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IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 34, NO. 12, DECEMBER 2016 3127

Dynamic Base Station Operation in Large-ScaleGreen Cellular Networks

Yue Ling Che, Member, IEEE, Lingjie Duan, Member, IEEE, and Rui Zhang, Senior Member, IEEE

Abstract— In this paper, to minimize the on-grid energy costin a large-scale green cellular network, we jointly design theoptimal base station (BS) ON/OFF operation policy and theon-grid energy purchase policy from a network-level perspective.We consider that the BSs are aggregated as a microgrid withhybrid energy supplies and an associated central energy storage,which can store the harvested renewable energy and the pur-chased on-grid energy over time. Due to the fluctuations of theon-grid energy prices, the harvested renewable energy, and thenetwork traffic loads over time, as well as the BS coordinationto hand over the traffic offloaded from the inactive BSs tothe active BSs, it is generally NP-hard to find a network-leveloptimal adaptation policy that can minimize the on-grid energycost over a long-term and yet assures the downlink transmissionquality at the same time. Aiming at the network-level dynamicsystem design, we jointly apply stochastic geometry (Geo) forlarge-scale green cellular network analysis and dynamic pro-gramming (DP) for adaptive BS ON/OFF operation designand on-grid energy purchase design, and thus propose a newGeo-DP design approach. By this approach, we obtain the optimalBS ON/OFF policy, which shows that the optimal BSs’ activeoperation probability in each horizon is just sufficient to assurethe required downlink transmission quality with time-varyingload in the large-scale cellular network. However, due to thecurse of dimensionality of the DP, it is of high complexity toobtain the optimal on-grid energy purchase policy. We thuspropose a suboptimal on-grid energy purchase policy with lowcomplexity, where the low-price on-grid energy is over purchasedin the current horizon only when the current storage leveland the future renewable energy level are both low. Simulationresults show that the suboptimal on-grid energy purchase canachieve near-optimal performance. We also compare the pro-posed policy with the existing schemes to show that our proposedpolicy can more efficiently save the on-grid energy cost overtime.

Index Terms— Base station on/off operation, hybrid energysupplies, on-grid energy cost minimization, energy storagemanagement, stochastic geometry, dynamic programming.

Manuscript received August 1, 2015; revised December 23, 2015 andApril 13, 2016; accepted June 28, 2016. Date of publication August 15,2016; date of current version December 29, 2016. This work was sup-ported by the SUTD-ZJU Joint Collaboration Grant (Project Number: SUTD-ZJU/RES/03/2014). (Corresponding author: Lingjie Duan.)

Y. L. Che is with the College of Computer Science and SoftwareEngineering, Shenzhen University, Shenzhen 518060, China, and also with theEngineering Systems and Design Pillar, Singapore University of Technologyand Design, Singapore 487372 (e-mail: [email protected]).

L. Duan is with the Engineering Systems and Design Pillar, SingaporeUniversity of Technology and Design, Singapore 487372 (e-mail:[email protected]).

R. Zhang is with the Department of Electrical and Computer Engineer-ing, National University of Singapore, Singapore 119077, and also withthe Institute for Infocomm Research, A*STAR, Singapore 138632 (e-mail:[email protected]).

Digital Object Identifier 10.1109/JSAC.2016.2600377

I. INTRODUCTION

THE dramatically increased mobile traffic can easily leadto an unacceptable total energy consumption level in the

future cellular network, and energy-efficient cellular networkdesign has become one of the critical issues for developing the5G wireless communication systems [1]. Due to the resultinghigh energy cost and the CO2 emissions, it is importantto improve the cellular network energy efficiency (EE) bygreening the cellular network [2]. It has been noted thatthe operations of base stations (BSs) contribute to most ofthe energy consumptions in the cellular networks, which areestimated as 60-80 percent of the total network energy con-sumptions [3]. Hence, reducing the BSs’ energy consumptionsis crucial for developing energy-efficient or green cellularnetworks.

In traditional cellular networks, BSs are usually denselydeployed to meet the peak-hour traffic load, which causesunnecessary energy consumption for many lightly-loaded BSsduring the low traffic load period (e.g., early morning). It isenvisioned that in the future energy-efficient 5G wireless com-munication system, the cellular network should dynamicallyshut down some BSs or adapt the BS transmissions accordingto the time-varying traffic load. Although appealing, due to thesignificant spatial and temporal fluctuations of the traffic loadin the cellular networks, optimal BS on/off operation designis a challenging problem [4]. For example, the authors in [3]studied optimal energy saving for the cellular networks byreducing the number of active cells, where simplified cellularnetwork model with hexagonal cells and uniformly distributedtraffic load is assumed. In [5], the authors proposed adaptivecell zooming scheme according to the traffic load fluctua-tions, but without considering downlink transmission qualityexplicitly. In [6], by studying the impact of each BS’s activeoperation on the network performance, the authors proposeda suboptimal BS on/off scheme that can be implemented ina distributed manner to save the BSs’ energy consumption.However, the impact of traffic fluctuation on the BS’s on/offdecisions as well as the downlink transmission quality werenot explicitly considered. The issue of downlink transmissionquality was considered in [7], where the BS’s transmit powerand cell range adaptations to the traffic load fluctuation wereproposed to improve the EE of the cellular network, but [7]only considered a single-cell scenario. Considering a large-scale heterogeneous cellular network, the dynamic small-cell BS on/off operation scheme has been studied in [8].In addition, we also have noticed there are some works

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3128 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 34, NO. 12, DECEMBER 2016

focusing on adaptive transmission design for other applications(e.g. [9]–[12]). Moreover, in [13], an energy group-buyingscheme was proposed to let the network operators make theday-ahead and real-time energy purchase as a single group,where the BSs of the network operators share the wirelesstraffic to maximally turn lightly-loaded BSs into sleep mode.

To more effectively reduce the carbon footprint, the energyharvesting (EH) enabled BSs, which are able to harvest cleanand free renewable energy (e.g., solar and wind energy) fromthe surrounding environment for utilization, have been devel-oped for the green cellular networks recently. For example,in [14], by assuming a renewable energy storage, the authorsapplied the dynamic programming (DP) technique to study theenergy allocations for a point-to-point transmission, to adaptto the time-selective channel fading. In [15], by using a birth-death process to model the harvested renewable energy levelat each BS for a large-scale K -tier green cellular network,the authors characterized an energy availability region of theBSs based on tools from stochastic geometry [16]. Variousissues of the EH-enabled wireless communications are alsodiscussed in [17]–[20]. However, it is noted that the availablerenewable energy in nature is limited and intermittent, and thuscannot always guarantee sufficient energy supply to power upthe BSs.

By combining the merits of the reliable on-grid energy andthe cheap renewable energy, hybrid energy supplied BS designhas become a promising method to power up the BSs [21].One of the main design issues is to properly exploit theavailable renewable energy to minimize the on-grid energycost or maximize the EE of the system. We note that someinitial work has been proposed to address this issues via, e.g.,the optimal packet scheduling [22], the optimal BS resourceallocation [23], and low-complexity online algorithm designbased on the Lyapunov optimization [24]. In [25]–[27], tomitigate the fluctuations of the renewable energy harvestedby each BS, the authors also considered energy cooperationand sharing between the BSs. Moreover, by applying theDP technique to adapt to the fluctuations of both the trafficloads and the harvested renewable energy, hybrid energysupplied BS on/off operation design has also been studied inthe literature. For example, in [28], by assuming each BS in thenetwork is supplied by either the renewable energy or the on-grid energy, the authors studied the BS sleep control problemto save the energy consumptions of all the BSs. In [29], byassuming each BS is jointly supplied by renewable energyand on-grid energy, the authors studied the joint optimizationof the BS on/off operation and resource allocation under auser blocking probability constraint at each BS. Due to thetraffic offloaded from the inactive BSs to the active BSs, allthe BSs in the network are essentially coordinated to supportto all the users in both [28] and [29]. However, due to thedimensionality curse of the DP [30], it is generally NP-hardto conduct a network-level BS coordination to decide theiroptimal on/off status. As a result, in [28] and [29], the authorsproposed a cluster-based BS coordination scheme to decidethe BSs’ on/off status in a large-scale network, where theBSs form different clusters, and the BSs in each cluster applythe DP technique to decide their on/off status. However, such

a cluster-based BS coordination scheme cannot achievenetwork-level optimal BS on/off decisions in general.

In this paper, we consider a large-scale cellular network,where all the BSs are aggregated as a microgrid withhybrid energy supplies and an associated central energy stor-age (CES). The microgrid works in island mode if it hasenough local supply from the renewable farm; otherwise,it connects to the main grid for purchasing the on-gridenergy [31]. By adapting to the fluctuations of the harvestedrenewable energy, the network traffic loads, as well as theon-grid energy prices over time, the microgrid applies theDP technique to decide the amount of on-grid energy topurchase as well as the probability that each BS stays activeat each time, so as to minimize the total on-grid energy costover time in the network. Unlike [28] and [29], we aim at anetwork-level optimal BS on/off operation policy design, suchthat the on-grid energy cost in the cellular network can beefficiently saved.

The key contributions of this paper are summarized asfollows:

• Novel large-scale network model with hybrid-energysupplied BSs: Based on Poisson point processes (PPPs),we first model the large-scale network by jointly con-sidering the mobility of mobile terminals (MTs), trafficoffloading from an inactive BS to its neighboring activeBSs, as well as BS frequency reuse for reducing thedownlink network interference level. Since all the BSsare supplied by the hybrid energy stored in the CES, wethen model the hybrid energy management at the CES,where the on-grid energy is purchased with time-varyingprice to ensure that the energy demands of all the BSs inthe network can be satisfied.

• New Geo-DP approach for dynamic network optimiza-tion: To pursue a network-level design, we jointly applystochastic geometry (Geo) for large-scale green cellularnetwork analysis and the DP technique for adaptive BSon/off operation and on-grid energy purchase, and thuspropose a new Geo-DP approach. By this approach,the microgrid centrally decides the optimal BSs’ activeoperation probability and the purchased on-grid energyin each time horizon, so as to minimize the total on-grid energy cost over all time horizons, under the BSs’downlink transmission quality constraint and the BSs’energy demand constraint.

• Network-level optimal policy design: We aim at optimaloffline closed-form policy design, which updates the BSs’on/off status and on-grid energy purchase decisions ina predictable future period. Although the optimal BSon/off policy and the optimal on-grid energy purchasepolicy are generally correlated and thus need to bejointly designed, we show that these two policies canbe separately designed without any loss of optimality.In particular, the optimal BS on/off policy shows thatthe optimal BSs’ active operation probability in eachhorizon is just sufficient to assure the required down-link transmission quality with time-varying load in thelarge-scale cellular network. However, due to the curseof dimensionality of the DP, it is of high complexity

CHE et al.: DYNAMIC BS OPERATION IN LARGE-SCALE GREEN CELLULAR NETWORKS 3129

to obtain the optimal on-grid energy purchase policy.We thus propose a suboptimal on-grid energy purchasepolicy with low-complexity, where the low-price on-gridenergy is over-purchased in the current horizon only whenthe current storage level and the future renewable energylevel are both low.

• Efficient network-level BS coordination to minimize theon-grid energy cost: By conducting extensive simulationsin Section VI, we show that the proposed suboptimalon-grid energy purchase policy can achieve near-optimalperformance. We also show that our proposed policyis robust to the prediction errors of the on-grid energyprices, the harvested renewable energy, and the networktraffic loads, and thus can be properly implemented inpractice. Moreover, we conduct a large-scale networksimulation to compare our proposed policy with the exist-ing schemes, and show that our proposed policy can moreefficiently save the on-grid energy cost in the network.

As a powerful tool, stochastic geometry has been widelyapplied to model the EH enabled wireless communicationnetworks. For example, besides [15], we also noticed thatthe EH-based ad hoc networks, cognitive radio networks,cooperative communication networks have been studiedin [32]–[34], respectively, by adopting the PPP-based networkmodeling. In our previous work [35], we also applied toolsfrom stochastic geometry to analyze the spatial throughput ofa wireless powered communication network, where the usersexploit their harvested radio frequency (RF) energy to powerup their communications. Although the network-level systemperformance can be characterized in these existing studies, theadaptation to the fluctuations of the network parameters (e.g.,the harvested renewable energy, the network traffic loads, andthe on-grid energy prices) has not been properly addressed.To our best knowledge, our newly proposed Geo-DP approachthat can lead to a network-level optimal adaptation policydesign has not been studied in the literature.

II. NETWORK OPERATION MODEL

We consider a large-scale cellular network, where the trafficloads, the on-grid energy prices, the available renewableenergy, as well as the wireless fading channels from each BSto the MTs are all varying over time in the network. The BSsare able to switch between active (i.e., on status) and inactive(i.e., off status) operation modes to save the total on-gridenergy cost over time. Supported by smart grid development,as illustrated in Fig. 1, we aggregate all the BSs as a microgridwith hybrid energy supplies and an associated CES to defendagainst the supply/load variation [31]. For efficient energymanagement, the cellular network deploys the CES in themicrogrid, which connects to both the local renewable farm(e.g., wind turbines or solar panels) and the power grid, andthus can store the harvested renewable energy (e.g., wind orsolar energy) from the environment and the purchased on-gridenergy from the power grid at the same time.1 All the BSsare connected with the CES and are powered up by its stored

1A CES is easier and cheaper to manage as compared to distributed storageat each BS. One can also view this CES as a collection of distributed storagewith perfect energy exchange links.

Fig. 1. Illustration of the cellular network supplied by both renewable energyand on-grid energy.

Fig. 2. Dynamic network operations over two different time scales: horizonsand slots.

hybrid energy. Similar to [7], it is assumed that the CES isable to charge and discharge at the same time. In the followingsubsections, we first model each BS’s operations over time,and then present the large-scale cellular network model basedon homogeneous PPPs. The hybrid energy management modelat the CES will be elaborated later in Section III.

A. Time Scales for Network Operations

As compared to the variations of the downlink wirelessfading channels from each BS to the MTs, the renewableenergy arrival rates, the network traffic loads, as well as theon-grid energy prices are all varying slowly over time [15].We thus consider the network operates over two differenttime scales [19]: one is the long time scale and is referredto as horizons, and the other is the short time scale and isreferred to as slots, as shown in Fig. 2. We define a horizonas a reasonably large time period where the renewable energyarrival rate, the network traffic load, and the on-grid energyprice all remain unchanged. Each horizon consists of N slots,and the wireless fading channels vary over slots. We focus onin total T horizons, 1 ≤ T < ∞, and assume each horizonhas a fixed duration τ > 0. For simplicity, we assume τ = 1hour in the sequel, and thus interchangeably use Wh and Wto measure the energy consumption in each horizon.

By adapting to the variations of the on-grid energy prices,the renewable energy arrival rates, the network traffic loads, aswell as the wireless fading channels, the microgrid centrally


decides the amount of on-grid energy to purchase and theactive operation probability of the BSs in the network for eachhorizon t ∈ {1, . . . , T }, which are denoted by G(t) > 0 andρ(t), respectively, so as to minimize the total on-grid energycost over all T horizons. Similar to [17], we consider theoptimal offline policy design, and assume the fluctuations ofthe renewable energy arrival rates, the network traffic loads,as well as the on-grid energy prices in all T horizons canbe accurately predicted [36]. We will show that even givenreasonable prediction errors, our approach works quite well inSection VI by simulation. In each horizon t , based on ρ(t)determined by the microgrid, each BS independently decidesto be active or inactive. If a BS decides to be active, it transmitsto its associated MTs with a fixed power level [37], denoted byPB > 0. If a BS decides to be inactive, it keeps silent and itsoriginally associated MTs are handed over to its neighboringactive BSs.

B. PPP-Based Network Model

This subsection models the large-scale cellular networkbased on stochastic geometry. We assume the BSs aredeployed randomly according to a homogeneous PPP, denotedby �(λB), of BS density λB > 0. For a given active operationprobability ρ(t) in horizon t , due to the independent on/offdecisions at the BSs, the point process formed by the activeBSs in each horizon t ∈ {1, . . . , T } is still a homogeneousPPP, denoted by �(λBρ(t)), with active BS density givenby λBρ(t). We assume the MTs are also distributed as ahomogeneous PPP, denoted by �(λm(t)), of MT densityλm(t) > 0 in horizon t . The MTs independently move in thenetwork over slots in each horizon based on the random walkmodel [38], and thus all �(λm(t))’s are mutually independent.We also assume �(λB) is independent with �(λm(t)),∀t ∈ {1, . . . , T }. Each MT is associated with its near-est active BS from �(λBρ(t)) in each slot of horizon t ,for achieving good communication quality. When an activeBS becomes inactive, its originally associated MTs willbe transferred to their nearest BSs that are still active asin [3], [5], and [22]–[29]. From [39], the resulting coverageareas of the active BSs in each slot comprise a Voronoi tessel-lation on the plane R

2. We refer to traffic load of an active BSas the number of MTs that are associated with it, i.e., thoseare located within the Voronoi cell of the active BS, as in [15].The following proposition studies the average traffic load of anactive BS.

Proposition 1: Given the BSs’ active operation probabilityρ(t) in horizon t , ∀t ∈ {1, . . . , T }, the average traffic load foran active BS from �(λBρ(t)) is given by D(t) = λm(t)

λBρ(t) .

The proof of Proposition 1 is obtained by noticing that D(t)equals the product of the MT density λm(t) and the averagecoverage area of each BS, where the latter term is 1

λBρ(t) from[16, Lemma 1], and thus is omitted here for brevity. FromProposition 1, the average traffic load D(t) at each BS isincreasing over the MT density λm(t), and decreasing over theBS density λB as well as the BSs’ active operation probabilityρ(t), as expected. Moreover, since the inactive BSs do nottransmit information to the MTs and thus have zero traffic

load, the average traffic load for each BS from �(λB) is alsoobtained as D(t) for any t ∈ {1, . . . , T }.

C. Frequency Reuse Model

To effectively control the potentially large downlink inter-ference, which is mainly caused by the nearby BSs thatare operating over the same frequency band, this subsectionpresents a random frequency reuse model to assign differentfrequency bands to the neighboring BSs. Specifically, weassume the total bandwidth available for the network is W Hz.To properly support the traffic load D(t), we assume thetotal bandwidth is equally divided into δ(t) bands in eachhorizon t , and each BS is randomly assigned with one outof δ(t) bands for operation as in [39]. We consider orthogonalmultiple access for the MTs in the Voronoi cell of each activeBS as in, e.g., [15] and [39], and each MT is assigned with achannel with fixed bandwidth B Hz for communication, where0 < B < W . Since each active BS is only assigned with oneband, by letting each BS’s required total bandwidth to supportits associated MTs be equal to the average bandwidth per band,i.e., D(t)B = W/δ(t), we obtain

δ(t) = W

B

1

D(t)= W

B

λBρ(t)

λm(t), (1)

by substituting D(t) = λm(t)λBρ(t) from Proposition 1. It is

observed from (1) that the number of bands δ(t) decreases asthe traffic load D(t) increases, as expected. For each horizont ∈ {1, . . . , T } with a given δ(t), due to the BSs’ randomoperation band selection as well as the independent on/offdecisions over horizons, the point process formed by the co-band active BSs is still a homogeneous PPP, denoted by�(λc

B(t)), with co-band active BS density λcB(t) = λBρ(t) 1

δ(t) .As a result, for each MT, it only receives interference fromall other active BSs that operate over the same band as itsassociated BS with probability 1/δ(t). In the next subsection,based on the PPP-based network model and the frequencyreuse mode, we present the downlink transmission model fromeach BS to its associated MT.

D. Downlink Transmission Model

We measure the downlink transmission quality between theBS and its associated MTs based on the received signal-to-interference-plus-noise-ratio (SINR) at the MTs. We assumeRayleigh flat fading channels with path-loss as in [15], [32],[35], and [39], where the channel gains vary over slots asshown in Fig. 2. Let �(λB ) = {X}, X ∈ R

2, denote thecoordinates of the BSs. In slot n ∈ {1, . . . , N} of horizont ∈ {1, . . . , T }, let h X (t, n) represent an exponentially dis-tributed random variable with unit mean to model Rayleighfading from BS X to the origin o = (0, 0) in the plane R

2.We assume h X (t, n)’s are mutually independent over any timeslot n ∈ {1, . . . , N}, any horizon t ∈ {1, . . . , T }, and anyBS X ∈ �(λB ). Suppose a typical MT is located at theorigin and is associated with the active BS X ∈ �(λBρ(t))in slot n of horizon t . We express the desired signal strengthreceived at the typical MT as |X |−αh X (t, n), where |X | isthe distance from the associated active BS X to the origin,


α > 2 is the path-loss exponent. Under the random fre-quency reuse model, since the received interference at thetypical MT is caused by the co-band BSs from �(λc

B(t)),we express the received interference at the typical MT as∑

Y∈�(λcB(t)),Y �=X PB |Y |−αhY (t, n). Thus, the received SINR

at the typical MT from BS X in slot n of horizon t , denoted bySINRo(t, n), ∀t ∈ {1, . . . , T },∀n ∈ {1, . . . , N}, is obtained as

SINRo(t, n) = |X |−αh X (t, n)∑

Y∈�(λcB(t)),Y �=X |Y |−αhY (t, n) + σ̂ 2 , (2)

where σ̂ 2 = σ 2

PB, with σ 2 denoting the noise power at

the typical MT, represents the normalized noise power overthe BS’s transmit power. It is also noted that |X | in (2)also represents the minimum distance from the typical MTto all the active BSs from �(λBρ(t)), regardless of theiroperating frequency bands, i.e., no other active BSs can becloser than |X |. By using the null probability of a PPP, theprobability density function (pdf) of |X | in (2) is then obtainedas f|X |(r) = 2πλBρ(t)re−λBρ(t)πr2

for r ≥ 0 [39]. We saya downlink transmission is successful if the received SINR atthe MT is no smaller than a predefined threshold β > 0.

III. HYBRID ENERGY MANAGEMENT MODEL

This section presents the hybrid energy management modelat the CES, by modeling the on-grid and renewable energyconsumptions of all the BSs in the network. In the follow-ing, we first model the energy consumption at both activeand inactive BSs. We then detail the hybrid energy man-agement at the CES so as to meet the energy demands ofthe BSs.

A. Energy Consumption at the BS

According to the BS energy consumption breakdown pro-vided by the practical studies in [40], various components ofthe BS, e.g., the power amplifier, base-band operation, andpower supply for power grid and/or back-haul connections,all contribute to the total BS energy consumption. It is alsoshown in [40] that the BS energy consumption can be wellapproximated by a linear power model, where the total energyconsumption of an active transmitting BS is affine/linear to itstraffic load, with the corresponding slope determined by thepower amplifier efficiency. Such a linear power model hasbeen widely adopted in the literature (see, e.g., [14] and [29]).We thus also adopt it to model the energy consumption foreach BS in this paper.

Specifically, for a given horizon t , although the traffic loadof each active BS generally varies over space, by applying ourPPP-based network model in Section II, the average energyconsumption of each active BS over space is obtained as

Pon(t) = Pa + PB

μD(t), t ∈ {1, . . . , T }, (3)

where the average traffic load D(t) of the active BS isgiven in Proposition 1, μ ∈ (0, 1) is the power amplifierefficiency, and Pa > 0 represents the active BS’s averageenergy consumption for supporting its basic operations andis taken as a constant [40]. For an inactive BS in horizon t ,

since it keeps silent in the horizon, we model its averageenergy consumption as a constant, which is given by

Pof f (t) = Ps, t ∈ {1, . . . , T }, (4)

where similar to Pa in (3), the constant Ps > 0 represents theaverage energy consumption of an inactive BS for supplyingits basic operations. We assume Pa > Ps [40]. Based on theenergy consumption model for each active or inactive BS, wepresent the hybrid energy management model at the CES tomeet all the BSs’ energy demand.

B. Energy Supplies at the CES

As shown in Fig. 1, the CES can store both the renewableenergy that is harvested from the local renewable farm andthe on-grid energy that is purchased from the power grid.In each horizon, the microgrid centrally decides the amountof on-grid energy to purchase from the power grid and theBSs’ active operation probability ρ(t), by jointly consideringthe BSs’ downlink transmission quality, the energy demandsof all the BSs in each horizon, and the hybrid energy storagelevel at the CES. We focus on the average energy consumptionof all the BSs normalized by spatial area. For a given activeoperation probability ρ(t) in horizon t , by considering the BSdensity λB and its average traffic load D(t) in each horizon t ,we can obtain the average energy consumption of all the BSsover the BSs’ on/off status and the network area in eachhorizon t ∈ {1, . . . , T } as

E(t) = λBρ(t)Pon(t) + λB(1 − ρ(t))Pof f (t) (5)(a)= λBρ(t)Pgap + λB Ps + PBλm(t)

μ. (6)

where equality (a) follows by substituting (3) and (4) into (5),and Pgap = Pa − Ps > 0. It is easy to find that the unit ofE(t) is given by W/unit-area. It is also observed from (6) thatE(t) increases monotonically over the BSs’ active operationprobability ρ(t) in each horizon t .

Denote the storage level of the CES at the beginning ofhorizon t as B(t) ≥ 0, the amount of on-grid energy topurchase in horizon t as G(t), and the renewable energy arrivalrate in horizon t as λe(t). All B(t), G(t), and λe(t) have thesame unit as E(t), i.e., W/unit-area. According to Fig. 1, tosatisfy the demanded energy of all the BSs in horizon t , weobtain the following energy demand constraint:

B(t) + G(t) + λe(t) ≥ E(t), t ∈ {1, . . . , T }. (7)

If the purchased on-grid energy G(t) and/or harvested renew-able energy λe(t) cannot be completely consumed by the BSsin the current horizon, their residual portions are both storedin the CES for future use. The dynamics of the storage levelB(t) is obtained as

B(t + 1) = min (B(t) + λe(t) + G(t) − E(t), C) , (8)

where 0 < C < ∞ is the normalized storage capacity of theCES over the network area, with unit given by W/unit-area.We assume C is given, and the initial storage level at thebeginning of horizon t = 1 is B(1) = 0 for simplicity.


IV. PERFORMANCE METRICS AND

PROBLEM FORMULATION

In this section, based on the network operation model andthe hybrid energy management model in Sections II and III,respectively, we propose a new Geo-DP approach to studythe cellular network and formulate the on-grid energy costminimization problem from the network-level perspective.In particular, we first use stochastic geometry to characterizethe downlink transmission performance from the BSs to theirassociated MTs. We then further apply DP to formulate theon-grid energy cost minimization problem under the BSs’successful downlink transmission probability constraint.

A. Successful Downlink Transmission Probability

As discussed in Section II, if a BS is active in a particularhorizon, it transmits to its associated MTs in each slot withinthis horizon, while the channel fadings from the BSs to theMTs as well as the locations of the MTs vary over slots.In this subsection, by applying tools from stochastic geometry,we study the active BSs’ successful downlink transmissionprobability to their associated MTs in each slot. Specifically,from Section II-B, due to the stationarity of the consideredhomogeneous PPPs for the active BSs and the MTs in eachhorizon as well as the independent moving of the MTs overslots, we focus on a typical MT in each slot of horizont ∈ {1, . . . , T }, which is assumed to be located at the origin ofthe plane R

2, without loss of generality. Denote the successfuldownlink transmission probability for the typical MT in slot nof horizon t as Psuc(t, n), ∀t ∈ {1, . . . , T }, ∀n ∈ {1, . . . , N}.According to Section II-D, for a target SINR threshold β, wedefine Psuc(t, n) for any t ∈ {1, . . . , T } and n ∈ {1, . . . , N} as

Psuc(t, n) = P (SINRo(t, n) ≥ β), (9)

with SINRo(t, n) for a typical MT given in (2). By applyingthe probability generating functional (PGFL) of a PPP [16],we explicitly express Psuc(t, n) in the following proposition.

Proposition 2: In slot n of horizon t , ∀t ∈ {1, . . . , T },∀n ∈ {1, . . . , N}, the successful downlink transmission prob-ability for the typical MT is

Psuc(t, n) =∫ ∞

0e−ue

−a uπλBρ(t) e

−b[

uπλB ρ(t)

]α/2

du (10)

with b = βσ̂ 2 and a = π λm(t)BW v(β), where B and W

are the fixed channel bandwidth for each MT and the totalbandwidth available in the network, respectively, as intro-duced in Section II-C, and v(β) = β2/α

∫ ∞β−2/α

11+uα/2 du.

When α = 4, with v(β) being reduced to v(β) =√β

(π/2 − arctan

(1√β

)), (10) admits the following closed-

form expression:

Psuc(t, n) = πλBρ(t)√

π

βσ̂ 2 exp

(ϒ(t)2

2

)

Q(ϒ(t)), (11)

where ϒ(t) =[πλBρ(t) + π λm(t)B

W v(β)] (

2βσ̂ 2)− 1

2 , and

Q(x) = 1√2π

∫ ∞x exp

(− u2

2

)du is the standard Gaussian tail

probability function.

Proposition 2 is proved using a method similar to thatfor proving [40, Th. 2], and thus is omitted for brevity.By using a similar method as in our previous work [35],one can also easily validate Proposition 2 by simulation.Moreover, from Proposition 2, due to the independent movingof the MTs as introduced in Section II-B, the expressions ofPsuc(t, n) are observed to be identical over all slots for a givent ∈ {1, . . . , T ]}. Thus, for notational simplicity, we omit theslot index n and use Psuc(t) to represent the typical BS’ssuccessful downlink transmission probability in any slot ofhorizon t in the sequel. The following proposition shows thevariation of Psuc(t) over the active BS density λBρ(t).

Proposition 3: For a general α > 2, Psuc(t) monotonicallyincreases over the active BS density λBρ(t) in each horizont ∈ {1, . . . , T }.

Proof: Since both e−a2

uπλBρ(t) and e

−b[

uπλB ρ(t)

]α/2

in (10)monotonically increase over λBρ(t) for any given u ∈ (0,∞),it is easy to verify that the resulting integral over u monoton-ically increases over λBρ(t). Proposition 3 thus follows.

As a special case with α = 4, Psuc(t) given in (11)also follows Proposition 3. From Proposition 3, as the activeBS density λBρ(t) increases, the desired signal strength ateach MT is substantially increased due to the largely short-ened distance between the MT and its associated active BS,which dominates over the increased downlink interference, andPsuc(t) is thus increased. To ensure the QoS for each BS’sdownlink transmissions, we consider a successful downlinktransmission probability constraint such that Psuc(t) ≥ 1 − εwith ε 1, t ∈ {1, . . . , T } [39]. Since Psuc(t) monotonicallyincreases over λB for any given ρ(t) > 0, we assume theBS density λB is sufficiently large, such that Psuc(t)|ρ(t)=1 ≥1 − ε always holds, to avoid the trivial case with no feasiblesolutions of ρ(t) for satisfying Psuc(t) ≥ 1 − ε.

B. Problem Formulation

Denote the on-grid energy price in each horizon tas a(t) ($/W). The total on-grid energy cost across all the BSsover all T horizons is thus obtained as

∑Tt=1 a(t)G(t), with

unit $/unit-area. To minimize the total on-grid energy costunder the energy demand constraint given in (7), the microgridcan take advantage of the on-grid energy’s price variations bypurchasing more on-grid energy when its price is low andstore it for future use, and purchasing less (or even zero) on-grid energy when its price is high. As a result, by jointlyconsidering the energy demand constraint and the successfuldownlink transmission probability constraint, we optimize theBSs’ active operation probability ρ(t) and the purchased on-grid energy G(t) in each horizon, and formulate the on-gridenergy cost minimization problem as

(P1) : min.ρ(t),G(t)

T∑

t=1

a(t)G(t)

s.t. Psuc(t) ≥ 1 − ε, ∀t ∈ {1, . . . , T }, (12)B(t) + G(t) + λe(t) ≥ E(t), ∀t ∈ {1, . . . , T },G(t) ≥ 0, ∀t ∈ {1, . . . , T }, (13)0 ≤ ρ(t) ≤ 1,∀t ∈ {1, . . . , T }, (14)B(t + 1) = min (B(t) + λe(t) + G(t) − E(t), C),∀t ∈ {1, . . . , T − 1},


where E(t) is determined by ρ(t) and is given in (6).Problem (P1) is a constrained long-term on-grid energy costminimization problem for a PPP-based large-scale networkwith a general path-loss exponent α > 2, which has notbeen reported in the existing literature to our best knowledge.By applying Proposition 3, The following proposition sim-plifies the successful downlink transmission probability con-straint and obtains an equivalent constraint of ρ(t).

Proposition 4: For a general α > 2, there always exists aminimum required BSs’ active operation probability ρmin(t),t ∈ {1, . . . , T }, which is the unique solution to Psuc(t) = 1−ε,such that Psuc(t) ≥ 1 − ε is equivalent to ρ(t) ≥ ρmin(t). Forthe special α = 4, the closed-form ρmin (t) = λm(t)B

λB W v(β) 1−εε

with v(β) given in Proposition 2.Proposition 4 can be easily obtained due to the fact

that Psuc(t) monotonically increases over ρ(t), as given inProposition 3. For the general case with α > 2, although theclosed-form expression of ρmin(t) does not exist in general, wecan always find its value numerically by using, e.g., decimalsearch method to find the root ρmin (t) for Psuc(t) = 1 − ε.For the special case with α = 4 , the closed-form ρmin (t)is obtained by using the same method as in our previouswork [35], which is omitted here for brevity. It is also observedthat for α = 4, the network becomes interference-limited whenPsuc is sufficiently high with Psuc(t) ≥ 1 − ε; and thus thevalue of ρmin(t) does not depend on the normalized noise σ̂ 2,and is determined by λm(t), β, and λB . The following lemmastudies the variation of ρmin(t) over the MT density λm(t).

Lemma 5: For a general α > 2, ρmin (t) is monotonicallyincreasing over the MT density λm(t) for any t ∈ {1, . . . , T }.

Proof: Please refer to Appendix A.It is easy to verify that Lemma 5 holds for the special case

with α = 4. It is also noted that when the MT density and thusthe required total bandwidth λm(t)B of the MTs increase, dueto the decreased number of bands δ(t) for frequency reuse, asgiven in (1), the downlink interference level increases. In thiscase, it is observed from Lemma 5 that the minimum requiredBSs’ active operation probability ρmin(t) also increases, suchthat more BSs need to be active to increase the desired signalstrength at the MT, so as to assure a high Psuc(t). Due to thevariations of MT density λm(t), it is also observed that ρmin (t)is also varying over time in general.

Therefore, for any general α > 2, by applying Proposition 4,we find an equivalent problem to problem (P1) as follows

(P2) : min.ρ(t),G(t)

T∑

t=1

a(t)G(t) (15)

s.t. G(t) ≥ max(E(t) − B(t) − λe(t), 0),

∀t ∈ {1, . . . , T }, (16)

ρmin(t) ≤ ρ(t) ≤ 1, ∀t ∈ {1, . . . , T }, (17)

B(t + 1) = min (B(t) + λe(t) + G(t) − E(t), C) ,

∀t ∈ {1, . . . , T − 1},where the new constraint (16) is obtained by combiningthe energy demand constraint B(t) + G(t) + λe(t) ≥ E(t)and the non-negative on-grid energy constraint G(t) ≥ 0 inproblem (P1), and the other new constraint (17) is obtained

by combining the constraints (12) and (14) in problem (P1), aswell as Proposition 4. In the next section, we focus on solvingproblem (P2) by using the DP technique.

V. POLICY DESIGN FOR ON-GRID ENERGY

COST MINIMIZATION

This section studies the optimal on-grid energy costminimization policy for solving problem (P2), which isessentially a constrained DP problem. The optimal on-gridenergy minimization policy consists of two parts. One isthe optimal BS on/off policy, which decides the optimalBSs’ active operation probability ρ(t) in each horizon t .The other is the optimal on-grid energy purchase policy, whichdecides the amount of on-grid energy G(t) to purchase ineach horizon t . To provide insightful results for our consid-ered highly dynamic system, we aim at closed-form policydesign, which is generally challenging for the constrainedDP problem [30], [41]. Moreover, since the battery update,given as the last constraint in (P2), correlates ρ(t) with G(t)in each horizon, we need to jointly design the optimal BSon/off policy and the optimal on-grid energy purchase policy ingeneral. In the following, by studying the cost-to-go functionthat is defined based on the Bellman’s equations [30], wefirst investigate the optimal BS on/off policy, and show thatthe optimal BS on/off policy and the optimal on-grid energypurchase policy can be separately designed, and then focus ondesigning the optimal on-grid energy purchase policy.

A. Cost-to-Go Function

In this subsection, we define the cost-to-go function forproblem (P2). Due to the fluctuations of the on-grid energyprices, the MT density, as well as the renewable energyarrival rates over time, the decision of G(t) and ρ(t) ineach horizon t are related to both current and future val-ues of the on-grid energy prices, the MT density, and therenewable energy arrival rates, as well as the current storagelevel B(t) at the CES. We thus define the system statein horizon t as �(t) = (B(t), (λe(t), . . . , λe(T )), (a(t), . . . ,a(T )), (λm(t), . . . , λm (T ))).

Let LG (t) = max(E(t)−B(t)−λe(t), 0), the constraint (16)in problem (P2) can be rewritten as G(t) ≥ LG (t). Basedon the Bellman’s equations, for a given system state �(t) inhorizon t , we then define the cost-to-go function Jt (�(t)) forproblem (P2) as

Jt (�(t))=

⎧⎪⎪⎨

⎪⎪⎩

min G(T )≥LG (T ),ρ(T )∈[ρmin (T ),1]

a(T )G(T ), if t = T,

min G(t)≥LG (t),ρ(t)∈[ρmin (t),1]

a(t)G(t)+ Jt+1(�(t+1)|�(t)),

if 1 ≤ t < T .

(18)

When 1 ≤ t < T , the first term a(t)G(t) in (18) representsthe instantaneous on-grid energy cost in the current horizon t ,and the second term Jt+1(�(t + 1)|�(t)) gives the minimizedon-grid energy cost over all the future horizons from t + 1to T , where for a given �(t) and thus B(t), B(t + 1) in�(t + 1) is updated according to (8). When t = T , onlythe instantaneous on-grid energy cost is considered in (18).By finding the cost-to-go function Jt (�(t)) in each horizon t ,


one can equivalently obtain the optimal BS on/off policy andthe optimal on-grid energy purchase policy, which gives theoptimal ρ∗(t) and G∗(t) in each horizon t for problem (P2),respectively. However, due to the curse of dimensionality, thecomplexity to find ρ∗(t) and G∗(t) to minimize the cost-to-go function in each horizon increases exponentially overthe number of horizons T [30]. In the next two subsections,due to the generally correlated BS on/off policy and on-gridenergy purchase policy, we first study the optimal BS on/offpolicy under a given on-grid energy purchase policy, andshowed that the joint design of the optimal BS on/off policyand the optimal on-grid energy purchase policy can actuallybe separately conducted. Then by substituting the obtainedoptimal BS on/off policy into the cost-to-go function (18), wefocus on the optimal on-grid energy purchase policy.

B. Optimal BS On/Off Policy

This subsection studies the optimal BS on/off policy forproblem (P2), by supposing that an arbitrary on-grid energypurchase policy is given, i.e., the microgrid knows the amountof on-grid energy G(t) to purchase for a given system state�(t) in each horizon t .

We first study the impact of storage level B(t) on the cost-to-go function Jt ( (t)) in the following lemma.

Lemma 6: The cost-to-go function Jt ( (t)) in horizon t isnon-increasing over the current storage level B(t).

Proof: Please refer to Appendix B.Next, by studying the impact of ρ(t) in the current horizon

on the storage level B(t + 1) in the next horizon, we obtainthe following lemma.

Lemma 7: For any given on-grid energy purchase policy,the cost-to-go function Jt ( (t)) in horizon t is non-decreasingover ρ(t).

The proof of Lemma 7 can be easily obtained by applyingLemma 6 and the fact that for any given storage level B(t)and purchase amount G(t) in the current horizon, the storagelevel B(t + 1) in the next horizon is non-increasing over ρ(t)in the current horizon according to (6) and (8), and thus isomitted here for brevity.

Moreover, given in the following proposition, Lemma 7 canbe exploited to provide an optimal and yet simple BS on/offpolicy to minimize the overall on-grid energy cost in all Thorizons.

Proposition 8 (Optimal BS On/Off Policy): The optimalρ∗(t) in each horizon t for problem (P2) is given by

ρ∗(t) = ρmin (t), ∀t ∈ {1, . . . , T }, (19)

where ρmin (t) is given in Proposition 4 and depends on time-varying MT density λm(t).

Proposition 8 is obtained due to the fact that Jt ( (t))in each horizon t is non-decreasing over ρ(t), as givenin Lemma 7.

Remark 9: From Proposition 8, since a small ρ(t) yieldsa low energy demand E(t) of the BSs, and thus a low on-grid energy cost in general, the optimal ρ∗(t) in each horizont is selected as the minimum required ρmin(t) which is justsufficient to assure the required downlink transmission quality.

Based on ρ∗(t), each BS independently decides its on/offstatus in horizon t . It is worth noting that since the trafficloads of the inactive BSs are handed over to their neighboringactive BSs, as described in Section II, although the exact on/offstatus of the BSs are determined independently, the network-level downlink transmission quality can still be assured withρ∗(t) = ρmin (t). It is also observed from Proposition 4 that theoptimal ρ∗(t) = ρmin(t) generally varies over time to adaptto the variations of the MT density λm(t).

Finally, it is worth noting from Lemma 7 that since Jt ( (t))is non-decreasing over ρ(t), ρ∗(t) = ρmin(t) may not be theonly optimal solution in some time horizons. However, fromProposition 2 and Proposition 4, it is observed that ρmin(t)is not related to the value of G(t) for any path-loss exponentα > 2. Thus, by always selecting ρ∗(t) = ρmin(t) for eachhorizon, the joint design of the optimal BS on/off policy andthe optimal on-grid energy purchase policy can be separatelyconducted without any loss of optimality. In the next subsec-tion, we will focus on the design of the optimal on-grid energypurchase policy.

C. Optimal On-Grid Energy Purchase Policy

This subsection studies the on-grid energy purchase policyfor problem (P2). By substituting ρ∗(t) = ρmin (t) into (6), wecan obtain the minimum value of E(t), which is denoted asEmin(t) = E(t)|ρ(t)=ρmin (t), given by

Emin(t) = λBρmin(t)Pgap + λB Ps + PBλm(t)

μ, (20)

and accordingly, we denote LminG (t) = LG (t)|E(t)=Emin (t) =

max(Emin(T )−B(T )−λe(T ), 0). Thus, with ρ∗(t) = ρmin (t),we can easily simplify the cost-to-go function for problem (P2)in (18) as

Jt (�(t))=

⎧⎪⎨

⎪⎩

minG(T )≥LminG (T ) a(T )G(T ), if t = T,

minG(t)≥LminG (t) a(t)G(t)+ Jt+1(�(t+1)|�(t)),

if 1 ≤ t < T .

(21)

where the storage level B(t + 1) in system state �(t + 1) isupdated from B(t) in system state �(t) as

B(t + 1) = min (B(t) + λe(t) + G(t) − Emin(t), C) . (22)

However, unlike the design of optimal BS on/off policy,due to the fluctuations of the on-grid energy price a(t) overtime, the cost-to-go function Jt (�(t)) in (21) is generallyneither non-increasing nor non-decreasing over G(t) in eachhorizon t . Although based on (21), one can always find theoptimal G∗(t), the complexity of finding G∗(t) in each horizonincreases exponentially over the total number of horizons T ,due to the curse of dimensionality for the DP problem.As a result, in the following, to obtain tractable and insightfulon-grid energy purchase policy for problem (P2), we focuson designing a suboptimal on-grid energy purchase policy, bystudying the optimal solutions of G∗(t) for the last horizon Tand the horizon T − 1. We also assume the storage capacityC is sufficiently large with C ≥ max (Emin(1), . . . , Emin(T )),


such that the BSs’ demanded energy for each horizon can beproperly stored.

First, we look at the last horizon with t = T , and assume thesystem state �(T ) = (B(T ), λe(T ), a(T ), λm(T )) in horizonT is given. From (21), it is easy to find that the optimal G∗(T )in the last horizon T is given by

G∗(T ) = max(Emin(T ) − B(T ) − λe(T ), 0). (23)

It is also noted that the optimal G∗(T ) is a myopic solution,which minimizes the instantaneous on-grid energy cost in thecurrent horizon. Moreover, when G∗(T ) is myopic, the optimalρ∗(T ) that minimizes E(T ) and thus the instantaneous on-gridenergy cost a(T )G(T ) is also a myopic solution.

Next, we consider the horizon with t = T − 1.We assume the system state (T − 1) = (

B(T − 1),(λe(T − 1), λe(T )), (a(T − 1), a(T )), (λm(T − 1), λm(T ))

)

is given. We also assume a reasonably large storage withcapacity C ≥ Emin(T )−λe(T ), such that for any given λe(T ),Emin(T ) can always be satisfied if the CES is full of energy.Based on (21), we jointly consider the impact of G(T − 1) onthe instantaneous on-grid energy cost in the current horizonT −1 and the future on-grid energy cost JT (�(T )|�(T −1)),where the storage level B(T ) in the next horizon T is updatedfrom B(T − 1) according to (22), and obtain the optimalG∗(T − 1) in the following proposition.

Proposition 10: Given the system state �(T −1) in horizonT − 1, the optimal G∗(T − 1) for problem (P2) is determinedas follows:

1) In the high current storage regime (B(T−1) ≥ Emin(T )+Emin(T − 1) − λe(T − 1) − λe(T )):

G∗(T − 1) = max(Emin(T − 1) − B(T − 1)

− λe(T − 1), 0). (24)

2) In the low current storage regime (B(T −1) < Emin(T )+Emin(T − 1) − λe(T − 1) − λe(T )):

– For high future renewable energy case (λe(T ) ≥Emin(T )): G∗(T − 1) is also given by (24).

– For low future renewable energy case (λe(T ) <Emin(T )):

G∗(T − 1)

=

⎧⎪⎪⎨

⎪⎪⎩

max(Emin(T − 1) − B(T − 1)− λe(T − 1), 0), if a(T − 1) ≥ a(T ),

Emin(T )+Emin(T − 1)−λe(T − 1) − λe(T )− B(T − 1), if a(T − 1) < a(T ).

(25)

Proof: Please refer to Appendix C.Observation 11: From Proposition 10, the decision of

G∗(T − 1) is jointly determined by the fluctuations of MTdensity, on-grid energy prices, the renewable energy arrivalrates in both current and future horizons. Moreover, the on-grid energy G∗(T − 1) is over-purchased only when all thefollowing three conditions are satisfied:

1) The current storage level B(T − 1) is within the lowcurrent storage regime;

2) The future renewable energy λe(T ) alone cannot to satisfythe demanded energy Emin(T ) in the future;

3) The current on-grid energy price is lower than the futurewith a(T − 1) < a(T ).

When all the three conditions are satisfied, the microgrid pur-chases more energy than the demanded in the current horizon,so as to ensure both current and future energy demands canbe satisfied. In addition, it is also observed that if the on-gridenergy prices a(T − 1) = a(T ), G∗(T − 1) is not affected bythe fluctuations of the on-grid energy prices and becomes amyopic solution in all cases of Proposition 10, just as G∗(T )in (23).

Finally, we extend the above observations for the optimalG∗(t) obtained in horizon T and horizon T − 1 to theon-grid energy purchase decision in an arbitrary horizont ∈ {1, . . . , T }, and propose a suboptimal on-grid energypurchase policy for problem (P2) in the following, by jointlyconsidering the impact of storage capacity C .

Proposition 12 (Suboptimal On-Grid Energy PurchasePolicy): Denote G�(t) as the suboptimal solution of thepurchased on-grid energy to problem (P2) in each horizont ∈ {1, . . . , T }. The microgrid over-purchases the on-gridenergy in horizon t if all the three conditions in the followingare satisfied at the same time:

1) Condition #1: Low current storage level(min (B(t) − Emin(t) + λe(t), C) <

∑Tk=t+1 Emin(k) −

∑Tk=t+1 λe(k));

2) Condition #2: Low future renewable energy(∑T

k=t+1 λe(k) ≤ ∑Tk=t+1 Emin(k));

3) Condition #3: Low current on-grid energy price (a(t) <min (a(t + 1), . . . , a(T ))).

Let ω(t) = min(∑T

k=t+1 Emin(k) − ∑Tk=t+1 λe(k), C

).

Given the system state (t) in horizon t , G�(t) is given by

G�(t)=

⎧⎪⎪⎨

⎪⎪⎩

max (ω(t) + Emin(t) − λe(t) − B(t), 0) ,if Conditions #1-#3 hold,

max(Emin(t) − B(t) − λe(t), 0),otherwise.

(26)From Proposition 12, the microgrid over-purchases the low-

price energy in the current horizon for future usage onlywhen the current storage and future renewable supply areboth low. It is also easy to verify that G�(t) = G∗(t) whent = T or t = T − 1. Moreover, when a(t) = a(t ′),∀t, t ′ ∈ {1, . . . , T } and t �= t ′, G�(t) becomes the myopicsolution max(Emin(t)−B(t)−λe(t), 0) for all horizons, whichis similar to the case with t = T − 1 in Proposition 10.Moreover, it is also easy to find that as compared to theDP-based approach to search the optimal G∗(t) in eachhorizon by applying (21), the proposed suboptimal on-gridenergy purchase policy is of low complexity to implement.We will later validate the near-optimal performance of theproposed suboptimal on-grid energy purchase policy for themulti-horizon scenario by simulations in Section VI.

To conclude, by combining the optimal BS on/off policyand the suboptimal on-grid energy purchase policy, given inProposition 8 and Proposition 12, respectively, the on-gridenergy cost in the network can be minimized.


Fig. 3. Network profiles on the variations of λm (t), λe(t), and a(t) for asingle day.

VI. SIMULATION RESULTS

This section studies the proposed network-level on-gridenergy cost minimization policy by providing extensivenumerical and simulation results. We first illustrate the adapta-tion of ρ(t) and G(t) over horizons by applying the proposedpolicy. We then validate the performance of the proposedsuboptimal on-grid energy purchase policy. After that, westudy the effects of the prediction errors in terms of thenetwork profiles λe(t)’s, λm(t)’s, and a(t)’s. At last, weconduct a large-scale network-level simulation to comparethe performance of the proposed policy with two referenceschemes.

Without specified otherwise, we consider the followingsimulation parameters in this section. We set the basic energyconsumptions of each BS in the active and inactive modes asPa = 130W and Ps = 75W, respectively, the transmit powerof each active BS as PB = 20W , and the power amplifierparameter as μ = 21.3% [40]. We also set the noise powerσ 2 = 10−9W, the targeted SINR level β = 2, the path-loss exponent α = 4, and the maximum outage ε = 0.05to ensure a sufficiently high downlink successful transmissionprobability Psuc(t) in each horizon. According to the real datameasured in [40], [42], and [43], we consider the variationsof the MT density λm(t), the solar energy arrival rate λe(t),as well as the on-grid energy price a(t) over a single day, andshow them in Fig. 3. In particular, instead of λm(t), Fig. 3shows the active MT ratio θ(t) for each horizon t . By denotingthe total MT density in the network as λall

m > 0, we can obtainthe MT density in each horizon as λm(t) = λall

m θ(t). We setλall

m = 8×10−3/m2, and the BS density as λB = 5×10−4/m2.We also set the normalized storage capacity C of the CES,given in (8), as C = 0.2 (W/m2).

A. Illustration for Dynamic Network Operation

In this subsection, we illustrate the dynamic adaptationof the BSs’ active operation probability and the amount ofon-grid energy to purchase over horizons, by applying theoptimal BS on/off policy and the suboptimal on-grid energy

Fig. 4. Adaptations of ρ∗(t) and G�(t) and the variation of B(t) for asingle day.

purchase policy, given in Proposition 8 and Proposition 12,respectively.

By applying the network profiles given in Fig. 3, Fig. 4shows the variations of the storage level B(t), as well as theadaptations of the BSs’ active operation probability and theamount of purchased on-grid energy to these network profilesover T = 24 hours. From Proposition 8, the optimal ρ∗(t) =ρmin(t) in each horizon, where ρmin(t) given in Proposition 4varies monotonically over the MT density λe(t). It is thusobserved from Fig. 4 that ρ∗(t) follows the exact variationtrend of λe(t) in Fig. 3. It is also observed that when the solarenergy arrival rate is substantially large from t = 7 to t = 19in Fig. 3, the storage level B(t) in Fig. 4 is also quite high,and achieves the capacity of the CES in most horizons fromt = 7 to t = 19. However, when the solar energy arrival rateis approaching to zero from t = 1 to t = 6 and from t = 20to t = 24 in Fig. 3, the storage level B(t) in Fig. 4 is alsoalmost zero in each of these horizons. Moreover, from t = 1to t = 5, since the storage level is almost zero in Fig. 4,but the MT density is not low and the on-grid energy priceis non-decreasing in Fig. 3, it is observed from Fig. 4 thatthe purchased on-grid energy follows the variation trends ofthe MT density and thus is myopic solution in each of thesehorizons. At horizon t = 6, it is observed from Fig. 3 thata(6) at t = 6 is the lowest value among all the on-grid energyprices over T horizons. Thus, from the suboptimal on-gridenergy purchase policy given in Proposition 12, it is notedthat the purchased on-grid energy G(6) at t = 6 achievesthe highest value among all the T horizons. From t = 7 tot = 19, due to the large storage level B(t), the purchasedon-grid energy is decreasing in these horizons and becomeszero from t = 10 to t = 18 in Fig. 4. At last, from t = 19to t = 24, due to the almost zero storage level in Fig. 4 aswell as the large MT density in Fig. 3, the purchased on-gridenergy is largely increased in these horizons in Fig. 4.

B. Suboptimal Policy Performance Validation

Since the proposed BS on/off policy in Proposition 8 isoptimal, the suboptimality of the proposed on-grid energy


TABLE I

COMPARISON OF TOTAL ON-GRID ENERGY COST∑T

t=1 a(t)G(t) UNDER OPTIMAL AND SUBOPTIMAL POLICES

minimization policy is caused by the suboptimality of theproposed on-grid energy purchase policy in Proposition 12.Thus, by applying the optimal BS on/off policy, we com-pare the performance of the suboptimal on-grid energy pur-chase policy in Proposition 12 with the optimal on-gridenergy purchase policy that is obtained by exhaustive search.To search the optimal G∗(t), we first find the search range ofG(t) in each horizon t . From (21), the minimum required G(t)is given by Gmin(t) = max(Emin(t)−B(t)−λe(t), 0). It is alsoeasy to obtain that to save the on-grid energy cost, the max-imum required G(t) is given by Gmax(t) = ∑T

k=t Emin(k) −∑T

k=t λe(k), which can just satisfy the energy demand ofall the BSs from the current to all future horizons. Then,we apply the DP technique from [30] to search the optimalG∗(t) ∈ [Gmin(t), Gmax (t)] in each horizon t , where the rangeof [Gmin(t), Gmax (t)] is quantized with a sufficiently smallstep-size 1.0 × 10−8. In Table I, we compare

∑Tt=1 a(t)G∗(t)

that is obtained by the optimal search with∑T

t=1 a(t)G�(t)that is obtained by applying the proposed suboptimal on-gridenergy purchase policy in Proposition 12. Due to the curseof dimensionality to apply the DP technique for searching theoptimal G∗(t), we only consider the total number of horizonsT ∈ {1, .., 5} in Table I, using network profiles starting fromt = 2 in Fig. 3 as an example. For total on-grid energy costswith network profiles starting from other t , t �= 2, we observesimilar performance as in Table I and thus omit them forbrevity. It is observed from Table I that both the optimal andsuboptimal total on-grid energy cost increases over T . It is alsoobserved that as the number of horizons T increases, since thenumber of optimal G∗(t) and suboptimal G�(t) with differentvalues in each horizon t also increases in general, the absoluteerror, given by

∑Tt=1 a(t)G�(t) − ∑T

t=1 a(t)G∗(t), increasesover T accordingly. However, it is observed that the absoluteerror at each T is quite small and is within 4.5 × 10−11. As aresult, the proposed suboptimal on-grid energy purchase policyin Proposition 12 and thus the proposed suboptimal on-gridenergy minimization policy in Section V can achieve near-optimal performance.

C. Effects of Prediction Errors

In this subsection, by applying our proposed on-grid energycost minimization policy in Section V, we study the effects ofthe prediction errors for λe(t)’s, λm(t)’s, and a(t)’s.

Specifically, we assume prediction errors �e(t), �m(t), and�a(t) exist in each horizon t for λe(t), λm(t), and a(t),respectively. We also assume each of �e(t)’s, �m(t)’s, and�a(t)’s are identical and independently distributed zero-meanGaussian random variables over different horizons, where thestandard deviations are denoted by ηe, ηm , and ηa , respectively.

Fig. 5. Effects of the prediction errors on the network performance.

Since the prediction errors �e(t), �m(t), and �a(t) can allbe large due to the large T = 24 under consideration, basedon the values of λe(t) ∈ [1 × 10−4 W/m2, 0.22 W/m2],λm(t) ∈ [2 × 10−4/m2, 1.3 × 10−3/m2], and a(t) ∈ [20 ×10−5 $/W, 5.9 × 10−5 $/W] in Fig. 3, we consider reason-ably large standard deviations for the prediction errors withηe = 0.1, ηm = 0.01, and ηa = 0.001 in each horizon,respectively. As a result, under the consideration of predictionerrors, the microgrid adopts λe(t)+�e(t), λm(t)+�m(t), anda(t) + �a(t) as the solar energy arrival rate, MT density, andon-grid energy price in each horizon t , respectively, to decideρ∗(t) and G�(t). However, since the storage level B(t) in eachhorizon can be perfectly known by the microgrid, the storagelevel B(t +1) in horizon t +1 is still updated according to theactual solar energy arrival rate λe(t) in horizon t . To show theeffects of the prediction errors on the network performance, weconsider four scenarios as follows: 1) no-error scenario, whereno prediction errors exist in any of a(t), λe(t), and λm(t);2) single-error scenario, where the prediction errors only existin one of a(t), λe(t), and λm(t); 3) double-error scenario,where the prediction errors exist only in two of a(t), λe(t), andλm(t); and 4) triple-error scenario, where the prediction errorsexist in all a(t), λe(t), and λm(t). In particular, for the single-error scenario, we consider the case with the prediction errorsonly in a(t), and for the double-error scenario, we considerthe case with the prediction errors only in a(t) and λe(t).We also observe similar network performance under othercases in each of these two scenarios, which are thus omittedfor brevity.

Fig. 5 compares the total on-grid energy cost∑T

t=1 a(t)G(t)over the number of horizons T under the four consideredscenarios. For each of the three scenarios with single-error,


double-error, and triple-error, at each T in Fig. 5, we consider1000 realizations of the T horizons with prediction errors,and take the average on-grid energy cost in T horizons overthe 1000 realizations as the total on-grid energy cost forcomparison. It is observed from Fig. 5 that the total on-grid energy costs under the three scenarios with single-error,double-error, and triple-error are all always very close to thatunder the no-error scenario. Moreover, although the predictionerrors generally increase over the single-error, double-error,and triple-error scenarios, the total on-grid energy cost ateach T only slightly increases along these three scenarios. Thisis mainly because that we focus on the average total on-gridenergy cost minimization in this paper, where the combinedprediction errors from a(t), λe(t), and λm(t), each of which isof zero-mean, do not largely affect the network performance.As a result, our proposed policy is robust to the predictionerrors for average on-grid energy cost reduction across thenetwork. It is also observed from Fig. 5 that the total on-gridenergy cost generally increases with the number of horizons T ,as expected.

D. Geo-DP Based Scheme Versus Reference Schemes

To show the performance of our proposed scheme based onthe Geo-DP approach, where the BSs are coordinated froma network-level to serve the MTs, this subsection conductsMonte Carlo simulations to compare the proposed scheme withtwo reference schemes, which are specified as follows.

First, we consider a simple reference scheme without BSs’mutual coordination. In this scheme, each BS individuallydecides whether to be active or not in each horizon: if thereexist MTs locating in a BS’s coverage, it keeps active, orbecomes inactive, otherwise. We assume the BS density λB

is sufficiently large, such that when all the BSs are active,the downlink transmission quality is assured in the network.Thus, since only BSs with no associated MTs become inactive,the downlink transmission quality is assured. The total energydemand of the BSs is calculated according to (3) and (4),depending on whether a BS is active or not, respectively.

Second, we consider a reference scheme with cluster-basedBS coordination, which has been proposed in the existingliterature to coordinate the BSs’ on/off operations in a large-scale network (see, e.g., [28] and [29]). However, it is notedthat due to the considered different performance metrics,the existing cluster-based BS coordination policy cannot beapplied directly. For example, in [28] and [29], the authorsconsidered a blocking probability constraint for the new MT’saccess as the QoS constraint, while we use the SINR-baseddownlink transmission quality as the QoS constraint. As aresult, we consider the following cluster-based BS coordi-nation scheme for comparison. Specifically, we assume eachcluster includes at most two BSs, and any two BSs that arelocated within L > 0 meters form a cluster. Each BS canbelong to at most one cluster. If a BS does not belong toany cluster, it decides its on/off status as that in the schemewith no BS coordination. For any two BSs that belong to onecluster, the BS that has less associated MTs becomes inactive,while the other becomes active and also helps to serve the

Fig. 6. Network performance comparison with two reference schemes.

MTs of the inactive BS. The total energy consumption of allthe BSs is also calculated as the same as that in the schemewith no BS coordination. It is easy to verify that the downlinktransmission quality can be assured with a small L, where theMTs are always connected to the active BSs that are locatedclosely for good communication quality.

To obtain the total on-grid energy cost under our proposedscheme and the two reference schemes, we conduct a large-scale network simulation. We generate �(λB) for BSs and�(λm(t)) for MTs in a square of [0m, 1000m]×[0m, 1000m],according to the method described in [16]. Due to the com-putation complexity that increases substantially over bothnetwork size as well as the number of horizons T , we setT = 3 and the number of slots within each horizon as N = 1in this simulation, and take network profiles of λe(t) and θ(t)from Fig. 3 for t ∈ {7, 8, 9}. For the cluster-based scheme,we use a small L with L = 100m to assure the downlinktransmission quality. We consider in total 20000 network real-izations, and take the average value over the 20000 realizationsas the network performance for each considered scheme. Forsimplicity, we assume identical on-grid energy price witha(t) = 1 ($/W) in each horizon t . In this case, it is easyto find that the on-grid energy purchase decision for all threeconsidered schemes is always myopic in each horizon fromSection V. Similar performance can also be observed for allthree schemes with non-identical on-grid energy prices, whichare thus omitted here for brevity.

Fig. 6 compares the total on-grid energy cost acrossT horizons over the total MT density λall

m . It is observed fromFig. 6 that as the total MT density λall

m increases, since theactual MT density λm(t) = λall

m θ(t) also increases, the totalon-grid energy cost of all three schemes increases accordingly,so as to properly serve the increased MTs in the network.It is also observed that at each value of λall

m , the total on-gridenergy cost under the proposed network-level BS coordinationusing the Geo-DP approach is always the minimum, thatunder the cluster-based scheme is always the medium, andthat under the scheme with no BS coordination is alwaysthe largest. Moreover, it is also worth noting that althoughwe only show the performance of the cluster-based scheme


with two BSs in one cluster, when the number of BSs in eachcluster increases, the performance of the cluster-based schemeis expected to gradually approach our proposed network-level BS coordination scheme. However, unlike our proposedclosed-form optimal BS on/off operation policy, which haslow-complexity to coordinate all the BSs’ on/off operationsin the network, the complexity of coordinating the increasednumber of BSs in each cluster can be largely increased forthe cluster-based scheme to assure the downlink transmissionquality [28], [29]. As a result, our proposed network-level BScoordination scheme based on the Geo-DP approach can moreefficiently solve the on-grid energy cost minimization problemfor a large-scale network.

VII. CONCLUSION

In this paper, we considered a large-scale green cellularnetwork, where the BSs are aggregated as a microgrid withhybrid energy supplies and an associated CES. We proposed anew Geo-DP approach to jointly apply stochastic geometry andthe DP technique to conduct network-level dynamic systemdesign. By optimally selecting the BSs’ active operation prob-ability as well as the amount of on-grid energy to purchase ineach horizon, we studied the on-grid energy cost minimizationproblem. We first studied the optimal BS on/off policy, whichshows that the optimal BSs’ active operation probability ineach horizon is just sufficient to assure the required downlinktransmission quality with time-varying load in a large-scalenetwork. We then proposed a suboptimal on-grid energy pur-chase policy, where the low on-grid energy is over-purchasedin the current horizon only when both the current storagelevel and future renewable energy level are both low. We alsocompared our proposed policy with the existing schemes,and showed that our proposed policy can efficiently save theon-grid energy cost in the large-scale network. It is also ofour interest to minimize the network-level on-grid energy costby jointly considering the uplink and downlink traffic loads inour future work.

APPENDIX APROOF TO LEMMA 5

Lemma 5 is proved by contradiction. From Proposition 4,for any given λm(t), ρmin(t) is the unique solution to Psuc(t) =1 − ε. We then suppose Psuc(t) = 1 − ε holds for the twofollowing cases: case 1 with ρmin(t) = ρ1 and λm(t) = λ1,and case 2 with ρmin (t) = ρ2 and λm(t) = λ2, where λ2 > λ1and ρ2 ≤ ρ1. From (10), since for any given u ∈ (0,∞),

both e−π λm (t)B

W v(β) uπλB ρ(t) and e

−b[

uπλBρ(t)

]α/2

monotonically

increase over ρ(t), and e−π λm (t)B

W v(β) uπλB ρ(t) monotonically

decreases over λm(t), we can find that Psuc(t) under case 1 isstrictly larger than that under case 2, which contradicts with theassumption that Psuc(t) = 1 − ε under both cases. As a result,when λm(t) increases, ρmin (t) must increase accordingly toensure that Psuc(t) = 1 − ε. Lemma 5 thus follows.

APPENDIX BPROOF TO LEMMA 6

Lemma 6 is proved based on the mathematical inductionmethod. First, at the last horizon t = T , the optimal G∗(T )

is given as G∗(T ) = max(E(T ) − B(T ) − λe(T ), 0). As aresult, G∗(T ) and thus JT ( (T )) = a(T )G∗(T ) are non-increasing over B(T ). Next, suppose at horizon t + 1, t ∈{1, . . . , T −1},Jt+1( (t +1)) is non-increasing over B(t +1).Then, at horizon t , when B(t) increases, since B(t + 1)in (8) is non-decreasing, the future cost Jt+1( (t + 1)| (t))is non-increasing. Moreover, similar to the case in horizon T ,the current cost a(t)G(t) is also non-increasing over B(t).Therefore, by combing the current and future costs, we findthat Jt ( (t)) is also non-increasing over B(t). Lemma 6 thusfollows.

APPENDIX CPROOF SKETCH OF PROPOSITION 10

First, for the case in high current storage regime, underthe assumption that C ≥ Emin(T ) − λe(T ), it is easy to findthat B(T ) ≥ Emin(T ) − λe(T ), where from (22) B(T ) =min (B(T − 1) + λe(T − 1) + G(T − 1) − Emin(T − 1), C)for a given B(T − 1). Thus, we obtain G∗(T ) = 0 from (23).As a result, according to (21), since JT (�(T )|�(T − 1)) = 0,G∗(T − 1) is given by (24). Next, for the case in lowcurrent storage regime, since G∗(T ) is not assuredto be 0 or Emin(T ) − B(T ) − λe(T ) in general, theproof is more complicated, and thus only the sketchof proof is provided for this case. Specifically, weconsider two options. In the first option, we assumemin(B(T − 1) + λe(T − 1) + G(T − 1) − Emin(T − 1),C) ≥ Emin(T ) − λe(T ) and thus G∗(T ) = 0. We findG∗(T − 1) according to (21) under this assumptionfor the first option. In the second option, we assumemin(B(T − 1) + λe(T − 1) + G(T − 1) − Emin(T − 1),C) < Emin(T ) − λe(T ) and thus G∗(T ) = Emin(T ) −B(T ) − λe(T ). Similarly, we can find G∗(T − 1) accordingto (21) under the corresponding assumption for the secondoption. Then, we compare the achieved JT (�(T − 1)) underboth options and take G∗(T − 1) that achieves a smallerJT (�(T − 1)) as the optimal solution for this case, which isgiven in (25). This completes the proof to Proposition 10.

REFERENCES

[1] K. Davaslioglu and E. Ayanoglu, “Quantifying potential energy effi-ciency gain in green cellular wireless networks,” IEEE Commun.Surveys Tuts., vol. 16, no. 4, pp. 2065–2091, 4th Quart., 2014.

[2] J. Wu, S. Rangan, and H. Zhang, Green Communications: TheoreticalFundamentals, Algorithms and Applications. Boca Raton, FL, USA:CRC Press, 2012.

[3] M. A. Marsan, L. Chiaraviglio, D. Ciullo, and M. Meo, “Optimal energysavings in cellular access networks,” in Proc. IEEE Int. Conf. Commun.Workshops, Jun. 2009, pp. 1–5.

[4] L. M. Correia et al., “Challenges and enabling technologies for energyaware mobile radio networks,” IEEE Commun. Mag., vol. 48, no. 11,pp. 66–72, Nov. 2010.

[5] S. Zhou, J. Gong, Z. Yang, Z. Niu, and P. Yang, “Green mobile accessnetwork with dynamic base station energy saving,” ACM MobiCom,vol. 9, no. 262, pp. 10–12, Sep. 2009.

[6] E. Oh, K. Son, and B. Krishnamachari, “Dynamic base station switching-on/off strategies for green cellular networks,” IEEE Trans. WirelessCommun., vol. 12, no. 5, pp. 2126–2136, May 2013.

[7] S. Luo, R. Zhang, and T. J. Lim, “Optimal power and range adaptationfor green broadcasting,” IEEE Trans. Wireless Commun., vol. 12, no. 9,pp. 4592–4603, Sep. 2013.


[8] S. Cai, Y. Che, L. Duan, J. Wang, S. Zhou, and R. Zhang, “Green 5Gheterogeneous networks through dynamic small-cell operation,” IEEE J.Sel. Areas Commun., vol. 34, no. 5, pp. 1103–1115, May 2016.

[9] K. Wu et al., “hJam: Attachment transmission in WLANs,” IEEE Trans.Mobile Comput., vol. 12, no. 12, pp. 2334–2345, Dec. 2013.

[10] G. Wang, S. Zhang, K. Wu, Q. Zhang, and L. M. Ni, “TiM: Fine-grainedrate adaptation in WLANs,” IEEE Trans. Mobile Comput., vol. 15, no. 3,pp. 748–761, Mar. 2016.

[11] L. Wang, K. Wu, J. Xiao, and M. Hamdi, “Harnessing frequency domainfor cooperative sensing and multi-channel contention in CRAHNs,”IEEE Trans. Wireless Commun., vol. 13, no. 1, pp. 440–449, Jan. 2014.

[12] H. Li, K. Wu, Q. Zhang, and L. M. Ni, “CUTS: Improving channelutilization in both time and spatial domain in WLANs,” IEEE Trans.Parallel Distrib. Syst., vol. 25, no. 6, pp. 1413–1423, Jun. 2014.

[13] J. Xu, L. Duan, and R. Zhang, “Energy group buying withloading sharing for green cellular networks,” IEEE J. Sel. AreasCommun., vol. 34, no. 4, pp. 786–799, Apr. 2016. [Online]. Available:http://arxiv.org/pdf/1508.06093v1.pdf

[14] C. K. Ho and R. Zhang, “Optimal energy allocation for wirelesscommunications with energy harvesting constraints,” IEEE Trans. SignalProcess., vol. 60, no. 9, pp. 4808–4818, Sep. 2012.

[15] H. S. Dhillon, Y. Li, P. Nuggehalli, Z. Pi, and J. G. Andrews, “Fun-damentals of heterogeneous cellular networks with energy harvest-ing,” IEEE Trans. Wireless Commun., vol. 13, no. 5, pp. 2782–2797,May 2014.

[16] D. Stoyan, W. S. Kendall, and J. Mecke, Stochastic Geometry and ItsApplications, 2nd ed. New York, NY, USA: Wiley, 1995.

[17] D. Gunduz, K. Stamatiou, N. Michelusi, and M. Zorzi, “Designingintelligent energy harvesting communication systems,” IEEE Commun.Mag., vol. 52, no. 1, pp. 210–216, Jan. 2014.

[18] S. Ulukus et al., “Energy harvesting wireless communications: A reviewof recent advances,” IEEE J. Sel. Areas Commun., vol. 33, no. 3,pp. 360–381, Mar. 2015.

[19] H. Li, J. Xu, R. Zhang, and S. Cui, “A general utility optimizationframework for energy-harvesting-based wireless communications,” IEEECommun. Mag., vol. 53, no. 4, pp. 79–85, Apr. 2015.

[20] J. Xu, L. Duan, and R. Zhang, “Cost-aware green cellular networks withenergy and communication cooperation,” IEEE Commun. Mag., vol. 53,no. 5, pp. 257–263, May 2015.

[21] T. Han and N. Ansari, “On optimizing green energy utilization forcellular networks with hybrid energy supplies,” IEEE Trans. WirelessCommun., vol. 12, no. 8, pp. 3872–3882, Aug. 2013.

[22] Y. Mao, G. Yu, and Z. Zhang, “On the optimal transmission policy inhybrid energy supply wireless communication systems,” IEEE Trans.Wireless Commun., vol. 13, no. 11, pp. 6422–6430, Nov. 2014.

[23] D. W. K. Ng, E. S. Lo, and R. Schober, “Energy-efficient resourceallocation in OFDMA systems with hybrid energy harvesting basestation,” IEEE Trans. Wireless Commun., vol. 12, no. 7, pp. 3412–3427,Jul. 2013.

[24] Y. Mao, J. Zhang, and K. B. Letaief, “A Lyapunov optimization approachfor green cellular networks with hybrid energy supplies,” IEEE J. Sel.Areas Commun., vol. 33, no. 12, pp. 2463–2477, Dec. 2015. [Online].Available: http://arxiv.org/pdf/1509.01886v2.pdf

[25] J. Xu and R. Zhang, “CoMP meets smart grid: A new communicationand energy cooperation paradigm,” IEEE Trans. Veh. Technol., vol. 64,no. 6, pp. 2476–2488, Jun. 2015.

[26] Y.-K. Chia, S. Sun, and R. Zhang, “Energy cooperation in cellularnetworks with renewable powered base stations,” IEEE Trans. WirelessCommun., vol. 13, no. 12, pp. 6996–7010, Dec. 2014.

[27] Y. Guo, J. Xu, L. Duan, and R. Zhang, “Joint energy and spec-trum cooperation for cellular communication systems,” IEEE Trans.Commun., vol. 62, no. 10, pp. 3678–3691, Oct. 2014.

[28] S. Zhou, J. Gong, and Z. Niu, “Sleep control for base stationspowered by heterogeneous energy sources,” in Proc. Int. Conf. ICTConverg. (ICTC), Oct. 2013, pp. 666–670.

[29] J. Gong, J. S. Thompson, S. Zhou, and Z. Niu, “Base station sleepingand resource allocation in renewable energy powered cellular networks,”IEEE Trans. Commun., vol. 62, no. 11, pp. 3801–3813, Nov. 2014.

[30] D. P. Bertsekas, Dynamic Programming and Optimal Control, vol. 1.Belmont, MA, USA: Athena Scientific, 2005.

[31] X. Fang, S. Misra, G. Xue, and D. Yang, “Smart grid—The new andimproved power grid: A survey,” IEEE Commun. Surveys Tuts., vol. 14,no. 4, pp. 944–980, 4th Quart., 2012.

[32] K. Huang, “Spatial throughput of mobile ad hoc networks poweredby energy harvesting,” IEEE Trans. Inf. Theory, vol. 59, no. 11,pp. 7597–7612, Nov. 2013.

[33] S. Lee, R. Zhang, and K. Huang, “Opportunistic wireless energyharvesting in cognitive radio networks,” IEEE Trans. Wireless Commun.,vol. 12, no. 9, pp. 4788–4799, Sep. 2013.

[34] T. A. Khan, P. Orlik, and K. J. Kim, “A stochastic geometry analysis ofcooperative wireless networks powered by energy harvesting,” in Proc.IEEE Int. Conf. Commun. (ICC), Jun. 2015, pp. 1988–1993.

[35] Y. L. Che, L. Duan, and R. Zhang, “Spatial throughput maximizationof wireless powered communication networks,” IEEE J. Sel. AreasCommun., vol. 33, no. 8, pp. 1534–1548, Aug. 2015.

[36] C. Joe-Wong, S. Sen, S. Ha, and M. Chiang, “Optimized day-aheadpricing for smart grids with device-specific scheduling flexibility,” IEEEJ. Sel. Areas Commun., vol. 30, no. 6, pp. 1075–1085, Jul. 2012.

[37] S. Sesia, I. Toufik, and M. Baker, LTE—The UMTS Long Term Evolu-tion: From Theory to Practice. New York, NY, USA: Wiley, 2009.

[38] F. Baccelli and B. Blaszczyszyn, Stochastic Geometry and WirelessNetworks: Theory, vol. 1. Norwell, MA, USA: NOW Publishers, 2009.

[39] J. G. Andrews, F. Baccelli, and R. K. Ganti, “A tractable approach tocoverage and rate in cellular networks,” IEEE Trans. Commun., vol. 59,no. 11, pp. 3122–3134, Nov. 2011.

[40] Energy Efficiency Analysis of the Reference Systems, Areasof Improvements and Target Breakdown. [Online]. Available:http://cordis.europa.eu/docs/projects/cnect/3/247733/080/deliverables/001-EARTHWP2D23v2.pdf

[41] A. Fu, E. Modiano, and J. Tsitsiklis, “Optimal energy allocation fordelay-constrained data transmission over a time-varying channel,” inProc. IEEE INFOCOM, Mar./Apr. 2003, pp. 1095–1105.

[42] A. Andreas and T. Stoffel. (2006). NREL Report No. DA-5500-56509.University of Nevada (UNLV), Las Vegas, Nevada (Data). [Online].Available: http://dx.doi.org/10.5439/1052548

[43] Hourly Ontario Energy Price. [Online]. Available: http://www.ieso.ca/Pages/Power-Data/price.aspx

Yue Ling Che (S’11–M’15) received thePh.D. degree from Nanyang TechnologicalUniversity, Singapore, in 2014. From 2014to 2016, she was a Post-Doctoral ResearchFellow with the Engineering Systems and DesignPillar, Singapore University of Technology andDesign. She is currently an Assistant Professorwith the College of Computer Science andSoftware Engineering, Shenzhen University, China.Her current research interests include greencommunications, wireless information and energy

transfer, cognitive communications, and stochastic geometry.

Lingjie Duan (S’09–M’12) received the B.Eng.degree from the Harbin Institute of Technologyin 2008, and the Ph.D. degree from The ChineseUniversity of Hong Kong in 2012. He is an Assis-tant Professor of Engineering Systems and Designwith the Singapore University of Technology andDesign (SUTD). In 2011, he was a Visiting Scholarwith the Department of Electrical Engineering andComputer Sciences, University of California atBerkeley, Berkeley, CA, USA. He is currently lead-ing the Network Economics and Optimization Lab-

oratory, SUTD. His research interests include network economics and gametheory, cognitive communications and cooperative networking, energy har-vesting wireless communications, and network security. He is an Editor ofthe IEEE COMMUNICATIONS SURVEYS AND TUTORIALS, and is a SWATTeam Member of the IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY.He currently serves as a Guest Editor of the IEEE JOURNAL ON SELECTED

AREAS IN COMMUNICATIONS Special Issue on Human-in-the-Loop MobileNetworks, and also serves as a Guest Editor of the IEEE Wireless Communi-cations Magazine. He also serves as a Technical Program Committee Mem-ber of many leading conferences in communications and networking (e.g.,ACM MobiHoc, IEEE SECON, INFOCOM, and NetEcon). He received the10th IEEE ComSoc Asia-Pacific Outstanding Young Researcher Award in2015, the Hong Kong Young Scientist Award (Finalist in Engineering Sciencetrack) in 2014, and the CUHK Global Scholarship for Research Excellencein 2011.


Rui Zhang (S’00–M’07–SM’15) received theB.Eng. (Hons.) and M.Eng. degrees from theNational University of Singapore in 2000 and 2001,respectively, and the Ph.D. degree from StanfordUniversity, Stanford, CA, USA, in 2007, all inelectrical engineering. From 2007 to 2010, he waswith the Institute for Infocomm Research, A*STAR,Singapore, where he currently holds a SeniorResearch Scientist joint appointment. Since 2010, hehas been with the Department of Electrical and Com-puter Engineering, National University of Singapore

where he is currently an Associate Professor. His current research interestsinclude energy-efficient and energy-harvesting-enabled wireless communica-tions, wireless information and power transfer, multiuser MIMO, cognitiveradio, smart girds, and optimization methods. He has authored or co-authored

over 200 papers. He has served for over 30 IEEE conferences as a memberof the technical program committee and the organizing committee. He iscurrently an Elected Member of the IEEE Signal Processing Society SPCOMand SAM Technical Committees, and serves as the Vice Chair of theIEEE ComSoc Asia-Pacific Board Technical Affairs Committee. He is anEditor for the IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, theIEEE TRANSACTIONS ON SIGNAL PROCESSING, and the IEEE JOURNALON SELECTED AREAS IN COMMUNICATIONS (Green Communications andNetworking Series). He was listed as a Thomson Reuters Highly CitedResearcher in 2015. He was a co-recipient of the Best Paper Award fromthe IEEE PIMRC in 2005, and the IEEE Marconi Prize Paper Award inWireless Communications in 2015. He was a recipient of the 6th IEEECommunications Society Asia-Pacific Best Young Researcher Award in 2011,the Young Investigator Award and the Young Researcher Award of theNational University of Singapore in 2011 and 2015, respectively.

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