![](https://csdnimg.cn/release/download_crawler_static/16650886/bg1.jpg)
Energy-Efficient Antenna Selection and Power
Allocation in Downlink Distributed Antenna
Systems: A Stochastic Optimization Approach
Yuzhou Li, Min Sheng, Yan Zhang, Xijun Wang and Juan Wen
Information Science Institute, State Key Laboratory of ISN, Xidian University, Xi’an, Shaanxi 710071, China
{yuzhou_li, juanwen}@stu.xidian.edu.cn, msheng@mail.xidian.edu.cn, {yanzhang, xijunwang}@xidian.edu.cn
Abstract—In this paper, by jointly considering antenna se-
lection and power allocation, we address the energy efficiency
(EE) maximization problem with delay performance taken into
account in downlink distributed antenna systems (DAS). To
characterise system EE, we first define a revenue-cost (RC)
function as the weighted difference between sum transmit rate
and total energy consumption. We then formulate the problem as
a stochastic optimization model, which maximizes the long-term
average RC value subject to network stability (used to depict
delay performance) and average power constraints. An Energy-
Efficient Antenna selection and Power allocation Algorithm (EE-
APA) is proposed based on Lyapunov optimization technique.
The EE-APA adapts to time-varying channel conditions and
stochastic traffic arrivals without requiring any corresponding
prior-knowledge. Moreover, the theoretical analysis shows that
the EE-APA can not only push the EE arbitrarily close to the
optimal at the cost of delay performance, but also quantitatively
control the EE-delay performance. Numerical results validate the
adaptiveness of the EE-APA and the correctness of the theoretical
analysis.
I. I NTRODUCTION
Green radio (GR) is becoming an inevitable trend for
future wireless network design [1], [2]. As a promising
candidate technique, distributed antenna systems (DAS) have
been introduced to cater for the green requirements, attributed
to the advantages of increasing capacity, reducing transmit
power, and extending the coverage [3]–[5]. By flexible antenna
configuration, adaptive power allocation and dynamic rate
adjustment, DAS can increase network energy efficiency (EE)
or spectral efficiency (SE) significantly.
There have been many researches on EE- or SE-oriented
issues in DAS from different perspectives. Power allocation
algorithms with different complexity are proposed in [3], [6]
to optimize the system EE in DAS. [7] tackles the energy con-
servation problem in the mobile downlink DAS. [8] maximizes
the downlink sum rate by jointly considering power allocation
and antenna selection. Sum rate maximization is studied in
[9] by optimization of pairings of distributed antenna ports
and users. [10] first establishes the ergodic capacity for DAS,
then investigates the effect of antenna placement on the system
performance.
This paper is supported by National Natural Science Foundation of China
(61231008, 61172079, 61201141, 61301176, and 91338114), 111 Project
(B08038), National S&T Major Project (2012ZX03004002-003), and Shaanx-
i Province Science and Technology Research and Development Program
(2011KJXX-40).
As one of the main common points, [3], [6]–[10] (and the
references therein) do not consider delay performance, while
it is an important metric to measure the quality of service
(QoS) of traffics. Further, [3], [6]–[10] study the network
EE or SE issues based on static models, i.e., snapshot-based.
However, practical network control decisions must be made
in the presence of stochastic traffic arrivals and time-varying
channel conditions. Besides, [3], [6] do not consider antenna
selection. It is a waste of energy to turn all the antennas always
on due to the circuit power consumption of antennas.
To this end, this paper combines antenna selection and
power allocation to address the EE maximization problem
with delay performance taken into account. The proposed
algorithm aims to be able to: 1) adapt to time-varying channel
conditions and match stochastic traffic loads without requiring
any prior-knowledge of channel statistics and traffic arrivals.
2) quantitatively reveal and control EE and delay performance.
To achieve the above target, we make improvements based
on the existing works mainly from the following two aspects.
• To model the time-variant and dynamic features of the
system, we focus on the long-term average (rather than
snapshot-based) performance by adopting stochastic op-
timization theory.
• We take both antenna selection and power allocation
into consideration, and we bridge and control EE-delay
performance by network stability constraint.
Specifically, to indicate the preference on transmit rate
and energy, we first define a RC function as the weighted
difference between sum transmit rate and total energy con-
sumption. We then formulate the EE maximization problem
as a stochastic optimization model, aiming at maximizing the
long-term average RC value under the constraints of the aver-
age power consumption of per antenna and network stability.
We devise an Energy-Efficient Antenna selection and Power
allocation Algorithm (EE-APA) to solve the formulation using
Lyapunov optimization technique. The EE-APA is a typical
online algorithm without requiring any prior-knowledge of
input rates and channel statistics. Besides, the theoretical
analysis shows that there is a waxing and waning relation
between EE and delay, and the EE-APA provides a quantitative
rule to control EE-delay performance.
The remainder of this paper is organized as follows. In
Section II, we formally describe the concerned scenario and
IEEE ICC 2014 - Wireless Communications Symposium
978-1-4799-2003-7/14/$31.00 ©2014 IEEE 4963