an independent channel deployent between different types of BSs, [27] shares all available channels between an MBS and all SBSs

11 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. XX, NO. XX, JANUARY 2XX 11 6 MBS coverage y (eter) SBS coverage UE QoS Satisfaction Ratio Proposed Optial SSSF Abdelnasser x (eter) Mean Per-UE QoS (Mb/s) Figure 3. Network scenario for a single-cell network. Figure 5. QoS satisfaction ratio for a single-cell network. Power Consuption (db) Proposed Optial SSSF Abdelnasser Mean Per-UE QoS (Mb/s) Figure 4. Overall power consuption for a single-cell network. therein, called co-channel deployent. The proposed resource scheduling schee in this paper allocates an optial power to each channel by taking both the channel gain and the QoS requireent of an associated UE into account, while [27] allocates an equal power to all channels in use. The proposed association schee in this paper allows UEs to be dynaically offloaded to SBSs for capacity enhanceent (i.e., open access ode), whereas [27] does not (i.e., closed access ode). Since the work in [27] considers only a single MBS, we set up a siilar network as Fig. 3, where there is a single MBS on the network with 4 SBSs and 2 UEs therein. Please note that due to this liitation, [27] is not used for perforance coparison in the following Section IV-D and Section IV-E. In this siulation, we have D X (proposed) = and D X (SSSF) = 6. 1) Power Consuption: Fig. 4 shows the overall power consuption, i.e., the total power used by an MBS and SBSs on the network, for the four different schees. As it can be seen in Fig. 4, the work in [27] uses ore power than the proposed ethod as well as Optial and SSSF. In contrast to the proposed ethod in this paper that dynaically anages the interference, [27] takes a conservative approach. In [27], when a UE is associated with an MBS, the MBS calculates the axiu allowable interference on the allocated channel for the UE, and then assigns the axiu power to the channel which is P M ax divided by the nuber of channels in use. On the other hand, the proposed schee in this paper as well as both Optial and SSSF allocates the iniu power to each channel while satisfying both SINR and QoS requireents for the associated UE. Therefore, our proposed work uch outperfors [27] in ters of the power consuption especially when the aount of downlink traffic is sall. Since we have D X (proposed) =, the proposed schee results in the optial solution. SSSF is also able to dynaically adjust the transission power, and thus, its power usage gradually increases as the average service deand increases. However, our proposed schee consues less power than SSSF. That is, considering both channel gain and QoS requireents results in a ore power-efficient solution than taking only the signal strength into account. 2) QoS Satisfaction Ratio: The Fig. 5 shows the QoS satisfaction ratio which is the ratio of the nuber of UEs with their QoS satisfied to the total nuber of active UEs on the network. As it can be seen in the figure, the satisfaction ratio of the work in [27] starts to drop when the ean QoS becoes larger than 2 Mb/s. On the other hand, the other ethods successfully satisfy the QoS requireents of all UEs until the ean QoS is 4.5 Mb/s. Due to the lack of freedo in controlling the downlink transission power, the work in [27] always allocates the fixed transission power to all active channels. This inflexibility in power allocation ay not be efficient, because it allocates ore than necessary aount of power to the UEs with high channel gains, while failing to satisfy the QoS requireent of UEs with low gains. The proposed ethod and the Optial, on the other hand, has a higher level of freedo in power control than [27], because

12 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. XX, NO. XX, JANUARY 2XX y (eter) Power Consuption (db) Proposed Optial SSSF x (eter) Mean Per-UE QoS (Mb/s) Figure 6. Network scenario for a sall-scale network. Figure 7. Overall power consuption for a sall-scale network. each channel anager allocates the iniu power level that satisfies both SINR and QoS requireents of the associated UE. When the average per-ue QoS is 5 Mb/s, the QoS satisfaction ratio of SSSF drops sharply, while it is not the case for both the proposed and optial schee even though both experience a sall aount of degradation. D. Sall-Scale Networks We have evaluated the proposed ethod on a sall-sized network where there are 3 MBSs on the network as shown in Fig. 6. The locations of these three MBSs for an equilateral triangle, eaning that the distance fro any MBS to either of the rest two is the sae. Each MBS is overlaid by 4 SBSs and 2 UEs. In this siulation, we have D X (proposed) = and D X (SSSF) = 18. Therefore, the perforance of the proposed schee will be exactly sae as that of Optial. 1) Power Consuption: The Fig. 7 shows the power consuption of the three ethods, the proposed, optial and SSSF, with respect to different ean per-ue QoS. The overall power use is the su of transission power used by all acro and sallcell BSs on the network. Although it is not shown in the figure, the difference between the overall power use and the aggregate MBS power use is trivial, eaning that MBSs use ost of the power consued in the network. This is because an MBS associates with uch larger nuber of UEs than SBSs due to the long transission range and a larger power budget. Thus, a UE associated with an MBS ay have a sall channel gain, aking the MBS use a high transission power to satisfy the UE s SINR and QoS requireent. On the other hand, an SBS has a sall nuber of associated UEs with a short distance to each. Therefore, it does not need uch power to satisfy the associated UE s QoS deand and SINR requireent. The overall power consuption becoes saturated when the ean per-ue QoS deand is approxiately 5 and 6 Mb/s, respectively, for SSSF and both the proposed and optial schees. QoS Satisfaction Ratio Proposed Optial SSSF Mean Per-UE QoS (Mb/s) Figure 8. QoS satisfaction ratio for a sall-scale network. 2) QoS Satisfaction Ratio: QoS satisfaction ratio is the nuber of UEs with their QoS satisfied to the total nuber of active UEs on the network. As it can be seen in Fig. 8, the QoS requireents of all UEs are fully satisfied when the ean per-ue QoS is equal to or less than 4 or 4.5 Mb/s, respectively, for SSSF or both the proposed and optial. Then, the QoS satisfaction ratio drops as the per-ue deand becoes larger. It is noteworthy that for the first one or two drops of the ratio, SSSF shows a steeper decline than the rest two. Since it already uses uch power when the ean per-ue QoS is 4 Mb/s, further increase in QoS causes a significant drops in the QoS satisfaction ratio. The increase in the QoS requireent will eventually let all BSs use the axiu transission power, which increases the interference level. Failing in achieving the satisfaction ratio of 1 eans there is at least one BS whose total power budget constraint is violated. Note that the violation of the power budget constraint akes a BS use an equal power allocation for all active channels. Since

13 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. XX, NO. XX, JANUARY 2XX Synchronized power update Unsynchronized power update 3 25 Power (watt) y (eter) Iteration x (eter) Figure 9. Convergence of the iterative power allocation procedure for a sallscale network. the equal power assignent takes away the freedo in power control fro a BS, any further increase of QoS requireents will yield ore UEs with their QoS unsatisfied. UEs in a SSSF network suffer uch ore QoS degradation as the average QoS deand increases copared to both the proposed and the optial schees. 3) Convergence: The speed of convergence deterines whether the proposed algorith is suitable for an online processing or not. We have evaluated the speed of convergence with two different setting as follows, while keeping the rest network configurations the sae. One is synchronized power update and the other is unsynchronized. In the synchronized power update setting, all active channel anagers update their power at the sae tie. In other words, on iteration t it is guaranteed that all the active channel anagers on the network have fished their power update procedures for the previous t 1 st iteration. On the other hand, the unsynchronized power update does not assue the synchronized power update. For exaple, when a channel anager runs its t th power update, it is possible that there are soe channel anagers that have not finished their t 1 iterations (or even the ones before the t 1 st iteration). In order to eulate the unsynchronized updates, we have added soe rando delay into the power update ethod. The Fig. 9 shows the convergence behaviors of the power update ethod under different settings. As expected, the unsynchronized setting requires ore iterations. In this sall-scale network, every MBS has two effective interfering cells, 7 both of which are 6 away. Therefore, when the update procedures are synchronized, all BSs will converge at the sae tie on a sall-scale network. Note that this is not the case for a large-scale network where each cell is exposed to the different nuber of effective interfering cells. 7 A cell is an effective interfering cell to another if the interfering cell is close enough to the interfered cell. For exaple, if an interfering cell is 6 away, it is an effective interfering cell. However, a cell which is 6 k away is not an effective interfering cell, because the interference fro the cell is too weak. Figure 1. Network scenario for a large-scale network. E. Large-Scale Networks We also carried out an evaluation on a large-scale network where there are 3 MBSs, each of which is overlaid by 4 SBSs and 2 UEs. MBSs are placed in a shape of a bee hive where there are 5 rows of MBSs with 6 MBSs per row as in Fig. 1. The rest configurations reain the sae as before. In this siulation, we have D X (proposed) = 22 and D X (SSSF) = 358. The proposed ethod has failed to find the optial solution in BS association and channel assignent for this network for having a nonzero value of D X (proposed). However, since the difference is not significant, the power consuption in Stage 2 is expected not to be deviated uch fro that of the optial ethod. 1) Power Consuption: The power consuption of BSs on a large-scale network is illustrated in Fig. 11, which has a siilar trend to Fig. 7. It is worth entioning that although the proposed ethod has a (trivially) different Stage 1 solution than that of the optial ethod, it is hardly seen on the power consuption. In both sall- and large-scale cases, the overall power use of both the proposed and optial becoes saturated around 6 Mb/s of the ean QoS. Also, both ethods outperfor SSSF in ters of power consuption, indicting that considering both channel gain and QoS requireent is ore energy-efficient than the one considering only the received signal strength. 2) QoS Satisfaction Ratio: Each cell on the large-scale network experiences ore interference than that on the sallsized network for the increased nuber of effective interfering cells. Fig. 12 shows the QoS satisfaction ratio of UEs on the large-sized network. As it can be seen in the figure, the ratio starts to drop when the ean QoS becoes larger than 2 and 3.5 Mb/s, respectively, for SSSF and both the proposed and optial, which was not the case on the sall-scale network. This is ainly because of the increased level of interference on the large-scale network. Having ore effective interfering cells on the network increases the level of interference to each cell, and thus results in a lower energy efficiency. The perforance

14 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. XX, NO. XX, JANUARY 2XX # Power Consuption (db) Proposed Optial SSSF Power (watt) Synchronized power update Unsynchronized power update Mean Per-UE QoS (Mb/s) Iteration Figure 11. Overall power consuption for a large-scale network. Figure 13. Convergence of the iterative power allocation procedure for a large-scale network. QoS Satisfaction Ratio Proposed Optial SSSF Mean Per-UE QoS (Mb/s) Figure 12. QoS satisfaction ratio for a large-scale network. degradation of the proposed ethod for having a non-optial solution in Stage 1 can be seen in Fig. 12. As the average QoS requireent becoes larger than 8 Mb/s, the proposed ethod results in a slightly lower QoS satisfaction ratio than the optial ethod, but the degradation is trivial. 3) Convergence: Due to the increased nuber of interfering cells, the iterative power update procedure on the large-scale network takes a couple of ore steps to converge as shown in Fig. 13. Still, the network reaches convergence in 6 or 7 iterations even when the power update is not synchronized. This fast convergence behavior on the large-scale network proves that the proposed schee scales well with the network size, aking it suitable for an online resource scheduling. V. CONCLUSION In this paper, we have proposed a distributed and energyefficient association and resource scheduling schee for twotier HetNets. We have forulated an optial user association proble and then proposed a resource allocation algorith in such a way that they can be solved efficiently by an iterative, distributed ethod. To be specific, we have forulated an optial user association and channel assignent proble for Stage 1 and then applied a relaxation and an iterative adjustent ethod so as to ake the proble tractable and low-coplex. In addition, we have transfored the proposed power assignent proble into a set of lightweight distributed procedures by using the decoposition structure for Stage 2. The coparison results and the evaluation studies on sall- /large-scale networks show that the proposed schee aintains a low power consuption while satisfying users QoS requireents with a low coputational load, which proves that the proposed schee can be used for an online resource scheduling for HetNets. REFERENCES [1] Cisco visual networking index: Global obile data traffic forecast update, , Cisco Systes, Inc., San Jose, CA, Cisco White Paper, Feb [2] R. Bolla, R. Bruschi, F. Davoli, and F. Cucchietti, Energy efficiency in the future Internet: A survey of existing approaches and trends in energyaware fixed network infrastructures, IEEE Counications Surveys & Tutorials, vol. 13, no. 2, pp , July 211. [3] E. Oh, B. Krishnaachari, X. Liu, and Z. Niu, Toward dynaic energyefficient operation of cellular network infrastructure, IEEE Counications Magazine, vol. 49, no. 6, pp , June 211. [4] A. Danjanovic, J. Montojo, Y. Wei, T. Ji, T. Luo, M. Vajapeya, T. Yoo, O. Song, and D. Malladi, A survey on 3GPP heterogeneous networks, IEEE Wireless Counications, vol. 18, no. 3, pp. 1 21, June 211. [5] P. Deestichas, A. Georgakopoulos, D. Karvounas, K. Tsagkaris, V. Stavroulaki, J. Lu, C. Xiong, and J. Yao, 5G on the horizon: Key challenges for the radio-access network, IEEE Vehecular Technology Magazine, vol. 8, no. 3, pp , July 213. [6] W. H. Chin, Z. Fan, and R. Haines, Eerging technologies and research challenges for 5G wireless networks, IEEE Wireless Counications, vol. 21, no. 2, pp , Apr [7] J. G. Andrews, S. Buzzi, W. Choi, S. V. Hanly, A. Lozano, A. C. K. Soong, and J. C. Zhang, What will 5G be?, IEEE Journal on Selected Areas in Counications, vol. 32, no. 6, pp , June 214.

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Inc., Natick, MA, [41] CVX: Matlab software for disciplined convex prograing, version 2., CVX Research, Inc., Taewoon Ki received the B.S. degree in Coputer Science and Engineering fro Pusan National University, Republic of Korea, in 28 and the M.S. degree in Inforation and Mechatronics fro Gwangju Institute of Science and Technology, Republic of Korea, in 21. He is currently pursuing the Ph.D. degree in coputer engineering at Iowa State University, Aes, IA. Fro 21 to 213, he was a Research Engineer at the Telecounications Technology Association, Republic of Korea. His research interest includes network odeling, optiization and protocol design on wireless networking systes, such as WLAN, sensor networks, cellular networks and heterogeneous networks. J. Morris Chang received the MS and PhD degrees in coputer engineering fro North Carolina State University, Raleigh, NC. He joined University of South Florida, Tapa, FL, in August, 216. He was on the faculty of the Departent of Electrical Engineering at Rochester Institute of Technology, Rochester, NY, fro 1993 to 1995, the Departent of Coputer Science at the Illinois Institute of Technology, Chicago, IL, fro 1995 to 21, and the Departent of Electrical and Coputer Engineering at Iowa State University, Aes, IA, fro 21 to 216. He received the IIT University Excellence in Teaching Award in His research interests include cyber security, wireless networks, energy-aware coputing, and object-oriented systes. His research projects have been supported by US National Science Foundation (NSF), US Defense Advanced Research Projects Agency (DARPA), and Altera. Currently, he is a handling editor of the Journal of Microprocessors and Microsystes, and the Associate Editor-in-Chief of IEEE IT Professional. He is a senior eber of the IEEE.