Downloaded from http://iranpaper.

ir
http://www.itrans24.com/landing1.html

Energy and Area Spectral Efficiency of Cell

Zooming in Random Cellular Networks
Atieh R. Khamesi and Michele Zorzi

Department of Information Engineering, University of Padova

Via Gradenigo 6b, 35131 Padova, Italy
{khamesi, zorzi}@dei.unipd.it

Abstract—In this paper, we study the Energy Efficiency (EE) Cell Zooming (CZ) was introduced in [1] as a technique
and Area Spectral Efficiency (ASE) of green random cellular to reduce energy consumption in cellular networks by fine-
networks which utilize the Cell Zooming (CZ) techniques. To this tuning the cell size via adaptation of the coverage radius
aim, using stochastic geometry, we derive a tractable expression
for the Ergodic Capacity in a Poisson Voronoi Tessellation (PVT) of a BS. Nowadays in the network planning phase, capacity
random cellular network in which both Base Station (BS) and and cell size are assigned statically based on the maximum
Mobile User (MU) locations are drawn randomly from two transmission power corresponding to the estimated peak traffic
independent Poisson Point Processes (PPPs). The performance load. However, the traffic pattern in cellular networks exhibits
of this network is examined under different MU densities and large fluctuations in both time and space. This characteristic
two CZ algorithms. Numerical evaluations show that there is
an optimum transmission power, which maximizes EE in PVT of mobile networks can be used for energy saving purposes
random cellular networks. On the other hand, increasing the through range adaptation techniques [6].
transmission power and the cell size does not improve ASE much More precisely, CZ is a technique to adjust the BS’s cov-
more after passing a threshold. The tradeoff between EE and erage area dynamically according to the network traffic load.
ASE is also presented.
[7] reported that CZ can decrease total power consumption
by approximately 20%. CZ is achieved differently in different
I. I NTRODUCTION
scenarios. For instance, when the traffic is low or the users
The next generation of mobile communication systems, are concentrated around the BS, the transmission power can
namely 5G, intends to improve some characteristics of the be reduced without any loss in expected Quality of Services
previous mobile generations, e.g., data rate, delay and cost in (QoS). As another example, in a low traffic scenario some BSs
addition to addressing new features, such as ubiquitous cov- can be switched off, while the others compensate the coverage
erage, device-to-device (D2D) communications, etc. Besides holes by increasing their power, a technique called zooming
achieving these goals, realization of green 5G is essential for out.
both environmental concerns, such as air pollution and carbon In order to address CZ, techniques such as Coverage Ex-
dioxide footprint, and also energy-related costs in the mobile tension Technology (CET) need to be adopted. In fact, CET
communication industry, which are important for end-users is not only limited to increasing transmit power, it can also
and telecommunication companies as well [1]. be obtained by relay and cooperative multi-point (CoMP)
In addition, the concept of small cells and random deploy- transmission [1]. Reference [8] gives an overview of the CZ
ment of Base Stations (BSs) in LTE and 5G, e.g., Heteroge- concept.
neous Network (HetNet), introduced a new area in cellular In another work [9], three algorithms were proposed to
network planning, named random cellular networks. In this implement CZ and their performance in a single cell scenario
regard, stochastic geometry came up as a novel and helpful was studied. The three proposed methods, namely Continu-
technique to deal with these random structures [2]. ous, discrete and fuzzy CZ algorithms, aim to dynamically
Recently, random networks have been studied through sev- adjust the BS transmission power in order to avoid constantly
eral aspects in the literature. In [3], stochastic geometry is working with maximum power emission. It was shown that all
exploited to propose a useful approach to deal with random the proposed techniques outperform the traditional approaches,
cellular networks. Besides, [4] studied spatial spectrum and assuming that the location of the users are known or can be
Energy Efficiency (EE) in a Poisson Voronoi Tessellation obtained by a location detection scheme.
(PVT) random cellular network using a Markov Chain (MC) Moreover, up to 57% of the total power in wireless mobile
channel access model. In another work [5], EE and Spatial communication is consumed by BSs [10]. Therefore, it seems
Spectral Efficiency (SSE) in random MIMO cellular networks crucial to find a strategy to reduce the BS power consumption
have been analyzed. or the number of active BSs. To this aim, turning off the
The approach followed in this paper is different from what serving macrocells is one of the techniques to improve the
has been done before, and provides a new expression for power saving efficiency without loss of throughput [11].
ergodic capacity which is less complex to compute and also To the best of our knowledge, the concept of CZ in random
to simulate. cellular networks, which is the main scope of this work, has

978-1-5090-1328-9/16/$31.00 ©2016 IEEE

Downloaded from http://iranpaper.ir
http://www.itrans24.com/landing1.html

different ways, for example based on equal distance partition,

1.5
so that
{ }
𝐷 2𝐷 (𝑁 − 1)𝐷
ℛ𝑐 = , ,..., ,𝐷 ,
𝑁 𝑁 𝑁
1
where 𝐷 is the maximum cell radius imposed by the maximum
transmitted power of a BS, 𝑃max and the BS density [12]. In
this scenario, the set of allowed transmission powers is
0.5 Rc { ( )𝛼 ( )𝛼 }
1 2
𝒫𝑡 = 𝑃max , 𝑃max , . . . , 𝑃max ,
𝑁 𝑁

which satisfies the QoS requirement of the MUs located at

0
0 0.5 1 1.5 the cell edge by keeping the received power at the prescribed
level. Alternatively, cell partitioning can also be determined
according to an equal power split.
Fig. 1. An example of PVT Random Cellular Network
In the second scenario, a general CZ method is considered.
In this case, under a low traffic situation, i.e., small MU
density, only a subset of the BSs remain active, while the
not yet been studied. In addition, in this paper we consider a others turn to sleep mode. In this case, we apply the thinning
random distribution of Mobile Users (MUs). To this aim, first operation to the PPP of the BS distribution [13], which results
we derive an expression for the ergodic capacity and then use in a 𝑝-thinned point process Φ̃𝐵 with density
it to formulate EE and Area Spectral Efficiency (ASE) in this
setting. We finally evaluate our results by numerical methods. ˜ 𝐵 = 𝑝 ⋅ 𝜆𝐵 ,
𝜆 (1)
The rest of the paper is organized as follows. In Section
II the system model and two CZ algorithms are introduced.
where 𝑝 is the retention probability, i.e., each BS switches off
Sections III and IV provide the ergodic capacity and EE
with probability (1 − 𝑝), independently of the location and of
and ASE in PVT random cellular networks, respectively.
the possibility that any other BS∈ Φ𝐵 switches off or remains
The numerical evaluations are reported in Section V. Finally,
active. 𝑝 can be determined based on the network parameters
Section VI concludes the paper and discusses some future
and the traffic profile.
works.

III. E RGODIC C APACITY

II. S YSTEM M ODEL
Without loss of generality, by exploiting the PPP charac-
In this work, we focus on downlink transmission in which teristics of the BS and MU locations, we can just focus and
each MU is associated with its nearest BS. The channel analyze the behavior of a typical MU located at the origin and
between the transmitter and the receiver is modeled by
√ its typical BS. Then the obtained results will be generalized
(1 + 𝑟)−𝛼 ℎ, where ℎ ∼ 𝒞𝒩 (0, 1) is an i.i.d. Rayleigh fading to the whole network.
channel coefficient and (1 + 𝑟)−𝛼 represents a non-singular To this aim, the Signal-to-Interference-plus-Noise Ratio,
path-loss model; where 𝑟 and 𝛼 are the transmission distance SINR, experienced by the typical MU associated with its
and the path-loss exponent, respectively. At the receiver side, nearest BS, BS𝑖 , is given by
there is also AWGN with normalized power 𝜎 2 .
Moreover, in our model a PVT random cellular network 𝑃𝑡 (1 + 𝑟𝑖 )−𝛼 ∣ℎ𝑖 ∣2
SINR = ∑ , (2)
is considered, where the BSs are located based on a Poisson 𝑃𝑡 (1 + 𝑟𝑗 )−𝛼 ∣ℎ𝑗 ∣2 + 𝜎 2
Point Processes (PPP), called Φ𝐵 , with density 𝜆𝐵 . Each BS 𝑗∈Φ𝐵 ∖{𝑖}
forms a circular coverage area of radius 𝑅𝑐 ∈ ℛ𝑐 around
itself. Figure 1 sketches an example of PVT random cellular where the channel coefficient between the typical MU and BSℓ
network with the circular coverage area of radius 𝑅𝑐 . ℛ𝑐 and is denoted by ℎℓ . Note that 𝑟ℓ , which denotes the distance from
equivalently 𝒫𝑡 , the set of allowed transmission powers, will the typical MU to BSℓ , is a random variable due to the random
be defined later based on the CZ scenarios. Also, we assume location of BSs. Besides, it is assumed that all BSs transmit
that MUs are randomly located based on Φ𝑀 , which is a PPP with the same power 𝑃𝑡 .
with density 𝜆𝑀 . The ergodic capacity is the average rate that is achievable
In this work, two CZ scenarios will be discussed. In the first by each user and is given by [14], [15]
case, a discrete CZ is adopted where each cell is divided into
𝑁 concentric circular zones. Cell partitioning can be done in 𝒞 = 𝔼 [log2 (1 + SINR)] . (3)
Downloaded from http://iranpaper.ir
http://www.itrans24.com/landing1.html

⎛ ⎡ ⎤
Lemma 1. The ergodic capacity per user in a PVT random ∏ [ ( )]
cellular network is given by ⋅ ⎝𝔼 Φ𝐵 ⎣ 𝔼h exp −𝑡𝑃𝑡 (1 + 𝑟𝑗 )−𝛼 ∣ℎ𝑗 ∣ 2 ⎦
𝑗∈Φ𝐵 ∖{𝑖}
∫ ∞ 2 ⎡ ⎤⎞
𝑒−𝑡𝜎 ∏ [ ( )]
𝒞= −𝔼Φ𝐵 ⎣ 𝔼h exp −𝑡𝑃𝑡 (1 + 𝑟𝑗 )−𝛼 ∣ℎ𝑗 ∣ 2 ⎦⎠ d𝑡
0 𝑡
( [ ∫ ∞[ ] ] 𝑗∈Φ𝐵
1
⋅ exp −2𝜋𝜆𝐵 𝑟d𝑟 1− (9)
𝑅𝑐 1 + 𝑡𝑃 𝑡 (1 + 𝑟)−𝛼 ⎛ ⎡ ⎤
∫
]) ∏
∞ 2
[ ∫ ∞[ ] (𝑒) 𝑒−𝑡𝜎 ⎝ 1
1 = ⋅ 𝔼 Φ𝐵 ⎣ ⎦
− exp −2𝜋𝜆𝐵 1− 𝑟d𝑟 d𝑡, (4) 0 𝑡 1 + 𝑡𝑃𝑡 (1 + 𝑟𝑗 )−𝛼
1 + 𝑡𝑃𝑡 (1 + 𝑟)−𝛼 𝑗∈Φ𝐵 ∖{𝑖}
0 ⎡ ⎤⎞
∏ 1
where 𝜎 2 is the noise power. Besides, 𝜆𝐵 , 𝑅𝑐 and 𝑃𝑡 are −𝔼Φ𝐵 ⎣ ⎦⎠ d𝑡.
1 + 𝑡𝑃𝑡 (1 + 𝑟𝑗 )−𝛼
the BS density, the cell radius and the transmission power, 𝑗∈Φ𝐵
respectively. (10)

Proof. By substitution of (2) in (3), we have Where (𝑎) comes ∫ ∞ 𝑒from Lemma 1 of [16], which states that
−𝑧

⎡ ⎛ ⎞⎤ log(1 + 𝑥) = (1 − 𝑒−𝑥𝑧 )d𝑧. The change of variable

(∑ 0 𝑧 )−1
−𝛼 2 2
⎢ ⎜ 𝑃 (1 + 𝑟 ) −𝛼
∣ℎ ∣ 2
⎟⎥ 𝑡 = 𝑧 𝑗∈Φ ∖{𝑖} 𝑃 𝑡 (1 + 𝑟𝑗 ) ∣ℎ 𝑗 ∣ + 𝜎 gives (𝑏). In
𝒞 =𝔼Φ𝐵 ,h ⎣log2 ⎝1 + ∑ 𝑡 𝑖
−𝛼
𝑖
2 2
𝐵
⎠⎦ (𝑐), the expectation and integral can be interchanged since
𝑃𝑡 (1 + 𝑟𝑗 ) ∣ℎ𝑗 ∣ + 𝜎
𝑗∈Φ𝐵 ∖{𝑖} the integrand is non-negative. Then, (𝑑) and (𝑒) follow from
[∫ (
(𝑎)
∞ −𝑧
𝑒 independence of the PPP Φ𝐵 and Rayleigh channel fading
= 𝔼Φ𝐵 ,h 1− property. The final result is obtained by using the probability
0 𝑧
⎛ ⎞⎞ ⎤ generating functional of a PPP Φ with density 𝜆, given by
[ ] ( ∫∫ )
⎜ 𝑃𝑡 (1 + 𝑟𝑖 )−𝛼 ∣ℎ𝑖 ∣2 ⎟⎟ ⎥ ∏
exp⎝−𝑧 ∑ ⎠⎠ ⎦ d𝑧 (5) 𝔼Φ 𝑓 (𝑥) = exp −𝜆 (1 − 𝑓 (𝑥)) d𝑥 .
𝑃𝑡 (1 + 𝑟𝑗 )−𝛼 ∣ℎ𝑗 ∣2 + 𝜎 2 ℝ2
𝑗∈Φ𝐵 ∖{𝑖} 𝑥∈Φ
[∫ 2
∞
(𝑏) 𝑒−𝑡𝜎
= 𝔼Φ𝐵 ,h
0 𝑡 To use the result of the previous lemma in the CZ frame-
⎛ ⎞
∑ work, we just need to substitute the proper BS density, 𝜆𝐵 ,
⋅ exp ⎝−𝑡 𝑃𝑡 (1 + 𝑟𝑗 )−𝛼 ∣ℎ𝑗 ∣2 ⎠ transmission power, 𝑃𝑡 ∈ 𝒫𝑡 , and cell radius, 𝑅𝑐 ∈ ℛ𝑐 .
𝑗∈Φ𝐵 ∖{𝑖} Compared to the other works [3]-[4] which derived the
( ) ] ergodic capacity in random networks, the approach and final
( )
−𝛼 2
⋅ 1 − exp − 𝑡𝑃𝑡 (1 + 𝑟𝑖 ) ∣ℎ𝑖 ∣ d𝑡 (6) expression in (4) is more tractable and less complex to
simulate in MATLAB and Mathematica. This result also takes
[∫
∞
𝑒−𝑡𝜎
2 advantage of stochastic geometry to reduce the simulation time
=𝔼Φ𝐵 ,h compared to the conventional Monte-Carlo method.
0 𝑡
( ⎛ ⎞
IV. E NERGY AND A REA S PECTRAL E FFICIENCY (EE &
∑
⋅ exp ⎝−𝑡 𝑃𝑡 (1 + 𝑟𝑗 )−𝛼 ∣ℎ𝑗 ∣2 ⎠ ASE)
𝑗∈Φ𝐵 ∖{𝑖} In this section, we investigate the performance of the CZ
⎛ ⎞⎞ ⎤
∑ scenarios in random cellular networks in terms of EE and ASE.
− exp ⎝−𝑡 𝑃𝑡 (1 + 𝑟𝑗 )−𝛼 ∣ℎ𝑗 ∣2 ⎠⎠ d𝑡⎦ (7) Along the lines of [15], [17], ASE is formulated as
𝑗∈Φ𝐵
∫ ASE = 𝜆𝑀 ⋅ 𝒞, (11)
∞ −𝑡𝜎 2
(𝑐) 𝑒
= where 𝜆𝑀 and 𝒞 are the MU density and the ergodic capacity
0 𝑡
⎛ ⎡ ⎛ ⎞⎤ of each user, respectively. Note that since we consider a
∑ random distribution for the users, we substitute the ratio of
⋅ ⎝𝔼Φ𝐵 ,h ⎣exp ⎝−𝑡 𝑃𝑡 (1 + 𝑟𝑗 )−𝛼 ∣ℎ𝑗 ∣2 ⎠⎦
the total number of active users over the cell area with the
𝑗∈Φ𝐵 ∖{𝑖}
⎡ ⎛ ⎞⎤ ⎞ MU density.
∑ Additionally, the EE of an active BS can be expressed as
−𝔼Φ𝐵 ,h ⎣exp ⎝−𝑡 𝑃𝑡 (1 + 𝑟𝑗 )−𝛼 ∣ℎ𝑗 ∣2 ⎠⎦⎠ d𝑡
𝑗∈Φ𝐵 𝑊 𝐿𝒞
EE = , (12)
(8) 𝑎𝑃𝑡 + 𝑃𝑐
∫ ∞ 2
where 𝑊 , 𝐿 account for the spectral bandwidth and the total
(𝑑) 𝑒−𝑡𝜎
= number of active users in a cell. Besides, in the denominator
0 𝑡
Downloaded from http://iranpaper.ir
http://www.itrans24.com/landing1.html

×10 -3
0.06 11
2
λ = 10 [1/km ]
M
10
λM = 50 [1/km2 ]
0.05 2
λM = 100 [1/km ] 9 p=1
p = 0.75

Energy Efficiency [Mbit/J]

Energy Efficiency [Mbit/J]

8 p = 0.5
0.04 p = 0.25
7

0.03 6

5
0.02
4

3
0.01
2

0 1
0 50 100 150 200 250 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Cell Radius [m] P t / P max

Fig. 2. Energy efficiency of a PVT random cellular network for different user Fig. 4. Energy efficiency of a PVT random cellular network for different
densities retention probabilities

5 V. P ERFORMANCE E VALUATION AND N UMERICAL

4.5
2
λM = 10 [1/km ] R ESULTS
2
λM = 50 [1/km ]
Area Spectral Efficiency [Mbps/km 2 ]

4
λ = 100 [1/km 2 ] In this section, we evaluate the performance of a green
M

3.5 PVT random cellular network in terms of EE and ASE

while adopting the CZ techniques. The system parameters are
3
summarized in Table I. Note that considering EE or ASE
2.5 individually does not give a comprehensive overview about
2 the network performance, since there is a tradeoff between
1.5
the two metrics.
First, the EE of the network for different MU densities is
1
depicted in Figure 2. As shown, in general the EE improves by
0.5 increasing the number of active users, since more MUs can be
0 served with the same power transmission level. However, for
0 50 100 150 200 250
a fixed 𝜆𝑀 , there is an optimum cell radius which maximizes
Cell Radius [m]
EE. The reason is that, although a larger cell size causes higher
Fig. 3. Area spectral efficiency of a PVT random cellular network for different ergodic capacity, on the other hand more transmission power
user densities is needed in this case to satisfy the QoS requirements for the
MUs located at the cell edge.
TABLE I Furthermore, Figure 3 shows that ASE grows monotonically
N ETWORK PARAMETERS with the MU density and the cell radius, however, it almost
𝑁 15
saturates when the transmission power approaches its maxi-
𝛼 3 mum value.
𝑎 1.5 Figures 4 and 5 illustrate the effect of the second CZ
𝜎2 −50 [dBm]
scenario for a PVT random cellular network. Note that we
𝑃max 44.77 [dBm]
𝑊 0.1 [MHz] assumed that there are enough resources to serve the MUs
𝜆𝐵 1 [/km2 ] even when decreasing the number of active BSs. As mentioned
𝜆𝑀 10 [/km2 ] in (1), 𝜆˜ 𝐵 is proportional to the retention probability, i.e.,
decreasing 𝑝 reduces the number of active BSs which serve
the specific number of users. Therefore, EE improves as 𝑝
of (12), 𝑃𝑐 denotes the non-transmission related power con- decreases. Note that in this work we consider a constant reten-
sumption, which corresponds to the hardware power consump- tion probability in order to study the performance in a simple
tion such as electronic circuits, processors, air-conditioners, scenario. Obviously, more elaborated thinning operation can
rectifiers and backup batteries [15]. Also, 𝑎 ≥ 1 represents enhance the results and opens a new direction for future works.
a scaling factor to compensate for the difference between Although reducing the BS density improves EE, it degrades
consumed and radiated power, which is caused by internal ASE as presented in Figure 5. It is also shown that the higher
losses, like the feeders. the BS density the faster the saturation of ASE.
Downloaded from http://iranpaper.ir
http://www.itrans24.com/landing1.html

0.5 0.06

0.45
Area Spectral Efficiency [Mbps/km 2 ]

0.05
0.4

Energy Efficiency [Mbit/J]

0.35
0.04
0.3

0.25 0.03

0.2
0.02
0.15 λ = 10 [1/km ]
2
p=1 M
p = 0.75
0.1 λ = 50 [1/km2 ]
p = 0.5 M
0.01 2
p = 0.25 λM = 100 [1/km ]
0.05

0 0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
P t / P max Area Spectral Efficiency [Mbps/km 2 ]

Fig. 5. Area spectral efficiency of a PVT random cellular network for different Fig. 6. Tradeoff between energy and area spectral efficiency of a PVT random
retention probabilities cellular network for different BS Densities

×10 -3
As a significant result of this paper, Figures 6 and 7 illustrate 11

the tradeoff between EE and ASE, revealing that improving 10

ASE does not always accompany with an EE enhancement. p=1
9
In fact, concavity of the curves proves the existence of an Energy Efficiency [Mbit/J] p = 0.75
p = 0.5
8
optimum point in tradeoff between EE and ASE. In other p = 0.25

words, after passing through the curve’s peaks, increasing ASE 7

degrades EE. Besides, it can be observed that this happens 6
approximately when ASE approaches its saturation region. The
5
result of this figure gives a useful perspective for network
planning. In addition, Figures 6 and 7 demonstrate that as 4

long as there are enough resources to serve the active users, 3

it is worth reducing the number of working BSs, a result that
2
could not have been obtained easily by individual analysis of
1
the ASE and the EE. 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Area Spectral Efficiency [Mbps/km 2 ]
VI. C ONCLUSION
Fig. 7. Tradeoff between energy and area spectral efficiency of a PVT random
In this work, we investigated the energy and area spectral cellular network for different retention probabilities
efficiency in a PVT random cellular network which utilizes cell
zooming techniques in transmission strategy. To this aim, using
stochastic geometry, we derived a novel expression for the In addition, more precise thinning and retention probability
ergodic capacity in random networks, which is less complex models are an interesting topic for future works.
and faster to simulate compared to the ones proposed before.
Two CZ algorithms have been considered in this work. R EFERENCES
Numerical evaluations showed that there is an optimum
[1] Z. Niu, Y. Wu, J. Gong, and Z. Yang, “Cell zooming for cost-efficient
cell radius, and equivalently a transmission power, which green cellular networks,” IEEE Communications Magazine, vol. 48,
maximizes EE. Besides, they revealed that by adopting the CZ pp. 74–79, November 2010.
algorithm based on the thinned point process, as the number [2] H. ElSawy, E. Hossain, and M. Haenggi, “Stochastic geometry for
of active BSs decreases EE increases and ASE degrades. Also, modeling, analysis, and design of multi-tier and cognitive cellular
wireless networks: A survey,” IEEE Communications Surveys Tutorials,
the tradeoff between EE and ASE was demonstrated and the vol. 15, pp. 996–1019, March 2013.
results showed that as long as there are enough resources to [3] J. G. Andrews, F. Baccelli, and R. K. Ganti, “A tractable approach
serve the MUs, the CZ technique based on the thinned point to coverage and rate in cellular networks,” IEEE Transactions on
Communications, vol. 59, pp. 3122–3134, November 2011.
process provides some gains. [4] X. Ge, B. Yang, J. Ye, G. Mao, C.-X. Wang, and T. Han, “Spatial
As future work, the effect of other CZ techniques in ran- spectrum and energy efficiency of random cellular networks,” IEEE
dom cellular networks can be investigated. Also, the concept Transactions on Communications, vol. 63, pp. 1019–1030, March 2015.
[5] A. R. Khamesi, B. Yang, X. Ge, and M. Zorzi, “Energy and spatial
of random MIMO cellular network and different types of spectral efficiency analysis of random MIMO cellular networks,” in 22nd
infrastructures are interesting items for future investigation. European Wireless Conference (EW), May 2016.
Downloaded from http://iranpaper.ir
http://www.itrans24.com/landing1.html

[6] S. Luo, R. Zhang, and T. J. Lim, “Optimal power and range adaptation
for green broadcasting,” IEEE Transactions on Wireless Communica-
tions, vol. 12, pp. 4592–4603, September 2013.
[7] V. Prithiviraj, S. B. Venkatraman, and R. Vijayasarathi3, “Cell zooming
for energy efficient wireless cellular network,” Journal of Green Engi-
neering, vol. 3, Jul 2013.
[8] K. C. Tun and K. Kunavut, “Green cellular networks: A survey, some
research issues and challenges,” KMUTNB: International Journal of
Applied Science and Technology, vol. 7, pp. 1–13, July 2014.
[9] R. Balasubramaniam, S. Nagaraj, M. Sarkar, C. Paolini, and P. Khaitan,
“Cell zooming for power efficient base station operation,” in 9th Inter-
national Wireless Communications and Mobile Computing Conference
(IWCMC), pp. 556–560, July 2013.
[10] D. Zhang, K. Yu, Z. Zhou, and T. Sato, “Energy efficiency scheme
with cellular partition zooming for massive MIMO systems,” in IEEE
Twelfth International Symposium on Autonomous Decentralized Systems
(ISADS), pp. 266–271, March 2015.
[11] J. Y. Kim, J. Kim, and C. S. Kang, “A novel BS power saving
scheme with virtual coverage management for green heterogeneous LTE
networks,” in 2015 International Conference on Computing and Network
Communications (CoCoNet), pp. 886–891, Dec 2015.
[12] R. W. Heath, M. Kountouris, and T. Bai, “Modeling heterogeneous
network interference using Poisson point processes,” IEEE Transactions
on Signal Processing, vol. 61, pp. 4114–4126, Aug 2013.
[13] D. Stoyan, W. S. Kendall, and J. Mecke, Stochastic geometry and its
applications. 2nd ed., John Wiley and Sons, 1996.
[14] A. Thornburg and R. Heath, “Ergodic capacity in mmWave ad hoc
network with imperfect beam alignment,” in IEEE Military Commu-
nications Conference (MILCOM), pp. 1479–1484, Oct 2015.
[15] M. Aldosari and K. Hamdi, “Trade-off between energy and area spectral
efficiencies of cell zooming and BSs cooperation,” in 5th International
Conference on Intelligent and Advanced Systems (ICIAS), pp. 1–6, June
2014.
[16] K. A. Hamdi, “Capacity of MRC on correlated Rician fading channels,”
IEEE Transactions on Communications, vol. 56, pp. 708–711, May
2008.
[17] M.-S. Alouini and A. Goldsmith, “Area spectral efficiency of cellular
mobile radio systems,” IEEE Transactions on Vehicular Technology,
vol. 48, pp. 1047–1066, Jul 1999.