A Stochastic Geometry Approach to Energy
Efficiency in Relay-Assisted Cellular Networks
Na Deng, Sihai Zhang, Wuyang Zhou, and Jinkang Zhu
Dept. of Elect. Eng. & Inform. Sci., University of Science & Technology of China, China, 230027.
Email: ndeng@mail.ustc.edu.cn,
{shzhang, wyzhou, jkzhu}@ustc.edu.cn.
Abstract—Though cooperative relaying is believed to be a
promising technology to improve the energy efficiency of cellular
networks, the relays’ static power consumption might worsen
the energy efficiency therefore can not be neglected. In this
paper, we focus on whether and how the energy efficiency of
cellular networks can be improved via relays. Based on the
spatial Poisson point process, an analytical model is proposed to
evaluate the energy efficiency of relay-assisted cellular networks.
With the aid of the technical tools of stochastic geometry, we
derive the distributions of signal-to-interference-plus-noise ratios
(SINRs) and mean achievable rates of both non-cooperative
users and cooperative users. The energy efficiency measured by
“bps/Hz/W” is expressed subsequently. These established expres-
sions are amenable to numerical evaluation and corroborated by
simulation results.
I. INTRODUCTION
With the rapid rise in the number of user equipments
(UEs) and base stations (BSs), the energy consumption of
cellular networks grows quite amazing. It is shown in [1]
that the energy consumed by BSs accounts for nearly 60-
70% of the total network energy. Therefore, improving the
energy efficiency of BSs becomes the fundamental challenge
to implement and spread green communications.
Recently, cooperative relaying has been in-depth studied
as a promising way to reduce the energy consumption of
cellular networks [2][3], which offers the possibility to extend
coverage and increase capacity, and provides more flexible
and cost-effective deployment options as well [4]. Compared
with BSs, RSs cover a much smaller area and require lower
transmit power. Meanwhile, the UEs covered by RSs generally
enjoy much higher average signal-to-interference-plus-noise
ratios (SINRs). In addition, RSs do not have a wired backhaul
connection, which makes their deployment cost largely lower.
All the above confirms that using cooperative relaying tech-
nique is capable of lowering the transmit power consumption
in cellular networks and the low power RSs are easy to be
deployed without modifying current cellular infrastructure.
However, the total power consumption of both BSs and
RSs consists of two parts, transmit power and other power
consumption. The transmit power consumption occupies only
a small part of the whole power consumption, which means
that large amount of power consumption, coined in this
This work was partially supported by NSFC (61172088), National programs
for High Technology Research and Development (SS2012AA011702), the
National Major Special Projects in Science and Technology of China under
grant 2010ZX03003-001 and 2010ZX03005-003.
paper as static power consumption, is contributed by signal
processing, battery backup, site cooling and etc. Therefore,
the transmit power saved by cooperative relaying technique
may not compensate for the additional power consumption
of RSs which leads to higher power consumption in cellular
networks.
The aforementioned discussions motivate us to investigate
whether and how the energy efficiency of cellular networks
can be improved via relays. The related works mostly focus
on regular network deployments, such as the hexagonal grid
model, merely estimated by Monte Carlo simulations [2][5][6].
However, the spatial deployment observed in actual commu-
nication networks is usually far from being regular. Mean-
while, the interference and the signal strength at a receiver
critically depend on the spatial positions of the interfering
transmitters, thereby mathematical techniques are needed to
explicitly model the node distribution. Stochastic geometry
theory has recently emerged as an essential tool to model
and quantify interference, mean achievable rate, and coverage
in cellular networks which is verified to be close to the
actual networks [7]. Consequently, this paper proposes an
analytical model for evaluating the energy efficiency of relay-
assisted cellular networks using stochastic geometry, instead
of relying on system simulations only. The distributions of
SINRs and mean achievable rates of both non-cooperative UEs
and cooperative UEs are derived. We use the ratio of spectral
efficiency to power consumption with unit bps/Hz/W as the
metric and further analyze the energy efficiency. Simulation
results present how the intensity of users affects the energy
efficiency and how much RS’s static power consumption
should be controlled below in order to obtain some energy
saving gains. Notably, our work serves as a pioneering effort
on the network design and planning, especially with respect
to energy efficient wireless communications.
II. N
ETWORK MODEL AND METRICS
We consider a relay-assisted downlink cellular network
shown in Fig. 1. The locations of BSs are modeled according
to a homogeneous Poisson point process (PPP) Φ
b
of intensity
λ
b
, and RSs are located according to another homogeneous
PPP Φ
r
of intensity λ
r
. Specifically, for a given PPP, the
number of points in a bounded area is a Poisson-distributed
random variable and those points are uniformly-distributed
within the area. A realization of the relay-assisted cellular
network with Poisson distributed BSs and relays portrayed by