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the impact of BS deployment, especially BS density on energy efficiency in ultra dense HetNets using the stochastic geometry theory. The minimum achievable ...
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IEEE WIRELESS COMMUNICATIONS LETTERS, VOL. 5, NO. 2, APRIL 2016

Energy Efficiency of Base Station Deployment in Ultra Dense HetNets: A Stochastic Geometry Analysis Tiankui Zhang, Jiaojiao Zhao, Lu An, and Dantong Liu Abstract—Ultra dense heterogeneous networks (HetNets), which involve densely deployed small cells underlaying traditional macro cellular networks, will be an enabling solution for extremely high data rate communications. However, the dense deployment of small cell base stations (BSs) inevitably triggers a tremendous escalation of energy consumption. In this letter, we investigate the impact of BS deployment, especially BS density on energy efficiency in ultra dense HetNets using the stochastic geometry theory. The minimum achievable data rate in terms of the traffic load in each tier is characterized, and then the minimum achievable throughput of the whole HetNets is obtained. Finally, the closed-form energy efficiency with respect to the BS deployment is derived. The simulation validates the accuracy of the theoretical analysis, and demonstrates that the energy efficiency maximization can be achieved by the optimized BS deployment. Index Terms—Energy efficiency, HetNets, stochastic geometry, ultra dense networks.

I. I NTRODUCTION

H

ETEROGENEOUS networks (HetNets), where various small cells are underlaid the traditional macro cells, have been thought as a promising paradigm to support the deluge of data traffic with higher spectral efficiency. The increasing network density at different tiers in HetNets can substantially improve the network capacity by extreme spatial reuse [1], i.e., the ultra dense HetNets in 5G cellular networks [2]. Nevertheless, the unprecedented growth in the cellular industry has pushed the limits of energy consumption in wireless networks, where energy consumption and corresponding costs has evolved as one of the major concerns faced by cellular networks. Although the dense deployed small cells are able to provide the extreme high data rate, they inevitably incur the increasing the energy consumption. As such, it is imperative to take the energy efficiency into account in the base station (BS) deployment stage, thereby reducing energy consumption as well as remaining profitability for network operators. Earlier lines of research [3] and [4] focused their attention on BS density optimization for energy saving in cellular networks. The impact of BS deployment strategies on the power consumption of hexagonal grid macro cells was investigated in

Manuscript received October 21, 2015; revised December 20, 2015; accepted January 3, 2016. Date of publication January 8, 2016; date of current version April 7, 2016. This work was supported in part by the National Natural Science Foundation of China under Grant 61461029, and in part by the Fundamental Research Funds for the Central Universities under Grant 2014ZD03-01. The associate editor coordinating the review of this paper and approving it for publication was R. Madan. T. Zhang and J. Zhao are with Beijing Key Laboratory of Network System Architecture and Convergence, Beijing University of Posts and Telecommunications, Beijing 100876, China (e-mail: [email protected]. cn; [email protected]). L. An is with Department of Electrical and Computer Engineering, North Carolina State University, Raleigh, NC 27606 USA (e-mail: [email protected]). D. Liu is with School of Electronic Engineering and Computer Science, Queen Mary University of London, London, U.K. (e-mail: [email protected]). Digital Object Identifier 10.1109/LWC.2016.2516010

[3]. Ref. [4] considered the energy efficiency of HetNets and analyzed the macro BS density’s impact on network energy efficiency. Recently, the authors of [1] discussed the spectral and energy efficiency of ultra dense HetNets under different BS deployment strategies via rigorous simulations. The aforementioned laid a good foundation on BS density optimization for energy saving. However, these works mainly depend on simulation analysis without tractable theory. The distinct characteristics and flexible location of the Heterogeneous BSs pose many challenges to the theoretical analysis and simulation validation for the HetNets. Modeling the HetNets by spatial Poisson point process (PPP) provides an effective and tractable method to analyze the performance of HetNets using the stochastic geometry theory [5]–[11], in terms of, coverage probability [5], outage probability [6] and average ergodic rate [7]. Furthermore, [8] and [9] characterized the downlink rate coverage with mean load approximation. Ref. [10] proposed an energy efficiency model considering the traffic load and the wireless channel effects. The authors in [11] analyzed the minimal BS density with service outage constraint to minimize the network energy cost in HetNets. In the ultra dense HetNets, the BS density in each tier and the proportion of BS density among tiers have a notable impact on the network energy efficiency [1]. In this letter, we adopt the stochastic geometry theory to analyze the energy efficiency with respect to the BS density in the ultra dense HetNets. The works in the literatures consider the network power consumption minimization [11], and we prefer to maximize the network energy efficiency, which is defined as the ratio of network throughput to total power consumption. Although the data rate of HetNets has been analyzed in in [8] and [9], they did not provide the close-form data rate expression to derive the closed-form network energy efficiency directly. The main contributions of this letter are as follows. We first characterize the minimum achievable data rate in terms of the traffic load in each tier, then obtain the minimum achievable throughput of the whole HetNets, and finally derive the network energy efficiency with respect to BS deployment. The work in this letter is capable of providing theoretical guideline for the energy efficient BS deployment in ultra dense HetNets. When considering the traffic load varying in short term, the BS density for energy efficiency maximization can be controlled by BS switch on/off. Once the long term statistical traffic load in the network is available, the optimal energy efficient BS density in each tier can be determined accordingly. II. S YSTEM M ODEL A. Cellular Network Model A downlink ultra dense HetNet is considered. K tiers of BSs are deployed in the network with the set K = {1, 2, · · · , K }.

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ZHANG et al.: ENERGY EFFICIENCY OF BASE STATION DEPLOYMENT IN ULTRA DENSE HETNETS

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The static power consumption of a BS in the kth tier is denoted as PCk , which is caused by signal processing, battery backup, as well as site cooling, and is independent with the BS transmit power. Then, the total power consumption of the tagged BS in the kth tier can be expressed as Pk = PCk + ξk P Tk

(2)

in which, ξk is load-dependent power consumption coefficient, which accounts for power consumption that scales with traffic load of the kth tier BSs. III. E NERGY E FFICIENCY A NALYSIS Fig. 1. An example of three tier HetNet, λ2 = 1.5λ1 and λ3 = 2λ1 .

We model the spatial distribution of the BSs in kth tier as a homogeneous PPP k with density λk in the two dimensional Euclidean plane. Since the transmit powers of BSs across tiers are different, the coverage regions of BSs form a weighted Poisson Voronoi Tessellation (PVT). Fig. 1 shows an example of coverage region of heterogeneous BSs in a three tier HetNet. We consider an independent distribution of user equipments (UEs) following the independent PPP with density λu . Since we focus on the impact of BS deployment on energy efficiency under a certain UE density in this letter, the kth tier BS density is normalized as λk = ρk λu , where ρk is defined as the BS density ratio factor of the kth tier. B. Channel Model The UE will associate with the BS from which it receives the largest mean received signal power. This typical UE is named as tagged UE and its serving BS named as tagged BS. The path loss and fast fading are taken into account when modeling the wireless channel gain. The path loss exponent is denoted as α, α > 2. The fast fading experienced by the tagged UE and the tagged BS Bo (belonging to the kth tier) is denoted by h k , which is assumed to be Rayleigh fading. We consider universal frequency reuse. As such, except the serving BS of the tagged UE, all the other BSs in the HetNet are potential interferers. The distance between the tagged UE and the tagged BS is denoted as dk . The transmit power of the kth tier BS is P Tk . Consequently, the received power of the tagged UE from its serving BS is P Tk h k dk −α . The received cumulative interference signal of the tagged UE from all other BSs in the HetNet is Ik , and the signal to interference plus noise ratio (SINR) of the tagged UE associated with Bo is S I N Rk =

P Tk h k dk−α Ik + σ 2

(1)

where σ 2 is the noise power. Ref. [5] has proven that the intercell interference dominates noise in cellular networks of even modest density. As a result, the noise power has no effect on the SINR values. In the following analysis we ignore the noise in SINR and use signal to interference ratio (SIR) instead. C. Power Consumption Model

Firstly we characterize the minimum achievable data rate in terms of the traffic load in each tier, then obtain the minimum achievable throughput of the whole HetNets, and provide the network energy efficiency with respect to BS deployment. We set that the kth tier BSs have a target SIR γk , where γk > 1 is the SIR threshold for an acceptable QoS, which means the user will be outage if the downlink SIR with its serving BS is less than γk . The number of UEs associated with the tagged BS in the kth tier is denoted as Nk , which can represent the traffic load of tagged BS in long term. Clearly, the number of UEs served by the tagged BS is a random variable which is determined by both the area of the region that the tagged BS serves and the UE density in the HetNets. Definition 1 (coverage probability): The coverage probability of the kth tier is defined as Pcov (γk ) = P (S I Rk > γk ). This definition can be interpreted as (i) the probability that the tagged UE can achieve a target SIR γk when associating with a BS in the kth tier, (ii) the average fraction of UEs who at any time achieve SIR γk in the kth tier. Based on the Corollary 1 in [5], the coverage probability of the HetNet can be written as   K  π k=1 ηk S I R k > γk = (3) P K C (α) k=1 β k k∈K   2 2/α where C (α) = 2πα csc 2π βk = ρk P Tk , and α , −2/ α η =β γ . k

k k

According to the Corollary 2 in [5], the probability that the tagged UE connected to a kth tier BS is ηk pk =  K (4) k=1 ηk which can be considered equivalently as the average fraction of UEs served by the BSs in the kth tier. Proposition 1: The coverage probability of the kth tier is ηk π Pcov (γk ) = . (5) K C (α) k=1 βk Proof: Since the probability that the tagged UE connected to the kth tier BSs can be thought of equivalently as the average fraction of UEs served by BSs in the kth tier, the average kth tier is given fraction of UEs who achieve  SIR γk in the   by P (S I Rk > γk ) = pk · P S I R j > γ j , then we have j∈K

Generally, BSs consist of two types of power consumptions: static power consumption and transmit power consumption [3].

Pcov (γk ) =

2/α −2/α

π ρk P Tk γk C(α)  K ρ P T 2/α k=1 k k

.



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IEEE WIRELESS COMMUNICATIONS LETTERS, VOL. 5, NO. 2, APRIL 2016

Definition 2 (minimum achievable data rate): The downlink minimum achievable data rate of the tagged UE associated with the kth tier BS is defined as the target data rate achieved in the condition with a predefined target SIR γk . In order to keep the derivation tractable, we assume that each BS equally allocates the frequency resource among its associated UEs. According to the Shannon theory, the minimum achievable data rate in bps of the tagged UE when it connects to a kth tier BS can be expressed as

W (6) log2 (1 + γk ) Rk = E Nk where W indicates the system bandwidth. We assume the Nk and γk to be independent for tractability [9]. With this assumption, the Rk is expressed as follows when the kth tier target SIR γk is determined, W Rk = (7) log2 (1 + γk ) E [Nk ] Proposition 2: The average number of UEs served by the tagged BS in the kth tier is pk (8) E [Nk ] = 1 + 1.28 . ρk Proof: Taking association probability into consideration, the equivalent BS density in the kth tier, denoted as λk , is λk pk [8]. We define the area of a typical PVT cell in the kth tier as Ak . Thus, the cell size is subject to a biased Gamma distribution with a shape parameter δ = 3.5 [8]. According to lemma 1 in [8], the probability generating function (PGF) of Nk is G Nk (z) = E exp (λu Ak (z − 1)) . Using the PGF, the probability mass function of Nk can be derived as G Nk n (0) n! 

n δ λu −(n+δ+1) δ (n + δ + 1) λu δ + = (9) n!

(δ) λ k λ k ∞ where (δ) = 0 x δ−1 exp (−x) d x is the gamma function. ∞  Since E [Nk ] = nP (Nk = n + 1) and δ = 3.5, we can P (Nk = n + 1) =

n=0

derive the average number of users in a kth tier cell as E [Nk ] = 1 + 1.28 λλuk , where λk = λpkk and λk = ρk λu . From the derived average number of UEs served by the tagged BS in the kth tier, we can obtain the minimum achievable data rate of the tagged UE in (7).  Definition 3 (minimum achievable throughput): According to the average fraction of UEs served by the BSs in the kth tier (4), the coverage probability of the kth tier (5), the minimum achievable data rate of the tagged UE associated with the kth tier BS (7), we can obtain the minimum achievable throughput of the whole HetNets as K (10) Rtotal = Pcov (γk ) λu pk Rk . k=1

By substituting (4), (5) and (7) into (10), we have ρk ηk2 log2 (1 + γk ) W π λu  K     Rtotal = k=1 K K C (α) ρk k=1 ηk +1.28ηk k=1 βk (11)

2/α −2 α where βk = ρk P Tk , ηk = βk γk / . The expression of (11) is related to the BS density ratio factor of kth tier ρk , the UE density λu , the target SIR of the kth tier γk and the kth tier BS transmit power P Tk . Definition 4 (network energy efficiency): The network energy efficiency is defined as the ratio of minimum achievable throughput to total power consumption in the HetNet, that is

Rtotal ηE E = K . k=1 λk Pk

(12)

Since the coefficient ξk in (2) is proportional with the traffic load of the BS in the kth tier, we set ξk = E [Nk ] . Thus, the power consumption of the BS in the kth tier can be expressed as Pk = (PCk + E [Nk ] P Tk ). Taking (11) into (12), we can get the network energy efficiency as Wπ C(α)

ηE E =

K

K

k=1 ρk

ρk ηk2 log2 (1+γk )    K ηk+1.28ηk ρk k=1 k=1 βk

 k=1  K

PCk + P Tk +1.28

ρk

P Tk ηk K



(13)

k=1 ηk

2/α −2 α where βk = ρk P Tk and ηk = βk γk / . The expression of (13) indicates that, the maximum network energy efficiency will be achieved if BS density in each tier is set properly according to the UE density, which will be demonstrated in detailed by the simulation. Special Case (Energy Efficiency in Two Tier Networks). We give an analysis of the two tier case where there are two types of BSs in the network, macro BSs and pico BSs with respective BS density ratio factor ρ1 and ρ2 . We consider a special case, that the two tiers have identical target SIR, i.e., γk = γ , ∀k. Then the network energy efficiency can be rewritten as,     2/α 2 2/α 2 B ρ1 P T1 +A ρ2 P T2    (14) ηE E = 2/α AB L 2k=1 ρk P Tk +ρ1 P T1 A+ρ2 P T2 B πγ

−2/ α , L = ρ1 PC1 +ρ2 PC2 , in which,  = W log2 (1 + γ ) C(α) 2  2/α 2/α 2/α A = k=1 ρk P Tk +1.28P T1 , and B = 2k=1 ρk P Tk + 2/α 1.28P T2 . We can see that the network energy efficiencyis a function of BS  density ratio factor ρ1 , ρ2 . Since ρ1 = λ1 λu and ρ2 = λ2 λu , given the traffic load, different ρ1 and ρ2 means different macro BS density and pico BS density, and both of them have impacts on network energy efficiency.

IV. S IMULATION A NALYSIS A two tier HetNet with macro BSs and pico BSs is modeled in the simulation. The system bandwidth is 10 MHz and the frequency reuse factor is one. The power path loss exponent α is set as 4, and the fast fading is a Rayleigh channel with the mean value of zero and the variance of one. The static power consumption of a macro and pico BS is 1000W, and 50W, whereas the transmit power of a macro and pico BS is 46 dBm and 30 dBm, respectively. We assume that all the BSs in both tiers have identical target SIR. The coverage of the whole HetNets is an area with 200 km radius and the

ZHANG et al.: ENERGY EFFICIENCY OF BASE STATION DEPLOYMENT IN ULTRA DENSE HETNETS

Fig. 2. Network energy efficiency with varying ρ1 . Note γ = 0 dB here.

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Fig. 4. Network energy efficiency with varying γ . Note ρ2 /ρ1 = 5 here.

we can see that with the increase of γ , the network energy efficiency curve will rise first and then drop. This is because the achievable data rate will increase as γ grows while the coverage probability will decrease as γ increases. V. C ONCLUSION

Fig. 3. Network energy efficiency with varying ρ2 /ρ1 . Note γ = 0 dB here.

locations of macro BSs and pico BSs are generated by PPP with respective density λ1 and λ2 . In the simulation, we set the UE density λu as 0.01 m−2 . Monte Carlo method is used to obtain the network energy efficiency with different BS deployment parameters by 10000 drops of BSs distribution. We investigate the network energy efficiency with variable BS density ratio factors in order to observe their impacts on the network energy efficiency as shown in Fig. 2 and Fig. 3. Fig. 2 gives the impact of macro BS density ratio factor ρ1 on network energy efficiency. The target SIR γ is set as 0 dB. It is shown that the simulation results are in line with the theoretical results, which validates the network energy efficiency expression (14). In addition, we can conclude that, if the UE density  λu and the ratio of pico BS density to macro BS density ρ2 ρ1 is determined, we can find an optimal ρ1 to get the maximum network energy efficiency. We investigatethe impact of pico BS density to macro BS density ratios ρ2 ρ1 on network energy efficiency in Fig. 3. We can see that with the increasing number of pico BSs in the HetNets, the network energy efficiency will first increase and then decrease due to the rise of power consumption caused by the increment of pico BSs. Therefore, in the ultra dense HetNets, the density of small cell BS should be carefully designed. Otherwise, over dense deployment of small cell BSs will attenuate the network energy efficiency. Furthermore, we evaluate the network energy efficiency with various target SIR γ in Fig. 4 to analyze the impact of γ on network energy efficiency with given ρ1 and ρ2 . First, the consistency between the theoretical results and the simulations validates the network energy efficiency expression. And also,

In this letter, we investigate the impact of BS deployment on energy efficiency in ultra dense HetNets using the stochastic geometry theory. We have derived the closed form expressions of the network energy efficiency in terms of the BS density. In the simulation, we analyze the impact of BS density on network energy efficiency. This work is capable of providing theoretical basis for energy efficient network planning in ultra dense HetNets. R EFERENCES [1] S. Yunas, M. Valkama, and J. Niemela, “Spectral and energy efficiency of ultra-dense networks under different deployment strategies,” IEEE Commun. Mag., vol. 53, no. 1, pp. 90–100, Jan. 2015. [2] Z. Gao, L. Dai, D. Mi, Z. Wang, M. Imran, and M. Shakir, “Mmwave massive-MIMO-based wireless backhaul for the 5G ultra-dense network,” IEEE Wireless Commun., vol. 22, no. 5, pp. 13–21, Oct. 2015. [3] F. Richter, A. Fehske, and G. Fettweis, “Energy efficiency aspects of base station deployment strategies for cellular networks,” in Proc. IEEE 70th Veh. Technol. Conf. Fall (VTC’09-Fall), Sep. 2009, pp. 1–5. [4] Y. S. Soh, T. Quek, M. Kountouris, and H. Shin, “Energy efficient heterogeneous cellular networks,” IEEE J. Sel. Areas Commun., vol. 31, no. 5, pp. 840–850, May 2013. [5] H. Dhillon, R. Ganti, F. Baccelli, and J. Andrews, “Modeling and analysis of K-tier downlink heterogeneous cellular networks,” IEEE J. Sel. Areas Commun., vol. 30, no. 3, pp. 550–560, Apr. 2012. [6] H.-S. Jo, Y. J. Sang, P. Xia, and J. Andrews, “Heterogeneous cellular networks with flexible cell association: A comprehensive downlink SINR analysis,” IEEE Trans. Wireless Commun., vol. 11, no. 10, pp. 3484– 3495, Oct. 2012. [7] M. Di Renzo, A. Guidotti, and G. Corazza, “Average rate of downlink heterogeneous cellular networks over generalized fading channels: A stochastic geometry approach,” IEEE Trans. Commun., vol. 61, no. 7, pp. 3050–3071, Jul. 2013. [8] S. Singh, H. Dhillon, and J. Andrews, “Offloading in heterogeneous networks: Modeling, analysis, and design insights,” IEEE Trans. Wireless Commun., vol. 12, no. 5, pp. 2484–2497, May 2013. [9] H. Dhillon and J. Andrews, “Downlink rate distribution in heterogeneous cellular networks under generalized cell selection,” IEEE Wireless Commun. Lett., vol. 3, no. 1, pp. 42–45, Feb. 2014. [10] D. Cao, S. Zhou, and Z. Niu, “Optimal combination of base station densities for energy-efficient two-tier heterogeneous cellular networks,” IEEE Trans. Wireless Commun., vol. 12, no. 9, pp. 4350–4362, Sep. 2013. [11] L. Xiang, X. Ge, C.-X. Wang, F. Y. Li, and F. Reichert, “Energy efficiency evaluation of cellular networks based on spatial distributions of traffic load and power consumption,” IEEE Trans. Wireless Commun., vol. 12, no. 3, pp. 961–973, Mar. 2013.