Minimum Power Consumption of a Base Station
with Large-scale Antenna Array
Zhiyuan Jiang, Sheng Zhou, and Zhisheng Niu
Tsinghua National Laboratory for Information Science and Technology (TNList)
Dept. of Electronic Engineering, Tsinghua University, Beijing, China
E-mail: jiang-zy10@mails.tsinghua.edu.cn, {sheng.zhou,niuzhs}@tsinghua.edu.cn
Abstract—In this paper we consider the minimum base station
(BS) power consumption given the sum rate requirement in large-
scale multiple-input-multiple-output (MIMO) systems. A single
cell with an M
tot
-antenna BS and N single-antenna users is
considered. The BS power consumption consists of two parts:
The part accounting for the total transmit power and the part
proportional to the number of active antennas. Specifically,
closed-form approximations (CFAs) of the optimal transmit power
and optimal number of active antennas are derived when the sum
rate requirement is high. A CFA of the ergodic sum capacity
upper bound for the downlink broadcast channel is also given.
I. INTRODUCTION
Recent years have witnessed the rapid growth of the
information and communication technology (ICT) industry,
which is becoming a significant part of the world energy
consumption. Particularly cellular networks are one of the
main energy consumers in the ICT industry. It is reported that
the base stations (BSs) are responsible for 80% of the total
energy consumption of cellular networks. Therefore, reducing
the energy consumption of BSs is the key to support future
development of cellular networks.
The concept of large-scale multiple-input-multiple-output
(MIMO) system is drawing much academic attention and
becoming an emerging technology, which scales up the num-
ber of BS antennas by an order of magnitude compared to
current state-of-the-art. It not only brings capacity gain but
also reduces the power consumption dramatically [1]. The
downlink channel of large-scale MIMO systems is in nature
the MIMO broadcast channel. The capacity of BC has been
studied intensively in the literature. In [2], the capacity region
of BC is shown to coincide with the dirty-paper coding
achievable rate region. The sum capacity is expressed by
a max-min problem in [3] and an uplink-downlink duality
is also found. Nonetheless, little is known for the ergodic
capacity of BC, especially when the channel matrix is non-
identically distributed (NID). On the other hand, the optimal
number of active radio-frequency (RF) chains is studied in [4],
however only simulation results are given. And the authors in
[5] considers the optimal active RF chains in a point-to-point
MIMO system.
This paper analyzes the minimum power consumption of
one BS with a large-scale antenna array given the user sum
This work is sponsored in part by the National Basic Research Program of
China (2012CB316001), the Nature Science Foundation of China (61201191,
60925002, 61021001), and Hitachi Ltd.
rate requirement. Specifically, we consider the communication
between a BS with M
tot
available antennas and N single-
antenna users. However only M out of M
tot
antennas are active
to support the rate requirement in the cell. In this paper, the
BS power consumption model is obtained from the EARTH
project [6]
P
BS
= P
0
+ MP
s
+Δ
P
P
t
, (1)
where P
0
is the static BS power consumption, P
s
is the BS
power consumption of each antenna and the corresponding RF
chain, Δ
P
is the transmit power coefficient related to power
amplifier (PA) efficiency, and P
t
is the total downlink transmit
power of all the active antennas. Among these coefficients,
P
s
and Δ
P
can be obtained from [6]. P
0
is regarded as a
constant and does not affect the optimization, therefore it is
omitted in the analysis hereinafter. The typical values of these
parameters are shown in Table I. Based on this model, the
rate-dependent parts of the BS power consumption not only
involve P
t
, which is directly related to the sum capacity, but
also include the number of active antennas M , which also has
a great impact on the sum capacity. The problem considered
in this paper is: Given the sum rate requirement and N users’
locations in the cell, what is the minimum base station (BS)
power consumption, i.e.
Minimize P
BS
,
s.t. R(P
BS
)
MP
s
+Δ
P
P
t
≤P
BS
≥ R
req
, (2)
where M and P
t
are jointly optimized. We assume the channel
state information (CSI) is perfectly known to the BS and users
prior to data transmission
1
.
The main contribution of this work is deriving the closed-
form approximations (CFAs) of the optimal number of active
antennas M
∗
and optimal transmit power P
∗
t
, along with
the minimum BS power consumption in large-scale MIMO
systems when the system sum rate is high. A CFA of the
downlink broadcast channel (BC) ergodic sum capacity upper
bound is derived to facilitate the analysis. All CFAs are verified
numerically.
1
In practice, this can be done using training sequences and channel
estimation methods [7].
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