Efficient Usage of Renewable Energy in Communication Systems using Dynamic Spectrum Allocation and Collaborative Hybrid Powering

Transcription

1 1 Efficient Usage of Renewabe Energy in Communication Systems using Dynamic Spectrum Aocation and Coaborative Hybrid Powering Taha Touzri, Mahdi Ben Ghorbe, Member, IEEE, Bechir Hamdaoui, Senior Member, IEEE, Mohsen Guizani, Feow, IEEE, and Bassem Khafi, Student Member, IEEE Abstract In this paper, we introduce a new green resource aocation probem using hybrid powering of communication systems from renewabe and non-renewabe sources. The objective is to efficienty aocate the power deivered from the different micro-grids to satisfy the networ requirements. Minimizing a defined power cost function instead of the net power consumption aims to encourage the use of the avaiabe renewabe power through coaboration between the base stations within and outside the different micro-grids. The different degrees of freedom in the system, ranging from assignment of users to base stations, possibiity of switching the unnecessary base stations to the seep mode, dynamic power aocation, and dynamic aocation of the avaiabe bandwidth, aow us to achieve important power cost savings. Since the formuated optimization probem is a mixed integer-rea probem with a non-inear objective function, we propose to sove the probem using the Branch and Bound B&B approach which aows to obtain the optima or a suboptima soution with a nown distance to the optima. The reaxed probem is shown to be a convex optimization which aows to obtain the ower bound. For practica appications with arge number of users, we propose a heuristic soution based on decomposing the probem into two sub-probems. The users-to-base stations assignment is soved using an agorithm inspired from the binpacing approach whie the bandwidth aocation is performed through the bub-search approach. Simuation resuts confirm the important savings in the non-renewabe power consumption when using the proposed approach and the efficiency of the proposed disjointed agorithms. Index Terms green communications, smart grids, efficient bandwidth aocation, power efficiency, renewabe energy, branch and bound. I. INTRODUCTION The dramatic increase of power generation costs and the increasing awareness about effects of carbon emissions resuted in a serious focus on reducing power consumption when designing modern industria systems [1 4]. As a resut, the deveopment of techniques that can sti achieve high system performances whie minimizing energy consumption has been the design focus of various networing systems, This wor was made possibe by NPRP grant # NPRP from the Qatar Nationa Research Fund a member of Qatar Foundation. The statements made herein are soey the responsibiity of the authors. This wor is an extended version of the wor accepted for presentation at the IEEE Goba Communications Conference GLOBECOM, San Diego, USA, Dec. 15. Taha Touzri, Mahdi Ben Ghorbe, and Mohsen Guizani are with Qatar University, Doha, Qatar e-mai: mguizani@ieee.org. Bechir Hamdaoui and Bassem Khafi are with Oregon State University, Oregon, USA. incuding sensor networs [5 8], cognitive radio networs [9 12], femtoce networs [13 16], coud networs [17 19], and others. Reying on renewabe energy sources has been one of the promising soutions to reduce carbon emissions [, 21], but their imited avaiabiity maes them unreiabe for ong term use. With the technoogica advances achieved in improving their energy efficiency, renewabe sources contributed about 19% of the goba word energy consumption in 12 [22]. With the continuous growth in teecommunications maret, communication systems become one of the biggest power consumers and CO 2 producers with an amount representing 2% of the goba CO 2 emissions in the word [23]. In 14, radio access networs contributed about 84 T W h in the tota word energy consumption and about 17 Mto CO 2 e in the tota carbon emissions [24]. Those numbers are expected to exponentiay increase in the coming years with the continuous growth of the teecommunications maret driven by the mutipication and variation of the teecommunication services and the exponentia increase of the required Quaity of Service QoS. According to [25, 26], base stations BSs are the highest components in terms of power consumption in the mobie networs. It is responsibe for about 6% of the tota power consumption. For that, many research attempts [27, 28] have focused on reducing BSs energy consumption through efficient resource aocation, increasing coaboration between BSs to serve users, optimizing the geographica positions taing into consideration the distribution of the served users, and improving the use of renewabe sources. In this wor, we consider a communication system where BSs connected to different micro-grids cooperate to minimize the goba power cost whie ensuring a reiabe service to the requesting users. Each micro-grid is equipped with renewabe sources but has the abiity to procure non-renewabe power from the main grid when needed. The main tas is to optimize resource aocation through coaboration between BSs to satisfy the required QoS of the different users whie minimizing the non-renewabe energy consumption by profiting from the avaiabe renewabe power. The chaenge consists in determining the users assignment to BSs depending on their reative channe gains as we as the renewabe power avaiabiity at each micro-grid. Our joint users assignment and resource aocation probem is formuated as a mixed-integer rea probem with noninear objective function and constraints. Soving this type of

2 2 probems is often chaenging, especiay with arge number of variabes. In our initia wor [29], we proposed a heuristic approach based on dividing the probem into two tass, users assignment tas and resource aocation tas, and proposed an adequate agorithm for each tas. In this paper, we compement it with a study of an optima soution using convex reaxation of the probem and the branch and bound method. This method aows to obtain a soution with a nown distance to the optima but its high computationa cost maes it impractica for rea impementation. Thus, we show that the heuristic soution represents a good aternative that achieves a tradeoff between optimaity and compexity. A. Literature Review Deveoping green communications is one of the major chaenges of the communication networs for 5G systems [3]. A recent survey [31] studied different wors on using renewabe sources to power BSs and showed their efficiency for a reiabe communication system. Authors in [32] proposed to power BSs using soar energy whie in [33], they focused on dimensioning the battery and the photovotaic pane used to suppy BSs. Using hybrid renewabe is shown to increase the energy efficiency by taing advantage of the different renewabe power sources. In this topic, different scenarios of hybrid wind-soar powering of the BSs were studied in the iterature [34 36]. One of the imits of renewabe sources is the discontinuity of the power generation which affects reiabiity of the service. Thus, hybrid renewabe and non-renewabe powering is required. The emergence of smart grids represents an opportunity to enhance power usage in teecommunication systems by expoiting the dynamic power pricing information. In a recent survey, Ero-Kantarci and Mouftah [37], showed the great savings that coud be achieved through the use of smart grid capabiities in optimizing powering communication networs. In addition, it was remared that ony few research groups have focused on optimizing the use of smart grids in communication systems. Of these wors, Bu et a. [38] presented a study of the best scheme to power base stations using smart grid with consideration of rea-time power prices provided by the smart grid and poution eve resuting from the power generation whie Ghazzai et a. [39] presented a compete framewor for a smart-grid powered LTE system and introduced a power aocation strategy based on evoutionary agorithms. Turning BSs to seep mode is one of the strategies that attracted a ot of attention. For this purpose, Hotamp et a. [4] proposed an optimized radio resource aocation agorithm where the achieved gain ranges between to 4% depending on the oad, the proposed agorithm incudes a seep mode duration estimation, resources sharing and antenna configuration. Micaef et a. [41] proposed to switch BSs to seep mode when the traffic oad decreases, the focus of this wor is how to seect the set of BSs to be switched to seep mode. Serving the same main purpose of the previous reference, Saer et a. [42] proposed two switching to seep mechanisms for base stations, the first is dynamic and depends on the rea time oad and the second is caed semi-static where resource aocation is panned for onger time periods. B. Contributions In this paper, we propose to sove a joint users-to-bs assignment and resource aocation probem for a group of BSs custered into a number of micro-grids, where each microgrid is powered through hybrid renewabe and non-renewabe power sources. The objective is to minimize the tota cost of procurement in the networ whie guaranteeing the required QoS for the users in the system. The contributions of this paper are summarized as foows: 1 A green resource aocation architecture using hybrid powering of the communication system from renewabe and non-renewabe sources. 2 Expoiting the optima performance using the reaxation approach based on the branch and bound method to present an ɛ-to-optima soution. 3 Proposing a suboptima soution based on di-associating the probem into two sub-probems; one for the users-to- BSs assignment and the other for the resource aocation and proposing efficient heuristic agorithms to sove each of them. 4 Taing into consideration the possibiity of switching BSs to the seep mode by studying a powering mode that contains this capabiity and studying its effect on power cost savings. 5 Studying the effect of the distribution of the renewabe power avaiabiity on the achieved cost gains. The remaining of this paper is organized as foows. Section II introduces the system mode and micro-grid powering architecture. Section III gives the mathematica probem formuation of the system and modes that govern the power cost in the system. Then, in Section IV we present how to expoit the B&B method to find the optima soution whie in Section V, we detai and anayze the proposed heuristic agorithms for resource aocation. Foowing that, we present a performance anaysis of the presented agorithms through extensive simuations in Section VI. Finay, the concusion is drawn in Section VII. II. SYSTEM MODEL We consider a set of L base stations aiming to serve K users through N sub-channes N >> K. We assume that the base stations are connected through M power-grids where each micro-grid m powers a group of L m base stations. Each micro-grid uses renewabe power to generate eectricity needed to feed the connected base stations. In addition to that, it is responsibe for purchasing the bac-up power from the main grid when needed as shown in Fig. 1. It is to be noted that BSs custering method into the microgrids is out of the scope of this paper. But, resuts of this wor coud be expoited to optimize the custering of the BSs. We consider to focus on the instantaneous management of the avaiabe power. Thus, we assume that BSs do not have the abiity to stoc power. The avaiabe instantaneous renewabe power at a micro-grid m is denoted by Pm renew assumed to incur free cost of usage whie the non-renewabe power has a unitary cost denoted α m per power unit. Thus, the cost of the power consumed by each micro-grid is equa to the cost of

3 3 BS 1,1 Micro-grid 1 BS 2,3 Micro-grid 2 BS 1,2 User 6 User 1 User 2 BS 2,2 Fig. 1. System powering architecture BS 3,1 User 3 User 4 User 7 BS3,2 Main power source Micro-grid 3 User 5 the power consumed by a BSs beonging to the micro-grid exceeding the avaiabe renewabe power. Mathematicay, the cost of the power at the micro-grid m is written as C m = α m [ L =1 ] + b m, P Pm renew, 1 with [ x ] + = maxx, and where P represents the power consumption of the base station, b m, is an index of the base stations connected to the micro-grid m i.e., b m, = 1 if base station is connected to micro-grid m and b m, =, otherwise, and Pm renew represents the generated renewabe power at this micro-grid. We consider a simpified mode for the base station power P. According to Arnod et a. [43], the power consumption of a base station consists of basicay two components. The first term is a function of the transmitted power which depends on the served users whie the second is independent of the oad and serves to ensure powering of the base station and ensuring some functionaities such as cooing. Thus, assuming a inear mode function of the transmitted power, the base station power can be written as foows P = ξ K =1 a P + P ide, 2 where a is the assignment index for users to base stations i.e., a = 1 if the -th user is served by the base station and a =, otherwise, P is the power transmitted by base station to the -th user, and ξ is the ampification factor for the transmitted power by the base station and P ide is the power consumed by the -th base station when ide. III. PROBLEM FORMULATION The aim of our wor is to improve the usage of the avaiabe renewabe power in different micro-grids through coaboration between the base stations in the same microgrid and in different micro-grids. Consider Eq. 1, the tota cost of the procured non-renewabe power by a micro-grids can be written as foows: [ L ] + C = α m b m, P Pm renew. 3 =1 The Quaity of Service QoS is ensured by a minimum throughput r req that needs to be guaranteed for each user for its successfu communication. The QoS may differ from one user to another depending on the user s running appications. The minimum rate constraint for each user is expressed as R r req, 4 where R is the achieved throughput by user, given by R = =1 a b c n og P g N b c n, 5 where n is the number of sub-channes aocated to user, b c is the sub-channe bandwidth, g is the channe gain between the base station and the user assumed to be the same for a sub-channes fast fading variations are not considered as we target reativey arge time-sot transmissions, and N is the noise power density. To avoid interference, we assume channe re-use not aowed and a sub-channes shared orthogonay between a base-stations. Thus, an additiona constraint is considered for sub-channes sharing K =1 =1 a n N. 6 Then, the probem consists of minimizing the cost function under minimum rate per user constraint, tota bandwidth constraint, and the assumption that each user must be served ony from one base station which can be written mathematicay as foows s.t. min { } a,n 1 L 1 K =1 =1 =1 =1 [ L ] + α m b m, P Pm renew a b c n og 2 K =1 1 + P g N b c n 7a r req, 7b a n N 7c a = 1,. 7d The ast constraint is added to indicate that each user is served by ony one base station. In this case, the aocated

4 4 power is deduced from the rate constraint 13d as foows P = a 2 r req n N b bc c n 1. 8 g The optimization probem 7 is a non-inear mixed integerrea minimization probem to determine the assignment of each user to the best BS in addition to the number of subchannes per user and the aocated power. The objective is to ensure the required data rates for a users whie minimizing the consumption power cost by profiting from the avaiabe renewabe power in the different micro-grids and variabiity of the channes gains between the different users. In conventiona power aocation probems, users-to-bss assignment depends mainy on the channe gains between the users and the BSs i.e., each user wi be assigned to the BS with the best channe gain. In our probem, the dependency of the cost function on the avaiabe renewabe power maes the probem more chaenging. In addition, further power cost reductions are possibe by using adaptive bandwidth aocation on the cost of an additiona compexity in the probem soving. IV. OPTIMAL SOLUTION USING BRANCH AND BOUND METHOD As dynamic spectrum, power aocation and user to base station assignment probem is a mixed integer non-inear optimization probem with a arge number of variabes, then finding the optima soution is a chaenging tas. For this type of probems, branch and bound method is shown to provide an ɛ-to-optima soution with a worst case exponentia time but a ess compex average time and a minimum time of poynomia compexity [44]. The method is proposed by A. H. Land and A. G. Doig in 196 [45] as a non-heuristic goba optimization method for non-convex probems. Its basic idea consists of partitioning the set of feasibe soutions into smaest subsets. Then, recursivey, compute an upper bound and a ower bound for each subset and a goba upper and ower bounds. The dimension of the probem is reduced rapidy by pruning the subset of feasibe sub-probems by eiminating the branches where a goba upper-bound is better than the branch ower bound. The agorithm of this method is described as foows 1 Compute an upper bound U and a ower bound L for the probem: The upper bound can be computed using one of the heuristic proposed agorithms or as a randomy seected soution, and the ower bound can be computed using a reaxation method. 2 If the found ower bound is a feasibe soution then it is the searched soution, otherwise create two branches by fixing one of the binary variabes one time to zero B 1 and one time to one B 2. 3 Compute ower bounds L 1, L 2 and upper bounds U 1, U 2 for B 1 and B 2, respectivey. 4 Set U to minu 1, U 2 and then if L 1 is greater than U then prune B 1 and if L 2 is greater than U then prune B 2. 5 Repeat the previous steps recursivey unti finding a soution within ɛ distance to the optima i.e., the difference between ower bound and upper bound is ess than ɛ, or parsing a the branches. Eiminating the unfeasibe branches reduces the compexity of the agorithm. For instance, if one variabe a is fixed to 1, using the constraint that L =1 a = 1, a variabes a, are set to. In addition, the choice of the binary variabe to fix is aso important. Usuay, the variabes with equa probabiities to the binary vaues are fixed firsty and their two possibe branches are parsed i.e, the variabe for which the rea soution is the cosest to.5. The fixing for 1 is done first since it requires ess computation as L 1 variabes are eiminated. The chaenging tas in this approach is obtaining the owerbound. We use a convex reaxation of the probem by converting the users-to-bs assignment binary variabes a into rea variabes reaxed variabe and adding constraints that require the reaxed variabes to be between zero and one. We show in the Appendix that the reaxed probem is convex. Soving the reaxed probem is sti chaenging as the reaxation of the binary variabes produces a probem with high dimensionaity 3 K L variabes to be soved. Observing the dependence of the bandwidth and the users-to-bs assignment variabes, we proceed with a variabe change 9 that reduces the number of variabes by one-third. Thus, we propose a new variabe, representing the percentage of sub-channes used by user through the -th BS: Using the property that = a =1 n 9 a = 1,, the origina variabes are re-obtained from the new joint variabe as foows n = 1 a = L 11 =1 x In addition, in order to derive easiy the Lagrangian of the probem we introduce a new variabe C m defined as foows { L } C m = max b m, P Pm renew, 12 =1 =1 The reaxed probem is then written as foows min { } P, 1 L 1 K [ L K s.t. C m =1 =1 α m C m b m, P C m og P =1 K =1 =1 ] Pm renew g N m 13a 13b 13c r req, 13d N 13e

5 5 As proven in the Appendix, the reaxed probem is convex. Thus, the prima and dua probem soutions are identica given the sacness condition which is guaranteed in our case existence of at east one feasibe soution. Then, by introducing non negative dua variabes β, {λ 1...λ m }, {γ 1...γ m }, and {µ 1...µ K }, the Lagrangian function is given by L = + α m C m L K λ m b m, P L K + β + K =1 =1 =1 =1 =1 µ r req N =1 Pm renew + C m γ m C m P og θ. 14 Then prima feasibiity K.K.T conditions are inferred from the Lagrangian derivatives as foows γ m = α m λ m [ β µ λ m b m, og 1 + P µ θ 1 + P θ θ P θ + P θ 15a ] = 15b =, 15c where θ = g N, whie the compementary sacness conditions are given by λ m L µ L K i=1 =1 i=1 b m, P P m + C m =, m 16a og P θ r req =, 16b γ m C m =, m 16c K N =. 16d i=1 =1 Then we define A m = K i=1 =1 b m, P P renew m, 17 such that C m = maxa m, A sub-gradient agorithm is then impemented, where the dua variabes are iterativey soved in the outer oop to satisfy the sacness conditions whie in the inner oop the K.K.T conditions are soved to determine the prima variabes P,, and C m. In particuar, in the case where C m is greater than zero, we can deduct from 16c that γ m = and from 15a that λ m = α m. Then, we sove 15b and 15c to obtain and P function of the Lagrangian parameters whie in the other case where C m = i.e., A m < ; we can deduct from 16a that λ m =, and P can be then be freey chosen such that we eep C m =, then we increase the power P and decrease the used bandwidth for the BSs beonging to the micro-grid m i.e., b,m = 1. V. DISJOINT USERS AND CHANNELS ASSIGNMENT As the probem is compex and even, the optima soution presented earier is impractica for arge number of users/channes, we then propose a suboptima efficient approach. We divide the probem into two sub-probems. First, we assume constant bandwidth aocation among a users and focus on assigning the users to BSs. Then, we optimize the aocated bandwidth to further optimize the cost of the power consumed by profiting from dynamic spectrum assignment. The two agorithms are incorporated successivey in a twostep iterative agorithm. A. Users-to-BS assignment In this part, we consider a fixed bandwidth sharing between the users and we focus on determining the assignment of users to the BSs. The optima soution to determine the best usersto-bs assignment is to perform an exhaustive search of a the possibe assignments and tae the combination that incur the east tota cost. Obviousy, this is not a practica soution as its compexity is exponentia. Aternativey, we propose a poynomia approach based on the bin-pacing to determine the users that wi be assigned to each base station. In our case, the BSs represent the bins whie the users are the objects to be paced. The difference, is that objects occupy different voumes depending on the pac as the power consumed differs from a BS to another. Our metric criterion for the decision is the resutant goba power cost in the whoe networ. Thus, each user wi be assigned to the base station incurring the owest power cost according to Eq. 3. As in usua binpacing agorithms, the order of pacing objects infuences the obtained performance. For that, we propose two approaches: Random users assignment: In this approach, we simpy assign the users in a random order. Athough, this method is imited in performance, it is suitabe for onine assignment as we need to assign users in their order of request of service without waiting for a users to search for the best order of assignment. Best users assignment: In this approach, as described in Agorithm 1, we search for the user that wi incur the owest power cost by checing with a users. Then, assign it and repeat the procedure unti assigning a users. Athough the compexity is mutipied by a factor capped by the number of users we need to parse, at each step, a users and compute the resutant power cost, this process notaby enhances the performance as the order of assignment of the users is very important to efficienty use the renewabe power in the micro-grids.

6 6 Agorithm 1 Users-to-base stations assignment. INPUT: Number of sub-channes per user: {n } 1 L. 1 K OUTPUT: Users-to-BSs assignment: {a. repeat for a users = 1 : K do Determine base station } 1 L 1 K to be assigned to user incurring owest power cost: = arg min c end for Assign user such that = arg min c unti A users assigned Number of iterations Distance to optima % Maximum number of recursive cas Average number of recursive cas Minimum number of recursive cas B. Bandwidth Aocation Dynamic spectrum aocation has shown its importance for power savings. Thus, we propose to assign the bandwidth adaptivey between the users in order to further reduce the goba power cost. As discussed earier, soving the goba probem optimay is computationay compex, therefore we propose to use an iterative two-step agorithm. In the first step, we optimize the users-to-bss assignment simiary to the previous section. Whie in the second step, we propose to optimize the bandwidth aocation. For the bandwidth aocation, inspired by the bubbe sort, we propose an agorithm that consists of searching recursivey the best possibe subchannes changes unti convergence. At each step, we parse a users and search, for every user, the best channe swap with another user that resuts in the argest reduction in power cost. We appy that change and restart the search again unti no further power savings coud be achieved. Agorithm 2 Bandwidth aocation. INPUT: Users-to-BSs assignment: {a } 1 L. 1 K OUTPUT: Number of sub-channes per user: {n } 1 L. 1 K repeat for a users 1 = 1 : K do search for the best sub-channe swap with another user 2 such that: 2 = arg min Cn 1 n 1 + 1, n 2 n end for unti no possibe cost decrease 2 = 1, 1. A. Compexity Anaysis VI. PERFORMANCE ANALYSIS 1 Branch and Bound Agorithm: The branch and bound proceeds with a tree binary search over the branches which are the binary variabes unti finding the optima soution. Thus, its worst case compexity is proportiona to 2 L K. This shoud be mutipied by the cost of computing the ower bound denoted by C r. For the best case, the soution can be found through a singe evauation of the ower bound if a feasibe soution is Fig. 2. B&B number of recursive cas as a function of the distance to optima soution for K = 1 users. found from this step. It is shown that this approach performs much better in practice by pruning the branches rapidy using the feasibiity constraints. For our probem, the condition of having ony one BS to serve a user heps to eiminate rapidy the branches. For instance, if a BS 1 is shown to serve a user, a other branches of BSs 2 1 serving the user. In order to show the practica compexity of this approach, we consider a sma scenario with K = 1 users, M = 2 micro-grids, and L = 3 BSs and compute the number of iterations to find an ɛ-to-optima soution for different vaues of ɛ. Fig. 2 shows that the minimum, average, and maximum number of iterations function of ɛ. We observe that the average is much coser to the minimum than the maximum which proves the efficiency of the pruning method. 2 Two-Step Agorithm: For the users-to-bs assignment Agorithm 1, the number of iterations needed to perform the assignment of a users is inear as a function of the number of users and the number of BSs in the networ. The easiest way to impement Agorithm 1 is to perform two oops, one on the users and one on BSs. Additionay, the operations inside the oops does not exceed the computing of a simpe function and a comparison. Thus, the compexity of Agorithm 1 is OK L when not considering the outer oop random user seection agorithm and it wi be mutipied by the number of users when considering the outer oop best user seection. For the bandwidth aocation, we need first to go through a users, and to search for the best sub-channe swap with another user. The search operation is performed by going through a possibe swaps and this is by going through a users and a sub-channes. Since sub-channes are a identica in terms of gains, and without considering the repeat oop, we wi have K 2 comparisons and K 2 possibe swaps. In the best case we need to perform the previousy described operations ony one time before deducing that there is no cost decrease. In the worst case, we need to perform the previous operations as much as the number of the sub-channes. Then the worst case compexity is N K 2. Thus, the compexity of the whoe agorithm wi be the sum of the compexities of these two steps mutipied by the number of iterations needed to converge denoted by N iter.

7 7 Via simuations, we verify the convergence of this two-step agorithm within few iterations not exceeding 1. To resume, we present in Tabe I, the compexity of the different agorithms. B. Simuation Resuts We consider a circuar area of diameter 6 Km where K users and L base stations are paced randomy. The channe gains are derived based on the pathoss mode g = η d c d,, where c is the channe gain for the reference distance d, d, is the distance between the base-station and the user, and η is the pathoss set to 3. We consider a tota bandwidth B = MHz divided into sub-channes of per sub-channe width b c = 15 KHz. The noise power is taen 1 dbm/hz. The minimum required throughput rate per user is set to r req = 5 Mbps. We consider that the base stations are grouped into M = 4 micro-grids so each micro-grid suppies two base stations. We assume that the non-renewabe power cost, α m, is equa for a micro-grids to focus on the effect of the renewabe power avaiabiity. The renewabe power Pm renew is set such that it is sufficient to serve an average number of users for the average spatia distribution in the networ. To iustrate the resuts, we consider the scenario where renewabe power is not considered in optimization and compute the incurred power cost and consider that as a reference. We represent the obtained performance as the reative cost gain with comparison to this reference cost. Fig. 3 iustrates the normaized power cost gain as a function of the number of users in the networ for the B&B method with ɛ =.8%. The method shows good performance as nown distance at most ɛ to optima soution in the way that it eeps coser to the optima bac curve than to ɛ-tooptima imit red curve. Normaized cost gain % Number of users Lower bound B&B for ε =.8%.8% to optima imit Fig. 3. Power cost gain as function of the number of users for optima, B&B ɛ-to-optima, and ɛ-to-optima cost gain distance. The performance of the heuristic agorithms are firsty compared to the ɛ-to-optima resuts obtained by the B&B method. Due to the computationa compexity of the B&B method, we restrain the simuations to a sma number of users in this comparison. Fig. 4 shows the power cost gain as a function of the number of users for B&B method, best user seection agorithm and random user seection agorithm with optimized bandwidth. Through this anaysis, we show that the best user seection agorithm combined with an optimized bandwidth aows to obtain ess than.8% to optimaity whie the random user seection agorithm is sighty farther than this bound. Normaized cost gain % Number of users B&B for epsion =.8% Fig. 4. Power cost gain as a function of the number of users Since one of the advantages of the heuristic agorithms is its abiity to sove the probem with more degrees of freedom, we study in the next simuations the performance of the proposed agorithms when considering a arger number of users 1 to users. Fig. 5 iustrates the normaized power cost gain as a function of the number of users in the networ with different heuristic agorithms. First, we note the net cost gain achieved by incorporating additiona features in the optimization agorithm. In particuar, the best user seection method for the users-to-bss assignment outperforms the random seection. In addition, optimizing the aocated bandwidth for each user aows further cost savings. Second, as the number of users requesting to be served increases, the cost gain decreases due to the increase of the consumed power which, at a certain step, harvests a the avaiabe renewabe power. In this case, the probem reduces to a tota power minimization probem and our approach becomes imited in performance compared to the optima approach. One important factor that impacts the obtained performance is the avaiabe non renewabe power in the micro-grids. For that, we denote the non renewabe to renewabe consumed power ratio by ρ and represent it in Fig. 6 as a function of the number of users. As expected, the bandwidth optimized agorithms aows to reach esser ratios than agorithms with uniform bandwidth which means esser consumption of nonrenewabe energy and higher utiization of the renewabe sources. The users seection agorithm aso heps in enhancing the usage of the renewabe resources as the best seection method reaches esser ratio than the random user seection. In order to show the optimaity of the proposed agorithms

8 8 TABLE I ALGORITHMS COMPLEXITY Agorithm best case worst case average Random user seection with Uniform bandwidth L K L K L K Best user seection with Uniform bandwidth L K 2 L K 2 L K 2 Random user seection with Optimized bandwidth 2K 2 + L KN iter 2N K 2 + L KN i ter - Best user seection with Optimized bandwidth 2K 2 + L K 2 N iter 2N K 2 + L K 2 N i ter - B&B method C r 2 L K C r L K C r Normaized cost gain % Best user uniform bandwidth Random user uniform bandwidth Number of users Fig. 5. Reative power cost gain as a function of the number of served users with constant renewabe power for a micro-grids. Normaized cost gain % Random user uniform bandwidth Best user uniform bandwidth Number of users 1 9 Fig. 7. Agorithms optimaity: reative power cost gain when renewabe power is not avaiabe. 8 ρ % Best user uniform bandwidth Random user uniform bandwidth Number of users increasing variabiity of the renewabe power eve across the micro-grids. We note that with the best user assignment agorithm, the cost gain increases when the variance increases. This is expained by the fact that the order of assignment of users-to-bss becomes more important in this case than in the equa renewabe case for which, due to the random distribution of users, optima assignment wi be most iey based on channe gains rather than renewabe power avaiabiity. Fig. 6. Non renewabe to renewabe consumed power ratio in the networ as a function of the number of users. for such a practica scenario arge number of users, we consider the case where the renewabe power is not avaiabe at a i.e., Pm renew =, m. In this case, the probem reduces to exacty the same as the tota power minimization which we too as a reference for computing the cost gains. We present the resuts in Fig. 7 which shows that without bandwidth optimization the best user seection agorithm incurs a oss of around 1% whie adding the bandwidth optimization aows a gain between 3 to 45% which represents the net gain of the dynamic aocation of the bandwidth. In the previous figures, we studied configurations where the same renewabe power amount is avaiabe in each micro-grid. In the foowing, we propose to study a more practica scenario where the avaiabe renewabe power is variabe across the different micro-grids. We present in Fig. 8 the cost gain with Normaized cost gain % Best user uniform bandwidth Random user uniform bandwidth Renewabe power standard deviation noramized by the average renewabe power % Fig. 8. Cost gain percentage as a function of the renewabe power standard deviation for K = 15 users.

9 9 In Fig. 9, we vary the number of micro-grids whie eeping the same number of base stations and the same tota renewabe power over a micro-grids to observe the effect of coaboration between the base stations. As the number of microgrids increases, the cost gain is expected to decrease as in the random users assignment due to non-possibiity of exchanging energy between BSs. But, with the best user assignment, the gain remains approximatey constant. The agorithm succeeds to compensate the oss incurred by the absence of coaboration between BSs by cassifying the users before assigning them. Power cost gain % Best user uniform bandwidth Random user uniform bandwidth Normaized cost gain % Random user uniform bandwidth Best user uniform bandwidth Number of micro grids Fig. 9. Cost gain percentage for different number of micro-grids for K = users. The possibiity of switching base stations to the seep mode when not serving any users coud hep in saving the power. We consider a new mode for the BS power where the component independent from the oad in the BS power consumption mode given by Eq. 2 is divided now into two terms; one term that is consumed ony if the BS is serving users caed P on P ide and one for the power consumed even in seep mode. The new mode is given by P = ξ K =1 a P + P on K =1 a > + P ide, 18 The effect of the seep mode is studied in Fig. 1. We vary the percentage of power that coud be saved through this seep mode and represent the power cost savings that coud be achieved. The normaized power cost gain sighty increases with the increase of the power needed to turn the BSs on as further savings coud be achieved when this amount increases. Hardware imitations due to components needed aways ON and system instabiity for ong-term due to recurrent switch of BSs imit the gains of this capabiity in practice. In order to further enhance the performances of the proposed agorithms, we propose to use a new objective function when evauating the power cost during the users-to-bss assignment tas. This new objective incudes the consumed renewabe energy at each micro-grid weighted with the degree of consumption of the renewabe energy in each micro-grid P on /P renew % Fig. 1. Effect of seeping mode: power cost gain as a function of the power needed to turn the BS ON for K = users. Mathematicay, this objective is written as foows [ L ] + O = α m b m, P Pm renew ω m = + =1 { L } ω m min b m, P ; Pm renew, =1 19 where ω m is the weight affected to the micro-grid and computed as foows { } L Pm renew min =1 b m,p ; Pm renew M m =1 P renew m { } min L =1 b m,p ; Pm renew Consider the configuration where a different renewabe power amounts are avaiabe in each micro-grid, Fig. 11 shows the power cost gain function of the number of users for two objective functions. The first is the one given by Eq. 3 FOF, whie the second is given by Eq. 19 SOF. The fina power cost gain is aways evauated using Eq. 3 which is our effective cost measure. The figure shows an improvement on the power cost gain up to 3% depending on the number of users when using the new objective function. VII. CONCLUSION We have introduced in this paper a new mode for powering base stations using hybrid renewabe and non-renewabe power sources. Whie base-stations are custered in groups of micro-grids, we proposed to minimize the goba power cost whie satisfying the users requirements through cooperation between BSs in the same micro-grids and between the different micro-grids. Two approaches are presented. The first aiming an ɛ-to-optima soution based on the branch and bound method, then a suboptima two-step agorithm using efficient heuristics for the users-to-bss assignment and bandwidth aocation tass. Important power cost gains are achieved through the proposed approaches due to the better usage of the renewabe powers across the micro-grids to serve the users.

10 1 Normaized cost gain % Number of users FOF SOF to get 2 = x P 2 = P og2 = og2 P θ P og2 θ P θ + P θ θ 2 + P θ 2 24a 2 24b 2 24c Fig. 11. Effect of the objective function: reative power cost gain as a function of the number of users when considering the new objective function. RELAXED PROBLEM CONVEXITY PROOF In the reaxed probem 13 the objective function is convex since it is the maximum of two convex functions and a constraints, except constraint 13d, are inear, that is why it wi be sufficient to prove the convexity of the minimum rate constraint 13d to prove the convexity of the whoe optimization probem. This is equivaent to proving that the {P function r, } defined as, =1..L {P r, } = =1..L =1 og P g N 21 is concave for a = 1..K. The Hessian of this function is written as foows H 1, H =..... Hm,n.., H M,N where the boc matrices H m,n are defined as H m,n = 2 P P P 2, 23 Since H is a boc diagona matrix thus it is sufficient to prove that a the H m,n are definite negatives to concude that H is a definite negative since the eigenvaues of H are the concatenation of a the eigenvaues of the matrices H m,n. Thus, et us compute the eigenvaues of H m,n. For that, we start by computing the partia derivatives in 23 where θ = g N. Then the H m,n matrices are given by: H m,n = og2 θ 2 + P θ 2 P 2 P P 25 The sum of the eigenvaues of the H m,n matrix is given by its trace as foow: ] trace [H m,n = θ 2 + P θ P 2 +, 26 and the product of the eigenvaues is given by its determinant ] det [H m,n =. 27 Since the determinant of the Hessian matrices are nu and the traces are negative, then the Hessian matrices H m,n are semi-definite negative and thus matrix H is aso semi-definite negative. Thus, we concude that the rate function is concave and the rate constraint is convex. REFERENCES [1] M. Ben Ghorbe, B. Hamdaoui, R. Hamdi, M. Guizani, and M. NoroozOiaee, Distributed dynamic spectrum access with adaptive power aocation: Energy efficiency and cross-ayer awareness, in IEEE Conference on Computer Communications Worshops INFOCOM WKSHPS, Apri 14, pp [2] D. Dechene and A. Shami, Energy-aware resource aocation strategies for te upin with synchronous harq constraints, IEEE Transactions on Mobie Computing, no. 99, pp. 1 1, 14. [3] M. Ben Ghorbe, B. Khafi, B. Hamdaoui, and M. Guizani, Power aocation anaysis for dynamic power utiity in cognitive radio systems, in IEEE Internationa Conference on Communications ICC, Jun. 15. [4] M. Guizani, B. Khafi, M. Ben Ghorbe, and B. Hamdaoui, Largescae cognitive ceuar systems: resource management overview, IEEE Communications Magazine, vo. 53, no. 5, pp , May 15. [5] B. Hamdaoui and P. Ramanathan, Sufficient conditions for fow admission contro in wireess ad-hoc networs, ACM SIGMOBILE Mobie Computing and Communications Review, vo. 9, no. 4, pp , 5. [6] X. Wang, D. Wang, H. Zhuang, and S. Morgera, Fair energy-efficient resource aocation in wireess sensor networs over fading TDMA channes, IEEE Journa on Seected Areas in Communications, vo. 28, no. 7, pp , September 1.

11 11 [7] S. Ehsan, B. Hamdaoui, and M. Guizani, Radio and medium access contention aware routing for ifetime maximization in mutichanne sensor networs, IEEE Transactions on Wireess Communications, vo. 11, no. 9, pp , 12. [8] N. Chachou, B. Hamdaoui, and M. Friha, WCDS-induced routing for data-aggregation in wireess sensor networs, in First Internationa Conference on Communications and Networing ComNet. IEEE, 9, pp [9] M. NoroozOiaee, B. Hamdaoui, and K. Tumer, Efficient objective functions for coordinated earning in arge-scae distributed osa systems, IEEE Transactions on Mobie Computing, vo. 12, no. 5, pp , 13. [1] Y. Beasmi, A. Kobbane, M. Koutbi, and J. Ben-Othman, Channe aocation strategies in opportunistic-based cognitive networs, in 8th Internationa Wireess Communications and Mobie Computing Conference IWCMC. IEEE, 12, pp [11] B. Hamdaoui, Adaptive spectrum assessment for opportunistic access in cognitive radio networs, IEEE Transactions on Wireess Communications, vo. 8, no. 2, pp , 9. [12] M. Ben Ghorbe, B. Hamdaoui, M. Guizani, and B. Khafi, Distributed earning-based cross-ayer technique for energy-efficient muti-carrier dynamic spectrum access with adaptive power aocation, IEEE Transactions on Wireess Communications, vo. PP, no. 99, pp. 1 1, 15. [13] N. Chachou and B. Hamdaoui, Upin performance characterization and anaysis of two-tier femtoce networs, IEEE Transactions on Vehicuar Technoogy, vo. 61, no. 9, pp , 12. [14] A. Hatoum, N. Aitsaadi, R. Langar, R. Boutaba, and G. Pujoe, Fcra: Femtoce custer-based resource aocation scheme for ofdma networs, in IEEE Internationa Conference on Communications ICC. IEEE, 11, pp [15] B. Hamdaoui, M. Eaoud, and P. Ramanathan, A deay-based admission contro mechanism for mutimedia support in ieee 82.11e wireess ans, Wireess Networs, vo. 15, no. 7, pp , 9. [16] A. Hatoum, R. Langar, N. Aitsaadi, R. Boutaba, and G. Pujoe, Qos-based power contro and resource aocation in ofdma femtoce networs, in IEEE Goba Communications Conference GLOBECOM. IEEE, 12, pp [17] T. Taeb and A. Ksentini, Foow me coud: interworing federated couds and distributed mobie networs, IEEE Networ, vo. 27, no. 5, pp , 13. [18] M. Dabbagh, B. Hamdaoui, M. Guizani, and A. Rayes, Energy-efficient coud resource management, in INFOCOM worshop on Mobie Coud Computing. IEEE, 14, pp [19] M. Bagaa, T. Taeb, and A. Ksentini, Service-aware networ function pacement for efficient traffic handing in carrier coud, in IEEE Wireess Communications and Networing Conference WCNC. IEEE, 14, pp [] H. A Haj Hassan, L. Nuaymi, and A. Peov, Renewabe energy in ceuar networs: A survey, in Onine Conference on Green Communications GreenCom, Oct 13, pp [21] M. Marsan, G. Bucao, A. Di Caro, M. Meo, and Y. Zhang, Towards zero grid eectricity networing: Powering bss with renewabe energy sources, in IEEE Internationa Conference on Communications Worshops ICC, June 13, pp [22] P. S. REN21, Renewabes 14: Goba Status Report. REN21 Secretariat Paris, France, 14. [23] C. A. Chan, A. F. Gygax, E. Wong, C. A. Lecie, A. Nirmaathas, and D. C. Kiper, Methodoogies for assessing the use-phase power consumption and greenhouse gas emissions of teecommunications networ services, Environmenta Science & Technoogy, vo. 47, no. 1, pp , 13, pmid: [Onine]. Avaiabe: [24] A. Fehse, G. Fettweis, J. Mamodin, and G. Biczo, The goba footprint of mobie communications: The ecoogica and economic perspective, IEEE Communications Magazine, vo. 49, no. 8, pp , August 11. [25] A. Chatzipapas, S. Aouf, and V. Mancuso, On the minimization of power consumption in base stations using on/off power ampifiers, in IEEE Onine Conference on Green Communications GreenCom, Sept 11, pp [26] C. Han, T. Harrod, S. Armour, I. Kriidis, S. Videv, P. M. Grant, H. Haas, J. Thompson, I. Ku, C.-X. Wang, T. A. Le, M. Nahai, J. Zhang, and L. Hanzo, Green radio: radio techniques to enabe energyefficient wireess networs, IEEE Communications Magazine, vo. 49, no. 6, pp , June 11. [27] X. Ge, X. Huang, Y. Wang, M. Chen, Q. Li, T. Han, and C.-X. Wang, Energy-efficiency optimization for mimo-ofdm mobie mutimedia communication systems with qos constraints, IEEE Transactions on Vehicuar Technoogy, vo. 63, no. 5, pp , Jun 14. [28] X. Ge, B. Yang, J. Ye, G. Mao, C.-X. Wang, and T. Han, Spatia spectrum and energy efficiency of random ceuar networs, IEEE Transactions on Communications, vo. 63, no. 3, pp , March 15. [29] M. Ben Ghorbe, T. Touzri, B. Hamdaoui, M. Guizani, and B. Khafi, Joint users-channes assignment for efficient use of renewabe energy in hybrid powered communication systems, in IEEE Goba Communications Conference GLOBECOM, Dec. 15. [3] X. Ge, H. Cheng, M. Guizani, and T. Han, 5g wireess bachau networs: chaenges and research advances, IEEE Networ, vo. 28, no. 6, pp. 6 11, Nov 14. [31] H. A Haj Hassan, L. Nuaymi, and A. Peov, Renewabe energy in ceuar networs: A survey, in IEEE Onine Conference on Green Communications GreenCom, Oct 13, pp [32] N. Tebiyi-Ersoy, E. Uysa-Biyiogu, K. Lebebiciogu, and T. Girici, Kaman prediction based proportiona fair resource aocation for a soar powered base station, in 21st Signa Processing and Communications Appications Conference SIU, Apri 13, pp [33] V. Chamoa and B. Sidar, Resource provisioning and dimensioning for soar powered ceuar base stations, in IEEE Goba Communications Conference GLOBECOM, Dec 14, pp [34] G. Schmitt, The green base station, in 4th Internationa Conference on Teecommunication - Energy Specia Conference TELESCON, May 9, pp [35] S. Paude, J. Shrestha, F. Neto, J. Ferreira, and M. Adhiari, Optimization of hybrid pv/wind power system for remote teecom station, in Internationa Conference on Power and Energy Systems ICPS, Dec 11, pp [36] M. Marsan, G. Bucao, A. Di Caro, M. Meo, and Y. Zhang, Towards zero grid eectricity networing: Powering bss with renewabe energy sources, in IEEE Internationa Conference on Communications Worshops ICC, June 13, pp [37] M. Ero-Kantarci and H. Mouftah, Energy-efficient information and communication infrastructures in the smart grid: A survey on interactions and open issues, IEEE Communications Surveys & Tutorias, vo. 17, no. 1, pp , Firstquarter 15. [38] S. Bu, F. Yu, Y. Cai, and P. Liu, Dynamic operation of bss in green wireess ceuar networs powered by the smart grid, in IEEE Goba Communications Conference GLOBECOM, Dec 12, pp [39] H. Ghazzai, E. Yaacoub, M.-S. Aouini, and A. Abu-Dayya, Optimized smart grid energy procurement for te networs using evoutionary agorithms, IEEE Transactions on Vehicuar Technoogy, vo. 63, no. 9, pp , Nov 14. [4] H. Hotamp, G. Auer, S. Bazzi, and H. Haas, Minimizing base station power consumption, IEEE Journa on Seected Areas in Communications, vo. 32, no. 2, pp , February 14. [41] G. Micaef, P. Mogensen, and H.-O. Schec, Ce size breathing and possibiities to introduce ce seep mode, in European Wireess Conference EW, Apri 1, pp [42] L. Saer, S.-E. Eayoubi, and T. Chahed, Minimizing energy consumption via seep mode in green base station, in IEEE Wireess Communications and Networing Conference WCNC, Apri 1, pp [43] O. Arnod, F. Richter, G. Fettweis, and O. Bume, Power consumption modeing of different base station types in heterogeneous ceuar networs, in Future Networ and Mobie Summit, June 1, pp [44] S. Boyd and J. Mattingey, Branch and bound methods, Notes for EE364b, Stanford University, pp. 6 7, 7. [45] A. H. Land and A. G. Doig, An automatic method of soving discrete programming probems, Econometrica: Journa of the Econometric Society, pp , 196.

12 12 PLACE PHOTO HERE Taha Touzri is currenty a Research Assistant at Qatar University in Doha, Qatar. He received the "Dipome d Ingenieur" from the Ecoe Poytechnique de Tunisie EPT in Tunis, Tunisia in 13. His research interests incude green communication, smart grids, and resource aocation for Dynamic Spectrum Access systems. Mahdi Ben Ghorbe S 1-M 14 is currenty a postdoctora feow at Qatar University in Doha, Qatar since September 13. He received the "Dipome d Ingenieur" from the Ecoe Poytechnique de Tunisie EPT in Tunis, Tunisia in 9 and the Ph.D in Eectrica Engineering from King Abduah University of Science and Technoogy KAUST, Saudi Arabia in 13. He received Exceency Feowship for his studies at EPT and the top student award in his University in June 9. He aso received Provost Award and Discovery Feowship to join KAUST in Sep 9. His research interests incude optimization of resource aocation and cooperative spectrum sensing performance for cognitive radio systems. Bechir Hamdaoui S 2-M 5-SM 12 is presenty an Associate Professor in the Schoo of EECS at Oregon State University. He received the Dipoma of Graduate Engineer 1997 from the Nationa Schoo of Engineers at Tunis, Tunisia. He aso received M.S. degrees in both ECE 2 and CS 4, and the Ph.D. degree in Computer Engineering 5 a from the University of Wisconsin-Madison. His research focus is on distributed resource management and optimization, parae computing, cooperative & cognitive networing, coud computing, and Internet of Things. He has won the NSF CAREER Award 9, and is presenty an AE for IEEE Transactions on Wireess Communications 13-present, and Wireess Communications and Computing Journa 9-present. He aso served as an AE for IEEE Transactions on Vehicuar Technoogy 914 and for Journa of Computer Systems, Networs, and Communications 7-9. He served as the chair for the 11 ACM MobiCom s SRC program, and as the program chair/co-chair of severa IEEE symposia and worshops incuding ICC 14, IWCMC 9-15, CTS 12, PERCOM 9. He aso served on technica program committees of many IEEE/ACM conferences, incuding INFOCOM, ICC, GLOBECOM, and PIMRC. He is a Senior Member of IEEE, IEEE Computer Society, IEEE Communications Society, and IEEE Vehicuar Technoogy Society. Mohsen Guizani S 85-M 89-SM 99-F 9 is currenty a Professor and Associate Vice President of Graduate Studies at Qatar University, Qatar. Previousy, he served as the Chair of the Computer Science Department at Western Michigan University from 2 to 6 and Chair of the Computer Science Department at the University of West Forida from 1999 to 2. He aso served in academic positions at the University of Missouri-Kansas City, University of Coorado-Bouder, Syracuse University and Kuwait University. He received his B.S. with distinction and M.S. degrees in Eectrica Engineering; M.S. and Ph.D. degrees in Computer Engineering in 1984, 1986, 1987, and 199, respectivey, a from Syracuse University, Syracuse, New Yor. His research interests incude Wireess Communications and Mobie Computing, Computer Networs, Mobie Coud Computing and Smart Grid. He currenty serves on the editoria boards of many Internationa technica Journas and the Founder and EIC of "Wireess Communications and Mobie Computing" Journa pubished by John Wiey He is the author of nine boos and more than 4 pubications in refereed journas and conferences. He guest edited a number of specia issues in IEEE Journas and Magazines. He aso served as member, Chair, and Genera Chair of a number of conferences. He was seected as the Best Teaching Assistant for two consecutive years at Syracuse University, 1988 and He was the Chair of the IEEE Communications Society Wireess Technica Committee and Chair of the TAOS Technica Committee. He served as the IEEE Computer Society Distinguished Speaer from 3 to 5. Dr. Guizani is Feow of IEEE, member of IEEE Communication Society, IEEE Computer Society, ASEE, and Senior Member of ACM. Bassem Khafi S 14 is currenty a Ph.D student at Oregon State University in Corvais, OR, USA. He received the "Dipome d Ingenieur" from Ecoe Superieure de Communications de Tunis SUP COM in Ariana, Tunisia in 12 and Masters of Science from Ecoe Nationae d Ingenieurs de Tunis ENIT in Tunis, Tunisia in 14. His research interests incude resource aocation in Dynamic Spectrum Access systems and performance anaysis for cooperative spectrum sharing.