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10.1109/TVT.2015.2481727, IEEE Transactions on Vehicular Technology
1
Blind Carrier Frequency Offset Estimation for MIMO-OFDM with
Constant Modulus Constellations via Rank Reduction Criterion
Weile Zhang and Qinye Yin
Abstract—In this paper, we propose a new blind carrier
frequency offset (CFO) estimator for multi-input multi-output
orthogonal frequency-division multiplexing (MIMO-OFDM) sys-
tems with constant modulus constellation. The proposed esti-
mator exploits a rank reduction criterion and works in the
general MIMO scenarios where no space-time block coding
is assumed. As compared to several existing competitors, the
proposed estimator does not suffer from performance error
floor as signal-to-noise (SNR) increases, and thus it can behave
better under the moderate and high SNR region. The Cramer-
Rao bound of CFO estimation for MIMO-OFDM with constant
modulus constellation is derived and the numeral results are
provided to corroborate the proposed studies.
Index Terms—Carrier frequency offset (CFO), multi-input
multi-output (MIMO), orthogonal frequency division multiplex-
ing (OFDM), constant modulus constellations.
I. INTRODUCTION
The orthogonal frequency division multiplexing (OFDM)
is deemed as the promising technique for broadband wire-
less communications. However, OFDM is sensitive to carrier
frequency offset (CFO) between transceivers that results in
inter-carrier interference (ICI) and performance deterioration.
Different kinds of CFO estimation methods have been de-
veloped during the past few years. Among these estimators,
the blind estimation has attracted specially large amount of
attention due to the improved spectral efficiency, especially for
continuous-transmission OFDM-based systems. For examples,
the CFO can be blindly obtained based on the kurtosis-type
criterion [1], the diagonality criterion [2], overampling [3], [4],
the presence of null subcarriers [5], [6], or the multi-antenna
redundancy [7]–[9].
Another class of blind CFO estimators has been proposed
for OFDM systems with constant modulus modulations [10]–
[13]. For example, a subspace based estimator was proposed
in [11] by exploiting the low-rank signal model and the
correlation among OFDM subcarriers. Another blind estimator
for OFDM with constant modulus constellations was proposed
in [12] by using the circular shifts of the received signal.
Based on the fact that the covariance matrix has a banded
structure in the absence of CFO, the work in [12] obtains
Copyright (c) 2015 IEEE. Personal use of this material is permitted.
However, permission to use this material for any other purposes must be
obtained from the IEEE by sending a request to pubs-permissions@ieee.org.
Manuscript received March 10, 2015; revised July 26, 2015; accepted
August 27, 2015. The review of this paper was coordinated by Prof. Justin
Coon. This work was supported by the National High-tech R&D Program of
China (No. 2015AA011306) and the National Natural Science Foundation of
China (NSFC) (No. 61302069 & 61302066 & 61172093 & 61172092), and
the Foundation for Innovative Research Groups of the NSFC (No. 61221063).
The authors are with the Ministry of Education Key Lab for Intelligent
Networks and Network Security, Xi’an Jiaotong University, Xi’an, Shaanxi,
710049, China. (email: {wlzhang, qyyin}@mail.xjtu.edu.cn).
CFO through minimizing the power of the elements outside
the band. Another low-complexity blind CFO estimator was
proposed in [13], where the cost function is designed as the
sum of the products of the signal amplitudes on each pair of
subcarriers from two successive OFDM blocks. Note that all
of these estimators [10]–[13] are designed for the case with
single transmit antenna.
On the other side, several estimators have been developed
for the multi-input multi-output (MIMO) OFDM systems with
constant modulus constellations [14]–[16], where multiple
transmit antennas are considered. For example, both the es-
timators proposed in [14] and [15] were designed for the
orthogonal space-time block coded (OSTBC) MIMO-OFDM
system. The work of [16] considered the general MIMO-
OFDM scenarios and developed a blind CFO estimator by
minimizing the components of the signal power spectrum
(MCSPS). The CFO estimate can be then obtained in closed
form with low computational complexity in [16]. However,
due to the inter-interference among the signals from multiple
transmit antennas, the estimator of [16] suffers from perfor-
mance error floor under the moderate and high signal-to-noise
(SNR) region.
In this paper, we propose a new blind CFO estimator for the
MIMO-OFDM systems with constant modulus constellation.
The proposed estimator exploits a rank reduction criterion and
differs from the existing competitors in the following aspects:
1) Different from [14], [15], the proposed estimator works
in the general MIMO scenarios where no space-time block
coding is assumed. 2) The proposed estimator does not suffer
from performance error floor as the SNR increases. Thus,
our estimator could substantially outperform [16] under the
moderate and high SNR region. 3) As compared to the existing
maximum likelihood (ML) estimator [7] which also works
for MIMO-OFDM as described in the Remark 3 of [7], the
proposed estimator not only can achieve better performance,
but also has the advantage of being able to work in the case
of equal number of transmit and receive antennas.
II. SYSTEM MODEL
Consider a MIMO OFDM system with a total of N sub-
carriers sequentially indexed with {k}, k = 1, 2, ··· , N. We
assume that the transmitter has M
t
antennas and the receiver
is equipped with M
r
(M
r
≥ M
t
) antennas. Without loss of
generality, we consider that all subcarriers are used for data
transmission, i.e., the system is fully loaded. In this paper we
consider the case of co-located multiple antennas, and only a
single common CFO appears in the different transmit-receive
antenna pairs [14]–[16]. For the more challenging scenarios
with multiple CFOs between the transceivers, we refer the