366 IEEE COMMUNICATIONS LETTERS, VOL. 21, NO. 2, FEBRUARY 2017
Load-Aware Energy Efficiency Optimization in Dense Small Cell Networks
Shie Wu, Zhimin Zeng, and Hailun Xia
Abstract—Energy efficiency (EE) has become a crucial metric
in dense small cell networks (DSCNs) due to the tremendous esca-
lation of energy consumption. Since small cell base stations (SBSs)
are randomly deployed, loads of them are usually different.
In this letter, we aim to maximize the load-aware weighted sum
of EEs (LWSEEs) across all subchannels in DSCNs jointly con-
sidering SBSs’ loads and users’ signal processing power through
power allocation. First, we design the EE weight as a function
of load factor (LF). Then, the LWSEE optimization problem is
formulated as a non-concave sum-of-ratios optimization and we
present the optimal LWSEE algorithm to tackle the problem
based on the concave-convex procedure method. Furthermore,
a simplified LWSEE (LWSEE-simp) algorithm where SBSs form
interference groups is developed to reduce the signaling overhead
in DSCNs. Simulation results show that SBSs’ sum-EEs can be
optimized according to their LFs and the optimal interference
group size exists in the LWSEE-simp algorithm.
Index Terms— Dense small cell networks, energy efficiency,
load-aware, power allocation, interference group.
I. INTRODUCTION
T
O ENABLE the exponential growth of data traffic, dense
deployment of small cells is introduced in the 5G net-
works. At the same time, due to the considerable amount of
energy consumption in dense small cell networks (DSCNs),
energy efficiency (EE) has captured much attention [1].
In general, a cell’s load is defined as the average resource
usage in it [2]. Inter-cell interference is affected by neighbor-
ing cells’ loads, especially for dense networks [3]. Therefore,
a load-coupling signal-to-interference plus noise ratio (SINR)
model is proposed in [2]. Based on this model, problems
of energy minimization [2]–[4] and sum of EEs (sum-EE)
maximization [5] are investigated. In [2] and [5], the authors
prove that operating at full load is optimal. MIMO-OFDM
system is considered in [3]. In [4], power allocation and user
association are jointly optimized in joint transmission scenario.
In these studies, transmit power of a base station (BS) on all
subchannels is equal, which may limit the EE performance.
In user association process, all users are assumed to have
the same traffic statistics so that a BS’s load is proportional to
the number of users associated with it [6]. In the network, the
random distribution of users and small base stations (SBSs)
inevitably results in load disparity. If a SBS’s load is low,
operators tend to concern more about its EE as its users’ rate
demands can be easily met; otherwise, SBS’s capacity should
Manuscript received September 28, 2016; accepted October 11, 2016. Date
of publication October 31, 2016; date of current version February 9, 2017.
This work is supported by Chinese National Nature Science Foundation
(61571062) and the Fundamental Research Funds for the Central Universities
(2014ZD03-01). The associate editor coordinating the review of this letter and
approving it for publication was N. Pappas.
The authors are with the Beijing Laboratory of Advanced Information
Networks, School of Information and Communication Engineering, Beijing
University of Posts and Telecommunications, Beijing 100876, China (e-mail:
wushie@bupt.edu.cn; zengzm@bupt.edu.cn; xiahailun@bupt.edu.cn).
Digital Object Identifier 10.1109/LCOMM.2016.2620173
Fig. 1. Considered network model
be paid more attention [7]. Therefore, the network sum-EE
should be optimized considering SBSs’ load conditions. How
to design EE coefficients is not given in [7]. In the letter, the
EE weighting function with respect to load is first derived.
Then we optimize SBSs’ transmit power on each subchannel
to maximize the weighted sum-EE in DSCNs while satisfying
users’ rate demands.
The main contributions are as follows. Firstly, we optimize
the SBSs’ sum-EEs based on their loads and present the
explicit expression of EE weights. Secondly, the optimal
power allocation is obtained using the concave-convex proce-
dure (CCCP) method. Thirdly, to reduce signaling overhead,
a simplified power allocation algorithm for SBSs is proposed
by forming interference groups.
II. S
YSTEM MODEL AND PROBLEM FORMULATION
A. System Model
We consider a downlink OFDMA network as illustrated in
Fig.1, where a macrocell and M small cells are deployed in
different frequencies [8]. SBSs’ load conditions are different.
For each SBS, the system bandwidth is divided into K
subchannels, each one with bandwidth B
0
[Hz]. Let M =
{1, 2,...,M} and K =
{
1, 2,...,K
}
denote the SBS set and
the subchannel set, respectively. Assume that the instantaneous
channel state information (CSI) is perfectly known. Each
user chooses its serving BS with the strongest reference
signal received power (RSRP). All subchannels in SBSs are
allocated to users in round robin way. We denote the small cell
user (SUE) occupying subchannel k in SBS m as u
(
m, k
)
,and
the received SINR on subchannel k can be calculated as
γ
mku(m,k)
=
p
mk
h
mku(m,k)
I
mku(m,k)
+ σ
2
(1)
where I
mku(m,k)
=
M
j=1, j=m
p
jk
h
jku(m,k)
and p
jk
is the
transmit power of SBS j on subchannel k. h
jku(m,k)
is the
channel gain from SBS j to SUE u
(
m, k
)
on subchannel k.
σ
2
is the power of additive white Gaussian noise. Then the
transmission rate of SUE u
(
m, k
)
on subchannel k is given by
R
mku(m,k)
= αB
0
log
2
1 + γ
mku(m,k)
(2)
where α represents implementation loss. Let p
sp
u(m,k)k
denote the
signal processing power of user u
(
m, k
)
on subchannel k [9].
1558-2558 © 2016 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.
See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.