IEEE COMMUNICATIONS LETTERS, VOL. 17, NO. 3, MARCH 2013 541
On the Energy Efficiency Optimality of
OFDMA for SISO-OFDM Downlink System
Qingjiang Shi, Weiqiang Xu, Dapeng Li, Yaming Wang, Xiaowei Gu, and Wenshu Li
Abstract—This letter considers energy–efficient resource allo-
cation for a general SISO-OFDM downlink system. A fundamen-
tal result is proven that OFDMA is optimal for achieving the
maximum energy efficiency measured by bits per joule. Using
the OFDMA solution structure, we turn the nonconvex energy–
efficient power allocation problem into a quasi–convex optimiza-
tion problem and propose an efficient power allocation algorithm
which requires solving at most two simple subproblems. The
achieved energy efficiency performance of the proposed power
allocation algorithm is verified via simulations.
Index Terms—Energy–efficient resource allocation, SISO–
OFDM downlink system, OFDMA.
I. INTRODUCTION
O
VER past decades, most efforts are made to improve the
system throughput or spectral efficiency of wireless net-
works, and various resource allocation methods are developed
to obtain higher QoS data transmission service in wireless
communication. Generally, high network throughput implies
large energy consumption. As a result, the current information
and communication technology contributes more and more
greenhouse gas emissions, which poses a challenge in cellular
system design. As a viable solution, energy–efficient system
design is becoming an increasingly important topic in wireless
communication and recently has gained a lot of attention in
both industry and academia [1].
So far, there are two main classes of energy efficient
system design methods. The first class is network planing.
For example, it is shown in [2] that, reducing cell size can
increase energy efficiency which is measured by the number
of bits transmitted per unit energy. In this letter, we focus on
the second class—energy-efficient resource allocation [1], [3]–
[7]. As opposed to the traditional spectral-efficient resource
allocation, dynamic resource allocation is designed to achieve
the maximum energy efficiency. Miao et. al. [3], [4] have con-
sidered energy efficiency optimization for an uplink OFDMA
system and showed that energy efficiency is improved by
rate adaption or adjusting the distribution of subchannels
among users. In [5], the authors assume flat–fading across
Manuscript received December 27, 2012. The associate editor coordinating
the review of this letter and approving it for publication was J. Armstrong.
Q. Shi, W. Xu, Y. Wang, X. Gu, and W. Li are with the School of Info.
Sci. & Tech., Zhejiang Sci-Tech University (ZSTU), Hangzhou 310018, China
(e-mail: qing.j.shi@gmail.com).
D. Li is with Nanjing University of Posts and Telecommunications, Nanjing
210003, China.
This work is supported by the National Nature Science Foundation of
China under grant 61272311, 61070063, 60702081, 61201162, the Key
Project of Chinese Ministry of Education under grant 212066, the Zhejiang
Provincial Science Foundation under grants LY12F02042, LQ12F01009, and
the Science Foundation of Zhejiang Sci-Tech University (ZSTU) under Grant
No. 1203805Y.
Digital Object Identifier 10.1109/LCOMM.2013.020413.122898
subcarriers and have considered energy-efficient bandwidth al-
location for a downlink OFDMA system. Accounting for QoS
constraints, [6] has studied the problem of energy-efficient
joint subcarrier allocation and rate/power allocations. Note
that, all the above works assume OFDMA system where no
inter-user interference exists. For interference-limited multi-
cell system/interference channel, [7] has studied distributed
energy-efficient power optimization based on a noncooperative
game method.
In this letter, we consider energy-efficient power optimiza-
tion for a general single cell SISO–OFDM downlink system
where subcarriers are allowed to be shared among users.
[8] has shown a fundamental result on the optimality of
OFDMA for spectral efficient resource allocation in SISO-
OFDM system. As a counterpart, an open question is whether
OFDMA is also optimal for energy-efficiency optimization.
This letter first answers this question by mathematical proof.
Then the nonconvex energy–efficient power allocation prob-
lem is simplified to a quasi-convex optimization problem
by using the OFDMA solution structure. Finally, a simple
energy-efficient power allocation algorithm is proposed which
requires only solving at most two simple subproblems.
The rest of the paper is organized as follows. In Section
II, we describe the system model and give the problem for-
mulation. In Section III, we prove the optimality of OFDMA
for energy efficiency. A simple power allocation algorithm is
proposed in Section IV. Section V demonstrates simulation
results while Section VI concludes the paper.
II. P
ROBLEM FORMULATION
Consider a single-cell SISO downlink communication sys-
tem where a base station (BS) sends signals to K users
over a frequency-selective channel. Using N -point FFT based
OFDM, the frequency-selective channel can be equivalently
viewed as N flat fading channel over N subcarriers [9]. The
system model can be described as
y
k,n
= h
k,n
K
k=1
√
p
k,n
x
k,n
+ z
k,n
,
n =1, 2,...N,k =1, 2,...,K.
(1)
where y
k,n
is the received signal by user k on subcarrier n,
h
k,n
denotes the channel coefficient between the user k and BS
on subcarrier n, x
k,n
∼CN(0, 1) is the transmitted signal for
user k on subcarrier n, p
k,n
is the transmission power used for
the user k’s signal, z
k,n
∼CN(0,σ
2
k,n
) is the additive white
Gassuan noise (AWGN).
By assuming that each user uses single-user detection (i.e.,
view other users’ signal as noise), the sum rate in nats/Hz of
1089-7798/13$31.00
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2013 IEEE