2072 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 58, NO. 4, MAY 2009
Correction of Carrier Frequency Offsets in OFDM-Based
Spatial Multiplexing MIMO With Distributed
Transmit Antennas
Kai Deng, Student Member, IEEE, Youxi Tang, Member, IEEE,
Shihai Shao, Student Member, IEEE,andKeSun
Abstract—This correspondence focuses on the correction of carrier
frequency offsets (CFOs) in orthogonal frequency-division multiplexing
(OFDM)-based spatial multiplexing multi-input–multi-output (MIMO)
with distributed transmit antennas, where the CFOs between the receiver
and each transmit antenna are possibly different. Considering macroscopic
fading and multipath Rayleigh fading, the average power of the intercar-
rier interference (ICI) caused by the CFOs is derived, and the optimal
CFO correction value is then obtained by maximizing the average signal-
to-interference-and-noise ratio (SINR). In particular, when the difference
between the minimum and maximum values of the CFOs is no more than
half of the adjacent subcarrier spacing, an upper bound of the average
ICI power can be obtained, and a closed-form solution of the optimal CFO
correction value is derived.
Index Terms—Carrier frequency offsets (CFOs), correction, distrib-
uted antennas, orthogonal frequency-division multiplexing (OFDM),
multi-input–multi-output (MIMO).
I. INTRODUCTION
It is known that the performance of orthogonal frequency-division
multiplexing (OFDM)-based spatial multiplexing multi-input–multi-
output (MIMO) [1], [2] is sensitive to the carrier frequency offset
(CFO) that is unavoidably present due to the possible carrier frequency
mismatch as well as the relative motion between the transmitter and
the receiver [3], [4]. Any CFO causes a loss in the orthogonality of the
subcarriers, which results in intercarrier interference (ICI) and hence
performance degradation [4]. Therefore, it is of primary importance
to accurately estimate this frequency offset and compensate for it
prior to detection. In conventional OFDM-based spatial multiplexing
MIMO [1], [2], since the antennas are centralized at the same geo-
graphic location, and the same oscillator is used for all the transmit
antennas, the CFOs between the receiver and each transmit antenna
can be considered to be identical, i.e., there exits only one CFO.
The problem of CFO estimation for this case has received significant
attention in the literature [4]–[7]. The CFO compensation is then easily
accomplished by a simple CFO correction process that is implemented
by multiplying the received signal by a complex exponential signal
exp(−j2πnε
0
/N ) in the time domain, where N is the number of
subcarriers, and ε
0
is the CFO correction value that is set equal to
the estimated CFO obtained by CFO estimation.
As a promising technique of future wireless communications, sys-
tems with distributed antennas have been attracting much research in-
terest in the recent years [8], [9]. In OFDM-based spatial multiplexing
MIMO with distributed transmit antennas, since the transmit antennas
are distributed at separated geographic locations, either different oscil-
Manuscript received April 11, 2008; revised July 18, 2008. First published
October 31, 2008; current version published April 22, 2009. This work was
supported in part by the National Natural Science Foundation of China under
Grants 60832007, 60572090, 60496313, and 60602009 and in part by the
Doctor Foundation of Higher Education Institutions of China under Grant
20050614009. The review of this paper was coordinated by Dr. C. Cozzo.
The authors are with the National Key Lab of Communications, University
of Electronic Science and Technology of China, Chengdu 610054, China
(e-mail: dengkai@uestc.edu.cn; tangyx@uestc.edu.cn; ssh@uestc.edu.cn;
sunke@uestc.edu.cn).
Digital Object Identifier 10.1109/TVT.2008.2005032
lators are possibly used for each transmit antenna [10], or the multipath
components from different transmit antennas may impinge on the
receiver from different angles of arrival [11], which leads to different
CFOs between the receiver and each transmit antenna. In this case,
the CFO estimation becomes more difficult, and the simple compen-
sation method used in conventional OFDM-based spatial multiplexing
MIMO is invalid. The estimation of multiple CFOs is addressed in
[10]–[13]. On the other hand, the CFO correction cannot completely
compensate for multiple CFOs, and we have to perform equalization to
compensate for them. In [14] and [15], some equalization methods are
introduced to compensate for multiple CFOs in distributed space–time
block coding (STBC) OFDM systems. However, to achieve a good
performance or reduce the computational complexity, these methods
usually assume that the system has a coarse frequency synchronization
mechanism so that the ICI power caused by the CFOs is small [14],
[15]. Therefore, an initial CFO correction process is still required to
reduce the ICI before equalization. As there exist multiple CFOs, a
problem arises on how to determine the CFO correction value ε
0
.As
far as we know, there has been little concentration on this issue.
This correspondence addresses the correction of CFOs in OFDM-
based spatial multiplexing MIMO with distributed transmit antennas,
where the CFOs between the receiver and each transmit antenna
are possibly different. The contributions of this correspondence are
summarized as follows. Taking macroscopic fading and multipath
Rayleigh fading into consideration, the average power of the ICI
caused by the CFOs is derived, and the optimal CFO correction value
is then obtained by maximizing the average signal-to-interference-and-
noise ratio (SINR, i.e., the ratio of the average signal power to the sum
of the average ICI power and the noise power). In particular, when the
difference between the minimum and maximum values of the CFOs is
no more than half the adjacent subcarrier spacing, an upper bound of
the average ICI power can be obtained, and a closed-form solution of
the optimal CFO correction value is derived.
The rest of this correspondence is organized as follows. In the next
section, we describe the system model to be used. Section III deals
with the correction of CFOs, and the optimal CFO correction value is
derived by maximizing the average SINR. Some numerical results are
given in Section IV. Finally, Section V concludes this correspondence.
II. S
YSTEM MODEL
We consider an OFDM-based spatial multiplexing MIMO system
with M
T
distributed transmit antennas and M
R
centralized receive
antennas, where the CFOs between the receiver and each transmit
antenna are possibly different. This scenario accounts for the downlink
of a single-user distributed-antenna system. We also assume that the
channel does not significantly change during one OFDM symbol
period, and that the CFOs remain constant over the observation time
interval [12].
The sampled signal of an OFDM symbol transmitted via the ith
transmit antenna is given by the N-point inverse fast Fourier transform
(IFFT) of the data symbols
x
i
(n)=
1
√
N
N−1
k=0
X
i
(k)e
j2πnk/N
,
n =0, 1,...,N −1,i=1, 2,...,M
T
(1)
where X
i
(k) is the data symbol to be transmitted at the kth subcarrier
from the ith transmit antenna.
To avoid the intersymbol interference (ISI), a cyclic prefix (CP)
is inserted in front of the OFDM symbol. Note that in the scenario
with distributed transmit antennas, the CP length N
g
should be equal
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