Self-Organized Energy-Efficient Cross-Layer Optimization for Device to Device Communication in Heterogeneous Cellular Networks

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1 Received November 23, 2016; accepted ecember 23, 2016, date of pubication January 10, 2017, date of current version arch 8, igita Object Identifier /ACCESS Sef-Organized Energy-Efficient Cross-Layer Optimization for evice to evice Communication in Heterogeneous Ceuar Networks ANAN SHAHI 1, ember, IEEE, KWAN SOON KI 2, Senior ember, IEEE, ELI E POORTER 1, ember, IEEE, AN INRI OERAN 1, ember, IEEE 1 I Lab, epartment of Information Technoogy, hent University - IEC, B-9052 hent, Begium 2 epartment of Eectronics and Eectrica Engineering, Yonsei University, Seou , South Korea Corresponding author: A. Shahid adnan.shahid@intec.ugent.be This work was supported in part by the European Union Seventh ramework Programme under rant P7/ IWT SAURAI Project, in part by the European Horizon 2020 Programme under Project ewine, in part by the Institute of Information and Communication Technoogy Promotion by the Korea government SIP under rant B , and in part by the Spectrum Sensing and uture Communication Patforms. ABSTRACT evice to device 2 communication brings numerous benefits for future heterogeneous ceuar networks. However, an energy-efficient design of such 2 communications is a critica chaenge due to the cochanne depoyment and imited power of users. In this paper, we present an energy-efficient sef-organized cross-ayer optimization scheme, which aims to maximize the 2 communication energyefficiency without jeopardizing the quaity of service QoS requirements of other tiers. Specificay, we mode the cross-ayer optimization, which incudes resource bock RB and power aocation using a noncooperative game. In the proposed scheme, each 2 transmitter user, which is a payer in the game, operates in a sef-organizing manner and seects the RBs and the power eves for enhancing its energy efficiency whie maintaining the QoS requirements of other heterogeneous parties. Concerning the computationay intense nature of the goba optimization probem, we decompose the probem into two subprobems: the RB aocation and the power aocation, and sove them iterativey in a game-theoretic manner. Simuation resuts demonstrate superior energy efficiency performance of the proposed scheme over conventiona schemes. In addition, it is aso shown via simuation that the performance of the proposed scheme degrades if the channe state information is not precisey avaiabe. INEX TERS 2 communication, noncooperative game, Nash equiibrium, cross-ayer optimization, sef-organization. I. INTROUCTION ue to the advent of rea-time bandwidth hungry appications such as video streaming, onine gaming, and mobie computing, there is a sharp increase in the bandwidth demand. In addition, it is predicted that by 2020 there are more than seven triion devices serving peope [1]. This avaanche in the traffic demand is a serious threat to the energy consumption for a future ceuar network, especiay handhed user equipments UEs. On the other hand, the energy consumption aso has a significant impact on the operating cost OPEX of service providers [2] due to the continuous increase in the network users. Thereby, the energy-efficient design of a wireess network is a worth investigating area to cope with the future wireess demands. evice to device 2 communication is a nove technoogy that provides range of benefits incuding proximity gain, reuse gain, efficient spectrum utiization and increased throughput [3]. The predominant difference with wireess oca area networks WLAN is that the 2 communication shares and reuses the icensed band, i.e., in-band underaid 2 under the direct contro of a ceuar network, whereas WLAN operates in an unicensed band and possesses high degree of uncertainty in the overa performance [4]. Thus, this study considers an energy-efficient in-band underaid 2 communication comprised of macroces, femtoces and 2 networks, which is indeed of vita importance owing to the expected heterogeneous nature of a future ceuar network [5]. VOLUE 5, IEEE. Transations and content mining are permitted for academic research ony. Persona use is aso permitted, but repubication/redistribution requires IEEE permission. See for more information. 1117

2 A. Shahid et a.: Sef-Organized Energy-Efficient Cross-Layer Optimization for 2 Communication espite the numerous benefits of the in-band underaid 2 communications, critica chaenges come aong with it due to the co-channe depoyment nature of the three-tier heterogeneous macro/femto/2 networks. One of the major chaenges is how to dea with the compicated three-tier interference components, which can be regarded as a rea botteneck in the overa performance of the 2 communications. These three-tier interference components cause a serious threat to the throughput satisfaction of not ony 2 communication users but aso of those in other tiers. In this study, we consider the downink case for 2 communication in a three-tier heterogeneous ceuar network. Within this context, the three-tier interference components are: macro-to-device, femto-to-device and deviceto-device. The first two interference components are termed as cross-tier whie the ast one is co-tier. A centraized cross-ayer optimization comprised of joint resource bock RB and power aocation can pay a vita roe in escaating the performance by managing the interference [6]. However, such a centraized contro of the 2 communication poses formidabe computationa compexity and information exchange overhead, which makes it hard to be impemented in practice [7]. Thus, sef-organized resource management approaches have drawn attentions because they can hep in providing range of benefits incuding reduced information exchange, ow compexity, scaabiity, and etc [8]. ost of the existing iterature on 2 communications focus on the spectrum efficiency defined as bits/sec/hz whie the energy efficiency defined as bits/j has been mosty ignored. In a rea depoyment scenario, the energy consumption of UEs is among of prime importance due to the imited battery ife. Thus, the energy-efficient design of a wireess network recenty attracts much attention from industry, academia and standardization bodies, which motivates us to expore the energy efficiency aspect of the sef-organized cross-ayer optimization for the 2 communication in a three-tier heterogeneous ceuar network. Accordingy, this study focuses on the maximization of the energy efficiency of the 2 communication without creating harmfu impact on other tiers. A. CONTRIBUTIONS In this study, a sef-organized cross-ayer optimization for the downink of the in-band underaid 2 communication in a three-tier heterogeneous ceuar network is modeed as a non-cooperative game. Such a game-theoretic approach provides a mathematica too for modeing an optimization probem with various conficting objectives and has been often utiized for soving various resource aocations probem for 2 communications [9] [11]. The main contributions of our work are categoricay defined as under: 1 Sef-organized energy-efficient cross-ayer optimization in terms of the joint RB and power aocation is modeed as a non-cooperative game, in which 2 transmitter users 2TUs are the payers of the game whie RBs and power eves are the actions associated with each payer. 2 In the proposed game, each payer interacts with the environment and determines its own action RBs and power eves with the concern of enhancing its own energy efficiency without jeopardizing the performance of macroce users, femtoce users and other 2 pairs. In order to achieve this, the utiity function for each 2TU is designed in a manner that it is aigned not ony with the energy efficiency of the 2 communication but aso to the cross-tier and cotier interference components so as to avoid harmfu impacts on other tiers. 3 Concerning the compexity of the joint RB and power aocation, the probem is decomposed into two subprobems: the RB aocation and the power aocation. In the RB aocation step, the aocation of RBs by each payer is carried out by assuming the simiar signa-tointerference-noise-ratio SINR under the power eves of others obtained in the previous iteration of the game. In the power aocation step, a non-cooperative power optimization game is utiized for seecting the power eves on the seected RBs in the first step. According to the designed agorithm, both the RB and power aocation is carried out independenty. Under the avaiabiity of the precise channe state information CSI, it is shown that the proposed game converges to the pure and unique Nash Equiibrium. In addition, it is aso shown how the performance of the proposed scheme variates if the CSI is not precisey avaiabe. 4 Simuations are carried out by comparing the proposed scheme with a round robin non-cooperative power optimization game RR-NPO and a spectrum-efficient scheme which iustrate the efficacy of the proposed scheme. B. RELATE WORK The reated work is divided into three categories: seforganized resource management [12] [14], spectrumefficient resource management in 2 communications [15] [18] and energy-efficient resource management in 2 communications [19] [21]. Sef-organized resource management has been expored for different networks in various ways incuding heuristic approaches, earning mechanisms, game theoretic approaches, and etc [12] [14]. The authors in [12] propose a utiity based SINR that reduces the cross-tier interference in a femtoce network. However, they do not cater the co-tier interference component, which is aso termed as the botteneck in performance enhancement in the co-channe environment. The authors in [13] propose a heuristic approach for resource aocation and power contro in a femtoce network. However, the assumption of their study is that the information needs to be thoroughy exchanged among a femtoce which is not practica in a rea environment. The benefit of incorporating a non-cooperative game for the probem under the 1118 VOLUE 5, 2017

3 A. Shahid et a.: Sef-Organized Energy-Efficient Cross-Layer Optimization for 2 Communication consideration is that it requires ess information exchange. The authors in [14] empoy a nove docitive Q-earning for sef-organized resource aocation in a femtoce network. However, it takes time to earn the mechanism for the optima strategies, which makes it unsuitabe for rea environments. The authors in [15] propose a distributed resource and power aocation for the in-band underaid 2 communication in a ceuar network by utiizing a Stackeberg game framework. The goa of the optimization probem is to enhance the capacity of the 2 communication without compromising the quaity of service QoS of the 2 users. The authors in [16] propose both centraized and distributed two-stage resource aocation schemes for 2 communications. Specificay, different poicies are taken into consideration whie expoiting the spectrum reuse. The throughput performance of the 2 communications using various resource sharing modes are anayzed in [17]. The authors in [18] propose an optima power aocation scheme for enhancing the spectrum efficiency of a 2 communication, in which a base station is powered by a sustainabe energy. However, the prime focus of the above schemes is on the spectrum efficiency of the 2 communication whie the energy efficiency is not considered. Aso, a straightforward change in the objective from the spectrum efficiency to the energy efficiency maximization in [15] [18] woud not ead to a stabiized energy-efficient soution with satisfying the QoS requirement due to the ack of interference management for the QoS satisfaction. The authors in [19] propose an energy-efficient resource aocation by expoiting a reverse iterative combinatoria auction game for 2 communications. They present a joint resource and power aocation for enhancing the upink energy efficiency of a system. However, the QoS requirement of the ceuar and 2 users are not constrained, which is an important issue for a successfu depoyment of a heterogeneous ceuar system. The authors in [20] propose a centraized energy-efficient power aocation in a custered 2 scenario, which is again not practica due to the formidabe computationa compexity and information exchange. The authors in [21] propose a distributed optima power aocation for a 2 communication by utiizing a game-theoretic framework. However, a power ony optimization for a given RB creates room for possibe improvement by utiizing a joint RB and power aocation, which wi be shown as significant from the simuation resuts. According to the best of the authors knowedge, a seforganized energy-efficient cross-ayer optimization for the in-band underaid 2 communication in a three-tier heterogeneous ceuar network whie keeping the QoS requirements of macroce and femtoce users has not been investigated yet and a straightforward extension of the resuts in [19] [21] woud not ead to a reduced compexity seforganized cross-ayer optimization soution. The foowing points makes our proposition unique and worth investigating. irst, most of the previous energy-efficient resource management in iterature consider an in-band 2 on a singe tier ceuar network whie a heterogeneous ceuar network is considered as typica in future ceuar network. In this study, an inband underaid 2 on a heterogeneous ceuar network comprised of macroces and femtoces is considered. Second, the proposed scheme is designed in a pure seforganizing manner without any invovement of a centraized entity, which gives various performance benefits incuding ow-cost, scaabiity and reduced compexity. Third, a owcompexity cross-ayer optimization agorithm comprised of the iterative RB and power aocation is proposed and is shown to provide a guaranteed convergence to a unique and pure Nash Equiibrium. The rest of this paper is structured as foows: the system mode and the probem formuation are presented in Section II. The proposed sef-organized cross-ayer optimization scheme is presented in Section III. Simuation resuts are presented in Section IV. inay, Section V concudes this paper. II. SYSTE OEL AN PROBLE ORULATION A. NETWORK OEL The network mode for a three-tier heterogeneous ceuar network empoying an in-band underaid 2 communication is shown in ig. 1. Concerning the co-channe depoyment, the three-tier interference components are aso shown in the figure. In the proposed sef-organization scheme for 2 communications in a three-tier heterogeneous ceuar network, each 2TU carries out the foowing steps iterativey: sensing, earning and tuning. In the sensing step, each 2TU senses the environment and acquires channe gain information. In the earning step, a non-cooperative game is empoyed at each 2TU for the evauation of RB aocation and power aocation. In the tuning part, the best action evauated in the earning step is updated by each 2TU. The objective of the proposed sef-organized scheme for 2 communications is to enhance its energy efficiency without creating harmfu impact on other tiers by expoiting the joint RB and power aocation. In order to achieve this, a noncooperative game is adopted in which each 2TU is a payer whie the joint RB and power eves as the action. A near optima soution for the game is provided as a ow compex iterative agorithm which is suitabe for the distributed sef-organization protoco. The performance of the proposed scheme is evauated under two conditions: perfect CSI avaiabiity and imperfect CSI avaiabiity. Athough each 2TU has the capacity to precisey acquire the CSIs from macroces, femtoces and other 2 pairs, the performance of the proposed scheme is aso anayzed under the imperfect CSI. Athough the channes from far apart base stations or other 2 pairs are hardy obtained in practice, the impact from such interferers is sma so that the simuation resuts can provide an upper bound on the performance of a practica system. The systems assumptions are: 1 Contro channes for QoS satisfaction: It is assumed that if any of the QoS requirements of macroce users, femtoce users, and 2 pairs is vioated, VOLUE 5,

4 A. Shahid et a.: Sef-Organized Energy-Efficient Cross-Layer Optimization for 2 Communication IURE 1. Proposed framework for the in-band underaid 2 communication in a heterogeneous ceuar network. the corresponding 2TU get an aert from the network via the contro channe. 2 Synchronization in RBs: A tight synchronization is assumed among transmitters in the network so that interference occurs ony whenever there is a transmission on the same RB. B. SYSTE OEL In this study, we consider the downink of a frequency reuse-1 OA-based muti-ceuar system comprised of J macroces, where each macroce is served by a macro base station BS at its center and is underaid with femtoces and 2 pairs. urthermore, there are tota K femtoces and L 2 pairs in the system. Each 2 pair is composed of a 2TU and a 2 receiver user 2RU. Note that, athough the proposed scheme is shown for the downink case, it can be directy appied for the upink case. Aso, the frequency reuse-1 means that each 2TU can have a compete access to the poo of RBs. The tota number of X macroce users UEs and Y femtoce users UEs are assumed to be randomy distributed within the coverage areas of the macroces and the femtoces. The tota poo of RBs is assumed in the system and the numbers of RBs acquired by each BS, BS and 2TU are denoted as S, T and Q respectivey, such that S, T and Q. or each 2TU, the tota number of R power eves are avaiabe for each seected Q RBs, whie the RBs and power eves of the BSs and BSs are assumed to be fixed. urthermore, et s and Rs denote the set of RBs and power eves such that s = {1, 2,..., } and Rs = {P1, P2,..., PR }. The transmission power of the jth BS, the kth BS and the th 2TU are denoted by P = j i h i h Pj,1, Pj,2,..., Pj,, Pk = Pk,1, Pk,2,..., Pk, and h i P = P,1, P,2,..., P,, respectivey, where Pj,g = 0 if the gth RB is not acquired by the jth BS, otherwise P 6= 0, and simiary for Pk,g and P j,g,g The maximum power constraint on the acquired S, T and Q RBs by the corresponding BS, BS and P 2TU are represented as P,P and P such that Pj,g AX AX AX P P P Pk,g PAX and P,g PAX, AX, respectivey. The performance of the proposed scheme is represented in terms of the energy efficiency of the 2 communication. The SINR at the th 2RU operating on the gth RB can, be given as in 2 at the top of the next page, where H,g Hj,g, Hk,g and Ha,g are the channe gains on the same RBs between the th 2TU and 2RU, between the jth BS and the th 2RU, between the kth BS and the th 2RU and between the ath 2TU and th 2RU,, δ and δ are the indicator variabes respectivey, and δgj gk g whether the gth RB is used by the jth BS, the kth BS and the th 2TU, respectivey, and finay, σ 2 is the noise power. Simiary, the SINRs on the gth RB of the jth BS and the kth BS at their corresponding users are represented in 3 and 4 at the top of the next page. The imperfect CSI is modeed as the deviation of channe estimate from the actua vaue of the channe and is written as: = H,g + κ,g H,g 1 is the channe estimation error and is modeed where κ,g by a zero-mean aussian random variabe with variance. oreover, the random variabes κ are indepenξ,g,g dent and identicay distributed i.i.d. on different RBs and on different tiers. Here we are assuming a minimum mean square error SE estimator where the CSI estimation error and the actua CSI are mutuay uncorreated [22], [23]. Simiary, the imperfect CSI for a the channe gains in 2-4, as shown at the top of the next page, can be modeed by 1, respectivey. The throughput of the th 2 pair and the average throughput of the jth BS and the kth BS with respected to their associated users, respectivey, can be represented VOLUE 5, 2017

5 A. Shahid et a.: Sef-Organized Energy-Efficient Cross-Layer Optimization for 2 Communication SINR,g = SINR j,g = SINR k,g = σ 2 + σ 2 + σ 2 + J j=1 P j,g H j,g δgj acro components J a=1,a =j P a,g H aj,g + δ ga acro components J j=1 P j,g H jk,g δgj acro components + K k=1 P,g H,g P k,g H k,g δgk emto components k=1 + emto components L a=1,a = P a,g H a,g δga 2 components =1 2 components, = {1, 2,..., L}, g s. 2 P j,g H jj,g, j = {1, 2,..., J}, g s. 3 K L + P k,g H kj,g δgk + P,g H j,g δg P k,g H kk,g K P a,g H ak,g a=1,a =k δ ga emto components + L =1 P,g H k,g δg 2 components, k = {1, 2,..., K}, g s. 4 as: j k = W = W = W δgj og SINR j,g, j = {1, 2,..., J}, 5 δgk og SINR k,g, k = {1, 2,..., K}, 6 δg og SINR,g, = {1, 2,..., L}, 7 where W denotes the system bandwidth. Aso, the energy efficiency bits/j of the th 2 pair can be represented as: W EE δg og SINR,g = δg P,g + p, c = {1, 2,..., L} 8 where p c is the circuit power which corresponds to the accumuated power consumption of a the eectronic devices invoved in signaing and backhauing, and is assumed to be constant in this study. C. PROBLE ORULATIONS In contempation of enhancing the energy efficiency of the 2 communications by expoiting a joint RB and power aocation, the optimization probem can be formuated as: B, C = arg max B [1,0]s,C R s s W δg og SINR,g δg P,g + p, c = {1, 2,..., L}, 9 subject to: C1 : R IN,, 10a C2 : j R IN, j, 10b C3 : k R IN, k, 10c ] C4 : P,g [ C5 : δ g 0, P AX Q,, g, 10d Q, 10e where B = [ δ1, δ 2,..., ] δ and C = [P,1, P,2,..., P, ] corresponds to the aocation of Q RBs and their corresponding power eves by each th 2TU. The constraints C1 - C3 represent the satisfaction of the minimum throughput requirements of the considered three-tier users, respectivey, the constraint C4 represents the minimum power aocation bound on each RB and the constraint C5 represents that maximum number of RBs acquired by each 2TU.. NOTATIONS The notations and assumptions presented in Tabe 1 wi be used throughout the rest of the paper. III. SEL-ORANIZE CROSS-LAYER OPTIIZATION USIN A NON-COOPERATIVE AE A. NON-COOPERATIVE AE A non-cooperative game is a powerfu mathematica too which has been utiized in various resource aocation probems in wireess networks [24]. In the probem formuation in Section II.C, we consider each 2TU is sefish and an irrationa payer which tends to increase its utiity function. Therefore, the probem presented in 9 and 10 can be modeed as a non-cooperative game. In this study, we mode the cross-ayer optimization task in the form of a joint RB and power aocation as a non-cooperative game. eneray, VOLUE 5,

6 A. Shahid et a.: Sef-Organized Energy-Efficient Cross-Layer Optimization for 2 Communication TABLE 1. Notation and assumptions. energy efficiency and is written as: W δg og SINR,g U A, A = δg P,g + p, c = {1, 2,..., L}. 11 efinition 1: or given B and C, the best response of the joint RB and power aocation for the th payer is represented as: B, C = arg max B [1,0]s,C R s s U B, C B, C 12 Primariy, the optima joint RB and power aocation is mathematicay intractabe and is an NP-hard probem. In order to reduce the compexity, the joint probem is decomposed into two suboptima subprobems: the RB aocation and the power aocation.. a game γ is represented by a tupe γ = { } L, {A }, {U.} L, where L is the finite set of payers, A denotes the action associated with the th payer and U is the reward or the utiity function beongs to the th payer. In other words, the utiity function imitates the eve of satisfaction to each payer. athematicay, the utiity function can be thought as a mapping function that maps the action A into the rea number R such that U : A R. Aso, et the actions of others payers can be represented by a vector A = {A 1, A 2,..., A 1, A +1,..., A L }. In the proposed scheme, a set of L 2TUs are the payers of the game which interact with the environment in a seforganizing manner and find out the best actions, in which the action comprised of two parts: the RB aocation and the power aocation. athematicay, the action of the th 2TU is represented as A = B, C, where B represents the indication vector for the aocation RBs among the tota poo of RBs whie C denotes the power eves on the RBs within the maximum power constraint. or given B and C, the RB and the power aocations of other payers are represented as B = { B 1, B 2,..., B 1, B +1,..., } B L and C = { C1, C 2,..., C 1, C +1,..., } C L. Since the goa of the proposed scheme is to enhance the energy efficiency of the 2 communications, the utiity function is set as the B. RESOURCE BLOCK ALLOCATION In the RB aocation subprobem, the foowing theorem provides an optima RB aocation at a given power aocation of others in the previous iteration by assuming its own power aocation to make the SINRs on the seected RBs equa. Note that the power aocation of each seected RB wi be carried out under the network constraints C1-C5. Theorem 1: A group of Q RBs among the poo of RBs is aocated to each th payer 2TU, if the foowing condition is satisfied: B = arg min B [0,1]s δ g I,g H,g, s.t. δg = Q, 13 where I,g = σ 2 + J j=1 P j,q H j,q δgj + K k=1 P k,q H k,q δgk + L a=1,a = P a,q H a,q δga denotes the accumuated interference on the gth RB at the th 2RU. Proof: iven power aocation of the th payer, the best response of the RB aocation can be written as: B = arg max U B B C. 14 [1,0]s Note that information about B is aso avaiabe in C so that B can be determined at a given C. Substituting 2 and 11 in 14 we get, W δ B g og P,g H,g I,g = arg max B [1,0]s δg P,g + p, c s.t. = Q. 15 δ g Assuming ρ to be the target SINR on the seected RB and substituting the power of 2TUs P,g = ρi,g in 15, we H,g 1122 VOLUE 5, 2017

7 A. Shahid et a.: Sef-Organized Energy-Efficient Cross-Layer Optimization for 2 Communication get B = arg max B [1,0]s s.t. which is equivaent to B = arg min B [1,0]s δ g which concudes the proof. W δg og ρ ρ, δg I,g + p c H,g = Q, 16 δ g I,g H,g, s.t. δg = Q, C. POWER ALLOCATION iven the RB aocation by each 2TU, the power aocation probem can be considered as a non-cooperative power optimization game γ p = { L, C }, U. L. Since the utiity function of the proposed scheme depends upon the behavior power eves of two or more payers, we mode the power optimization probem via a non-cooperative power optimization game [25]. Then for a given RB power aocation of a other payers, the best response of the th payer is given by C = arg max U C C R s C s. 17 The payers invoved in a non-cooperative power optimization game optimize their power eves independenty on each seected Q RBs in the resource bock step. Since the goa of the overa game is to enhance the energy efficiency of the 2 communication without jeopardizing the performance of other tiers, the power optimization is carried out within the network constraints C1 - C5. Note that changes in the power aocation of each payer impact significanty on the other payers. Thus, it is of prime importance whether the proposed scheme can converge to an equiibrium point where a the competing infuences are baanced. 1 THE EXISTENCE AN UNIQUENESS O THE Nash EQUILIBRIU { In a non-cooperative game, the set of actions C = C 1, C2,..., } C L is termed as the Nash Equiibrium if none of the payer can change the action by increasing the utiity function. The strict definition of Nash Equiibrium is represented as in the foowing definition. efinition 2: In the energy-efficient non-cooperative power optimization game, a Nash Equiibrium for the given { power aocation of a the payers C = C 1, C2,..., } C L exists in the game if the foowing inequaity is satisfied, U C, C U C, C. 18 In other words, a Nash Equiibrium is defined as a stabe optima point in which none of the payers can change the actions profitaby. The existence of such a Nash Equiibrium is justified with the beow-presented theorem. Theorem 2 [26]: A Nash Equiibrium exists in a noncooperative power optimization game γ p = {L, { C }, {U.} L }, if the foowing two conditions are satisfied: 1 { C } to a non-empty, convex and compact subset of some Eucidean space. 2 The utiity function U C, C is continuous and quasi-concave. efinition 3: Let U C be a function that maps from a convex set θ of n-dimensiona vectors to a rea number. Then, U. is quasi-concave if for any C1, C 2 θ, and C 1 = C 2, } U λc λ C 2 min {U C, U C irst the existence is proved. Since the power aocation vector C is confined within the power constraints, condition 1 in Theorem 2 is satisfied. Aso, in order to prove that U is quasi-concave, define the upper contour set µ of U C, C as } µ = {C 0 U C, C µ, µ R, 20 where a vector S 0 means that each eement in S is nonnegative. In accordance with the preposition C.9 in [27], the utiity function U C, C is stricty quasi-concave in C if and ony if the upper contour set µ is convex for a µ R. In addition, if µ < 0, the upper contour set becomes the whoe space { C } so that µ is stricty convex for µ 0. or C µ, the utiity function satisfies W U C, C δg og SINR,g = δg P,g + p µ. c 21 Therefore, the upper contour set µ is equivaent to: µ = { C 0 W δg og SINR,g } δg P,g + p c µ which is convex and it concudes the proof for condition 2. In the contempation of the uniqueness of a noncooperative power optimization game, the foowing theorem is presented. Theorem 3 [28]: A non-cooperative power optimization game γ p posses a unique Nash Equiibrium if the beow-isted conditions satisfied: 1 Positivity: U C > 0. 2 onotonicity: if C1 > C 2, U C 1 > U C 2. 3 Scaabiity: β > 1, βu C > U βc. VOLUE 5,

8 A. Shahid et a.: Sef-Organized Energy-Efficient Cross-Layer Optimization for 2 Communication The utiity function U. used in this paper has a simiar form to that in [29] and can be proved to satisfy the above conditions in a simiar way.. PROPOSE ALORITH In Section III.B, the optima Q RB aocation of each 2TU is shown at a given power aocation of others and the same SINR assumption whie satisfying the constraints C1-C5. Aso, in Section III.C, it was proven that a non-cooperative power aocation game using the utiity function of the energy efficiency of each 2TU within the constraints C1-C5 provides a pure and unique Nash Equiibrium if the CSIs and actions of other payers are assumed to be known. Thus, the proposed Agorithm 1 empoys two steps iterativey at each 2TU: the RB aocation and the power aocation step. In the RB aocation step, the aocation of Q RBs among the poo of RBs is carried out by each 2TU with the concern of minimizing the impact of interference in the three-tier heterogeneous ceuar network. Here, the given power aocation of other users are the resuts obtained in the power aocation step of the previous iteration. In the power aocation step, a non-cooperative power optimization game with discrete power eves is utiized for seecting the power eves on the seected RBs in the RB aocation step of the current iteration. The detaied procedure is given as foows: In the proposed game, the best response of the RB and the power aocation in 14 and 17 depends on the power eves of other 2TUs i.e., C, which is hardy obtained in practice. However, the power eves of other 2TUs impacts on tota interference I,g so that the proposed agorithm can be operated approximatey at the cost of sight performance degradation ony with the tota interference information at each 2RU, simiary as in [27]. IV. SIULATION RESULTS AN ANALYSIS In this section, the performance of the proposed seforganized energy-efficient scheme is evauated in terms of the energy efficiency as the performance measure incuding the convergence performance, the energy efficiency distribution, and the impact of varying Q, and 2 pairs on the average energy efficiency in the three-tier network. In addition, the throughput satisfaction of the 2 pairs whie empoying the proposed scheme is evauated and compared by using the Jains fairness index [30]. or the comparison, two distributed sef-organizing schemes using a round robin noncooperative power optimization game abeed as RR-NPO and a spectrum-efficient game abeed as spectrum-efficient are utiized which can be considered as the representatives for those enhancing the energy efficiency by a power aocation ony simiary as in [21] and for those enhancing the energy efficiency by using a joint RB and power aocation simiary as in [31]. A. SIULATION SETUP We consider the downink of an OA-based threetier heterogeneous ceuar network operating at the carrier Agorithm 1: Proposed Sef-Organized RB and Power Aocation Using Non-Cooperative ame Input: A ink gains that connect macroces, femtoces and 2 pairs on the poo of RBs for both perfect CSI avaiabiity and imperfect CSI avaiabiity. Randomy initiaize the RBs and power aocation by each 2TU Set the proposed scheme maximum iteration count: ITER1 Set the proposed non-cooperative power optimization game maximum iteration count:iter2 Output: Resource bock and power aocation, A { B, C } Aocate same power on each RB whie the maximum iteration ITER1 has passed or the convergence is achieved do Step-1: Resource bock aocation for each 2TU payer do { } B arg maxb [0,1] s δg I,g, s.t. H C5 { B } { } B end Step-2: Power aocation Initiaize C 0, whie the maximum iteration ITER2 has passed or the the Nash Equiibrium point has achieved do for each 2TU payer do ind { C } arg maxr s U C s, C, s.t. C1-C5 By expoiting the power eves of the best RBs in terms of maximization of the utiity function { } { } C C end end end return A { B, C } frequency of around 2Hz that cosey foows the 3PP TR or simpicity, a singe macroce J =1 is assumed with a radius of 1000m. In the macroce, it is assumed that K femtoces with radius of 40m and L 2 pairs with distance of 25m are randomy ocated in an underaid manner. The BS or each BS is ocated at the center of the corresponding ce and X UEs and Y UEs are randomy depoyed within the coverage of the macroce and femtoces. Since we consider the three-tier heterogeneous network based on ong term evauation LTE, the frequency band is divided into RBs, each of bandwidth 180KHz in frequency and 0.5ms in time domain. Each RB is comprised of 12 subcarriers with a spacing of 15KHz and consist of 7 O symbos. urther, we consider the tota poo of RBs = VOLUE 5, 2017

9 A. Shahid et a.: Sef-Organized Energy-Efficient Cross-Layer Optimization for 2 Communication and = 50 which represents an LTE impementation with a system bandwidth of W = 4.5Hz and 9Hz, respectivey. With incorporating the guard intervas of 0.5Hz and 1Hz, respectivey, the system bandwidth becomes 5Hz and 10Hz, respectivey, which is in accordance with the LTE specifications. The number of RBs for each 2TU is assumed that Q {2, 3, 4, 5, 6} whie those for the BS and each BS are fixed at T = 10 and S = 25. The maximum powers of the BS and each BS are set to P AX = 43dBm and P AX = 23dBm, respectivey. The maximum power on each RB of a 2TU is set to P AX =23-10 og 10 QdBm. Aso, R = 100 discrete power eves uniformy distributed in the range from 80 to 23dBm are assumed. inay, the constant circuit power of p c = 100 mw, simiary as in [32] and the noise spectra efficiency is set to N 0 = 141dBW/Hz. The path oss PL mode that we have utiized in this study is in accordance to the 3PP [33], [34], where PL modes are given as 1 or macroce and femtoce outdoor: PLdB = og 10 d; 2 or macroce and femtoce indoor: PLdB = og 10 d; 3 or 2 system: PLdB = og 10 d. Aso, the og-norma shadowing with the shadowing factor of 8dB and 4dB are utiized for the indoor and the outdoor mode, respectivey. The variance of channe estimation error is considered to be: ξ,g = The performance of the proposed and comparative counterpart schemes are evauated over 500 different reaizations of the ocation of network entities and the fading channe among them. B. CONVERENCE PERORANCE EVALUATION The convergence performance of the proposed scheme for each perfect and imperfect CSI avaiabiity is evauated and compared for the cases: L = 25 and L = 35 as shown in ig. 2. The ack of CSI avaiabiity degrades the performance of the proposed scheme with perfect CSI and this trend increases from 10% to 15%, respectivey, with the increase of 2 pairs. Athough a three schemes require simiar number of iteration for convergence, the proposed scheme for each condition outperforms the other two schemes. Specificay, the spectrum-efficient scheme performs worst so that it becomes apparent that enhancing the spectrum efficiency without considering the required power resuts in a nonsatisfactory energy efficiency performance. It is shown that, athough the energy efficiency is considered, a power-ony aocation with a round robin or random RB aocation as in conventiona schemes is not sufficient. urthermore, athough the energy efficiency of each 2 pair decreases as the 2 pair density increases, the improvement by using the proposed scheme over two conventiona schemes increases from 23% and 52% to 35% and 98%, respectivey. C. ENERY EICIENCY ISTRIBUTION The energy efficiency distributions according to the various reaizations on the ocations of the network entities and fading IURE 2. Convergence performance. IURE 3. Energy efficiency distribution. channes among them are iustrated for the proposed and the two conventiona schemes in ig. 3. The resuts are potted for two different 2 pair densities L = 25 and L = 35 for each of the scheme. It is ceared from the distribution aso that the performance trend of the proposed scheme under two CSI conditions remains simiar as did for the convergence anaysis. On the other hand, it is aso apparent that the spectrum-efficient scheme performs worst again through the whoe distribution, which again confirms the importance of considering the energy efficiency. Aso, a round-robin or random RB aocation used in the RR-NPO scheme is shown to be very inefficient and the joint aocation of RB and power eve by considering the interference in the proposed scheme can provide a significant gain through the whoe distribution. ore precisey, the min-max energy efficiency bounds, defined as the interva of energy efficiency from 5% to 95%, of the proposed scheme with perfect CSI, the proposed scheme with imperfect CSI, the RR- NPO scheme and the spectrum-efficient scheme are [ bits/J], [ bits/J], [ bits/J] and [ bits/j] for L = 25 and [ bits/J], [ bits/J], [ bits/J] and [ bits/J] for L = 35, respectivey.. IPACT O VARYIN Q, AN L The impacts of varying Q and on the energy efficiency of the 2 communications are iustrated in VOLUE 5,

10 A. Shahid et a.: Sef-Organized Energy-Efficient Cross-Layer Optimization for 2 Communication IURE 4. Impact of varying and Q on the energy efficiency a: L = 25 and b L = 35. igs. 4a and 4b, when L = 25 and L = 35, respectivey. As the number of RBs acquired by 2TU increases at a fixed amount of tota RBs, the energy efficiency of each scheme increases. rom the resuts, it is shown that the proposed scheme, with both CSI conditions, improves faster than the two conventiona schemes, which comes from the significant advantage of the joint RB and power aocation of the proposed scheme. Aso, comparing the resuts of the = 50, L = 25 case, the reative performance improvement of the proposed scheme becomes more significant as decreases or L increases, i.e., 2 resource utiization over tota resource QL increases, which shows the efficiency of the proposed scheme again. IURE 6. airness index. E. AIRNESS INEX IURE 5. Impact of 2 density on the energy efficiency. In ig. 5, the impact of varying the 2 pair density on the energy efficiency is shown. ue to the co-channe depoyment among the heterogeneous parties, the energy efficiency can be improved by empoying a arger poo of RBs because an increase in the number of RBs provides more opportunities to reduce the interference. However, as the 2 resource utiization increases decreases or L increases, the proposed scheme shows more gracefu degradation in the energy efficiency of each 2 pair than the conventiona schemes. On the other hand, the performance degradation of the proposed scheme, whie considering perfect and imperfect CSI, increases with the increase of 2 pairs which is due to the increase in competition in the non-cooperative game Athough the energy efficiency is of the prime interest in this study, the throughput performance of the proposed scheme is compared with the conventiona schemes in ig. 6 using the Jains fairness index formua given as P 2 L =1 I f L = PL, 23 L =1 I2 where I = E 9 denotes the average throughput of the th 2 pair and the fairness index fl, 0 fl 1, indicates a eve of satisfaction among 2 pairs in terms of the fairness in the average throughput. rom the resut, it is shown that athough the proposed scheme focuses on the energy efficiency, the throughput performance of the proposed scheme with perfect CSI remains amost the same to that of the spectrum efficiency scheme whie that of RR-NPO scheme deteriorates. On the other hand, the throughput performance of the proposed scheme with imperfect CSI aso sighty variates as compared to its perfect CSI counterpart and spectrum efficient scheme and this is due to the sight degraded performance of it whie achieving the Nash Equiibrium. This is due to the efficiency of the joint RB and power aocation by minimizing required power by reducing interference whie managing the required QoS. VOLUE 5, 2017

11 A. Shahid et a.: Sef-Organized Energy-Efficient Cross-Layer Optimization for 2 Communication V. CONCLUSION In this study, we propose a sef-organized cross-ayer optimization for enhancing the energy efficiency of the 2 communications without creating harmfu impact on other tiers by empoying a non-cooperative game in a three-tier heterogenous ceuar network. Specificay, each 2 pair iterativey performs the sensing, earning and tuning steps for jointy optimizing the RB and power aocation to enhance its energy efficiency in a distributed manner without jeopardizing the user performance in other tiers. In order to achieve the energy efficiency maximization whie maintaining the QoS requirement of other parties, the utiity function is designed to consider not ony the energy efficiency of its own but aso the interference to other tiers. The joint RB and power aocation agorithm for each 2TU is proposed by iterativey appying an optima RB seection for given other users power eves determined in the previous iteration and power aocation on the seected RBs using the proposed noncooperative game. The performance of the proposed scheme with both CSI conditions is evauated and compared with conventiona RR-NPO and spectrum-efficient schemes. The resuts iustrates that superior performance of the proposed scheme is achieved in terms of the energy efficiency over the conventiona schemes. urthermore, the performance gap between the proposed scheme and the conventiona schemes increases as 2 pair density increases, which makes it an attractive option for dense environments. This study can be extended by considering the asynchronous OA and it is worth investigating to see the existence of Nash Equiibrium for this case. REERENCES [1] K. opper, C. B. Ribeiro, and J. 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12 A. Shahid et a.: Sef-Organized Energy-Efficient Cross-Layer Optimization for 2 Communication [33] 3PP Organizationa Partners 3PP urther advancements for e-utra physica ayer aspects, Tech. Rep. TR , [34] ETSI, Seection procedures for the choice of radio transmission technoogies of the umts, UTS Technica, Sects, Tech. Rep. TR European Teecommunications Standards Institute, Sophia Antipois, rance, UTS 30.03, ANAN SHAHI 15 received the B.Eng. and.eng. degrees in computer engineering with speciaization in communication from the University of Engineering and Technoogy, Taxia, Pakistan, in 2006 and 2010, respectivey, and the Ph.. degree in information and communication engineering from Sejong University, South Korea, in He is coordinating and activey invoved in the research activities of the research project ewine. rom 2007 to 2012, he served as a Lecturer with the Eectrica Engineering epartment, Nationa University of Computer and Emerging Sciences, Pakistan. rom 2012 to 2015, he was a Ph.. Research Assistant with Sejong University. In 2015, he was a Post-octora Researcher with Yonsei University, South Korea. rom 2015 to 2016, he was with the epartment of Computer Engineering, Taif University, Saudi Arabia. He is currenty a Post-octora Researcher at ILab, epartment of Information Technoogy, hent University, Begium. His research interests incude next generation wireess communication and networks with prime focus on resource management, interference management, cross-ayer optimization, sef-organizing networks, sma ce networks, device-to-device communications, machine-to-machine communications, and 5 wireess communications. r. Shahid received the Prestigious BK 21 Pus Postdoc Program at Yonsei University. He is activey invoved in various research activities. He is aso serving as an Associate Editor of the IEEE ACCESS. KWAN SOON KI S S 04 was born in Seou, South Korea, in He received the B.S. summa cum aude,.s.e., and Ph.. degrees in eectrica engineering from the Korea Advanced Institute of Science and Technoogy, aejeon, South Korea, in 1994, 1996, and 1999, respectivey. rom 1999 to 2000, he was with the epartment of Eectrica and Computer Engineering, University of Caifornia at San iego, La Joa, CA, USA, as a Post-octora Researcher. rom 2000 to 2004, he was a Senior ember of the research staff with the obie Teecommunication Research Laboratory, Eectronics and Teecommunication Research Institute, aejeon. Since 2004, he has been a Professor with the epartment of Eectrica and Eectronic Engineering, Yonsei University, Seou. His research interests incude signa processing, communication theory, information theory, and stochastic geometry appied to wireess heterogeneous ceuar networks, wireess oca area networks, wireess 2 networks and wireess ad doc networks, and are recenty focused on the new radio access technoogies for 5. Prof. Kim served as an Editor of the Journa of the Korean Institute of Communications and Information Sciences from , as an Editorin-Chief of the Journa of KICS since 2013, as an Editor of the Journa of Communications and Networks JCN since 2008, and as an Editor of the IEEE TRANSACTIONS ON WIRELESS COUNICATIONS He received the Post-octora eowship from Korea Science and Engineering oundation in He received the Outstanding Researcher Award from Eectronics and Teecommunication Research Institute ETRI in 2002, the Jack Neubauer emoria Award Best System Paper Award, the IEEE TRANSACTIONS ON VEHICULAR TECHNOLOY from the IEEE Vehicuar Technoogy Society in 2008, and the L R& Award: Industry-Academic Cooperation Prize, L Eectronics, ELI E POORTER 11 received the master s degree in computer science engineering from hent University, Begium, in 2006, and the Ph.. degree from the epartment of Information Technoogy, hent University, in He is now a Professor with ILab, hent University, Begium. In addition to teaching severa courses, he is a Research Coordinator of mutipe nationa and internationa projects reated to future wireess networks. He is part of the program committee of severa conferences and is the author or co-author of more than 90 papers pubished in internationa journas or in the proceedings of internationa conferences. He is aso the creator of the patented IRA architecture, a fexibe communication framework for heterogeneous networked devices. His main research interests incude wireess network protocos, network architectures, wireess sensor and ad hoc networks, future Internet, sef-earning networks, and next-generation network architectures. INRI OERAN 96 received the degree in eectrica engineering and the Ph.. degree from hent University, Begium, in 1987 and 1992, respectivey. She was a part-time Professor with hent University, in She is a Staff ember with ILab, a core research group of IEC with research activities embedded in hent University and University of Antwerp. She is coordinating the research activities on mobie and wireess networking and eading a research team of about 30 members at ILab-hent University. She is the author or co-author of more than 700 pubications in internationa journas or conference proceedings. Her main research interests incude the Internet of Things, ow power wide area networks, highdensity wireess access networks, coaborative and cooperative networks, inteigent cognitive radio networks, rea-time software defined radio, fexibe hardware/software architectures for radio/network contro and management, and experimentay-supported research. She has a ongstanding experience in running and coordinating nationa and EU research funded projects. At the European eve, she is active in the uture Networks research area, where she has been coordinating severa P7/H2020 projects CREW, WiSHUL, ewine, and ORCA and participating in other projects ed4ire, ORE, LEX, and ex5ware. VOLUE 5, 2017