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Characterizing Energy Efficiency and Deployment. Efficiency Relations for Green Architecture Design. Yan Chen, Shunqing Zhang, and Shugong Xu. Huawei ...
Characterizing Energy Efficiency and Deployment Efficiency Relations for Green Architecture Design Yan Chen, Shunqing Zhang, and Shugong Xu Huawei Technologies, Co. Ltd., Shanghai, China Email: {eeyanchen, sqzhang, shugong}@huawei.com

Abstract—Global warming and climate changing is among the major challenges in the 21st century. In wireless communications, green architecture design is an urgent demand for operators, not only because of the social responsibilities but also their willingness to reduce the network construction and operating cost. Previous literatures tried to tackle deployment cost and energy efficiency in a separated manner. However, these two aspects are interacting with each other and the design of green architecture needs a holistic consideration of both. In this paper, we try to shed some light on the green architecture design by analytically characterizing the open relations between energy efficiency and deployment efficiency, which is found somehow different from our intuition and there might not be a simple tradeoff between the two. This study has positive impact on the future network planning and optimization.

green cellular solution. In particular, we are target to answer the following two questions: • How to evaluate the efficiency of BS deployment and energy consumption in a quantitative framework? • How to characterize the relations between the energy efficiency and the deployment efficiency? Since the power consumption of base stations contributes to the energy bill, which is counted as part of the operating cost, the relations between energy efficiency and deployment efficiency is not straight forward. As we will show later, there may not be a simple tradeoff between the two. This study also gives some preliminary ideas on the future wireless network planning and optimization.

I. I NTRODUCTION

II. S YSTEM M ODEL AND D EFINITIONS

As the data traffic volume increases dramatically in the coming future, more BSs are needed, it inevitably pushes the related energy consumption climbing too. Facing such situation, how should a network be deployed to maintain operators profits and at the same time keep their energy bill low deserves great consideration. As a result, the study of BS deployment problems in the cellular networks becomes a very active research area recently. One direction is focusing on the financial aspects of the BS deployment. For example, [3] provided a comprehensive view of the deployment strategies for heterogeneous wireless networks, which contains a careful treatment of the Capital Expenditure (CapEx) and Operational Expenditure (OpEx) of the wireless network and [4] analyzed the financial impact of the home network deployment. The other direction is dealing with the energy efficiency of the wireless systems without the consideration of deployment cost. For example, [5] and [6] considered the deployment strategies in the cellular networks to improve the energy efficiency of the whole network. [7] compared different cell sizes and concluded that smaller cells are more favorable for high energy efficiency. However, only transmit power is counted therein. All the above literatures are trying to tackle the deployment cost and energy efficient transmission separately. The conclusions on the favorable cell sizes therein are drawn from either aspect but not from joint consideration. The objective of this paper is to give some answer from theoretical aspects by studying the relationships between the deployment cost, service guarantee, and the energy efficiency under different deployment strategies (cell sizes), which shall serve as the guidance for future network planning and part of the overall

We consider the deployment of homogenous BSs on a given round area A with radius RA . The mobile users are assumed to be uniformly distributed in this area with density ρu , so that the deployment of BSs is also uniform with the frequency reuse factor1 f . Moreover, the required number of BSs N in the area 2 /λR2 , A depends on the cell radius R in the light of N = RA where λ ∈ (0, 1) stands for the non-overlapped ratio. A. Propagation and Interference Model In wireless communications, the channel attenuation is mainly contributed by path loss. In the downlink direction, the received signal power at distance d from the BS can be modeled as Pr (d) = κ0 GPt /dα , where Pt is the transmit power of the BS, κ0 and α are the path loss coefficient and exponent, respectively, and G is the antenna gain. Without consideration of interference, the received signal-to-noise ratio 2 t = κσ02GP (SNR) is simply γ 0 (d) = Prσ(d) 2 dα , where σ is the noise power on total bandwidth. On the other hand, let I(d) be the total interference aggregated from all external cells, the signal-to-noise-andPr (d) interference ratio (SINR) at distance d is γ I (d) = I(d)+σ 2. In the calculation of I(d), we consider the fluid model2 used in [8], which replaces a given number of BSs by an equivalent continuum of transmitters spatially distributed with density N 1 = πλR ρ = πR 2 2 . Based on the fluid model, the external A

1 In general, the frequency reuse factor f is chosen to be 1, 3, 7 or some fractional numbers as for fractional frequency reuse in the LTE standard). 2 Note that the equivalence between the fluid model and the traditional hexagonal model has been verified in [8] for any TDMA/OFDM systems.

978-1-4244-6826-3/10/$26.00 ©2010 IEEE

interference on each element surface zdzdθ at distance z from the receiver is ρκ0 GPt z −α zdzdθ. By integrating over A (excluding its own cell), we obtain I(d) as  2π  RA −d ρκ0 GPt z −α z dzdθ I(d) = f 0 R−d  2κ0 GPt  = (2R − d)2−α − (RA − d)2−α (1) f (α − 2)λR2

CapEx

cCa

BS equip.

cC BS

Site installation and buildout

cC Site

Backhaul transmission equip.

cC BT

Radio Network Controller (RNC) equip. OpEx

cOp

Backhaul transmission lease

cO BT

Site lease

cO Site

Operation & maintenance

cO OM

Electric power

cO Pw

B. Definitions and Clarifications In this subsection, we shall give the formal definition of the two key metrics for the design of radio access networks, i.e. energy efficiency (EE) and deployment efficiency (DE). Definition 1 (Total Network Throughput): The average site throughput, T site (R), is defined to be the delivered information bits averaged over different mobile users within the coverage of the BS site and the total network throughput, T net , is thus defined as the summation of the average site throughput within the network area A (unit: bits). Definition 2 (Energy Efficiency): The network EE is defined as the ratio of the total network throughput per unit bandwidth over the network energy consumption within a given period (unit: bits/Joule): ΓEE = T net /E net

(2)

where E net is the network energy consumption, which is the sum energy consumption of all sites within the given area A. Definition 3 (Deployment Efficiency): The network DE is defined as the ratio of the total network throughput per unit bandwidth over the network deployment cost of the network within the given period (unit: bits/e): ΓDE = T net /cnet

(3)

where cnet denotes the network deployment cost, which is the summation of Capital Expenditure (CapEx) and total Operational Expenditure (OpEx) over the period considered. Specifically, the notations and breakdowns of Capex and OpEx are classified in Table I. III. C HARACTERIZATION OF DE-EE T RADEOFF In this section, we shall derive the tradeoff relationship between DE and EE. We first express the network EE and DE both as functions of the cell size R and then eliminate R to show the direct relationship between EE and DE. A. Network Energy Consumption The network energy consumption is the product of number of sites and per-site average energy consumption, i.e. E net = N E site , where the latter is the accumulation of energy consumption over a given time period T . In the paper, we model the site power consumption Psite as the sum of two parts [5]: • Power consumption linearly scales with the site transmit power Pt , denoted as aconv ∗ Pt , in which aconv is the power conversion efficiency, accounting for the power amplifier (PA) efficiency, feeder loss, and extra loss in transmission related cooling, etc.

cC RN C

TABLE I C ATEGORIES AND NOTATIONS OF C AP E X AND O P E X [3].

Power consumption independent of transmit Pt of a site, denoted as bsite , which includes circuit power for signal processing battery backup as well as transmission independent site cooling consumption, etc. Furthermore, for power saving consideration, we assume the BS has the ability to ideally turn off the PA and other transmit related components when not transmitting. As a result, the transmission related power is consumed only during effective working period. Therefore, the site power consumption can be expressed as  aconv · Pt + bsite , BS transmitting (4) Psite = BS not transmitting bsite , •

Note that this can be taken as an achievable lower bound of the power consumption of a site under green power saving technologies. The transmit power Pt is determined under the constraint that the cell edge user, the bottleneck of the network deployment, is guaranteed with a minimum rate C. According to Shannon formula C = B log2 (1 + γ(R))/f , the required  SINR at distance R should satisfy γ(R) ≥ 1 2Cf /B − 1 , where B is the communication bandwidth and stands for the SNR gap between practical schemes and the shannon bound. Based on the system model described in II-A, the cell edge SNR, with (w) and without (w/o) considering interference, is ⎧ ⎨κ0 GPt /σ 2 · R−α , w/o

−1 γ(R) = 2 RA 2−α 2 α σ R ⎩ + κ0 GPt , w (α−2)λf 1 − R −1 As a result, the transmit power Pt required is ⎧ Cf /B 2 α ⎪ ⎨ 2  −1 · σ κR0 , σ 2 Rα Pt (R) =  /κ0  2−α  , ⎪ R  2 ⎩ Cf /B 1− RA −1 − (α−2)λ 2

w/o I wI

(5)

−1

which are both functions of cell size R. Define the effective working period of a site as the time the site transmits at full load, which is modeled by an equivalent ratio of time fraction, denoted as ηe in the paper, meaning that in ηe T time out of the total period T , the site works at full load and in the rest of the (1 − ηe )T time, the site remains idle. Note that given the uniform user distribution and traffic

cC BS

cC RN C

cC BT

cC Site

Macro

c0

Micro

1 c 2 0

1 c 4 0 1 c 4 0

1 c 4 0 1 c 4 0

3 c 2 0 1 c 2 0

Annual OpEx

cO BT

cO Site

cO OM

cO Pw

1 c 4 0 1 c 4 0

1 c 4 0 1 c 8 0

1 c 16 0 1 c 20 0

c1 E site (R)

Total CapEx

Macro Micro

c1 E site (R)

TABLE II C AP E X AND O P E X BREAKDOWN FOR M ACRO /M ICRO BS S [3].

layout in the whole target area A, the ratio ηe for each site can be approximated as a function of the corresponding cell size R in the light of 2 ηe = R2 /Rref ,

(6)

where Rref is the maximum cell radius that can still supports the required traffic load distributed on the target area A. In other words, with cell radius Rref , all sites need to always work at full load. Moreover, eqn. (6) implies that the larger the cell size, the busier the BS will be, since more users (heavier traffic load) need to be served in that cell. Hence, the network energy consumption can be calculated as E net = N (R) [ηe (R) · asite Pt (R) + bsite ] T

(7)

B. Network Deployment Cost Consider two candidate BS types, namely macro BS and micro BS. A macro BS usually serves for a coverage with radius ranging from 500 m to a few kilometers while a micro BS serves for a comparatively smaller area with radius less than 500 m. The breakdowns of the total CapEx and annual average OpEx per cell (normalized by the equipment cost of a macro BS, denoted by c0 , unit: e) are listed in Table II, where the relative ratios for each elements are suggested by [3] with 10 year evenly distributed CapEx. In addition, note that in OpEx calculation, the electricity power bill of a site is closely related to its energy consumption in terms of cO Pw = c1 · E site (R), where c1 is the electricity charge per of unit e/Joule (or equivalently, c1 /3.6 ∗ 106 e/kWatt·hour). Based on Table II, the annual average cell deployment cost as a function in R can be expressed as cCO (R) = cCa (R)/10 + cOp (R)  0.86c0 + c1 E site (R), = 0.57c0 + c1 E site (R),

R ≥ 0.5 (8) 0.1 ≤ R < 0.5

The network deployment cost is thus calculated by summing the average cost over N (R) sites, i.e. cnet = N (R) · cCO (R)

(9)

C. Total Network Throughput Based on Definition 1, the total network throughput is the sum throughput of all sites normalized by the total transmission bandwidth, i.e T net (R) = N (R) · T site (R)/B, where the average site throughput T site (R) given by T site (R) = C site (R) · ηe (R) · T,

(10)

where C site (R) represents the average transmission rate of the site given BS transmit power Pt (R), T stands for the given time period, and ηe has been illustrated in subsection III-A. The average rate C site (R) is calculated as the arithmetic mean of each user’s achievable rate within the cell. In this paper, we assume the BS transmits with fixed power but rate adaptation is applied for downlink transmission so that the mobile user near the BS enjoys a larger rate. For practical consideration, we assume M -level Adaptive Modulation and Coding (AMC) scheme is applied at each BS3 and the applied region of the m-th AMC level (counting from the center, m = m 1, . . . , M ) is the ring between m−1 M R and M R, whose area is   2 2 R R 2m − 1 2 Am (R) = π m − π (m − 1) = πR . M M m2 Moreover, given the transmit power Pt (R), the rate in the mth ring is determined by the lowest supportable capacity in that zone (which is also function of R), i.e.  m −α  κ0 Pt (R) M R /f. Cm (R) = B log2 1 + m I( M R) + σ 2 Given the uniform user distribution density ρu , the average rate of the whole cell is M M  ρu Am (R)Cm (R) 2m − 1 C site (R) = m=1 = Cm (R), ρu πR2 m2 m=1 Note M = 1 implies the special case that all users within a cell have the same rate, i.e. the minimum required rate C. Finally, by substituting C site (R) and ηe (R), we get the final result of total network throughput T net (R). D. DE-EE Relation According to the definitions 2 and 3 given in section II-B, as well as the results obtained in eqn. (7), (9), and (10), the network EE and DE can be calculated as follows: ΓEE (R) =

T net (R) E net (R)

and

ΓDE (R) =

T net (R) . cnet (R)

Hence, given any specific cell size R, we can find a corresponding point on the DE-EE tradeoff curve. Traversing all possible values of R gives the complete DE-EE tradeoff curve, as will be shown in the next section. In what follows, we shall provide some insights about the DE-EE tradeoff by sketching the relationship for some special case. In particular, we consider the interference case and make the three assumptions below to ease the derivation: 1) RA  R, i.e. the target area A is large. In this case, the transmit power reduces to Pt (R) = A1 · Rα , where  −1 ξ σ2 2 . A1 = − κ0 2Cf /B − 1 (α − 2)λ 3 The M levels may not corresponds to the same spectrum efficiency for different BSs. For instance, CTC-1/3 with BPSK and QPSK are used for large cells while CTC-1/2 with QPSK and 16QAM are used for small cells.

Notation

Value

Notation

Value

B

10 M Hz

f

1

κ0

10−3

σ2

−134 dB (−174 dBm/Hz)

C

0.5B bps

M

1

c0

0.02 M e

c1

0.1 e/kWh

asite

21.45 (macro)

bsite

354.44 (macro)

asite

7.84 (micro)

asite

71.5 (micro)

RA

10 km

Rref

2 km

IV. N UMERICAL E XAMPLES AND D ISCUSSIONS

TABLE III S IMULATION PARAMETERS . VALUES OF asite AND bsite FOR MACRO AND MICRO BS S ARE SUGGESTED BY [5].

Consequently, the network energy consumption becomes E net (R) = A2 · Rα + A3 · R−2 (11) 2 R asite 2 bsite T, A3 = RA T where A2 = A1 2A Rref λ λ 2) R ≥ 500m, i.e. we only consider deploying macro BSs. In this case, combined with the first assumption, the average annual total deployment cost reduces to cnet (R) = c1 A2 · Rα + (c1 A3 + A4 ) · R−2 (12) where

2 A4 = 0.86c0 · RA /λ

3) Cm (R) ≡ C, i.e. all users in the network have the same rate C bits/sec. In this case, the total network throughput can be reduced to a constant R2 C · T. (13) T net = A5 = 2A Rref λ Based on such assumptions, we have A5 , A2 · Rα + A3 · R−2 A5 ΓDE (R) = . α c1 A2 · R + (c1 A3 + A4 ) · R−2 ΓEE (R) =

In conclusion, there might be an optimal cell radius R that maximizes either EE or DE, but there might not be such a R that maximized both EE and DE simultaneously. The choice of an optimal cell radius becomes an multi-objective Pareto optimization problem and the result heavily depends on the definition of “optimal”. A major contribution of our work is the provision of a theoretical curve between EE and DE such that each point on the curve is a possible working point.

(14) (15)

E. Network Deployment Consideration Taking the derivatives of ΓEE (R) and ΓDE (R) with respect to (w.r.t) R and setting them to zero, we get two α-related cell radius thresholds for EE and DE, respectively, as follows:   1 2A3 α+2 EE , (16) Rth (α) = αA2 1   2(c1 A3 + A4 ) α+2 DE (α) = . (17) Rth αc1 A2 Given the range of cell radius R ∈ [Rmin , Rmax ] and a target deployment scenario (which corresponds to a specific α), the EE and DE may have the following three types of variation trends w.r.t the cell radius R. Take EE as an example, EE • Rth ≤ Rmin , EE increases monotonically with R; EE EE • Rmin < Rth < Rmax , EE firstly increases (R < Rth ) EE ) with R and the maximum and then decreases (R > Rth EE ; EE is achieved when R = Rth EE • Rth ≥ Rmax , EE decreases monotonically with R.

In this section, we give some numerical examples to illustrate how EE and DE vary with the cell radius R and what is the relationship between the two given different deployment scenarios. Simulation parameters are listed in Table III. Fig. 1 depicts the power consumption of each site and the whole network. Note that the transmit power is only part of the site power consumption. In particular, when R is small or α is small (corresponds to rural or suburb areas), the nontransmit related power becomes dominant. This explains why the network power consumption decreases as the cell radius increase when either R or α is small. On the other hand, when R and α grow larger, due to the large impact of path loss, the transmit power becomes dominant and the curves go up with increasing R. Fig. 2 shows how the site cost and network cost vary with the cell radius R. A jump at R = 500 m is due to the change of BS type from micro BS to macro BS, which upgrades the equipment cost. Moreover, as explained above, for large α (e.g. dense urban), as R gets large, the transmit power becomes dominant power consumption and increases sharply and so is the energy bill4 . This is why the total network cost increases again for large R and α. Fig. 3 depicts the EE and DE curves with increasing R. It might be a little contradictory with our intuition about how EE varies with R, namely the EE would increase monotonically with decreasing cell size, as shown in [7]. However, that is because only transmit-related energy has been considered. When transmit-independent power consumption is included, the monotonicity may not be preserved. In fact, the variation trend of EE and DE w.r.t R depends on the threshold values we derived in (16) and (17). Finally, Fig. 4 gives the EE-DE relations. In particular, we show both how the transmit EE (left) and the total EE (right) vary with DE. The tradeoff curves on the left match our intuition better, however, since it considers transmit power only in the energy consumption calculation, it does not give the correct picture of the EE-DE relationship. In fact, when transmit independent power consumption is considered (right), the relationship changes and somehow deviates from our intuition. In particular, there might no longer be a tradeoff between DE and EE for some deployment scenarios (e.g. α = 3.5, flat suburb). Another interesting observation is that, for large α (e.g. α = 4.5, dense urban), two different EE 4 Note here we do not set a limit on the maximum site transmit power. In practical scenarios, there would be such a constraint due to hardware limit, which would change the shape of the cost curves. However, for theoretical derivative of design insight, we temporarily ignore the constraint.

Power consumption (dB)

macro 40 30 20 10 0 −10 −20 −30

Transmit power 0

0.5

1

1.5

2

α = 3.5 α=4 α = 4.5

70 65 60

micro macro

55 50 45

4

0

0.5

R (km)

1

1.5

2

x 10 8

3.5 3 2.5 2 1.5

α = 3.5 α=4 α = 4.5

1 0.5 0

40

−4

x 10

Energy Efficiency (bits/Joule)

micro

−3

75

Transmit Energy Efficiency (bits/Joule)

Site power 50

Network power consumption w interference (dB)

60

0

500

7 6 5

α = 3.5 α=4 α = 4.5

4 3 2 1

1000

Deployment Efficiency (bits/$)

0

0

500

1000

Deployment Efficiency (bits/$)

R (km)

Fig. 4.

EE-DE tradeoff for different path loss exponents α.

Network annual cost w interference (M Euro)

Fig. 1. Transmit power, site power, and network power consumption as functions of cell radius R.

Site annual cost w interference (K Euro)

35

α = 3.5 α=4 α = 4.5

30

micro 25

20

15

10

macro

0

0.5

1

1.5

2

α = 3.5 α=4 α = 4.5

18 16 14 12

macro

10 8

V. C ONCLUSION AND F UTURE W ORK

6 4 micro 2 0

0

0.5

R (km)

Fig. 2.

the best possible EE performance. Moreover, we may gain insights on the optimal cell size for green cellular architecture design from the results obtained above. Specifically. for any target network throughput and given deployment budget, we can first calculate the corresponding deployment efficiency, say Γ∗DE , from which we can then decide the maximum achievable energy efficiency, say Γ∗EE , from Fig. 4. Finally, from Fig. 3, we get the optimal cell size R∗ corresponding to Γ∗EE .

20

1

1.5

2

R (km)

Annual average site and network cost as functions of cell radius R.

values may result in the same DE value. This is because in large path-loss case, both very small R or very large R result in high deployment cost but for different reasons: the former is because of the increasing number of sites while the latter is due to the sharply increasing electricity bill in OpEx. Note that the curves in Fig. 4 are the Pareto frontiers of DE and EE, that is, given any target value of DE, the curves give −3

x 10

900

α = 3.5 α=4 α = 4.5

Energy Efficiency (bits/Joule)

0.9 0.8

Deployment Efficiency (bits/Euro)

1

0.7

micro

0.6

macro

0.5 0.4 0.3 0.2 0.1 0

0

0.5

1

R (km)

1.5

2

α = 3.5 α=4 α = 4.5

800 700 600

micro 500

macro

400 300 200 100 0

0

0.5

1

1.5

2

R (km)

Fig. 3. EE and DE as function of cell radius R (normalized by the system bandwidth B).

In this paper, we have defined deployment efficiency to describe the effectiveness of BS deployment and energy efficiency to evaluate the effectiveness of energy use. We successfully characterized the analytical relations between the two, which turns out to be not a simple tradeoff. Future works may study the impact of employing new technologies on the tradeoff relations, including relay, distributed antenna systems, network MIMO and etc. R EFERENCES [1] P. Grant, Green Radio C The Case for More Efficient Cellular Base Stations, University of Edinburgh, 2009. [Online]. Available: http://www.see.ed.ac.uk/∼pmg/green radio.ppt [2] G. P. Fettweis and E. Zimmermann, “ICT energy consumption - trends and challenges,” in Proc. of 11th International Symposium on Wireless Personal Mulitimedia Communications, Lapland, Finland, Sept 2008. [3] K. Johansson, “Cost effective deployment strategies for heterogeneous wireless networks,” Ph.D. dissertation, KTH Information and Communication Technology, Stockholm, Sweden, Nov 2007. [4] H. Claussen, L. T. W. Ho, and L. G. Samuel, “Financial analysis of a pico-cellular home network deployment,” in in Proc. IEEE International Communications Conference (ICC), Giasgow, Scotland, June 2007. [5] F. Richter, A. J. Febske, and G. P. Fettweis, “Energy efficiency aspects of base station deployment strategies in cellular networks,” in Proc. of IEEE 70th Vehicular Technology Conference (VTC Fall), Anchorage, USA, Sept 2009. [6] A. J. Febske, F. Richter, and G. P. Fettweis, “Energy efficiency improvements through micro sites in cellular mobile radio networks,” in Proc. of 2nd International Workshop on Green Communications, parallel with IEEE GLOBECOM, Honolulu, USA, Dec 2009. [7] B. Badic, T. O’Farrel, P. Loskot, and J. He, “Energy efficiency radio access architectures for green radio: Large versus small cell size deployment,” in Proc. of IEEE 70th Vehicular Technology Conference (VTC Fall), Anchorage, USA, Sept 2009. [8] J.-M. Kelf and M. Coupechoux, “Cell breathing, sectorization and densification in cellular networks,” in Proc. of 7th Intl Symposium on Modeling and Optimization in Mobile, Ad Hoc, and Wireless Networks (WiOPT), Seoul, Korea, June 2009.