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Gaoning He, Shunqing Zhang, Yan Chen, and Shugong Xu. Huawei Technologies, Co. Ltd., Shanghai, China. Email: {hegaoning, sqzhang, eeyanchen, ...
2013 IEEE Wireless Communications and Networking Conference (WCNC): PHY

Spectrum Efficiency and Energy Efficiency Tradeoff for Heterogeneous Wireless Networks Gaoning He, Shunqing Zhang, Yan Chen, and Shugong Xu Huawei Technologies, Co. Ltd., Shanghai, China Email: {hegaoning, sqzhang, eeyanchen, shugong}@huawei.com

Abstract—To meet the global challenge of reducing greenhouse gas emissions and the explosive demand of wireless data traffic, green architecture design is becoming a critical issue for mobile network operators. Heterogeneous deployments of different cell types have been used to fulfill the challenges mentioned above. In this respect, a critical concern for operators is how to deploy small cells in a green manner such that the global network is spectrum-efficient as well as energy-efficient. In this paper, we characterize the spectrum efficiency (SE) and energy efficiency (EE) for heterogenous wireless networks, taking into account realistic network power consumption model and dynamic network configuration. We give first order closed form analysis to address this issue and show that SE and EE may not be contradictory to each other as in the traditional networks. Our study also provides useful insights for the modeling and deployment of future green wireless networks. Index Terms—Spectrum efficiency, Energy efficiency, SE-EE tradeoff, Green Radio

DE-EE tradeoff relation has been discovered for heterogeneous network in [5]. However, research efforts to extend the SE-EE tradeoff relation in the heterogeneous scenario are still quite limited due to the following reasons. •

I. I NTRODUCTION



With the increasing demand for high-quality data services and the popularity of smart terminals, the energy consumption of current wireless communication networks shows continuous growth for several years. It has been predicted that the wireless industry will be responsible for more than 0.7% of global CO2 emission by the year 2020, which may raise environmental issues for the sustainable development of wireless communications. In order to reduce the energy consumption and environmental impact of the wireless industry, Green Radio (GR) technology has been proposed and widely accepted as one of the key enabling technologies in the recent years, and international collaborative projects including Mobile Virtual Centre of Excellence (MVCE) Green Radio project [1] and Energy Aware Radio and neTwork tecHnologies (EARTH) [2] have devoted significant research efforts towards novel GR technologies. As a new research framework, four fundamental tradeoffs [3] was developed to fully characterize the complicated system performance and provide a common platform to compare different GR technologies, which contains the tradeoff among spectrum efficiency (SE), energy efficiency (EE), deployment efficiency (DE) and other system parameters. Among the proposed four tradeoff relations, SE-EE strikes a balance between the system capability and the operating efficiency, which provides an insightful guideline for the dynamic power management in the homogeneous networks and attracts numerous research attentions in the recent years [4]. Recently, the

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Dynamic Topology Management Due to the coverage maintenance issues, base stations (BSs) in the homogeneous topology cannot be dynamically adjusted and the green strategies are mainly focusing on the efficient power management. While in the heterogenous network, if the coverage issues can be resolved by other BSs, we can further reduce the static power consumption by turning off some pico/femto BSs during off-peak periods. Hence, to consider the SE-EE tradeoff relation in the heterogeneous network, dynamic network topology management to switch on/off BS will be considered as an essential part. Deployment Overhead In the homogeneous network deployment, to provide the whole coverage and maintain the minimum rate requirement will be the main target and the associated static power consumption overhead is uniform to the whole network. However, in the heterogenous environment, the overhead would no longer be uniform and the optimal deployment strategy should be jointly considered, including the reward of the network throughput and the deployment overhead for different types of cells. In addition, the heterogeneous network size and throughput capability may also affect the SE and EE tradeoff curves.

In this paper, we will address the above issues and investigate the SE-EE tradeoff. To be more specific, we investigate the SE-EE tradeoff relation for a two-tier heterogeneous network considering realistic base station power model and dynamic network topology management. We derive the closedform expressions for SE-EE tradeoff relation under some reasonable assumptions and asymptotic cases. Numerical results will be provided thereafter to validate our theoretic claims. The rest of the paper is organized as follows: In section II we introduce the system model and some basic definitions. In section III, we study the SE-EE tradeoff for a two-tier heterogeneous wireless network and we completely characterize the SE-EE relation with close-form formula. Finally, numerical results are provided in section IV followed by conclusions in section V.

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II. S YSTEM M ODEL AND D EFINITIONS A. System model and assumptions In this paper, we consider a two-tier wireless network model with macro BS and small cell BS whose signal coverages are geographically overlapped in a certain service area. In practice, macro cells have very large coverage radius (e.g., r0 = 1 kM) used for signal coverage and small cells have much smaller coverage radius (e.g., r1 = 50 meters) dedicated for highspeed data offloading. Ideally, we would assume that the macro cell radius is much larger than the small cell radius, i.e., r0 ≫ r1 . For simplicity reasons, in this paper we consider the heterogeneous network area A within one macro cell coverage. We assume that n small cells are non-overlapped distributed in A and each small cell has two different working modes: active mode or sleep mode. A small cell is in active mode if there is at least one user in its coverage. A small cell is in sleep mode if there is no active user is its coverage. We further assume that user terminals are distributed in A following poisson distribution Pois(λ), each with the same date transfer rate R. A key challenge of heterogeneous network deployment is how to cope with inter-tier and intra-tier interference on one operator’s spectrum band. One method is to do “frequency sharing”, i.e., allocate a fraction of licensed spectrum to small cells while keeping the whole licensed spectrum for macro cells as it is. Another method is to do “frequency division”, i.e., allocate different spectrum bands to macro cells and small cells. The “frequency division” method is becoming a trend for future small cell deployment as more and more countries are considering to allocate more spectrum for small cell deployment. In this paper, we focus on the case of “frequency division”. The study of the “frequency sharing” would be provided in another paper. Following the frequency division scheme, we assume that the small cell layer is operated on bandwidth ωB and the macro layer is operated on bandwidth (1−ω)B, where B is the total system bandwidth and the partition factor ω ∈ [0, 1]. We also assume that macro or small cell BS transmits signals to multiple user terminals using orthogonal and equal bandwidth. The wireless channel is assumed to be frequency-flat. Thus, the throughput of macro cell T0 and the throughput of a small cell T1 can be written as ( ) ( ρ0 B0 g0 ρ0 g0 ) T0 = k0 B0 log 1+ 2 = (1 − ω)B log 1+ 2 (1) σ B0 σ ) ( k 1 ∑ ρ1 B1 g1 T1 = (2) B1 log 1+ Ij + σ 2 B1 j=1 where k0 and k1 are the number of users served by macro cell and small cell, respectively. More precisely, in this paper k0 is the number of users in the coverage of the macro cell but NOT in the coverage of any small cell, k1 is the number of users in the coverage of a small cell. B0 = (1 − ω)B/k0 and B1 = ωB/k1 are the per user bandwidth for macro cell user and small cell user, respectively. Ij is the inter cell interference in

the small cell layer, ρ0 and ρ1 are the transmit power spectrum density of macro BS and small cell BS, respectively. g0 = ζ0 r0−φ and g1 = ζ1 r1−φ are the channel gains of macro user and small cell user, respectively. φ is the path loss exponent, ζ0 and ζ1 are the path loss coefficients. B. Definitions In this part, we give the formal definition of spectrum efficiency and energy efficiency which are recognized as the key metrics for the design of green wireless networks. First, we give the definition of network throughput. The network throughput is defined as the total transmission rate of all BSs in all layers. In our model, the network throughput is defined as the total transmission rate of the macro cell and all the n small cells, i.e., TNet = T0 + nT1 Second, we define the network power consumption. In practice, the power consumption of a heterogeneous wireless network can be considered as the summation of the average power consumption of different classes of BS sites, i.e., ∑ i PNet = N i PSite i i where i is the BS class index, N i and PSite are the number of BS sites and site average power consumption in class i, respectively. In general, the power consumption of a BS site includes many components, e.g., power losses from circuit power of signal processing, converter, power supply, radio frequency, A/D D/A, battery backup, antenna feeder, site cooling consumption, etc. In [6] it is shown that the BS transmit power and BS site power has a linear relation for LTE/LTEA systems. Therefore, the BS site power consumption of any class i can be approximated as a linear model, as follows: { i i i NTX PSleep PTX = (0 i ] (3) PSite = i i i i i i NTX PBase + µ PTX PTX ∈ 0, PMax i i where PTX is the BS transmit power, PBase is the power consumption when BS transmits at the minimum non-zero power, µi is the slope of the traffic-dependent power consumption, i.e., BS transmit power and traffic have a near-linear relation, i PSleep is the power consumption during sleep mode which is i normally smaller than PBase . It is shown in [7] that network energy can be significantly saved by putting BSs into sleep mode, i.e., dynamically switching off some components inside BS when there is little or nothing to transmit. In this paper, we will analyze the network SE and EE taking into account the realistic power model (3) and the impact of dynamic BS sleeping. Some typical parameters for BS power model of different classes are listed in Table 1. We now give the definitions of network spectrum efficiency and energy efficiency, as follows: • Spectrum efficiency (SE) is defined as the ratio of the network throughput over the network bandwidth:

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ηSE =

TNet (bit/sec/Hz) B

(4)

BS type

i PBase

i PSleep

i PM ax

µi

NiT

Macro

130 W

75 W

20 W

4.7

6

Micro

56 W

39 W

6.3 W

2.6

2

Pico

6.8 W

4.3 W

0.13 W

4

2

TABLE I P OWER MODEL PARAMETERS FOR DIFFERENT BS



CLASSES

macro BS are

 ( ηSE ln 2 )  λ0 e (1−ω)K −1 (1 − ω)B M e − 1 PTX = γ0 [ ( ηSE ln 2 ) ] ωB λ1 e ωK −1 S PTX = e −1 γ1

[8].

Energy efficiency (EE) is defined as the ratio of the network throughput over the average network power consumption Pnet : ηEE =

TNet (bit/joule) PNet

(5)

The proof can be found in Appendix A. Since the expressions of transmit power are quite complex under general situation, it would be more interesting to characterize the system under some typical assumptions.

III. SE-EE T RADEOFF FOR H ETEROGENOUS W IRELESS N ETWORKS In this section, we study the SE-EE relation for the twotier heterogeneous network model with sparse small cell deployment, i.e., the inter site distance between adjacent small cells are much larger than the coverage radius so that the inter small cell interference Ij in equation (2) is sufficient small and can be omitted when calculating the overall network power consumption. The analysis of dense small cell scenario (very short inter-site distance) would be from another paper. Suppose that the transmit power of macro cell BS and the transmit power of small BS in equation (1) and (2) shall support the rate requirement from the corresponding users. From equation (1), the achievable rate of a macro cell user can be written as R=

( (1 − ω)B ρ0 g0 ) log 1 + 2 k0 σ

(6)

Note that in our model k0 is a random variable following Poisson distribution. For a certain rate requirement R, the transmit power per Hz ρ0 is function of k0 . Therefore, the transmit power of macro cell BS can be written as pM TX = (1 − ω)Bρ0 which is function of random variable k0 . Similarly, the achievable rate of a small cell user is ωB ρ1 g1 ) R= log 1 + 2 k1 σ

where ηSE = KR/B represents the network spectrum efficiency, γ1 = g1 /σ 2 and γ0 = g0 /σ 2 represent the SNR of small cell user and macro cell user, respectively. λ1 = λπr12 and λ0 = λπ(r02 − nr12 ) represent the average number of users served by a small cell BS and served by the macro BS, respectively. K = λπr02 = λ0 + nλ1 is the averaged total number of users in the considered network. n is the number of small cells.

(

(7)

pTX,1 (k1 ) is the transmit power of small cell on the frequency band ωB/k1 . The total transmit power of a small cell BS is pSTX = ωBρ0 which is function of random variable k1 . We now have the following lemma:

Corollary 1: Following Lemma 1, for a two-tier heterogeneous system with sufficient large number of users K and sufficient small cell coverage of small cells r0 ≫ r1 , the average transmit power of macro BS and small cell BS can be approximated as (1 − ω)B αηSE (e − 1) γ0 ≈ βηSE

M PTX ≈ S PTX λ0 ln 2 (1−ω)K

(8) (9)

λ1 B ln 2 γ1 K .

and β = where α = Proof: The proof follows immediately from the limitation rule: lim (ex − 1) = x. The detailed proof is not provided x→0 here due to lack of space. This implies that when the small cell coverage is relatively small (compared to the macro cell coverage) the transmit power of macro cell BS would scales exponentially with the network traffic (equivalent to ηSE ) and the transmit power of small cell BS would scales only linearly with the network traffic. Based on the BS linear power model (3) and the results above, we derive the following key theorem in this paper. Theorem 1: (SE-EE Relation) For a two-tier heterogeneous network with sufficient large number of users K and sufficient small cell coverage of small cells r0 ≫ r1 , the network SE-EE relation can be expressed as ηEE ≈

BηSE aηSE + b (eαηSE − 1) + c

where

Lemma 1: For a two-tier heterogeneous wireless network, given macro cell radius r0 , small cell radius r1 , user distribution Pois(λ) and assume each user has the same traffic demand R, the average transmit power of small cell BS and

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S a = nNTRX µS β, (1 − ω)B M b = NTRX µM , γ0 S S M M c = nNTRX PBase + NTRX PBase .

(10)

B 20 MHz

R 1 Mbps

σ2 -174 dBm

φ

ζ1 = ζ2

3.5

1

ω

Small cell radius r =100 meters

5

2.5

0.3

1

x 10

η

=(B/c) η

EE

TABLE II S YSTEM PARAMETERS USED IN NUMERICAL EVALUATION .

n=60 SE

n=50

Energy efficiency ηEE (bit/joule)

2

The proof can be found in Appendix B. The theorem above characterizes the SE-EE relation of a two-tier heterogeneous wireless network under assumption of large number of users K and relatively smaller coverage of small cells r0 ≫ r1 . From Theorem 1, we have the following result:

n=40 1.5 n=30 1

n=20

0.5 Approximation Exact 0 10

Corollary 2: For a two-tier heterogeneous network with sufficient large number of users K and sufficient large number of small cells n, the SE-EE relation is ) 1 ( −1 −1 ηEE ≈ cηSE + ϵ (11) B

In this section, numerical results are provided to validate our theoretical claims. Some key system parameters are listed in Table IV. First, based on the considered two-tier heterogeneous network model, we compare in Fig. 1 the exact SE-EE relation and the approximated SE-EE relation derived in (10) in Theorem 1 for different number of small cells n, assuming that the macro cell radius is r0 = 1000 meters and small cell radius is r1 = 100 meters. As expected, the approximation curves are very close to the exact SE-EE relation curves. When the number of small cells n is small, SE exponentially decreases with EE, this is because when n is small the exponential part dominates the denominator in (10). When the number of small

13 14 15 16 17 Spectrum efficiency ηSE (bps/Hz)

18

19

20

Small cell radius r1=50 meters

4

12

x 10

Energy efficiency ηEE (bit/joule)

n=250

n=200

10

The proof can be found in Appendix C.

IV. N UMERICAL E VALUATION AND D ISCUSSION

12

Fig. 1. SE-EE tradeoff for two-tier heterogeneous wireless network with one macro cell and n small cells deployed within the macro cell coverage. The location of user terminals follows Poisson distribution. The Macro cell radius is r0 = 1000 meters and the small cell radius is r1 = 100 meters.

S M where ϵ = nNTRX µS Kγ11α1 + NTRX µM Kγ00α0 . For practical small −1 cell systems ϵ ≪ cηSE , which implies that the PA power consumption is much less than the static part, the energy efficiency of the system scales linearly with its spectrum efficiency B ηEE ≈ ηSE c

This result is somewhat surprising since it is contradictory to our intuition of “increasing SE must be done at the cost of EE reduction” as shown in [3] for the homogeneous scenario. However, when shifting to the case of heterogeneous networks with sufficient large number of small cells, spectrum efficiency and energy efficiency are not necessary contradictory and they can be simultaneously improved. This is because in small cell dominated heterogeneous networks the network power consumption is mainly contributed by static power. In this case, when the number of users is sufficient large, the transmission rate is increased without significant increase of power consumption any more.

11

8

n=150

6

n=100 n=50

4

2 Approximation Exact 0 10

11

12

13 14 15 16 17 Spectrum efficiency ηSE (bps/Hz)

18

19

20

Fig. 2. SE-EE tradeoff for two-tier heterogeneous wireless network with one macro cell and n small cells deployed within the macro cell coverage. The location of user terminals follows Poisson distribution. The Macro cell radius is r0 = 1000 meters and the small cell radius is r1 = 50 meters.

cells n is large, SE behaves as a linear function of EE, which coincides with our discovery in Corollary 2. Second, Fig. 2 shows the same comparison result for shrinked small cell radius r1 = 50 meters. As expected, when small cell radius is reduced our approximation results become even closer to the exact SE-EE curves. This observation is valid for the assumption r0 ≫ r1 in Theorem 1. Finally, from both figures we note that the maximum EE is achieved at different n for different SE regions. The difference is more significant when the small cell radius is smaller. This means for a target SE, there exists an optimal small cell deployment to maximize the network EE, especially when the small cell coverage is small.

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V. C ONCLUSION In this paper, we have defined and characterized the relation between spectrum efficiency and energy efficiency for the heterogenous wireless networks. We derive close-form expression for SE-EE tradeoff relation under asymptotic cases. From our theoretical and numerical results, we found that for heterogeneous wireless network with sufficient large number of small cells, the spectrum efficiency and energy efficiency has a linear relationship. This discovery is somewhat surprising and contradictory to traditional results in homogeneous networks. Our result implies that spectrum efficiency and energy efficiency may not be two contradictory factors for future heterogeneous wireless networks. To the best of our knowledge, this phenomenon has not be addressed in any other previous work. Our results provide useful insights for the architecture design of future green wireless networks. Future works will consider the case of frequency sharing between macro cell and small cells as mentioned in the system model section and may also focus on the case of non-uniform spatial traffic distribution. A PPENDIX A P ROOF OF L EMMA 1 Proof: From equation (7) we have the average transmit power of small cell BS (considering log2 (·)) [ 2 )] σ 2 ωB [ ( k1 R ln 2 ) ] σ ωB ( k1 R S ωB PTX = E 2 −1 = E e ωB −1 g1 g1 where ( R ln 2 )k ) ( R ln 2 ∞ ( k1 R ln 2 ) ∑ e ωB λ1 λ1 e ωB −1 −λ E e ωB = e 1 =e k! k=0

and by applying (12) into (A) we have ] [ ( R ln 2 ) 2 λ1 e ωB −1 σ ωB S PTX = −1 e g1

S M where PTX and PTX are functions of ηSE given by Lemma 1, S PBase = P(x1 > 0)pSBase = (1 − e−λ1 )pSBase + e−λ1 pSSleep represents the average value of pSBase . Then from equation (8), (9) and (12), we can show that

lim ηEE =

r1 r0

→0

BηSE aηSE + b (eαηSE − 1) + c

where the value of a, b and c are listed in (10). This completes the proof. A PPENDIX C P ROOF OF C OROLLARY 2 Proof: When n is sufficient large, we know from λ0 = λπ(r02 −nr12 ) that λ0 would be sufficient small. This means that when large number of small cells is deployed in the network, not many users will be served by the macro BS. In this case, 1+λ0 we know that α0 = (1−ω)K is also sufficient small, which λ0 α M implies PTX → γ0 ηSE , since eαηSE − 1 → αηSE . Then (10) can be reduced to B BηSE = −1 ηEE ≈ λ1 β λ0 α cη c + γ1 ηSE + γ0 ηSE SE + ϵ S M where ϵ = nNTRX µS λγ11β + NTRX µM λγ00α . Therefore, we have −1 ηEE ≈

) 1 ( −1 cηSE + ϵ B

This completes the proof. ACKNOWLEDGEMENT This paper is partially supported by the National High Technology Research and Development Program of China (863 Program 2012AA011400) and the National Basic Research Program of China (973 Program 2012CB316000). R EFERENCES

Similarly, from equation (6) we have [ 2 )] 0 R ln 2 σ (1 − ω)B ( k(1−ω)B M =E PTX e −1 g0 ) [ ( R ln 2 ] 2 σ (1 − ω)B λ0 e (1−ω)B −1 = e −1 g0 This completes the proof. A PPENDIX B P ROOF OF T HEOREM 1 Proof: From equation (5), the energy efficiency of a twotier heterogeneous network containing one macro cell and n small cells can be expressed as E (KR) BηSE )= ηEE = ( S S M M nPTotal + PTotal E npTotal + pTotal BηSE ( S ) ( M ) = S S M M S nNTRX PBase +µ PTX + NTRX PBase +µM PTX Bη ) SE (12) =( S S M P M +nN S µSP S +N M µMP M nNTRXPBase +NTRX Base TRX TX TRX TX

[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] R. Tafazolli, “EARTH - energy aware radio and network technologies,” in Proc. of Next Generation Wireless Green Networks Workshop, Pairs, France, Nov 2009. [3] Y. Chen, S. Zhang, S. Xu, and G. Y. Li, “Fundemantal Tradeoffs on Green Wireless Networks,” IEEE Commun. Mag., vol. 49, no. 6, pp. 30 – 37, Jun. 2011. [4] G. Miao, N. Himayat, Y. G. Li, and D. Bormann, “Energy-Efficient Design in Wireless OFDMA,” in Proc. of IEEE International Communications Conference (ICC), Beijing, China, May 2008, pp. 3307 – 3312. [5] G. He, S. Zhang, Y. Chen, and S. Xu, “Energy efficiency and deployment efficiency tradeoff for heterogeneous wireless networks,” in Proc. of IEEE Global Telecommunications Conference (Globecom), California, USA, Dec. 2012. [6] G. Auer, V. Giannini, C. Desset, I. Godor, P. Skillermark, M. Ollsson, M. A. Imran, D. Sabella, M. J. Gonzalez, O. Blume, and A. Fehske, “How much energy is needed to run a wireless network?” IEEE Trans. Wireless Commun., vol. 18, no. 5, pp. 40 – 49, Oct. 2011. [7] I. Ashraf, F. Boccardi, and L. Ho, “Sleep mode techniques for small cell deployments,” IEEE Commun. Mag., vol. 49, no. 8, pp. 72 – 79, Aug. 2011. [8] K. Johansson, “Cost effective deployment strategies for heterogeneous wireless networks,” Ph.D. dissertation, KTH Information and Communication Technology, Stockholm, Sweden, Nov 2007.

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