IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 58, NO. 1, JANUARY 2009 165
A Comparison of Frequency-Domain
Block MIMO Transmission Systems
Reza Kalbasi, Member, IEEE, David D. Falconer, Life Fellow, IEEE,
Amir H. Banihashemi, Senior Member, IEEE, and Rui Dinis, Member, IEEE
Abstract—Block transmission techniques, with appropriate
cyclic prefix and frequency-domain processing schemes, have
been shown to be excellent candidates for digital transmission
over severely time-dispersive channels, allowing good performance
with implementation complexity that is much lower than tradi-
tional time-domain processing schemes. Orthogonal frequency-
division multiplexing (OFDM) modulation is the most popular
block transmission technique. Single-carrier (SC) modulation
using frequency-domain equalization (FDE) is an attractive alter-
native approach based on this principle. In this paper, we propose
two new receiver structures for multiple-input–multiple-output
(MIMO) channels employing SC (MIMO-SC) modulation and
FDE schemes. These receivers have a hybrid structure with
frequency-domain feedforward and time-domain feedback filters
for intersymbol interference (ISI) and interference cancellation.
The proposed schemes are compared with different MIMO sys-
tems employing OFDM modulation (MIMO-OFDM) receivers in
terms of performance [bit error rate (BER) and throughput]
and complexity. Our performance results show the superiority of
MIMO-SC approaches relative to MIMO-OFDM in terms of the
BER performance for the simulated scenarios. Also, the simulation
results show that the proposed hybrid MIMO-SC receivers yield a
higher throughput than a MIMO-OFDM system.
Index Terms—Bit error rate (BER), decision feedback
equalizer (DFE), frequency-domain equalization (FDE), layered
space–time (LST), multiple-input–multiple-output (MIMO)
system, orthogonal frequency-division multiplexing (OFDM),
single carrier (SC).
I. INTRODUCTION
F
UTURE-GENERATION wireless systems are required to
support a high quality of service at high data rates. For
such high data rates, we can have severe time-dispersion effects
with a very long intersymbol interference (ISI) span. In this
case, the conventional time-domain equalization schemes are
Manuscript received February 11, 2006; revised January 29, 2007 and
July 28, 2007. First published April 18, 2008; current version published
January 16, 2009. An earlier version of this paper was presented at the Fifth
IEEE Workshop on Signal Processing Advances in Wireless Communications,
Lisbon, Portugal, July 11–14, 2004. The review of this paper was coordinated
by Prof. M. Juntti.
R. Kalbasi is with ArrayComm LLC, San Jose, CA 95131 USA (e-mail:
rkalbasi@arraycomm.com).
D. D. Falconer and A. H. Banihashemi are with the Broadband Communi-
cations and Wireless Systems Center, Department of Systems and Computer
Engineering, Carleton University, Ottawa, ON K1S 5B6, Canada (e-mail:
ddf@sce.carleton.ca; ahashemi@sce.carleton.ca).
R. Dinis is with the Institute for Systems and Robotics, Instituto Superior
Técnico, Technical University of Lisbon, 1049-001 Lisbon, Portugal (e-mail:
rdinis@ist.utl.pt).
Color versions of one or more of the figures in this paper are available online
at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TVT.2008.923655
not practical since the signal processing requirements are very
high. This can be more serious when conventional time-domain
equalization methods are employed in high-data-rate multiple-
input–multiple-output (MIMO) systems.
Cyclic prefix (CP)-assisted block transmission techniques
employing frequency-domain equalization (FDE) schemes are
known to be excellent candidates for severe time-dispersive
channels, allowing good performance and implementation com-
plexity that is much lower than those of traditional time-domain
equalization techniques. Orthogonal frequency-division multi-
plexing (OFDM) [1] is the most popular frequency-domain
technique. Single-carrier (SC) modulation using FDE tech-
niques is another valuable candidate for highly dispersive
channels in broadband wireless communications [2], [3]. In
both cases, a CP is appended to each block, eliminating the
interblock interference and converting the linear convolution
that is associated with the channel into a circular convolution
with respect to the useful part of the block. This allows low-
complexity fast Fourier transform (FFT)-based receiver imple-
mentations. Although OFDM simplifies the equalization at the
receiver, it has a high peak-to-average-power ratio and is more
sensitive against the presence of frequency offset and phase
noise [4]–[6].
It is well known that when we have deep frequency notches
in the in-band region, the performance of linear equalizers can
be very poor. In this case, it is better to employ a nonlinear
equalizer, namely, a decision feedback equalizer (DFE), which
presents a good performance/complexity tradeoff, provided that
the error propagation is limited [7], [8]. In conventional DFEs,
data is filtered by the feedforward filter symbol-by-symbol,
and decisions are immediately fed back through the feedback
filter to remove the postcursor ISI. Due to the delay in FFT
processing, it is not practical to implement the feedback filter in
the frequency domain. For this reason, a hybrid time-frequency
SC-FDE was proposed in [2] and [9], employing a frequency-
domain feedforward filter and a short time-domain feedback
filter. The feedback filter is relatively simple to implement since
it has only a small number of taps, and it can significantly
outperform a linear FDE. An iterative DFE with frequency-
domain feedforward and feedback has been proposed in [10]
and [11]. Using iterative schemes, improved performance is
achieved, whereas the complexity is increased.
Kadel [12] explored the possibility of combining the FDE
with diversity techniques. Later, Clark [13] presented the
potential of frequency-domain adaptive algorithms with di-
versity techniques. With the recent exploding interest in
MIMO systems, MIMO equalizers have attracted significant
0018-9545/$25.00 © 2009 IEEE
166 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 58, NO. 1, JANUARY 2009
attention [14]–[16]. However, MIMO channel equalization
presents a significant challenge because MIMO receivers
should simultaneously cancel ISI and cochannel interfering
substreams. Time-domain MIMO equalizers have been intro-
duced in [17]–[19].
In this paper, we present a comparison among various un-
coded and coded frequency-domain block transmission systems
(linear and nonlinear SC and OFDM receivers) with multiple
antennas. First, we extend the ideas of Falconer et al. [2]
to multiple antenna systems. The feedforward filter is im-
plemented in the frequency domain and is designed to par-
tially suppress ISI and interference, whereas the feedback
signal is generated in the time domain to further remove the
ISI and interference. The SC-FDE and OFDM receivers are
compared based on two measures—bit error rate (BER) and
throughput.
This paper is organized as follows. Section II describes the
system model. In Section III, the different MIMO frequency-
domain block transmission systems are presented. Section IV
presents the signal processing complexity of the proposed tech-
niques. The performance of the proposed receivers is evaluated
in Section V. Finally, Section VI concludes this paper.
Notations: Lowercase (uppercase) fonts denote time
(frequency) samples; bold fonts denote vectors and matrices;
(·)
T
, (·)
∗
, and (·)(i, j) represent the transpose, the complex-
conjugate transpose, and the (i, j)th entry of a matrix, respec-
tively; I
N
denotes the identity matrix of size N ; e
i
denotes
the ith unit vector, and the vect(·) operator is defined as
vect([v
1
,...,v
k
]) = [v
T
1
,...,v
T
k
]
T
, where v
1
,...,v
k
are
column vectors.
II. S
YSTEM MODEL
We consider a discrete-time complex baseband model
for an SC-MIMO system with P transmit and N receive
antennas. The data is transmitted in blocks of M data
symbols a
p
(m)(m =0,...,M − 1) from the transmitter p at
a symbol rate 1/T. Each block is preceded by a CP to make the
linear convolution of the channel equivalent to a circular con-
volution. At the receiver, the CP is discarded, and the received
signals are sampled at I/T, where I>1 gives a fractionally
spaced receiver whose performance is less sensitive to the
sampling phase [20]. It is assumed that the channel is quasi-
stationary; furthermore, perfect channel estimation and syn-
chronization are assumed at the receiver. The N -dimensional
received signal at the sampling instant m can be expressed as
r(m)=
P
p=1
M−1
k=0
h
p
(mT/I − kT )a
p
(k)+n(mT/I)
m =0,...,MI − 1 (1)
where r(m)=[r
1
(m),...,r
N
(m)]
T
, and h
p
(mT/I − kT )=
[h
p1
(mT/I − kT ),...,h
pN
(mT/I − kT )]
T
(p =1,...,P),
with h
pn
denoting the sampled channel impulse response
between transmitter p and receiver n. n(·) is the N-dimensional
noise vector with mean zero and covariance matrix σ
2
I
N
.The
data symbols are assumed to be uncorrelated complex random
variables, which are selected from a given constellation (e.g., a
QPSK constellation). We define
A
p
(l)=
M−1
m=0
a
p
(m)exp
−j2πml
M
l =0,...,M − 1 (2)
N(l + kM)=
MI−1
m=0
n(mT/I)exp
−j2π(l + kM)m
MI
l =0,...,M − 1,k=0,...,I − 1
(3)
H
p
(l + kM)=
MI−1
m=0
h
p
(mT/I)exp
−j2π(l + kM)m
MI
l =0,...,M − 1,k=0,...,I − 1.
(4)
After the FFT operation on a block of MI samples of
(1), the corresponding MI frequency-domain samples can be
expressed as
R(l + kM)=
P
p=1
H
p
(l + kM)A
p
(l)+N(l + kM)
l =0,...,M − 1,k=0,...I− 1. (5)
If we define the NI-dimensional vectors R
l
= vect([R(l),
R(l+M),...,R(l+(I −1)M]); H
p
l
=vect([H
p
(l),...,H
p
(l+
(I − 1)M)]); and N
l
= vect([N(l),...,N(l +(I − 1)M)]),
then (5) can be expressed as
R
l
=
P
p=1
H
p
l
A
p
(l)+N
l
,l=0,...,M − 1. (6)
The transmitted symbols are assumed to have unit average
power, i.e., E[|a
p
(m)|
2
]=1.
III. H
YBRID TIME–FREQUENCY RECEIVERS
Here, hybrid time–frequency domain layered space–time
(LST) DFE (LST-DFE) and hybrid time–frequency MIMO-
DFE receivers are introduced. The hybrid time–frequency do-
main LST-DFE receiver for detecting the P streams of data
symbols, shown in Fig. 1(a), consists of P successive multiple-
input–single-output (MISO) hybrid time–frequency domain
DFEs. At each stage, the “best” substream data block, in the
MMSE sense,
1
is selected, detected by a MISO-DFE, and
transformed to frequency domain by an FFT operation. Then,
this substream is subtracted from the received signal in the
frequency domain, and the residual signal is passed to the next
1
Since the complexity of computing the MMSE for all streams and selecting
the best one for each stage is very high, a suboptimum scheme is used in our
simulations. In this suboptimal approach, the streams are ordered and detected
based on the first-stage MMSE. We observed that the suboptimum and optimum
approaches have similar performance.