Cooperative Small Cell HetNets with Sleeping and Energy Harvesting

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1 Cooperative Small Cell HetNets with Sleeping and Energy Harvesting Abdllah Alqasir 1, Ahmed E. Kamal 1 1 Iowa State University (ISU), Ames, Iowa, United States, {aalqasir, kamal}@iastate.ed Abstract This paper considers a heterogenos network Het- Net where a macro base station (MBS) coexists with many small base stations (SBSs). SBSs can be deactivated and pt to sleep to save energy and are eqipped with two power sorces, harvested energy (HE) sorce and a power grid sorce, where irst the SBS will se its available HE to serve the associated sers. Then, the SBS will reqest any shortage o its energy rom other active or deactivated SBSs which have srpls o HE. Finally, i there is still shortage in energy, the SBS will se the power drawn rom the grid. This transer o energy is acilitated throgh the se o the promising technology o the smart grid (SG). We investigate the grid energy minimization problem by optimizing both the transmission power and activation/deactivation (Dynamic Sleeping) o the SBSs. Moreover, a decomposition o the problem into a convex optimization problem and sers association according to the best SINR is proposed. Then, we derived a closed orm o the optimal transmission power and se the IPOPT algorithm to ind the Lagrangian variables. The reslts clearly show the advantages o or model operational strategy. Index Terms Energy Eiciency, 5G, Energy Harvesting, Smart Grid, Sleeping strategy. I. INTRODUCTION The rapid increase in the wireless access devices is boosting the demands or higher rates and better coverage. However, higher rates reqire higher energy consmption, hence increasing the CO emission cased by the wireless commnication networks 1. Recently, energy harvesting has been considered as one o the promising soltions or sstainable wireless commnications. Energy Harvesting (EH) technology converts the ambient energy to electric energy. Sch technology can be sed in celllar networks to help redce the carbon ootprint o wireless networks. For Example, a solar panel with.6 sqare meter, can harvest p to 5 watts with conversion eiciency o 14% 3. Sch energy level can sstain the operation o small cells with power management. On the other hand, the advanced technology o smart grids (SG) made energy cooperation between wireless networks dierent components easible. The concept o SG can be regarded as as an electric system that ses inormation and two-way power low in an integrated ashion to achieve an eicient and sstainable system 4. Exploiting sch technology cold provide enormos opportnities or wireless networks. One approach is by tilizing the SG to transer harvested energy rom on BS to another, with high transer eiciency. Several researches have dealt with powering celllar BSs with renewable energy sorces. In 5, 6, the athors highlighted the importance o combining renewable energy systems and the smart grid or developing an energy eicient celllar network. In 7, the athors ormlated a constrained optimization problem in order to minimize the total cost incrred by the Celllar Networks operators, by harvesting and transerring the energy throgh the SG. Additionally, the athors o 8-1, sed the dynamic sleeping to activate and deactivate BSs in order to minimize the energy drawn rom the grid. In 9 they ormlate an optimization problem or the system, and de to the problem s NP-hardness, they proposed a greedy decomposition to tackle the problem. On the other hand, the athors o 1 considered a model where the small BSs are powered solely by harvested energy, and minimized the grid energy by optimizing the Macro BS active probability and Small BSs transmission power. However, none o the previos stdies considered tilizing the harvesting sorce o the sleeping Small BSs to redce the power acqired rom the grid. In this work, the deactivated BS will keep harvesting then injecting the energy to the SG to aid other SBSs and increase the network eiciency. Moreover, other SBSs will orward their extra RE into the SG to other SBSs. The goal o this work is to minimize the power driven rom the grid by exploiting the harvested energy as mch as possible. Thereore, in order to beneit rom the RE and minimize the power driven rom the grid, or model will psh the network to deactivate as many SBSs as possible and tilize the sleeping SBSs in harvesting energy. However, to ensre qality o service, we set a minimm reqired rate or every ser that the network shold not violate. This paper is organized as ollows: Section II describes the proposed Energy Harvesting system model. The problem ormlation with the proposed decomposition is given in Section III. Section IV discsses the selected nmerical reslts o the simlation. Finally, the paper is conclded in Section V. II. SYSTEM MODEL We consider a heterogenos network where a Macro BS (MBS) and several Small BSs (SBSs) co-exist. The MBS is deployed to provide coverage while the SBSs are deployed to provide higher qality o service (QoS) or sers. MBS and SBSs operate in dierent reqency bands e.g., OFDMA, and thereore, there is no intererence between them. However, between the SBSs intererence is considered, since resing the available resorce provides higher throghpt. Fig.(1) shows the architectre o the network where SBSs are eqipped with energy harvesting methods (solar panels or example.) and are serving sers nder their coverage. Moreover, every SBS is connected to the Smart Grid with a two way connection. A. Energy Harvesting Model For SBSs Let = 1,..., F denote the set o the SBSs that are randomly distribted in the macro cell coverage area, while

2 Table I: List o Notations Fig. 1: A network with SBSs powered by renewable energy and connected to a smart grid. Notation Description SBS index. User index. c Resorce block index. n Time slot index. τ Dration time o every slot. B max Maximm battery capacity. p c n Transmission power rom to by c. B n Battery level o SBS dring slot n. λ n Injected energy into the SG by dring n. hr n HE or every SBS dring n. μ n Drawn energy rom the SG by dring n. h c n Commnication channel between and by c dring n. η The transer eiciency o the SG. x c n The binary association between and throgh c dring n. y n The SBS ON/OFF stats dring n ω Available bandwidth. E b The energy consmption o the SBS basic circit. =1,..., U and c =1,..., C denote the set o a randomly distribted sers covered by the SBSs and the set o available resorce blocks in the network, respectively. Moreover, we consider a time slotted system with ixed dration τ, and n =1,..., N denote the index o the slot nmber. Frthermore, every ser is assmed to be associated with only one SBS. The SBSs harvest energy rom a renewable sorce (e.g. wind, solar... etc), where the amont o harvested energy or every SBS and time slot n is denoted by hr n and it ollows the trncated Gassian distribtion 11. Moreover, every SBS is eqipped with a battery to store its harvested energy with a maximm capacity o B max with battery level at time slot n is Bn. However, de to the stochastic natre o the energy harvesting, every BS is connected to a nonrenewable energy sorce to compensate or the renewable energy shortage. In other words, every SBS is set to se the energy rom renewable sorce irst, and then reqest power orm the grid. However, the promising technology o Smart grid which allows a two-way low o power 4, can be sed here to transer the harvested energy between SBSs, i.e., the SBS with srpls harvested energy will transer it to other SBSs that ser rom renewable energy deicit. Thereor, at the end o every time slot, the SBS will either transer the srpls o its harvested energy or reqest energy rom other SBSs to compensate its deicit. I the energy srpls o the other SBSs cannot match the energy demand o the SBS with the shortage, then the SBS will reqest a non-renewable energy rom the smart grid directly. Hence, every SBS is eqipped with two power sorces: the non-renewable power rom the grid and the power rom the renewable sorces. Thereore, the transmission power between ser and BS sing resorce block c, dring the time slot n is: p c n =pc,g n+pc,r n, where p c,g n is the power drawn rom the grid and pc,r n is the power drawn rom the renewable sorce (inclding the energy transerred rom other SBSs). Let λ n and μ n denote the amont o the harvested energy the BS is injecting into or receiving rom the smart grid at the end o slot n, respectively. The the amont o the harvested energy that is transerred into the smart grid eqals the harvested energy that is drawn rom the smart grid, where η is the transer eiciency. μ n =ηλ n (1) Thereore, at time slot i =1the battery will be zero, and at the end o every slot i =1,,...N the battery storage will be the sm o the harvested energy sbtracting the transmission power and the transerred energy B i B max, where B i is deined as: B i = i hr n n= i n=1 =1 p c,rnτ i λ n () n=1 B. User Association and Achievable Rate Let x c be a binary indicator that is eqal to 1 i ser and SBS are associated sing resorce block c, or otherwise. Also, let z be a binary indicator that is eqal to 1 i ser is associated with SBS, or otherwise. y indicates the SBS on/o stats, where y =i the SBS is OFF (where there are no sers associated with it), and y =1i the SBS is ON. However, a deactivated SBS will keep harvesting energy and injecting it into the smart grid to serve other active SBSs. Moreover, the intererence at a ser which is associated with SBS rom all other SBSs at a time slot n will be: I c n = p c jinh c in, (3) j i Then, the signal to intererence and noise ratio SINR or every ser is: γ c n = pc nhc n I c n+ωn, (4) where h c n denotes the channel gain rom SBS to ser sing resorce block c at time slot n, ω is the available bandwidth or every channel, and N is the channel noise spectral density which is assmed to be Additive White Gassian Noise AWGN, and ωn is the noise variance σ. Ths, the data rate or every ser sing a single channel will be as ollow: R c n =ω log(1 + γ c n) (5)

3 and this reqires predicting the harvestable energy and channel conditions.. Optimization or every slot separately, and this is not globally optimal, bt more realistic. III. PROBLEM FORMULATION In this section, an optimization problem, which minimizes the non-renewable energy consmption o the transmission power or a cooperative heterogenos network is ormlated. First, we ormlate a problem where sers association, sleeping strategy and energy minimization are perormed within a single optimization problem. There are two problems, the irst is optimizing over N slots and this reqires predicting the harvestable energy and channel conditions, where the second is optimizing or every slot separately, and this is not globally optimal, bt more realistic, hence we ocs on the second problem in this paper. The problem can be stated as ollows: given the nmber o sers and SBSs, the problem will solve the ser association, sleeping strategy and power consmption, then at every time slot the optimization problem will recalclate the sers association and the transmission power, while not changing the stats o the SBSs, this will help simpliy the problem since the time slot is relatively very short. However, de to the non-convexity o the problem we present a more tractable and a convex approximation where we decople the sers association and sleeping strategy rom the energy minimization. We can then mathematically state the main optimization problem as below: Problem F : Minimize p c n,λ n,μ n,y,z,x c sbject to x c R min =1 F,U,N,C,,n, p c,gnτ + E b y (6) =1 x c Rn, c, n (7) p c,rnτ B n 1+μ n,, n, (8) B n B max, n, (9) μ n =ηλ n, n, (1) p c n P max, n, (11) x c 1, c, (1) =1 z =1,, (13) =1 U =1 z #osbss y z,, (15) =1 Constraint (7) represents the QoS or every ser. The constraints rom (8) to (11) are dealing with energy transer and cooperation between SBSs, while constraints rom (1) to (15) are dealing with the sers association and SBSs sleeping strategy. Constraint (8) represents the energy consmption casality where the BS cannot se energy more than what is available. Constraint (9) limits the battery capacity. Constraint (1) is or energy conservation, where the total injected energy into the smart grid eqals the total received energy by all BSs. Constraint (11) limits the maximm allowed transmission power or every BS. Constraint (13) represents the sers association with the FBSs, where every ser is associated with a single FBS and no ser is allowed to associate with more than that. Constraint (14) evalates z, where i there is at least one ser that is associated with the SBS, then z is one, or zero otherwise. Similarly, constraint (15) captres the sleeping strategy o the variable y, where i there is at least one ser associated with the FBS then this FBS is kept on, otherwise it will be trned o. However, de to the copling o the ser associations and sleeping strategy with energy harvesting, the above problem is clearly intractable and diiclt to solve. Since we have three binary variables (y, z, and x c ) with or dierent indices (,, and c), the time needed to ind the optimal soltion will increase exponentially as the network size increases linearly. This is de to the act that the problem is a Mixed Integer NonLinear problem (MINLP), or which there is no eicient algorithm or solving it. Thereore, we present an approximation (Γ), where we decople the sers association and sleeping strategy rom the rest o the problem, and perorm the sers association according to the highest SINR or all sers. Ths, the rest o the problem will be a convex optimization problem as ollow: Problem Γ: Minimize N p n,λ n,μ n =1 n=1 =1 sbject to x c R min =1 p c,gnτ + E b y x c R n, c, n (8) (11) (16) where R c n =ω log(1 + pc nhc n σ ) The problem (Γ) is convex, since the objective nction (16) is linear and all the constraints are convex 1. Thereore, we can se the lagrangian to obtain the optimal soltion o (16). The Lagrangian o (16) is given in (17), where α n,ρ n,ζ n,ξ n,β n are the lagrangian mltipliers. C xc #ous z x c,,, (14) The Karsh-Khn-Tcker (KKT) conditions or problem (Γ) is as ollows:

4 + F,N,n=1 L = ζ n F,N,U,C,n,, U,C, p c,gnτ + E b y + =1 N =1 n=1 p c,rnτ B n 1 μ n + α n =1 n=1 (17) Rn+ c x c R min + =1 N ξ n μ n ηλ n + =1 n=1 N =1 n=1 N U β n ρ n B n B max p c n P max p c,g n = τ α n ωhc n σ + p c nhc n+β n =,, c, n (18) p c,r n = α n ωhc n σ + p c nhc n ρ nτ (19) +ζ nτ (n 1)τ+β n =,, c, n λ n = ρ n+ζ n ηξ n =, n () μ n = ζ n+ξ n =, n (1) Using (18)-(19), the closed orm expressions or the transmission power can be obtained as ollows: p c,gn = α nωln (τ + β n) σ h c n pc,rn () 15 sers and N =4. From the igre we can see that sing sleeping SBSs to harvest energy and transer it to other SBSs provide better perormance than the noncooperative approach. On the other hand, or approximated approach perorms close to the optimal soltion o F. While the optimal took longer times ( hors) the approximated approach took mch shorter time (seconds). However, or R min 1Mbps the optimal approach perormed better since it was able to trn o an extra SBS. However, as the R min increases, the perormance o the approximate approach is keeping p with the optimal while the noncooperative approach is increasing ast. Pg in Watts Optimal Proposed Soltion Uncooperative p c,rn = α nωln τ(ζ n(n 1) ρ n) + β n σ h c,gn n pc (3) Note that the optimal powers are nctions o the Lagrangian mltipliers. To ind the optimal Lagrangian mltipliers, the Interior Point Algorithm or Large Scale Nonlinear Programming, Interior Point OPTimization (IPOPT) was sed 13. IV. SIMULATION RESULTS In this section, simlation reslts are provided to demonstrate the perormance o the proposed model in Fig.1. In all simlations (nless stated otherwise.), the time slot dration is set to 1 ms (i.e., τ = 1ms). The available bandwidth ω =5MHz, the maximm transmission power p max =1watt and the noise spectral density is N = 1 16 W/Hz. The energy transer eiciency η =.9. The initial battery level are set to zeros, while the battery sizes B max =6J. The harvested energy levels are given by a trncated normal distribtion with a mean eqal to. and standard deviation is.7, the trncated normal distribtion is set to have vales higher than In Fig., we compare the soltion o the main problem (F) as the optimal soltion to or proposed approach or (Γ) and to a noncooperative approach (where the deactivated SBSs harvest no energy). In this simlation we have 6 SBSs with Minimm Reqired Rate (Mbps) Fig. : Comparing the Optimal with The Approximation. In Fig.3, we investigate the eect o the η parameter and the increase in the R min on the amont o power sed rom both sorces ( P r and P g ). In this simlation we sed 1 SBSs (where the optimization problem trned o one o them is sed to harvest energy) and 3 sers while N = 4.As the reslts show, or η =.9, the network will rely solely on P r ntil the R min reaches 1.3Mbps then we see that the P g start increasing to provide the necessary power to match the increase o sers demands. A similar pattern happens in both η =.5 and η =.65, with lower R min reqired to trigger the se o power rom the grid (P g ). This is nderstandable since the lower the eiciency means the lower the energy transerred between SBSs in the network. On the other hand, or lower minimm rate (R min 1Mbps), P r or the three scenarios are very close to each other, despite the dierence in eiciencies, this is de to the act that or lower rate almost all SBSs are sing their harvested energy and not receiving or transerring it throgh the network where the η actor will come into eect.

5 Pr and Pg in Watts Pr Pg η=.9 η=.65 η=.5 problem into a convex optimization problem and sers association according to the best SINR. Then, we calclated the closed orm o the optimal transmission power and sed the IPOPT algorithm to ind the Lagrangian variables. Finally, the reslts showed the perormance speriority over the case with the deactivated SBSs not cooperating with the other active SBSs in harvesting the energy. Additionally, the reslts showed the beneit o densiying the network o more SBSs, where they will cooperate in adding more HE Minimm Reqired Rate (Mbps) Fig. 3: The Minimm Rate Compared to the Eiciency. Fig.4 shows the eect o increasing the nmber o BSs and the nmber o sers on the amont o injected energy λ. As in the igre, we have two trends. First, the increasing nmber o SBSs will increase the amont o injected energy (λ) into the network. Second, as the nmber o sers in the network increases λ decreases ntil it becomes almost zero. This can be explained as the nmber o sers increases, the active SBSs will have no energy let to inject into the network, and only the deactivated SBSs that will be injecting energy into the network. Injected Energy into the smart grid ( λ) in Jols U=3 sers U=35 sers U=4 sers U=45 sers Nmber o SBSs in The Network Fig. 4: Nmber o OFF BSs to the Amont o Injected Energy vs. the Smart Grid. REFERENCES 1 M. Z. Shakir, K. A. Qaraqe, H. Tabassm, M. S. Aloini, E. Serpedin and M. A. Imran, Green heterogeneos small-cell networks: toward redcing the CO emissions o mobile commnications indstry sing plink power adaptation, in IEEE Commnications Magazine, vol. 51, no. 6, pp. 5-61, Jne 13. A. Kwasinski and A. Kwasinski, Increasing sstainability and resiliency o celllar network inrastrctre by harvesting renewable energy, in IEEE Commnications Magazine, vol. 53, no. 4, pp , April G. Piro et al., HetNets Powered by Renewable Energy Sorces: Sstainable Next-Generation Celllar Networks, in IEEE Internet Compting, vol. 17, no. 1, pp. 3-39, Jan.-Feb X. Fang, S. Misra, G. Xe and D. Yang, Smart Grid The New and Improved Power Grid: A Srvey, in IEEE Commnications Srveys & Ttorials, vol. 14, no. 4, pp , Forth Qarter 1. 5 H. Al Haj Hassan, A. Pelov and L. Naymi, Integrating Celllar Networks, Smart Grid, and Renewable Energy: Analysis, Architectre, and Challenges, in IEEE Access, vol. 3, pp , G. Piro et al., HetNets Powered by Renewable Energy Sorces: Sstainable Next-Generation Celllar Networks, in IEEE Internet Compting, vol. 17, no. 1, pp. 3-39, Jan.-Feb. 13. doi: 1.119/MIC J. Leithon, T. J. Lim and S. Sn, Energy exchange among base stations in a Celllar Network throgh the Smart Grid, 14 IEEE International Conerence on Commnications (ICC), Sydney, NSW, 14, pp C. Y. Chang, K. L. Ho, W. Liao and D. s. Shi, Capacity maximization o energy-harvesting small cells with dynamic sleep mode operation in heterogeneos networks, 14 IEEE International Conerence on Commnications (ICC), Sydney, NSW, 14, pp Y. H. Chiang and W. Liao, Green Mlticell Cooperation in Heterogeneos Networks With Hybrid Energy Sorces, in IEEE Transactions on Wireless Commnications, vol. 15, no. 1, pp , Dec Y. Song, H. Wei, M. Zhao, W. Zho, P. Dong and L. Zhao, Optimal Base Station Sleeping Control in Energy Harvesting Heterogeneos Celllar Networks, 16 IEEE 84th Vehiclar Technology Conerence (VTC-Fall), Montreal, QC, 16, pp A. Alsharoa, H. Ghazzai, A. E. Kamal and A. Kadri, Optimization o a Power Splitting Protocol or Two-Way Mltiple Energy Harvesting Relay System, in IEEE Transactions on Green Commnications and Networking, vol. PP, no. 99, pp S. Boyd and L. Vandenberghe, Convex optimization. Cambridge niversity press, Wächter, A.: An Interior Point Algorithm or Large-Scale Nonlinear Optimization with Applications in Process Engineering. PhD thesis, Carnegie Mellon University, Pittsbrgh, PA, USA, Janary 14 A. Masadeh, A. E. Kamal and Z. Wang, Cognitive Radio Networking with Cooperative and Energy Harvesting, accepted or pblication in the proceedings o the IEEE VTC Fall 17. V. CONCLUSIONS In this paper, energy harvesting in cooperative SBSs heterogenos networks with dynamic sleeping strategy was investigated, where the deactivated SBSs are cooperating with the rest o the network by harvesting then injecting the energy to the network. Each o the SBSs is eqipped with a harvesting device and a inite battery to store the HE. We ormlated an optimization problem aiming at minimizing the transmission power driven rom the grid nder ser QoS constraints. Moreover, we proposed a decomposition o the