Availability-Aware Cell Association for Hybrid Power Supply Networks with Adaptive Bias

Transcription

1 Avaiabiity-Aware Ce Association for Hybrid Power Suppy Networks with Adaptive Bias Fanny Parzysz, Member, IEEE, and Christos Verikoukis, Senior Member, IEEE 1 ariv: v2 [cs.it] 12 Ju 2017 Abstract New chaenges have emerged from the integration of renewabe energy sources within the conventiona eectrica grid which powers base stations (BS). Energy-aware traffic offoading brings a promising soution to maintain the user performance whie reducing the carbon footprint. Focusing on downink ceuar networks consisting of on-grid, off-grid and hybrid BSs, we propose a nove poweraware biased ce association where each user independenty partitions BSs into two sets and appies different association biases for each, depending on the type of power, renewabe or not, that can be requested for service. The gain provided by such strategy regarding the probabiity of power outage and the average grid power consumption is investigated. To capture their dua nature, the bias appied for association with a hybrid BS is not constant among users nor over time, and is dynamicay taiored to the fuctuations of the BS battery eve, the user power requirement and the estimated power consumed to serve other users potentiay associated with the same BS. Such approach aows to efficienty share the avaiabe energy among BSs and turns high heterogeneity in the BS powering into advantage. Index Terms Downink ceuar networks, user association, energy harvesting, bias optimization, power avaiabiity, energy consumption, stochastic geometry. I. INTRODUCTION The next-generation (5G) systems are expected to serve an unprecedented number of devices, estimated at over six connected terminas per person [1], and to argey rey on sma-ce base stations (BS), i.e. ow-powered radio access nodes having a coverage range from some tens Fanny Parzysz was with the Eectronics Department, University of Barceona, Spain (e-mai: fanny.parzysz@ieee.org). Christos Verikoukis is with the Teecommunications Technoogica Centre of Cataonia (CTTC), Castedefes, Spain (e-mai: cveri@cttc.es).

2 2 to some hundreds meters. The fast escaation of the energy demand, together with increasing environmenta concerns on greenhouse gas emissions, has urged the integration of renewabe energy sources [2 5], resuting in networks with heterogeneous power suppy, composed of (i) on-grid BS, soey connected to the conventiona carbon-based power grid, (ii) off-grid BSs, soey reying on energy harvesting and (iii) hybrid BSs, combining both types of power suppy. Traffic offoading was originay proposed to boost the network capacity, by everaging underused spectrum across the different existing radio access technoogies [6, 7] and efficienty rerouting the user traffic towards avaiabe pico-bss, femto-bss or WiFi hot spots. But it aso pays a fundamenta roe in green wireess ceuar networks. A wide range of energy-aware offoading strategies has been proposed for on-grid networks [8 10]. However, such conventiona approaches do not encompass the unique chaenges raised by energy harvesting [11]. Firsty, renewabe energy is generay unreiabe and unpredictabe, depending on the weather condition. Secondy, the traffic oad may not be distributed in accordance to the energy harvesting random process, eading to energy waste in parts of the network and energy shortage in other parts. Thirdy, the coexistence of different power suppies within the same network, each having its own operating characteristics, cas for a refined management of the avaiabe energy. Optimizing the user association issue in sma-ces networks with heterogeneous power suppy has been investigated in the iterature with the objective of minimizing the grid energy consumption, e.g. in [11 13], maximizing the data rate [14, 15], baancing the trade-off existing between traffic deay and power consumption [16] or minimizing the outage probabiity due to energy shortage [17]. The proposed optimized decisions are processed at a centra (possiby virtua) node or are impemented in a distributed manner through iterative agorithms. Athough in both cases, optimaity is reached ony through extensive causa (possiby non-causa) information exchange on the instantaneous channe and battery states, the extra cost of such additiona signaing is generay ignored in the evauation of the overa energy performance and thus, questions the gains provided by centraized strategies. This motivates us to rather focus on distributed one-shot ce association schemes, where each user associates with a BS independenty of others, using oca CSI/BSI ony, and in a seforganized manner. But the resuted information shortage, jointy with the uncertainty in the energy arrivas and battery imitations, (i) ets the possibiity for users to associate with a BS that cannot guarantee service due to ow battery eve and (ii) may resut in poor energy management, by excessivey draining the BS batteries at each time sot or conversey, by underusing the avaiabe

3 3 renewabe energy. Whie this first issue has been addressed in our previous work [18], we here propose to reguate the energy consumption from both grid and renewabe suppies by the use of association weights, or biases, that are appied to artificiay squeeze or extend the BS coverage. A genera framework has been proposed in [19] to assess the impact of biases on the performance of muti-tier networks with RF energy harvesting, and severa anayses have been provided, notaby in [15, 20] for throughput optimization and outage probabiity respectivey. But the strategies proposed in these works consider association biases which ony depend on the BS tier, irrespective of the BS current battery eve or the user power requirement. The use of such constant biases cannot capture the dua nature of hybrid base stations, since it does not differentiate in this case the consumed carbon-based grid energy and the renewabe one, harvested from the environment. Dynamicay adapting the association biases to the instantaneous energy resource and user requirement opens perspectives on green traffic offoading that have not been expored so far. Contributions: In this paper, we aim to minimize the power consumed from non-renewabe sources whie meeting a received power constraint at any served users, by utiizing the poweraware ce association of [18] and proposing for it a nove strategy based on adaptive biases. To our best knowedge, this work is the first to propose and anayze non-constant adaptive biases for user association. Different from existing schemes, our approach is user-centric and ony requires periodica broadcast of the BS battery eves. Each user computes, independenty from others, the energy required by neighboring BSs to satisfy a received power constraint over one time sot and then, partitions BSs depending on whether or not it can be served from renewabe energy. Next, biasing is appied for association decision to prompt users to be served by BSs having sufficient renewabe green power. In this work, we propose a nove approach where biases are dynamicay taiored, at each user and time sot, to the energy stored in the BS battery, the user required power, accounting for path-oss and shadowing, but aso the estimated power consumed to serve other users potentiay associated with the same BS. Next, adjusting the association biases aows to reguate the average amount of energy stored in the BS battery, and thus to contro the probabiity of power outage and the grid power consumption. Anayzing such trade-off is the second objective of this work. As most of sma-ce infrastructures are opportunisticay depoyed, resuting in irreguary-shaped networks, modeing the node position as random variabes aows to anayze the network performance using toos of

4 4 TABLE I CONSIDERED NOTATIONS k/j / B / λ Considered BS / User Power buffer state / Lowest buffer state providing avaiabiity -BS position in the network (PPP / density) P (A) A () j G () j / Λ (A) / Λ (G) Subset of Avaiabe -BSs, serving user j from renewabe energy Subset of Non-avaiabe -BSs, serving user j from the grid suppy (p ) / P(G) (p ) Probabiity to associate with a -BS and request green/grid power, given a battery state U / ω User position in the network (PPP / density) Ω (A) / Ω (G) P Rx / P (max) Tx p kj Density of the users served by a -BS from renewabe source/grid suppy Received power constraint / Maximum power consumed from the grid suppy Power required to send data from BS k to user j P (A ) T (m ) / P (G ) T (m ) Probabiity that a -BS consumes exacty m power units from the battery / grid P (G) v () / P () Average power consumed from the grid at a -BS Probabiity vector and transition matrix of the battery states at a -BS stochastic geometry and aeviates the need for extensive time-consuming Monte-Caro simuations. We thus present a comprehensive anaysis for the proposed strategy and derive cosed-form expression for the performance gain. Finay, we show that dynamicay associating with BSs depending on the current battery eve achieves significant power saving whie, at the same time, taking advantage of higher network heterogeneity. The paper is organized as foows. The network mode and main assumptions are described in Section II. The proposed ce association with adaptive biases is presented in Section III and its performance is anayzed in Section IV. Numerica simuations are presented in Section V and Section VI concudes this paper. II. SYSTEM MODEL AND ASSUMPTIONS We describe in this section the network mode, the assumptions for energy harvesting, together with the battery mode at off-grid and hybrid base stations. Tabe I summarizes the notation used in this paper.

5 5 A. A PPP-based network We consider a downink ceuar network which consists, as in [11], of (i) on-grid BSs (OG- BS), connected to the power grid, (ii) energy-harvesting BSs (EH-BS), soey powered by energy scavenging and (iii) hybrid base stations (HY-BS) which are both connected to the power grid and provided with energy harvesting faciities. The BSs of type, with {OG, EH, HY}, are distributed according to an independent homogeneous PPP B, with density λ. Next, users are distributed according to an independent homogeneous PPP U, with density ω, and are assumed in coverage of more than one BS. Served users are separated in time, frequency or both (OFDMA), impying that there is no intra-ce interference, as in [21]. We further assume a power-imited framework, where the avaiabe time-frequency resource is arge enough to accommodate any user requiring service, as ong as sufficient power is avaiabe. Such baseine assumption provides a tractabe benchmark for performance anaysis and is supported by the densification of next-generation ceuar networks, where BSs serve ony a few users each. B. Channe attenuation and Required power The channe mode accounts for path-oss and shadowing. A inks are assumed mutuay independent and identicay distributed. First, the path-oss from BS k to user U j is given by κr α k,j, where r k,j is the distance between them, κ is the free-space path-oss at a distance of 1m and α is the path-oss exponent. Second, the shadowing attenuation χ k,j from BS k to U j foows a og-norma distribution, with zero-mean and standard deviation σ. Since fast fading can be hardy tracked for ce association, it is not taken in to account. As in [18], we consider a power aocation which minimizes the transmit power required to satisfy a received power constraint P Rx. More commony envisaged for upink transmissions, such a mode aows more efficient use of the renewabe energy avaiabe in the battery [4, 12]. A BS with ow power in its battery can nevertheess serve nearby users, with ow power requirement. p kj is defined as the power requested by user j to receive data from BS k, i.e. Whie the required power p kj constraint P (max) Tx respect to BS k. p kj = P Rx κr α k,j χ k,j. (1) is imited by the battery eve at EH-BSs, we assume a power at both OG-BSs and HY-BSs. If p kj > P (max) Tx, user j is decared in outage with

6 6 C. A Markov chain mode for the battery We assume a sotted-time mode, with a sot duration of τ = 1. The amount of power 1 that is avaiabe in the buffer of EH-BSs and HY-BSs are broadcast towards users at the beginning of a time sot, as part of signaing in contro channes. We assume that the time sots at EH-BSs, OG-BSs and HY-BSs match, and that battery broadcasts are performed simutaneousy. Based on such information, users perform ce association during this time sot, and are seected for service at the end of it. Effective data transmission occurs in the next time sot and a seected users are served simutaneousy. Both EH-BSs and HY-BSs are equipped with batteries, or power buffers, potentiay with distinct energy harvesting capabiities. We assume that the power stored in a battery is soey issued from renewabe sources, and conversey, that a the green power is stored in the battery before consumption. This impies that the power consumed from the grid suppy does not affect the battery eve. As in [18, 22], both the harvested and consumed powers are continuous random variabes but are discretized into a finite number of eves for the purpose of anaysis. The battery fuctuations, as broadcast at each time sot, depend soey on the previous battery states, the user associations at previous time sot and the power harvested during τ. They are thus modeed by a finite-state Markov chain. For {EH, HY}, we respectivey define ε (), () and L () as the step size (or power unit), the current battery eve and the battery capacity of a -BS (in power units). In addition, the probabiity that the battery has power units is denoted as v () [ ] and the probabiity vector of the battery states as v () = v () 0 v () 1... v () L. We aso denote as P () q the probabiity to go from state to state q from one time sot to the next one at a -BS. [ The reated transition matrix is referred as P () = P () ]. q Without oss of generaity, a genera energy harvesting mode is considered, where the power arrivas foow a Poisson process of intensity λ e. Such a mode is used for exampe for soar photo-votaic panes, but the anaysis proposed in this work is vaid for other harvesting processes, by considering other function P H. Regarding the mode for battery depetion, we assume as in [18, 22] that the power p kj consumed to send data from BS k to user j is rounded up to the nearest battery unit. Given that the battery eves are broadcast ony periodicay, more than one user can associate with 1 The transmission and harvesting processes are considered within the duration of one time sot, such that the anaysis proposed in this paper is based on power rather than energy, without oss of generaity.

7 7 the same BS based on the same battery state information. Therefore, from one time sot to the foowing one, the battery eve is decreased by an amount of power equa to the sum of the powers requested by a users seected during this time sot. The probabiity P () T (m ) to consume a tota of m power units given that -BS k has power units in its battery is equa to ) ( P () T (m ) = P j p kj = m, (2) where the summation is over the set of users served by BS k. We assume that associated users are seected for service in ascending order of their required transmit power. The computation of this probabiity is one of the major chaenges soved in Section IV. III. BIASED CELL ASSOCIATION WITH ADAPTIVE BIASES This section describes the considered ce association with BS partitioning and adaptive biases. The case with EH-BSs ony is first described, next extended to the genera case. We concude by discussing on the particuar case of HY-BSs. A. User association for homogeneous networks [18] We first focus on networks consisting of EH-BSs ony, for which a ce association jointy accounting for the BS avaiabe power and the user power requirement of Eq. (1) has been proposed in [18]. It is performed in three steps, briefy restated in the foowing: Step 1: Estimating the BS power avaiabiity: A base station BS k is decared avaiabe for user j if the amount of power k ε (broadcast at the beginning of the current time sot) is sufficient to accommodate the requested power p kj in addition to the estimated power P k\j consumed by other users potentiay associated with BS k, i.e. p kj + P k\j k ε where Pk\j ωυ 2/α 2/α + 1 (p kj) 2 α +1 (3) ( ) ( 2 ( ) 1 α 2 2/α Υ = π P and Rx exp µ + 1 2/α κ ζ 2 ζ σ 2) ζ = 10/ n(10) The estimate P k\j characterizes the BS avaiabiity and is computed independenty at each user. If overestimated, users wi more ikey decare BSs as unavaiabe. If underestimated, too many users may associate with the same BS, eading to power outage. We highight that a BS may be avaiabe for one user and not for another one.

8 8 Step 2: Effective association: Then, each user effectivey associate with the avaiabe BS that minimizes the required transmit power. No muti-ce transmission nor custering is assumed in this work. Step 3: User seection: Finay, each BS seects the users which can be served among the associated ones. Since users associate with a given BS based on an estimate of the tota power consumption, such BS may not be abe to serve a associated users To maximize the number of served users, each BS seects associated users in ascending order of their power requirement, ti a associated users are seected or ti the battery is empty. We refer the reader to [18] for further detais on the ce association. Such strategy has been shown to provide significant reduction of the probabiity of power outage, exceeding 50% in case of bursty energy arrivas, whie requiring itte extra overhead to broadcast the BS battery eves at each time sot. B. Appication to networks with heterogeneous power suppy Different from the anaysis of [18], we now move onto considering genera networks, consisting of EH-BS, HY-BS and OG-BS. 1) Step 1: BSs partitioning: To minimize the power consumed from the conventiona grid suppy, users are prompted to associate in priority with base stations which can guaranty service soey using the power issued from renewabe source, i.e. the power harvested from the environment and stored in the battery. By appying the power-avaiabiity criteria of Eq. (3), each user partitions neighboring -BSs into two sets. If the battery eve is high enough compared to the required power, a -BS is decared avaiabe and power from renewabe source wi be requested if user j associates with it. The sub-set of corresponding BSs is denoted by A () j, with A for avaiabe. Otherwise, BSs are decared non-avaiabe and power from the grid suppy wi be requested. This subset of BSs is denoted as G () j, with G for grid. We highight that such partitioning is different from one user to another and jointy depends on the battery eve and the power requirement. Defining g (p kj ) = p kj + A () P () k\j, j { BS k B : g (p kj ) k ε ()} and (4) { ( BS k B : g 1 k ε ()) } p kj P (max) Tx. (5) G () j

9 9 Remarks: For OG-BSs, A (OG) j G (EH) j to A () j = (HY-BSs with P (max) Tx nor to G () j = (equivaenty HY-BSs with empty battery) and for EH-BSs, = g 1 EH ( ε (EH) ) at each instant). Any BS which beongs neither is not considered for ce association. 2) Step 2: Effective association: A user j associates with the base station BS k which consumes the ess biased power to satisfy the received power constraint P Rx : k = arg min k A j {p kj } k = arg min k G j {p kj } and k = arg min {β kj p kj } where β kj = k {k,k } β A if k A j (6) β G if k G j In this, β kj denotes for a power bias, or association weight, which is appied for ce association of user j with BS k. Such biases aow to contro traffic off-oading, from BSs with ow battery to BSs with higher battery. Together with the association request, each user announces the requested power suppy. If BS k A j, user j requests renewabe energy, whether it is an EH-BS or a HY-BS. Otherwise, it requests grid suppy, whether it is an OG-BS or a HY-BS. 3) Step 3: User seection: Both EH-BSs and HY-BSs may need to drop users which cannot be served given their effective battery eve. Whie HY-BSs can consume extra grid power to serve such users, power outage is decared at EH-BSs. C. On the particuar case of hybrid BSs HY-BSs are both provided with energy harvesting faciities and access to the power grid. Whie a user can ony request renewabe power (resp. grid power) if associated with an EH-BS (resp. OG-BS), it is free to choose the power source if associated with a HY-BS. We do not assume that grid power is consumed at a HY-BS ony if the battery is empty. As discussed in Section V, this significanty improves the network performance. Another consequence is that HY-BSs manage two sets of users, one being served with renewabe suppy and one with grid suppy. Different from existing iterature on biased ce association, the bias appied by a user for associating with a HY-BS is not constant over the whoe set of HY-BSs. It varies from one time sot to the other and from one user to the other, according to the user power requirement and the battery eve fuctuations. As far of our knowedge, this is the first non-constant adaptive bias proposed for ce association. IV. PERFORMANCE ANALYSIS OF CELL ASSOCIATION WITH ADAPTIVE BIASES As iustrated in Figure 1, the association biases significanty impact the probabiity for a user to be served using power from the conventiona grid suppy. Setting β A cose to zero forces users

10 10 (a) βa = 0.1 (b) βa = 2 Fig. 1. Probabiity to be served using power from conventiona grid suppy (ω = 20, π(100)2 (EH) λe (HY) = 0.1L, λe = 0.05L, PRx = 60dBm, βg = 1, Red circes: OG-BSs, Yeow squares: HY-BSs, Green diamonds: EH-BSs) to associate with a BS equipped with harvester as soon as energy is avaiabe. On the contrary, by increasing βa, users are more ikey associated with HY-BSs or OG-BSs and requesting power from the grid, such that batteries are maintained at a higher eve throughout the network. In this section, we anayze the proposed scheme to aow the quantification of such trade-off. A. Probem characterization for bias optimization Monte-Caro simuations may rapidy turn out to be excessivey time-consuming in regard to the considerabe number of sampes necessary to average both the node ocations and the battery eve fuctuations [23]. As a consequence, we propose to anayze the performance of the proposed strategy in terms of the probabiity of power outage Pout and the average power per (G) (G) area unit, POG + PHY, that is consumed from the grid suppy at both OG-BSs and HY-BSs. At a given time sot, the current battery eves, as broadcast by HY-BSs and EH-BSs, fuy determine the BS partitioning into sets A and G and give the probabiity of association to an EH-BS, a HY-BS or an OG-BS. Reciprocay, such probabiity affects the power consumption, from green or carbon-based power suppy, and thus, determines the battery eves at the next time sot. Thus, to any pair of biases (βa, βg ) corresponds an equiibrium distribution of the battery states at EH-BSs and HY-BSs, and of the number of users served by EH-BSs, HY-BSs and OGBSs. Characterizing such equiibrium is essentia to compute the performance of the proposed strategy. Whie the Markov chain anaysis described in Subsection IV-B aows to compute the

11 11 stationary distributions for v (HY) and v (EH), the stochastic geometry toos used in Subsection IV-C aow to characterize (i) the average number of avaiabe and non-avaiabe -BSs per area unit, i.e. the density of sets A 0 and G 0, for a typica user U 0, (ii) the probabiity of association with an EH-BS, a HY-BS or an OG-BS, and (iii) the density of users served by any -BS, for a given set of biases (β A, β G ) and battery probabiity vector v (HY) and v (EH). Performance is deduced in subsection IV-D. B. On the stationary distribution of the battery states The stationary distribution of v = [ v (EH) v (HY)] is numericay soved by adapting the agorithm proposed in [18] to networks with heterogeneous power suppy. We restate its main steps, as an overview of the anaysis proposed in next sub-sections. Inspired from the fixedpoint method, a first guess v (0) for the soution (e.g. uniform distribution) is considered, then successive approximations of the stationary distribution are computed as v (i+1) = v (i) P, where P = P(EH) 0 and P () is the transition matrix of the Markov chain modeing the 0 P (HY) battery at -BSs. The i th iteration consists of: Step 1: BS partitioning: Given v (i), compute the densities of A and G, respectivey denoted as Λ (A) and Λ (G). Step 2: Effective association: Deduce the probabiity P (A) (p ) (resp. P(G) (p )) to associate with an EH-BS or a HY-BS (resp. an OG-BS or a HY-BS) and to request renewabe power (resp. carbon-based power), for any battery state. Step 3: User seection: Compute the density Ω (A) (p ) (resp. Ω(G) (p )) of users served by a -BS using power from the green (resp. grid) suppy, for any state. Step 4: Power consumption: Using Theorem 1 of [18], deduce from the density Ω (A) (p ) the probabiity P (A ) T (m ) that a given -BS consumes exacty m power units from the battery. Simiary, compute the probabiity P (G ) T (m ) to consume m units from the power grid. Then, derive the new transition matrix P and vector v (i+1) as in [18]. In this agorithm, steps 1 and 2 characterizes the network from the point of view of the typica user, whie steps 3 and 4 move onto the perspective of a base station. The equiibrium distributions of the battery states at EH-BSs and HY-BSs are not independent and have to be jointy computed. In the foowing, we extend the anaysis proposed in [18] for step 1 to networks with heterogeneous suppy. Then, we fuy anayze steps 2 and 3 which incude

12 12 the nove association biases proposed in this paper. For the benefit of the reader, cosed-form expressions required for step 4 and derived in [18] are summarized in the Appendix. C. Characterization of the set of served users We consider the i th iteration of the soution agorithm. The biases are set to (β A, β G ) and the probabiity vectors of the BS battery state are equa to v (HY) (i) for more readabiity and start the anaysis by two definitions. First, the power coverage p (cov,) and v (EH) (i). We drop the index (i) is defined as the maximum power issued from renewabe sources that can be requested by a user served by a -BS (EH-BS or HY-BS) having power units in its battery. For any U j in coverage of -BS k, with g as given in Eq. (4)-(5). p (cov,) the energy harvesting rate, impying that p (cov,eh) p kj p (cov,) k g 1 ( k ε ()) (7) depends on the received power constraint P Rx and on is generay not equa to p (cov,hy). Second, we define as the owest buffer state providing avaiabiity of -BS k. For U j requiring p kj, 1 < g (p kj ) p (cov,) 1 < p kj p (cov,) (8) 1) Density of A 0 and G 0 (Step 1 of the agorithm): From the properties of dispaced PPPs, the point process modeing the powers p k0 k is distributed according to a non-homogeneous PPP on R + of density Λ (p) = λ Υ (P Rx ) 2 α p 2 α. Next, retaining out of this PPP ony the BSs which are avaiabe for U 0 is an independent thinning, whose properties aow to compute the density of A () 0. The retention probabiity that a -BS (EH- or HY-BS) has enough avaiabe power to serve U 0 using renewabe suppy is equa to is computed as in Eq. (14) of [18]: Λ (A) with p (cov) as given in Eq. (7). 1 (p) = v () =0 Λ (p (cov) ) + L v () = L, such that the density Λ (A) of A() 0 v () Λ (p), (9) = Now considering a network with heterogeneous power suppy, we deduce from Eq. (9) the density of G () 0, i.e. the set of -BSs (HY-BSs or OG-BSs) for which grid power is required: Λ (G) (p) = Λ (p) Λ (A) (p) if p P(max) Tx Λ (p) Λ (A) (P(max) Tx ) otherwise In particuar, for EH-BSs, Λ (G) EH (p) = 0, p and, for OG-BSs, Λ(G) OG (p) = Λ OG(p), p P (max) Tx. (10)

13 13 2) Probabiity of association with an -BS (Step 2 of the agorithm): We move onto computing the probabiity that U 0 associates with a base station of type {OG, EH, HY}. As described in Step 2 of Subsection III-B, U 0 associates with -BS 0 if the power p required to satisfy the received power constraint P Rx, weighted by the correct bias β, is minima among a other BSs. First, et assume that -BS 0 G () 0, i.e. -BS 0 consumes grid power to serve U 0, impying that β = β G. Leveraging the reduced Pam distribution [24], Y {EH, OG, HY}, the set of Y-BSs (excuding -BS 0 if Y =) has the same properties as B Y and can be partitioned into the subsets A (Y) 0, for which the association bias β A is appied, and G (Y) 0, for which the bias β G is appied. Therefore, the typica user U 0 associates with -BS 0 k A (Y) 0, β G p < β A p k0 p < β A β if Y G p k0 (11) k G (Y) 0, β G p < β G p k0 p < p k0 We now denote G as the point process modeing such scaed power: { G = t k = β } { } A p k0 : k A (Y) 0 t k = p k0 : k G (Y) 0. (12) β G Y {EH,OG,HY} Given that it is aso a PPP, the void probabiity of PPP aow to compute the probabiity that U 0 associates with -BS 0 G () 0 : P (G) (p ) = exp ( Λ (G) (p ) ) p > p (cov,) 0 otherwise where is the battery eve at -BS 0 and Λ (G) the density of G. In particuar, P (G) EH (p ) = 0,. We now compute Λ (G). For a BS k in A (Y) 0, we denoting the owest buffer state providing avaiabiity for a user U j requiring p kj = t k β G β A, i.e. p (cov,) 1 (13) < t k β G β A p (cov,). (14) Once again everaging the properties of dispaced PPP, the process modeing the {t k } forms a PPP on R + and its density is computed in a simiar way as Λ (A) (Eq.(14) of [18]): 1 L ( ) Λ (βa) Y (t) = v () Λ (p (cov,) βg ) + Λ t. (15) β A =0 v () = Note that if β A β G. Therefore, the density of G is expressed as: Λ (G) (p) = Λ (βa) EH (p) + Λ(βA) (p) + Λ(G) HY HY (p) + Λ(G) OG (p) (16)

14 14 In this, Λ (βa) EH (p)+λ(βa) HY (p) corresponds to the base stations (EH- or HY-BSs) which are decared avaiabe for U 0 (bias β A is appied). Λ (G) HY (p)+λ(g) (p) refers to base stations (OG- or HY-BSs) which are decared non-avaiabe (bias β G is appied). BS 0 A simiar anaysis can be conducted to compute the probabiity that U 0 associates with - OG A () 0, i.e. using bias β A. Focusing on U 0, the power requirements p k0 of a other Y-BSs for which the same bias β A is appied are distributed according to a PPP of density Λ (A) EH (p) + Λ(A) HY (p), whie the scaed power requirements β G β A p k0 of a other Y-BSs (for which bias β G is appied) are modeed according to a PPP with density ( Λ (βg) (p) = Λ p β ) A Λ (βa) HY (p), (17) β G with Λ (βa) HY computed as in in Eq. (15) but exchanging β A and β G. Denoting the battery eve at -BS 0, the probabiity that U 0 associates with -BS 0 A () 0 is s.t.: P (A) exp ( Λ (A) (p ) ) p p (cov,) (p ) = with In particuar, P (A) OG (p ) = 0. Λ (A) (p) = Λ (A) EH 0 otherwise (p) + Λ(A) HY (p) + Λ(βG) HY (p) + Λ(G) OG ( p β ) A β G 3) Density of users served by an -BS (Step 3 of the agorithm): So far, the anaysis has targeted the typica user s perspective. To characterize the point process of users served by a given -BS and compute the overa consumed power, we move onto the BS perspective and consider a typica base station of type, denoted as -BS 0. The point process modeing the powers p 0j, j required by surrounding users foows a non-homogeneous PPP on R + of density Ω(p) = ωυ (P Rx ) 2 α p 2 α. Remark: Foowing Step 3 of the ce association procedure, each base station seects the users that can be served among the ones which are associated with it and in ascending order of their biased power requirement, given the battery eve imitation. As the power avaiabiity criteria is based on an estimate, there exists a non-zero probabiity that too many users are associated, given the current battery eve, and have to be dropped (at EH-BSs) or served using grid power (at HY-BSs). Simuations show that the probabiity that too many users are associated regarding the battery eve is negigibe. We thus approximate the set of users seected by any EH-BS or HY-BS by the set of users associated with it.

15 15 Retaining out of the PPP modeing the powers p 0j, j ony the users associated to -BS 0 corresponds to an independent thinning, with retention probabiity P (A) (p ) if -BS 0 A () j and P (G) (p ) if -BS 0 G () j, as computed in previous subsection. Denoting the battery eve, the set of users which are served from renewabe energy has a density equa to p [ ] Ω (A) (p ) = dω(t)p (A) (t )1 t p (cov,) dt (18) 0 0 Simiary, the set of users which are served from the grid suppy forms PPP on R +, with density: p [ ] Ω (G) (p ) = dω(t)p (G) (t )1 p (cov,) < t P (max) Tx dt (19) We highight that the densities of the served users jointy depend on both probabiity vectors v (HY) and v (EH) via P (A) and P (G), whether it is a EH-BS, a HY-BS or a OG-BS. Such resut concudes the anaysis necessary to run the agorithm proposed in Section IV-B. D. Computation of considered performance metrics Once the stationary distribution for both v (HY) and v (EH) is known, the performance of the proposed strategy with adaptive biases can be computed. First, the probabiity of power outage is a good measure of the battery eve at EH-BSs and gives insight of the network genera behavior, as we wi show in Section V. A power outage at the typica user U 0 occurs if it cannot find any base station to associate with, due to weak channe or power shortage at surrounding EH-BSs. Therefore, from the void probabiity of PPPs, the probabiity of power outage is expressed by: ( ( )) P out = exp exp ( ) Λ P (max) (20) Λ (A) EH p (cov,eh) L {HY,OG} where Λ (A) EH is the density of avaiabe EH-BSs and Λ HY / Λ OG is the tota density of HY-/OG-BSs. The first term is the probabiity that no EH-BS is can be found within the maximum feasibe power coverage p (cov,eh) L. The second term refers to the probabiity that none of the HY-BSs and OG-BSs satisfies the maximum transmit power constraint P (max) Tx. Note that the effect of the biases are impicity captured in the first term ony and is particuary noticeabe when the network is poory provided with access to the power grid (ow densities λ HY and λ OG ). Next, we move onto the average power per area unit consumed from non-renewabe sources, at both OG-BSs and HY-BSs. Denoting P (G OG) T (m) the probabiity that a OG-BS consumes m units (computed in step 4 of the agorithm), we have: P (G) OG = λ OG m P (G OG) T (m). (21) m 1 Tx

16 16 Regarding HY-BSs, the probabiity that a HY-BS consumes m units from the power grid depends aso on its current battery eve. A fuy-charged HY-BS has much ess probabiity to resort to the grid suppy than HY-BSs with ow battery eve. We denote P (G HY) T (m ) the probabiity that a HY-BS consumes m units from the power grid given that units are stored in the battery. Recaing that v (HY) is the probabiity to have power units in the battery, the average power per unit area consumed from the carbon-based grid suppy at HY-BSs is equa to P (G) HY = λ HY L =0 m 1 Once again, the impact of (β A, β G ) is impicit and both P (G) OG stationary distribution of the battery states at EH-BSs and HY-BSs. mv (HY) P (G HY) T (m ). (22) and P(G) HY jointy depend on the V. SIMULATIONS AND PERFORMANCE RESULTS In this Section, we vaidate the anaysis proposed earier and investigate the performance achieved by the proposed biased ce association, by comparison with conventiona poicies. A. Simuation set up and reference schemes In the foowing, the proposed poicy is referred as CA-Aβ, for ce association with adaptive biases. Without oss of generaity, we can set β G to 1 and et β A vary. If not specified, we consider the simuation parameters of Tabe II. For performance comparison, we consider the three foowing reference schemes: Conventiona biased ce association (CA-Fβ): association biases are fixed and depends on the BS type, regardess of the user required power or the BS current battery eve as in [15, 19, 20]. Biases are denoted as β EH, β HY and β OG. Conventiona non-biased ce association (CA-noβ): each user simpy associates with the avaiabe BS that consumes the ess transmit power (i.e. β = 1, ). Idea scheme (Best-CA): batteries are assumed aways fu. This reference gives an upperbound on the achievabe performance and is used to efficienty compare a wide range of simuation parameters. The proposed power-aware ce association takes advantage of (i) the power-avaiabiity criteria, (ii) the abiity for users to choose their power suppy and (iii) the adaptive biases. The performance enhancement brought by the avaiabiity criteria has aready been investigated in

17 17 TABLE II SIMULATION PARAMETERS Network PPP Power κ / α 1 / 4 λ e / N e 10%L / 30 P Rx -65dBm σ 4dB ω 50 π100 2 P (max) Tx 500mW A sim 1km 2 β G 1 L / εl 1000 / 750mW [18]. To isoate its impact and fairy anayzing the gain provided by two other design parameters, we assume, for CA-Fβ, CA-noβ and Best-CA, that EH-BSs periodicay broadcast their battery eve, so that users determinate their power avaiabiity. Remark: The performance obtained by Monte-Caro simuations and by cacuation is potted in the two foowing figures. As observed, the pots show a good agreement between the computationa and simuated resuts, which vaidates the approximation used to compute the density of served users and the agorithm of Section IV-B. B. On the probabiity of power outage We first consider a network where a sma-ce BSs are provided with energy harvesting faciities and distributed according a PPP of density λ = 1 πr 2, i.e. when BSs are R meters away one from each other in average. We assume that c% of them are aso connected to the power grid, i.e. λ HY = c πr 2, λ EH = 1 c πr 2 and λ OG = 0. Figure 2 investigates, for different vaues of R, c and β A (with β G = 1), the power outage probabiity achieved using biased association. It depicts the ratio of the power outage obtained with CA-Aβ over the outage obtained in the idea case Best-CA (with fu batteries), i.e. (P (Aβ) out P (Best) out )/P (Best) out ( of power outage is dominated by the term exp {HY,OG} Λ. Given that the probabiity ( )), computing such P (max) Tx ratio aows to isoate the gain issued from the different schemes and battery management. As observed, the probabiity of power outage monotonicay decreases with β A, iustrating the fact that users are prompted to attach to HY-BSs with grid suppy and that more energy is stored in the batteries without being consumed. The oss decreases ti 0, i.e. batteries are aways fu and the outage probabiity cannot be further reduced. As iustrated in Figure 2, both CA-Aβ and CA-Fβ provide fairy simiar performance. Indeed, ony users sufficienty far from HY-BSs may be in power outage and have thus to be served

18 18 Probabiity c=0.4 R=70m R=80m R=90m CA-Aβ - Anaysis CA-Aβ - Simuation CA-Fβ c= β A (for CA-Aβ) / β EH (for CA-Fβ) Fig. 2. Loss in the overa power outage, with β G = 1, for a network consisting of c% of HY-BS and (1-c)% of EH-BS by the cosest avaiabe EH-BS. This suggests that the power outage probabiity is mosty impacted by the power-avaiabiity checking, performed prior to ce association, rather than by the adaptive biases. Thus, for the rest of this paper, we move onto investigating the on-grid power consumption. C. On the on-grid power consumption 1) First insights: Figure 3 depicts the tota on-grid power consumed over the simuation area A sim using CA-Aβ and iustrates the baance between the stationary distribution of the battery eve and the overa on-grid consumption. Increasing β A first aows to consume ess power from the grid. For exampe, with λ HY = 40% 1 π80 2, more than 2W are saved by taking β A = 4 rather than β A β G = 1. With a higher β A, users ocated far from both HY-BSs and EH-BSs are prompted to seect non-renewabe energy for service even if, at a given time sot, sufficient renewabe energy is stored in the battery of an EH-BS or a HY-BS. As a consequence, the battery eve has higher probabiity to store more power units at next time sot, and thus, more users can be served from renewabe energy. Yet, passed a certain threshod, increasing β A has a detrimenta effect on the on-grid power consumption. Indeed, the battery eve is kept useessy high and users are et requesting too often grid power, given the channe conditions, power demand and BS density. 2) Advantages of etting users decide on the power suppy: Figure 4 further investigate such trade-off in a network deprived of OG-BSs, with varying overa density λ = 1 πr 2 but aways constituted of 40% of HY-BSs and 60% of EH-BSs. We focus on the gain in the tota on-grid

19 Consumption (W) β A m - 5W m - 10W m - 10W m - 0W Anaysis Simuation Fig. 3. Tota on-grid power consumption over A sim, with λ HY = c 1 πr 2, β G = 1 and an offset of n Watts - Legend: c, R, n. As the power consumption noticeaby depends on the BS-user distance, we have subtracted a fixed offset to the obtained on-grid power consumption in Figure 3, for the soe purpose of carity. This offset aows to pot in the same figure the performance achieved for a arge range of BS densities. power consumption P (Aβ,G) HY (resp. P (Fβ,G) HY ) provided by considering the biased strategy CA-Aβ (resp. CA-Fβ), over the non-biased strategy CA-noβ. It is computed as ϱ = P(xβ,G) HY P (No,G) HY Note that the denominator incudes P (Best,G) HY P (No,G) HY P (Best,G) HY, x = A (resp. F ) (23) as an offset to isoate the gain provided by biasing. The scaed consumption P (No,G) HY P (Best,G) HY can be understood as the maximum feasibe range for performance improvement. We observe that, in denser networks (R 80m), most users are served from renewabe energy sources whatever it be CA-Aβ, CA-Fβ or CA-Noβ. The gain ϱ achieved by biasing is thus imited. However, when the network density decreases, the avaiabe renewabe power is not sufficient to manage a users in the network. Significant gain is obtained by considering biased ce associations as they prevent far users (requesting arge amount of power) to competey depete batteries and thereby, to deprive nearby users to access renewabe suppy in future time sots. For exampe with R=90m, 21%-gain is achieved by CA-Aβ over CA-Noβ, which corresponds to around 9W over A sim. In addition, the proposed CA-Aβ outperforms the conventiona CA-Fβ by etting users decide on the power source at HY-BSs, impying that on-grid power may be consumed even if the battery is not empty. The resuted gain is particuary visibe when β EH = β HY = 1 and β A = β G = 1,

20 20 40 Gain ϱ R=70m R=80m R=90m R=95m CA-Aβ CA-Fβ β A (for CA-Aβ) / β EH (for CA-Fβ) Fig. 4. Gain ϱ (%) in the on-grid power consumption for a fixed proportion of HY-BSs, with λ HY = πr 2 and β G = 1 (β HY = 1). in which case ϱ = 0 for CA-Fβ and ϱ > 0 for CA-Aβ. Indeed, with the conventiona CA-Fβ, batteries at HY-BSs are empty most of the time and stricty foow the fuctuation of the power unit arrivas. Each power unit is immediatey consumed. This has three main drawbacks: (i) in case of power cut, HY-BSs become unavaiabe ti sufficient energy is harvested, and the network must be handed by EH-BSs soey, which can cause severe data oss and ong system recovery, (ii) itte response is offered by HY-BSs to user traffic variations or increase in their power requirement, (iii) as a avaiabe power units are immediatey consumed, the batteries at HY-BSs continuousy suffer high eve variations, which can drasticay reduce their overa ifetime. On the contrary, the proposed ce association with adaptive biases provides a simiar battery management at both HY-BSs and EH-BSs, eads to smoother fuctuations of the battery eve and aows a better power management in the time, from one sot to another. 3) Advantages of the proposed adaptive gains: In Figure 5, we consider a network with fixed density λ = 1 π80 2 but with varying proportion of HY-BSs. We note that the case R=80m has been chosen on purpose since CA-Aβ and CA-Fβ achieve simiar performance gain for c=0.4, as iustrated in Figure 4. First, when most of base stations are hybrid (e.g. c=80%), the gain ϱ remains rather imited for CA-Aβ (resp. CA-Fβ) and is achieved for β A β G = 1 (resp. β EH β HY = 1), impying that distinguishing the type of BS powering for ce association does not provide much power gain. The conventiona CA-Fβ sighty outperforms the proposed CA-Aβ in this case. Given the high homogeneity of such network, preventing batteries to be

21 21 25 Gain ϱ c=0.2 c=0.25 c=0.4 c=0.6 c=0.8 CA-Aβ CA-Fβ β A (for CA-Aβ) / β EH (for CA-Fβ) Fig. 5. Gain ϱ (%) in the tota on-grid power consumption over No-β, with λ HY = c π80 2 and β G = 1 (β HY = 1). empty as does the proposed strategy, tends to increase the on-grid power consumption. Yet, this resut does not account for the three main drawbacks detaied earier. On the contrary, when the proportion of HY-BSs is decreasing, the proposed ce association significanty outperforms the non-biased strategy CA-Noβ and more than 23% of gain is obtained when ony 20% of base stations are HY-BSs (c=0.2). In this case, the optima β A is such that β A β G and increases when the proportion of HY-BSs diminishes, thus preventing far users to request renewabe energy, even if feasibe at a given instant. Moreover, distinguishing ce association based on the type of powering used for data transmission (as in CA-Aβ) rather than on the type of BS (as in CA-Fβ) significanty improves the network performance. Whie 23% of gain is obtained with the proposed strategy, ony a 16%-gain is reached with conventiona biased ce association, which represents an additiona gain of 3W (Figure 3). Indeed, the proposed CA-Aβ provides a better distribution of the power avaiabe throughout the network, not ony among EH-BSs but aso among HY-BSs. In addition, the range of β A for which high power gain is achieved is much arger than for CA-Fβ. Thus, the proposed ce association sti provides satisfying performance gain even if the set (β A, β G ) is away from its optimum. This trend is aso observed in Figure 4, for ower network densities. 4) Performance in highy heterogeneous networks: As ast resut, we anayze the impact of OG-BSs and assume as basis a network of density λ = 1 π80 2 and constituted of 40% of HY-BSs and 60% of EH-BSs. To this network, we progressivey add OG-BSs, by varying their density

22 Gain ϱ 10 5 r=150m r=200m r=300m r=600m r β A (for CA-Aβ) / β EH (for CA-Fβ) Fig. 6. Gain (%) in the tota on-grid power consumption over No-β, with λ HY = 0.4, λ π80 2 OG = 1 πr 2 and β G = 1 (β HY = 1 / optima β OG). λ OG = 1 πr 2. The case r refers to the case anayzed earier, i.e. without OG-BSs. As iustrated in Figure 6, the conventiona biased strategy CA-Fβ does not benefit from additiona OG-BSs. The gain ϱ remains quite constant for any r. As their batteries are most of the time empty, HY-BSs tend to behave ike OG-BSs and the network is equivaent, in terms of user association, to having ony EH-BSs and OG-BSs/HY-BSs, with respective densities 0.6 π80 2 λ OG π80 2. This bois down to the case anayzed in Figure 4. On the contrary, the proposed ce association is significanty impacted by additiona OG-BSs, as expained in the foowing. The ower the density of OG-BSs is, the higher shoud be the bias β A to maximize ϱ. Yet, the variation of the maxima gain ϱ (iustrated by red crosses) as a function of r is concave and upper-bounded by the case r=300m. The increasing part (r 300m) is in ine with what has been observed in Figures 4 and 5. Litte gain is obtained in networks consisting in majority of BSs connected to the grid suppy. When the overa network density is decreasing, the distance between a user and its serving BS is onger, more transmit power is required and increasing β A to prompt users to request grid suppy maintains higher battery eve and thus, aows a better energy distribution among BSs. Yet, when r 300m, the density of OG-BSs is too ow to affect performance resuts. The power gain ϱ starts to decrease and tends to the case r. Given such observation, we can concude that the proposed ce association argey takes advantage of the high heterogeneity of the networks. and

23 23 VI. CONCLUSION We have addressed the issue of the heterogeneity in the base station powering and have proposed a nove user association with adaptive biases. The provided gain is three-fod. First, users do not partition BSs depending on their effective type, but depending on the power suppy, renewabe or not, that is used for data transmission. Second, users associated with a HY-BS are et free to decide on the power suppy to be used, and may request power from the grid even if the battery is not empty. Third, the power coverage of BSs as perceived by users is controed by adaptive biases, which are set at each user and at each time sot, depending on the current BS battery eve, the power required to satisfy a received power constraint and the estimated power consumed to serve other users potentiay associated with the same BS. We have shown that this nove strategy significanty outperforms conventiona poicies, particuary in power-constrained networks, with ow density or with imited access to the grid power suppy. Moreover, it aows a better distribution of the avaiabe renewabe energy among base stations and thereby, takes advantage of higher heterogeneity in the BS powering. APPENDI We briefy re-state the cosed-form expressions obtained in [18] and used in step 4 of the agorithm. Given Ω (A) (p ) in Eq. (18), the probabiity P(A ) (m ) that a -BS consumes exacty m power units from the battery is computed recursivey as: T P (A ) T (m ) = where P sum () = and ( ) P Σ m,ω (A) (p ), p(cov) P sum() if m 0 otherwise. ( ) P Σ m, Ω (A) (p ), p(cov) m=1 P Σ (0, Ω, P ) = exp ( Ω(P )) P Σ (m, Ω, P ) = m q m q P Σ (m q, Ω, P ) q=1 (24) The probabiity P (G ) T (m ) to consume m units from the power grid is computed in a simiar manner, using Ω (A) (p ) of Eq. (19).

24 Finay, the transition matrix P () = P q = m P(A ) T [ ] P () is given by q (m ) P () H (q + m) q L P L = m P(A ) T (m ) q L +m P() H (q) (25) with P () H (m) the probabiity that a -BS harvests m power units during a time sot. 24 REFERENCES [1] S. Buzzi, C. L. I, T. E. Kein, H. V. Poor, C. Yang, and A. Zappone, A Survey of Energy-Efficient Techniques for 5G Networks and Chaenges Ahead, IEEE Journa on Seected Areas in Comm., vo. 34, no. 4, pp , Apri [2] H. Farhangi, The path of the smart grid, IEEE Power and Energy Magazine, vo. 8, no. 1, pp , January [3]. Fang, S. Misra, G. ue, and D. Yang, Smart Grid - The New and Improved Power Grid: A Survey, IEEE Comm. Surveys Tutorias, vo. 14, no. 4, pp , Fourth [4] Y. Mao, Y. Luo, J. Zhang, and K. B. Letaief, Energy Harvesting Sma Ce Networks: Feasibiity, Depoyment and Operation, ariv preprint ariv: , [5] Huawei, Shenzhen, China, Green Energy Soution. [Onine]. Avaiabe: hw htm [6]. Huang and N. Ansari, Energy sharing within EH-enabed wireess communication networks, IEEE Wireess Communications, vo. 22, no. 3, pp , June [7] B. Han, P. Hui, V. Kumar, M. V. Marathe, G. Pei, and A. Srinivasan, Ceuar traffic offoading through opportunistic communications: a case study, in Proc. of the 5th ACM workshop on Chaenged networks. ACM, 2010, pp [8] T. Han and N. Ansari, Enabing Mobie Traffic Offoading via Energy Spectrum Trading, IEEE Trans. on Wireess Comm., vo. 13, no. 6, pp , June [9] S. Singh, H. S. Dhion, and J. G. Andrews, Offoading in heterogeneous networks: Modeing, anaysis, and design insights, IEEE Trans. on Wireess Comm., vo. 12, no. 5, pp , May [10]. Chen, J. Wu, Y. Cai, H. Zhang, and T. Chen, Energy-Efficiency Oriented Traffic Offoading in Wireess Networks: A Brief Survey and a Learning Approach for Heterogeneous Ceuar Networks, IEEE Journa on Seected Areas in Comm., vo. 33, no. 4, pp , Apr [11] S. Zhang, N. Zhang, S. Zhou, J. Gong, Z. Niu, and. Shen, Energy-Aware Traffic Offoading for Green Heterogeneous Networks, IEEE Journa on Seected Areas in Comm. [12] D. Liu, Y. Chen, K. K. Chai, T. Zhang, and M. Ekashan, Two-Dimensiona Optimization on User Association and Green Energy Aocation for HetNets With Hybrid Energy Sources, IEEE Trans. on Comm., vo. 63, no. 11, pp , Nov [13]. Liu,. Huang, and N. Ansari, Green energy driven user association in ceuar networks with dua battery system, in IEEE Int. Conf. on Comm. (ICC), May 2016, pp [14] J. Rubio, A. Pascua-Iserte, J. de Omo, and J. Vida, User association for oad baancing in heterogeneous networks powered with energy harvesting sources, in Gobecom Workshops (GC Wkshps), Dec. 2014, pp [15] Y. Song, M. Zhao, W. Zhou, and H. Han, Throughput-optima user association in energy harvesting reay-assisted ceuar networks, in Sixth Int. Conf. on Wireess Comm. and Signa Proc. (WCSP), Oct [16] D. Liu, Y. Chen, K. K. Chai, and T. Zhang, Optima user association for deay-power tradeoffs in HetNets with hybrid energy sources, in IEEE 25th Annua Int. Symposium on Persona, Indoor, and Mobie Radio Comm. (PIMRC), Sept. 2014, pp