Energy Efficiency Maximization for MIMO-OFDMA Systems with Imperfect CSI
Jing Mao, Chen Chen, Xiaoning Zhang, HaigeXiang
School of Electronics Engineering and Computer Science
Peking University
Beijing, China
e-mail:{maojing, c.chen, zxn, xianghg}@pku.edu.cn
Abstract—Unlike the previous work on efficiency (EE) for
multiple input multiple output (MIMO) orthogonal frequency
division multiple access (OFDMA) systems with assuming the
availability of perfect channel state information (CSI), this
paper investigates robust resource allocation to improve the
system EE under imperfect CSI. Considering the estimation
error and the feedback delay, we formulate a combinatorial
problem involving subcarrier assignment and power allocation
to maximize the EE subject to a transmit power constraint and
a minimum rate constraint. By relaxing the integral
constraints, we develop a joint subcarrier and power allocation
algorithm which can be implemented by one-dimension search.
The simulation results demonstrate that the proposed
algorithm can achieve a comparable EE performance with the
optimal algorithm. Moreover, with taking imperfect CSI into
account, the proposed algorithm can achieve higher EE when
compared with a nonrobust algorithm.
Keywords-energy efficiency; resource allocation; multiuser;
MIMO-OFDMA
I. INTRODUCTION
The concept of green communication is promoted due to
large energy consumption brought by the high volumes of
data traffic in recent years. As multiple input multiple output
(MIMO) orthogonal frequency division multiple access
(OFDMA) has been widely adopted by all major wireless
communication systems, energy efficient MIMO-OFDMA
systems play a crucial role in realizing green communication
and networks.
It is not surprising that energy efficiency (EE) for
MIMO-OFDMA systems has attracted a lot of interest in the
field of academia and industry [1]-[3]. In [2], a near-optimal
resource allocation algorithm is proposed in LTE-based
MIMO-OFDMA systems with guaranteeing the minimum
user rate requirement. In [3], Tang et al. investigate the EE-
spectral efficiency (SE) tradeoff in MIMO-OFDMA
broadcast channel. However, the above works assume that
the perfect channel state information (CSI) is available at the
transmitter and receiver. In practice, it is impossible to obtain
the perfect CSI due to channel estimation errors, prediction
errors, quantization errors and feedback delay.
The effect of imperfect CSI on EE has been extensively
studied for MIMO systems [4]-[6] and OFDMA systems [7]-
[9]. Considering the additive bounded CSI uncertainty model,
a robust precoding aiming at the EE maximization is given
for the point-to-point MIMO channel [6]. In [4], the number
of users and power allocation is optimized to maximize the
EE in uplink virtual MIMO systems based on statistical CSI.
In [9], Wang et al. study a resource allocation algorithm in
multi-cell OFDMA wireless networks from the EE
perspective. Nevertheless, to the best of our knowledge, no
work considered the MIMO-OFDMA case assuming
imperfect CSI.
In this paper, we focus on the EE optimization in MIMO-
OFDMA systems when transceivers only acquire imperfect
CSI. Considering the channel estimation and prediction error,
we formulate a combinatorial problem to maximize the EE
subject to a total power constraint and a minimum rate
constraint. By considering subcarrier time-sharing relaxation,
we transform the problem to a convex problem, whose
optimal value is an upper bound to the maximum EE. Based
on the analysis of the solution of the convex problem, we
propose a suboptimal algorithm which can be implemented
by one-dimension search. The simulation results show that
the EE yielded by the suboptimal algorithm is nearly the
same as the maximum EE of the system. Moreover, we also
confirm that our proposed algorithm can achieve higher EE
than a non-robust algorithm which does not take into account
imperfect CSI.
II. SYSTEM MODEL AND PROBLEM FORMULATION
Consider a single-cell MIMO-OFDMA system where
one base station (BS) serves K users via N subcarriers. The
BS is equipped with M
T
antennas, and each user has MM
T
antennas. As stated before, assuming the perfect CSI at the
BS and users is unrealistic due to many factors such as
channel estimation error and feedback delay. In this paper,
we assume that the channel across different pairs of transmit
and receive antennas are independent. Thus, the MIMO-
OFDM channel prediction problem becomes an OFDM
channel prediction problem. According to [10], the perfect
frequency-domain channel coefficient between the BS and
user k on subcarrier n,
, can be represented as
,
where
and
denote the nominal channel and the
CSI error. The entries of
, denoted as
, are indepen-
dent and identically distributed (i.i.d.) zero mean circularly
symmetric complex Gaussian (ZMCSCG) variables with
variance
. Note that
's are correlated on different
subcarriers for a specified user k and the value of
is
determined by the estimation error, distribution and
temporal autocorrelation of the time-domain fading channel