CONTRIBUTED P A P E R Single Carrier Modulation With Nonlinear Frequency Domain Equalization: An Idea Whose Time Has Come VAgain In high-speed single-carrier digital communication systems, processing blocks of signals using Fast Fourier Transforms is an efficient way to equalize (compensate) for interference between transmitted symbols. By Nevio Benvenuto, Senior Member IEEE , Rui Dinis, Member IEEE , David Falconer, Life Fellow IEEE , and Stefano Tomasin, Member IEEE ABSTRACT | In recent years single carrier modulation (SCM) has again become an interesting and complementary alternative to multicarrier modulations such as orthogonal frequency division multiplexing (OFDM). This has been largely due to the use of nonlinear equalizer structures implemented in part in the frequency domain by means of fast Fourier transforms, bringing the complexity close to that of OFDM. Here a nonlinear equalizer is formed with a linear filter to remove part of intersymbol interference, followed by a canceler of remaining interference by using previous detected data. Moreover, the capacity of SCM is similar to that of OFDM in highly dispersive channels only if a nonlinear equalizer is adopted at the receiver. Indeed, the study of efficient nonlinear frequency domain equalization techniques has further pushed the adoption of SCM in various standards. This tutorial paper aims at providing an overview of nonlinear equalization methods as a key ingredient in receivers of SCM for wideband transmission. We review both hybrid (with filters implemented both in time and frequency domain) and all-frequency-domain iterative struc- tures. Application of nonlinear frequency domain equalizers to a multiple input multiple output scenario is also investigated, with a comparison of two architectures for interference reduction. We also present methods for channel estimation and alternatives for pilot insertion. The impact on SCM transmission of impairments such as phase noise, frequency offset and saturation due to high power amplifiers is also assessed. The comparison among the considered frequency domain equalization techniques is based both on complexity and performance, in terms of bit error rate or throughput. KEYWORDS | Decision-feedback equalizers; digital modulation; discrete Fourier transforms; multiple antennas I. INTRODUCTION EqualizationVthe compensation of the linear distortion caused by channel frequency selectivityVis an essential component of digital communications systems whose data symbol rate is higher than the coherence bandwidth of typically encountered channels. Intersymbol interference that afflicts serial data transmission has traditionally been mitigated by equalization implemented in the time domain with linear filtering, usually with a transversal structure, hence the designation linear equalizer [1]. Due to the tradeoff between equalization of the channel impulse re- sponse to remove intersymbol interference (both pre- cursors and postcursors) and noise enhancement at the decision point, a linear equalizer yields less than ideal performance in terms of bit error rate, especially in Manuscript received March 25, 2008; revised January 29, 2009. Current version published December 23, 2009. N. Benvenuto and S. Tomasin are with the Department of Information Engineering, University of Padova, Italy (e-mail: [email protected]; [email protected]). R. Dinis is with IT (Instituto das Telecomunicaço ˜es) and FCT-UNL (Faculdade de Cie ˆncias e Te ´cnologia da Universidade Nova de Lisboa), Lisbon, Portugal (e-mail: [email protected]). D. Falconer is with the Department of Systems and Computer Engineering, Carleton University, Ottawa, Canada (e-mail: [email protected]). Digital Object Identifier: 10.1109/JPROC.2009.2031562 Vol. 98, No. 1, January 2010 | Proceedings of the IEEE 69 0018-9219/$26.00 Ó2010 IEEE Authorized licensed use limited to: Oulu University. Downloaded on January 14, 2010 at 08:18 from IEEE Xplore. Restrictions apply.
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CONTRIBUTEDP A P E R
Single Carrier Modulation WithNonlinear Frequency DomainEqualization: An Idea WhoseTime Has ComeVAgainIn high-speed single-carrier digital communication systems,
processing blocks of signals using Fast Fourier Transforms is an efficient way to
equalize (compensate) for interference between transmitted symbols.
By Nevio Benvenuto, Senior Member IEEE, Rui Dinis, Member IEEE,
David Falconer, Life Fellow IEEE, and Stefano Tomasin, Member IEEE
ABSTRACT | In recent years single carriermodulation (SCM) has
again become an interesting and complementary alternative to
multicarrier modulations such as orthogonal frequency division
multiplexing (OFDM). This has been largely due to the use of
nonlinear equalizer structures implemented in part in the
frequency domain by means of fast Fourier transforms,
bringing the complexity close to that of OFDM. Here a nonlinear
equalizer is formed with a linear filter to remove part of
intersymbol interference, followed by a canceler of remaining
interference by using previous detected data. Moreover, the
capacity of SCM is similar to that of OFDM in highly dispersive
channels only if a nonlinear equalizer is adopted at the receiver.
Indeed, the study of efficient nonlinear frequency domain
equalization techniques has further pushed the adoption of
SCM in various standards. This tutorial paper aims at providing
an overview of nonlinear equalization methods as a key
ingredient in receivers of SCM for wideband transmission. We
review both hybrid (with filters implemented both in time and
frequency domain) and all-frequency-domain iterative struc-
tures. Application of nonlinear frequency domain equalizers to
a multiple input multiple output scenario is also investigated,
with a comparison of two architectures for interference
reduction. We also present methods for channel estimation
and alternatives for pilot insertion. The impact on SCM
transmission of impairments such as phase noise, frequency
offset and saturation due to high power amplifiers is also
assessed. The comparison among the considered frequency
domain equalization techniques is based both on complexity
and performance, in terms of bit error rate or throughput.
KEYWORDS | Decision-feedback equalizers; digital modulation;
discrete Fourier transforms; multiple antennas
I . INTRODUCTION
EqualizationVthe compensation of the linear distortion
caused by channel frequency selectivityVis an essential
component of digital communications systems whose data
symbol rate is higher than the coherence bandwidth of
typically encountered channels. Intersymbol interference
that afflicts serial data transmission has traditionally been
mitigated by equalization implemented in the time domainwith linear filtering, usually with a transversal structure,
hence the designation linear equalizer [1]. Due to the
tradeoff between equalization of the channel impulse re-
sponse to remove intersymbol interference (both pre-
cursors and postcursors) and noise enhancement at the
decision point, a linear equalizer yields less than ideal
performance in terms of bit error rate, especially in
Manuscript received March 25, 2008; revised January 29, 2009. Current version
published December 23, 2009.
N. Benvenuto and S. Tomasin are with the Department of Information Engineering,
Digital Object Identifier: 10.1109/JPROC.2009.2031562
Vol. 98, No. 1, January 2010 | Proceedings of the IEEE 690018-9219/$26.00 �2010 IEEE
Authorized licensed use limited to: Oulu University. Downloaded on January 14, 2010 at 08:18 from IEEE Xplore. Restrictions apply.
dispersive channels. Other types of equalizers have there-fore been proposed, especially ones with a nonlinear
structure denoted as decision feedback equalizer (DFE),
where, after a first transversal filter aiming at reducing the
precursors of the equivalent pulse at the detection point, a
linear feedback filter, whose input is the sequence of past
detected data symbols, removes by cancellation the inter-
symbol interference due to postcursors. Hence, the struc-
ture is nonlinear with respect to the received signal.Indeed, due to the feedback of detected data symbols, the
DFE is hard to analyze. However in general, its perfor-
mance is much better than that of a linear equalizer and
can come close to that of an optimum sequence detector,
e.g., implemented by the Viterbi algorithm, for a much
lower complexity [2].
The signal processing complexity (number of arithme-
tic operations per data symbol) in time domain equaliza-tion, exemplified by the number of transversal filter tap
coefficients, increases at least linearly with the number of
data symbol intervals spanned by the channel impulse
response. Frequency domain processing of blocks of signals,
using discrete Fourier transforms (DFT), provides lower
complexity per data symbol, and has therefore recently
emerged as the preferred mitigation approach to channel
frequency selectivity, for next-generation broadband wire-less systems with bit rates of tens or hundreds of megabits/s.
In this overview paper, we survey frequency domain equal-
ization structures, mostly based on the DFE principle, for
single carrier wireless digital transmissions.
Serial or single carrier modulation (SCM), in which
data symbols are transmitted in serial fashion, has been
the traditional digital communications format since the
early days of telegraphy. An alternative is multicarriertransmission, where multiple data streams, each modu-
lating a narrowband waveform, or tone, are transmitted in
parallel, thus allowing each tone to be separately equalized
by a simple gain and phase factor. Multicarrier transmis-
sion has become popular and widely used within the last
two decades, due mainly to its excellent complexity/
performance tradeoff for data symbol rates far above
coherence bandwidths, and also for its flexible linkadaptation ability [3]–[5]. Among the first military and
commercial multicarrier systems were the Collins Kineplex
and General Atronics KATHRYN HF radio systems [6], [7]
of the 1950s and 1960s. The KATHRYN system used DFT
signal processing at the transmitter and receiver. With the
realization that the eigenvectors of a linear system are
sinusoids, multicarrier transmission was recognized as an
optimal format for frequency selective channels in the early1960s [8], [9]. Generation and block processing of
multicarrier signals in the frequency domain, are enor-
mously simplified by implementing the DFTs by fast
Fourier transforms (FFTs), as was recognized by Weinstein
and Ebert in 1971 [10], yielding a signal processing
complexity that grows only logarithmically with the channel
impulse response length. This realization, and the ever-
growing demand for higher data rates on wireless and wiredsystems propelled the application of multicarrier transmis-
sion to i) digital subscriber line transmission standards,
where it is generally known as discrete multitone transmission,
ii) IEEE 802.11a wireless LAN and iii) digital audio and video
broadcast standards, where it is known as orthogonalfrequency division multiplexing (OFDM), or orthogonalfrequency division multiple access (OFDMA). The early
success of OFDM in standards after more then twenty yearssince the pioneering implementations, has been marked by
Bingham in his landmark paper: Multicarrier modulation fordata transmission: an idea whose time has come, [3].
A related development in the early 1970s was the
realization that frequency domain processing techniques
could also be used to facilitate and simplify equalization of
SCM systems [11]. More recently, as an alternative to the
first OFDM applications in wireless standards, Sari et al.[12]–[14] pointed out that traditional SCM could enjoy an
implementation simplicity/performance tradeoff similar to
that of OFDM for highly frequency selective channels with
the inverse DFT moved at the receiver. (A simpler struc-
ture, with applications to diversity reception, was proposed
by Clark [15] a few years later.) Indeed, this is true only for
a nonlinear frequency domain equalizer. In fact, only the
performance of a DFE can come close to or even exceedthat of OFDM [16]. SCM waveforms have the additional
advantage that for a given signal power their range of
amplitude, measured by the peak-to-average ratio, is signif-
icantly less than that of multicarrier signals. As a result,
their transmitted spectra and performance are less affected
by transmitter power amplifier nonlinearities. This allows
cheaper and more efficient high power amplifiers to be
used for transmitting SCM signals. A further benefit ofSCM is its greater robustness to frequency offset and phase
noise than that of OFDM [17] (see also [18]).
These features of robustness to radio frequency hard-
ware impairments make single carrier with frequency
domain equalization an attractive alternative to OFDM,
especially for cost- and power consumption-sensitive next-
generation wireless user terminals which transmit uplink
to base stations [19]. Thus frequency domain implementa-tions of SCM receivers can be said to be an idea whose time
has come again after a hiatus of about 20 years. However
the status of SCM now is not that of a potential replacementof OFDM, but rather of a complement to it. As we will see,
traditional SCM can morph to a special form of multicarrier
transmission, which can be called DFT-precoded OFDM. As
such, it is a form of generalized multicarrier transmission
[20] (see also [21] and [22]).SCM in the form of DFT-precoded OFDM has been pro-
posed by the European 6th framework program WirelessINitiative NEw Radio (WINNER) project as the uplink trans-
mission format for wide area cellular scenarios, mainly on
the basis of its radio frequency impairment robustness
properties. WINNER downlink and local area uplink trans-
missions rely on OFDMA, mainly because of its flexibility
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and transmission channel adaptability properties [23]. TheThird Generation Partnership ProjectVLong Term Evolution(3GPP-LTE) and now LTE-Advanced standards group also
propose DFT-precoded OFDM, which they call single carrierfrequency division multiple access for the uplink of next-
generation wide area cellular broadband wireless systems,
again with OFDMA used in the downlink [24], [25]. These
initiatives and standards activities are contributing to the
International Mobile Telecommunications Advanced (IMT-Advanced) initiative of the International Telecommunica-
tions Union. The 802.16m Task Group of the IEEE 802.16
Wireless metropolitan area network standards group has
recently been formed to contribute to IMT-Advanced. At the
time of writing, its proposed standard has not been finalized,
but versions of single carrier frequency domain equalization,
as well as OFDM, have been considered for uplinks. The
earlier 802.16a standard, which led to the WiMAX wirelessmetropolitan area concept, has three transmission modes:
two based on versions of OFDM and one based on SCM.
The rest of the paper is organized as follows. In Section II
we provide the basic principles and signal structure of SCM
frequency domain nonlinear equalization. In Section III, we
present various nonlinear equalization techniques imple-
mented in the frequency domain for a single antenna system
and using the direct knowledge of the channel frequencyresponse. These structures will be extended to the case of
transmitters and receivers with multiple antennas in
Section IV, where we also describe an iterative equalizer
fully implemented in the frequency domain. Channel
estimation methods for the proposed structures are investi-
gated in Section V. Impacts of phase noise and other
disturbances on implementations of the nonlinear frequency
domain equalizers are considered in Section VI. Section VIIcompares SCM with OFDM, with a focus of the considered
nonlinear frequency domain equalization structures. Lastly,
conclusions are outlined in Section VIII.
Notation: � denotes the complex conjugate, T denotes
the transpose, H denotes the Hermitian (transpose and
complex conjugate) operator. The DFT of sequence fsng,n ¼ 0; 1; . . . ; P� 1, is
Sp ¼XP�1
n¼0
sne�j2�npP ; p ¼ 0; 1; . . . ; P� 1: (1)
The inverse DFT (IDFT) of sequence fSpg, p ¼ 0;1; . . . ; P� 1, is
sn ¼1
P
XP�1
p¼0
Spej2�npP ; n ¼ 0; 1; . . . ; P� 1: (2)
IN denotes the N � N identity matrix. Circular convolution
among signals x and y is denoted as ðx� yÞ.
II . SYSTEM DEFINITIONS AND THEFINGERPRINT OF SINGLE CARRIERFREQUENCY DOMAIN EQUALIZER:TRANSMISSION FORMAT
A wireless mobile transmission is characterized by a slowly
time-varying multipath channel between each pair of
transmit and receive antennas in a multiple input-multiple
output (MIMO) scenario. For a system with NT transmit
and NR receive antennas, we denote the impulse response
of the time-invariant channel from antenna i to antenna jas h
ðj;iÞCh ð�Þ, i ¼ 1; 2; . . . ;NT, j ¼ 1; 2; . . . ;NR. Upon trans-
mission of signal �s ðiÞðtÞ from antenna i, the received signal
at antenna j can be written as (baseband equivalent model)
�rðjÞðtÞ ¼XNT
i¼1
Zhðj;iÞCh ð�Þ�s
ðiÞðt� �Þ d� þ wðjÞðtÞ (3)
where �wðjÞðtÞ is the noise term, which we assume to be
complex Gaussian with zero mean and power spectral
density N0.
Traditionally, a SCM signal is generated as a
sequential stream of data symbols, at regular time instants
nT, for n ¼ . . . ; 0; 1; 2; . . ., where T is the data symbol
interval, and 1=T is the symbol rate. Although generally
receivers perform oversampling, for the sake of a simplernotation, we assume also that the received signal is
filtered and sampled with rate 1=T. Hence we describe the
transmission system by an equivalent discrete-time model
the cascade of the transmit filter, the channel and the
receive filter. By indicating with sðiÞn the symbol transmit-
ted from the ith antenna, the received signal after samp-ling can be written as
rðjÞn ¼XNT
i¼1
XNh�1
‘¼0
hðj;iÞ‘ s
ðiÞn�‘ þ wðjÞn (4)
where wðjÞn is the noise term with variance �2w.
In order to allow frequency domain block equalizationof the received signal, the convolutions in (4) must be
circular and this can be achieved in different ways.
As we will first consider the single input-single output
case, we drop the antenna index for sake of a simpler
notation. The MIMO case is considered in Section IV.
A. Circular and Linear ConvolutionThe transmitted signal fsng depends on the informa-
tion signal fdng but, in general, the two may not coincide.
We examine conditions such that each linear convolution
in (4) appears as a circular convolution between the
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channel impulse response and the information datasignals dn.
Let us consider the sequence of data symbols in blocks
of M, fdng, n ¼ 0; 1; . . . ;M� 1; and the Nh-size sequence
fhng, n ¼ 0; 1; . . . ;Nh � 1, with M > Nh. We define the
periodic signals of period P, drepP;n ¼ dðn mod PÞ, and
hrepP;n ¼ hðn mod PÞ, n ¼ 0; 1; . . . ; P� 1, where in order to
avoid time aliasing, P � M and P � Nh.
Now, the circular convolution between fdng and fhngis a periodic sequence of period P defined as
xðcircÞn ¼ ðh� dÞn ¼
XP�1
‘¼0
hrepP;n�‘drepP;‘: (5)
Then, if we indicate with fDpg, fHpg and fXðcircÞp g,
p ¼ 0; 1; . . . ; P� 1, the P-point DFT of sequences fdng,n ¼ 0; 1; . . . ; P� 1, fhng, and fxðcircÞ
n g, n ¼ 0; 1; . . . ; P� 1,
respectively, we obtain
XðcircÞp ¼ HpDp; p ¼ 0; 1; . . . ; P� 1: (6)
The linear convolution with support n ¼ 0; 1; . . . ; MþNh � 2 is
xðlinÞn ¼XNh�1
‘¼0
h‘dn�‘: (7)
By comparing (7) with (5), it is easy to see that only if
P � Mþ Nh � 1, then
xðlinÞn ¼ xðcircÞn ; n ¼ 0; 1; . . . ; P� 1: (8)
To compute the convolution between the two finite-length
sequences fdng and fhng, (8) requires that both sequences
be completed with zeros (zero padding) to get a length of
P ¼ Mþ Nh � 1 samples. Then, taking the P-point DFT ofthe two sequences, performing the product (6), and taking
the inverse transform of the result, one obtains the desired
linear convolution.
However, there are other conditions, some of which are
listed below, that yield a partial equivalence between the
circular convolution fxðcircÞn g and the linear convolution
xn ¼XNh�1
‘¼0
h‘sn�‘; (9)
where fsng depends on fdng.
Overlap and Save: We consider as the transmitted signalsn ¼ dn, n ¼ 0; 1; . . . ;M� 1 and assume P ¼ M. We verify
that (9) coincides with (5) only for the instants n¼Nh�1,
Nh; . . . ;M� 1, [26]. In other words, the equivalence
between the linear and the circular convolution holds
always on a subset of the computed points.
Cyclic Prefix: An alternative to overlap and save is to
consider, instead of the transmission of the data sequencefdng, an extended sequence fsng that is obtained by
partially repeating fdng with a cyclic prefix of L � Nh � 1
samples, [26]:
sn ¼dn n ¼ 0; 1; . . . ;M� 1
dMþn n ¼ �L; . . . ;�2;�1.
�(10)
Moreover, assume P ¼ M. It is easy to prove that (9)
coincides with (5) for n ¼ 0; 1; . . . ;M� 1. Moreover, the
equivalence (6) in the frequency domain holds for DFTs ofsize P ¼ M, the data block size. This arrangement is used
also in multicarrier communications [11].
Pseudo Noise (PN) Extension: Consider a sequence fsng,obtained by fdng with the addition of a fixed sequence pn,
n ¼ 0; 1; . . . ; L� 1, of L � Nh � 1 samples, i.e.,
sn ¼dn n ¼ 0; 1; . . . ;M� 1
pn�M n ¼ M; . . . ;Mþ L� 1.
�(11)
The first data block is also preceded by the sequence fpng.Moreover, now P ¼ Mþ L. The sequence fpng can contain
any symbol sequence, including all zeros (zero padding)
[27], [28], or a PN symbol sequence, denoted PN extension
or unique word. The choice of the extension is also influ-
enced by other factors, such as channel estimation [29]. It
can be easily proved, that (9) coincides with ðh� sÞn for
n ¼ 0; 1; . . . ; P� 1, where now the circular convolution ison sn instead of dn.
With reference to the noisy MIMO scenario (4), we can
organize the transmitted signal fsng into blocks of size P,
each obtained by extending with a PN sequence a data block
of size M. Moreover, at the beginning a PN sequence is
transmitted first. Let fsnþkPg, n ¼ 0; 1; . . . ; P� 1 be the kth
block and let fHðj;iÞp g be the P-size DFT of the channel
impulse response fhðj;iÞ‘ g. Then we obtain
RðjÞp ðkÞ ¼XNT
i¼1
Hðj;iÞp SðiÞp ðkÞ þWðjÞp ðkÞ;
p ¼ 0; 1; . . . ; P� 1 (12)
where WðjÞp ðkÞ is the noise term in the frequency domain,
which according to the hypothesis on fwng is i.i.d. with
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variance �2W ¼ P�2
w. Note that in this arrangement theDFTs are of size P ¼ Mþ L instead of size M as in the cyclic
prefix arrangement. Moreover, in this arrangement, an
additional PN extension is required before the first data
block. Among the advantages of this format are a simple
channel estimation, by using the PN sequence [29], and the
possibility of implementing an efficient frequency domain
(FD) nonlinear equalizer, as detailed in Section III. Gen-
erally, the PN extension yields a reduced bit error rate withrespect to the cyclic prefix, since in the latter case data
detection errors affect both the information data and the
cyclic prefix, thus reducing the intersymbol interference
cancellation capabilities of the nonlinear equalizer. In the
following we will consider operations on a single data block
and we will drop the index k from FD signals.
B. Signal GenerationAs described in the previous section, the data symbol
sequence may be organized into DFT blocks, which may
include PN extensions, or to which cyclic prefixes areappended, thus facilitating DFT processing and FD
equalization at the receiver. The resulting data sequences,
with or without extensions and prefixes, are low pass
filtered for bandlimiting and spectrum-shaping purposes,
before being up-converted to the carrier frequency.
Fig. 1 shows a generalized multicarrier transmitter archi-
tecture [19], [20], [22], which can be adapted to generate a
wide variety of signals, including SCM signals, as well asOFDM, OFDMA, multicarrier code division multiple access
(CDMA), etc. Because its processing occurs in the FD, it is
easy to generate signals with arbitrary spectra, and to insert
FD pilot tones for channel estimation (see Section V). Com-
plexity is not a major issue since processing is done with
DFTs and IDFTs, implemented by FFTs. In the figure, the
IDFT block is preceded by a general pre-matrix operation,
which may include a DFT, spreading, a selection mechanismand/or an allocation to multiple transmitting antennas in a
MIMO or space-time code. Recognition of this generalized
structure can also be found in [30]–[32].
Generation of a SCM signal block proceeds as follows.
After coding and serial to parallel (S/P) conversion, blocks
of N coded data symbols are mapped to the FD by a N-pointDFT. The resulting FD data components are mapped by the
pre-matrix time-frequency-space selector to a set of M � Ndata-carrying subcarriers, and then processed by a
M–point inverse DFT to convert back to the time domain
(TD). The resulting samples are parallel-to-serial (P/S)
converted and appended with a prefix or extension for
transmission. The simplest frequency mapping is to Ncontiguous subcarrier frequencies, with the remainingM� N being padded with zeroes. In this case, the output
samples are expressed as
sn¼1
M
XN�1
‘¼0
d‘XN�1
p¼0
ej2�p n�‘MNð Þ
M
¼XN�1
‘¼0
g n� ‘M
N
� �d‘; n¼0; 1; . . . ;M�1 (13)
where
gðnÞ ¼ ej2�ðN�1Þn
M1
M
sin �NnM
� �sin �n
M
� � (14)
while fsng, n ¼ �L;�Lþ 1; . . . ;�1, contains the cyclicprefix.
This is recognized as a block of data symbols serially
transmitted at intervals of M=N samples. The sampled
pulse waveform given by (14) is a circular version of a sinc
pulse with zero excess bandwidth, limited to a bandwidth
N=MT. SCM signals generated in this way are called DFT-precoded OFDM signals by the WINNER project [23], and
local single carrier FDMA (SC-FDMA) by the 3GPP-LTEstandards body [24], [25]. For (13), smM=N ¼ N=Mdm, thus
the DFT-precoded OFDM waveform at data symbol inter-
vals depends only on a single data symbol, and therefore
has a significantly lower peak to average power ratio than
that of a corresponding OFDM waveform, whose sample
Table 1 Computational Complexity of Equalizer Structures
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Then, if fb‘g, ‘ ¼ 1; 2; . . . ;NFB, are the coefficients of the
feedback filter, the signal at the input of the decision
element is
~dn ¼ zn þ yn; n ¼ 0; 1; . . . ;M� 1 (23)
and
yn ¼XNFB
‘¼1
b‘ sn�‘ (24)
is the feedback signal. Note that, as indicated in Fig. 3,
for each block the first NFB data symbols, which initializethe feedback part of the DFE, coincide with the PN
symbols fpng.The computational complexity of the HDFE structure
is ðP=MÞ log2ðPÞ þ NFB � ðP=MÞ, as two P-size (I)DFTs
and one multiplication is performed for each block of Mdata symbols, while a feedback filter of size NFB is applied
on the detected data.
Starting from the channel frequency response, two
design methods are outlined: zero forcing and minimum
mean square error (MSE).
Zero Forcing: According to the zero forcing criterion, all
interferers must be canceled by the feedback filter. Firstly,
let the P-size DFT of the feedback filter be fBpg, p ¼ 0;1; . . . ; P� 1. As detailed in [16] the feedforward filter is
simply given by
Cp ¼1
Hpð1� BpÞ: (25)
Let’s define the NFB � NFB Toeplitz matrix AZF having as
first row the first NFB coefficients of the DFT of f1=jHpj2g,p ¼ 0; 1; . . . ; P� 1. Let’s also define the NFB-size columnvector vZF, having as elements the first NFB coefficients of
the IDFT of f1=jHpj2g, p ¼ 0; 1; . . . ; P� 1. Then the
feedback filter that removes interference is the solution of
the linear system AZFb ¼ vZF, [16]. Since AZF is a Toepliz
matrix, the reduced complexity Levinson-Durbin algorithm
[26] can be used to solve the system, with complexity
OðN2FBÞ. Additionally, observe that, if NFB � Nh, the
Fig. 3. The HDFE structure.
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elements of both AZF and vZF can be computed as 2NFB-sizeDFTs of f1=jHpj2g.
Minimum Mean Square Error: According to the mini-
mum MSE criterion, the coefficients of the feedforward
and feedback filters are chosen to minimize the sum of the
power of the filtered noise, and the power of the residual
interference. In particular, the MSE at the detection point
is given by
J ¼ E j~dn � dnj2
(26)
which, assuming that pn is i.i.d. with the same statistics of
dn, by the Parseval’s equation becomes in the FD
J ¼ 1
P2EXP�1
p¼0
j~Sp � Spj2" #
: (27)
Then, using (23) in the FD and substituting (12) for Rp and
(24) in the FD for Yp we have
J ¼ 1
P2EXP�1
p¼0
ðCpHp � 1ÞSp � BpSp þ CpWp
�� ��2" #: (28)
By assuming that a) the past detected data symbols are
correct ðSp ¼ SpÞ, b) both noise and data symbols are i.i.d.
and statistically independent of each other, J can bewritten as
J ¼ 1
P2
XP�1
p¼0
CpHp � Bp � 1�� ��2�2
D þ jCpj2�2W (29)
where �2D is the variance of the data in the FD.
Setting the gradient of J with respect to fCpg,p ¼ 0; 1; . . . ; P� 1, to zero, yields the following relation
between feedforward and feedback coefficients [16]
Cp ¼H�pð1� BpÞ
jHpj2 þ �2W
�2D
; p ¼ 0; 1; . . . ; P� 1: (30)
We define now the NFB-size Toeplitz matrix AMMSE whose
first row comprises the first NFB coefficients of the DFT of
f1=ð�2DjHpj2 þ �2
WÞg, p ¼ 0; 1; . . . ; P� 1, and the column
vector vMMSE whose NFB elements are the first NFB
coefficients of the IDFT of f1=ð�2DjHpj2 þ �2
WÞg, p ¼ 0;1; . . . ; P� 1.
By substituting (30) into (29) and setting the gradient
of J to zero with respect to the feedback coefficients b, it is
seen that b is provided by the solution of the linear system
of NFB equations with NFB unknowns AMMSEb ¼ vMMSE.
We note that the complexity of the minimum MSE method
is similar to that of zero forcing. Once the feedback filter is
determined, the feedforward filter is given by (30). Note
that the minimum MSE solution will reduce to the zeroforcing solution when �2
W ! 0.
The computational complexity for the design of HDFE
is reported in Table 2.
C. Frequency Domain Linear EqualizerThe FD linear equalizer with PN extension can be
considered as a particular case of the HDFE, as there is no
feedback filter, i.e., fBp ¼ 0g, p ¼ 0; 1; . . . ; P� 1 in (30).
Moreover, we should note that there exists also a linear FD
equalizer with cyclic prefix whose analysis is easily derivedfrom the HDFE. We recall from the Introduction that the
linear equalizer structure yields less than ideal perfor-
mance in dispersive channels. Hence, although it received
some attention in the recent literature [39], it will not be
considered further in this paper.
D. HDFE With Feedback as a Noise PredictorThe HDFE with feedback as a noise predictor
(HDFE-NP) scheme is illustrated in Fig. 4. If fzng, n ¼0; 1; . . . ; P� 1, is the output of the feedforward filter,implemented in the FD, we form, for n ¼ 0; 1; . . . ;M� 1,
[40], [41]
~zn ¼ zn � sn (31)
yn ¼XNFB
‘¼1
b‘~zn�‘ (32)
~dn ¼ zn þ yn: (33)
To minimize noise and intersymbol interference in ~dn,
the feedback filter, with input ~zn, i.e., the disturbance in zn
(assuming sn ¼ sn), needs to remove the predictable
components of zn to yield the prediction error signal ~dn
to be ideally a white noise. This configuration has a few
advantages over the HDFE scheme, when adaptive
Table 2 Computational Complexity of Parameter Design
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methods are used to updated filter coefficients, as
discussed in Section V-C.
Concerning the filter design of the HDFE-NP using the
minimum MSE criterion, a derivation of the minimum
MSE HDFE shows that the optimum feedforward filter is
the same as that of the linear equalizer while the feedback
filter coincides, apart from the sign, with the feedback ofthe HDFE. Note that now the feedforward filter design
does not depend on the feedback design: this may be an
advantage for the HDFE-NP.
The complexity of HDFE-NP, both in terms of struc-
ture and filter design, is the same as that of HDFE.
E. Overlap and Save Implementation of HDFEAll the FD equalizers presented in the previous sub-
sections require the use of special transmission formats
based either on cyclic prefix or PN extension. This has two
major consequences: a) frequency domain equalization cannot be applied on transmissions complying with standards
that do not include the transmission format and b) the use
of prefixes or sequences yields a reduced bandwidth
efficiency with respect to a conventional SCM transmis-
sion. In order to overcome both issues while still using FD
equalization, a HDFE scheme has been proposed that
exploits the overlap and save principle (see Section II-A) to
allow HDFE on an extensionless transmission [42], [43],
resulting in the ELHDFE scheme. Moreover, in [42] a
technique for channel estimation for the resulting system is
proposed.
We should say that, while linear filters, and in par-
ticular linear equalizers, implemented in the FD by the
overlap and save method, have been proposed since the’80s [44]–[47], nonlinear HDFEs in the FD are a more
recent development. In the ELHDFE the received signal is
divided into blocks of P samples, partially overlapping over
L samples. The kth block of size P has elements
rnðkÞ ¼ rkMþn; n ¼ 0; 1; . . . ; P� 1 (34)
where M ¼ P� L. An example of block sample partition-
ing with overlapping is shown in Fig. 5. Although for
ELHDFE the transmit signal coincides with the data signal,
i.e., sn ¼ dn, detection is performed on blocks of size M.
Hence, for the ease of notation we define the data block of
size M as
dnðkÞ ¼ dkMþn; n ¼ 0; 1; . . . ;M� 1
0 otherwise.
n(35)
Fig. 4. The HDFE-NP structure.
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Then, using (4) and (35), the received signal can be
rewritten as (see equation at bottom of page). Due to theabsence of extension in the transmission, the convolution
between the transmitted signal and the channel is not
circular. The first Nh � 1 samples of frnðkÞg are affected by
interblock interference from fdnðk� 1Þg (second term of
the summation), as well as intersymbol interference (first
term of the summation). The central samples of frnðkÞgare affected only by intersymbol interference while the last
L samples of frnðkÞg include both intersymbol interferenceand interblock interference due to fdnðkþ 1Þg.
The ELHDFE structure is similar to that of Fig. 3,
where the feedforward filter is implemented in the FD,
while the feedback filter is implemented in the TD. As a
distinctive feature of the ELHDFE, the feedback filter tries
to remove also the interblock interference due to
fdnðk� 1Þg by operating continuously on the detected
symbols rather than being fed with the PN sequence. Onthe other hand, the interblock interference due to
fdnðkþ 1Þg can not be removed by the feedback and
hence only the first M samples of each equalized block are
detected while the last L samples are discarded. The
corresponding data symbols will be recovered from the
next block frnðkþ 1Þg, which partially overlaps with
frnðkÞg, as from Fig. 5.
The computational complexity of ELHDFE is the sameas that of HDFE, as for each processed block of P sample,
M symbols are detected.
Filter Design: For the design of the filter coefficients that
minimize (26) a linear system of equations must be solved
[42], [43], where complexity for evaluating the system
matrix isOðP2Þ, while for determining the solution isOðP3Þ.
As the computational complexity may become too high for
large P, in [42] it has been proposed to design the equalizeras for the HDFE, resulting in additional distortion due to
interblock interference. However this approach results in a
close approximation (with a slight performance degrada-
tion) to the ideal equalizer parameters, provided that the
overlapping blocks are much longer (e.g., by a factor of 20
to 40) than the longest expected channel impulse response,
and if the overlap is half a block [42].
F. Bi-Directional Feedback FilterThe feedback of the HDFE processes samples at the
output of the feedforward filter in increasing temporal order
and this conditions both the filter design and the perfor-
mance, due to error propagation. As for TDDFE [48], [49],
better performance is obtained by a bidirectional HDFE
(BiHDFE), that processes samples both in the increasing and
decreasing order (i.e., backwards in time) [50].
The BiHDFE comprises two equalizers: a) a directHDFE that processes the received samples in increasing
order and b) a backward HDFE that processes the received
samples backward. The two equalizers perform indepen-
dent detections to be used as feedback signals. The direct
HDFE has already been described in detail in Section III-B.
Here we describe backward HDFE which operates on the
time-reversed signal
r n ¼ rP�1�n; n ¼ 0; 1; . . . ; P� 1: (37)
Let f C
pg, p ¼ 0; 1; . . . ; P� 1, be the frequency re-
sponse of the feedforward filter whose output in the TD
where the data signal is split into NT parallel streams, each
one associated to a different transmit antenna. Byemploying NR � NT antennas at the receiver it is possible
to separate the NT data streams, at least in theory. As an
example, we have Bell Laboratories layered space-time
(BLAST) coding architectures [55]–[57]. This concept can
also be extended to space-division multiple access
techniques where we employ multiple antennas at the
base station to increase the number of simultaneous users
in a given cell, allowing a significant increase in the systemspectral efficiency, while reducing the transmit power
requirements for the mobile terminals [58], [59].
At the receiver, we need to separate the streams.1 The
performance can be improved by employing interantenna
interference cancellation schemes. For flat fading MIMO
channels the antenna separation is relatively simple, since
we can just invert the channel matrix. However, for
frequency-selective channels the receiver can be muchmore complex.2 In fact, we need to jointly separate the
streams associated to different transmit antennas and to
equalize the channel. A way of achieving this is by employing
MIMO TD equalizers as proposed in [60]–[62]. However, as
with other TD receivers, their complexity can be very high
for severely time-dispersive channels and FD implementa-
tions are strongly recommended. The frequency domain
equalization designs described in the previous section can beextended for MIMO scenarios. Several hybrid DFE schemes
were proposed for MIMO systems [63]–[65].
In fact, for MIMO receivers we can consider two
alternative detection schemes [62]:
• MIMO-DFE or detection with parallel interference
cancellation (PIC). In this case, detection consists
of NT parallel detection stages, where symbols of
all streams at a given instant are detectedsimultaneously by linear processing of the received
signal and partial cancellation of interference from
the other streams and residual intersymbol inter-
ference using previously detected data.
• Layered space-time DFE (LST-DFE) or detection
with successive interference cancellation (SIC)
where we detect one stream at a time and cancel
interference from already detected streams, as wellas the residual intersymbol interference for the
stream that is being detected. It is desirable to rank
the streams according to some quality measure
(ideally it should be the bit error rate (BER) or
mean square error for each stream after the corres-
ponding detection stage; to simplify the receiver,
the average power associated to each stream could
also be employed) and to detect the streams fromthe best to the worst.
These receivers are closely related to SIC and PIC receivers
for CDMA [66]. Although the PIC structure is in general
more complex, it allows a parallel design, which can be
advantageous from the implementation point of view. More-
over, the detection delay for PIC structures is much lower
than for the SIC structure and it is not necessary to rank the
streams. Surprisingly, typical performance is worse for PICapproaches, since detection of worse streams is affected by
high interference of the best streams [62], [67].
The approach taken here is similar to that of [68] and
[69], which considered TD processing.
The received FD signal at frequency p corresponding to
(12) with the block index k dropped, is now a NR-size
column vector Rp ¼ ½Rð1Þp ; Rð2Þp ; . . . ; RðNRÞp �T , given by
Rp ¼XNT
i¼1
HðiÞp SðiÞp þWp; p ¼ 0; 1; . . . ; P� 1 (46)
where HðiÞp ¼ ½Hð1;iÞp ;Hð2;iÞp ; . . . ;HðNR;iÞp �T is the NR-size
column vector representing the channel frequency response
from transmitter i ¼ 1; 2; . . . ;NT, SðiÞp represents the FD
signal from transmitter i and Wp ¼ ½Wð1Þp ;Wð2Þp ; . . . ;WðNRÞp �T
is the FD white noise vector with E½WpWHp � ¼ �2
W INR.
A. The MIMO-HDFEThe HDFE designs described in Section III can be
extended for MIMO scenarios [63], [64]. The MIMO-HDFE
1The streams can be associated with different antennas of the samemobile terminal (as in BLAST systems) or with different mobile terminals(as in space-division multiple access systems).
2For systems with FD processing the receiver complexity can be keptlow since the channel can be modeled as parallel flat fading channels.
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consists of a FD feedforward filter and a TD feedback filterwith a temporal span of NFB taps. The structure is fully
connected, where cross-feedbacks are implemented, to feed
back all the past decisions from all streams into the detection
of each stream. In the MIMO-HDFE all NT stream symbols
at a given instant are detected simultaneously and on
detecting stream i (i ¼ 1; 2; . . . ;NT, we use a feedforward
filter with FD coefficients collected into the row vector
fCðiÞp ¼ ½Cði;1Þp ; Cði;2Þp ; . . . ; Cði;NRÞp �g, and feedback filters with
TD coefficients collected into the row vector
fbðiÞ‘ ¼ ½bði;1Þ‘ ; . . . ; b
ði;NTÞ‘ �g, ‘ ¼ 1; 2; . . . ;NFB.
The output in FD of the ith stream is ZðiÞp ¼ CðiÞp Rp. The
corresponding TD signal zðiÞn is obtained by IDFT of fZðiÞp g.At detection point, the signal can be written as
~dðiÞn ¼ zðiÞn þ
XNFB
‘¼1
bðiÞ‘ sn�‘ (47)
where sn ¼ ½sð1Þn ; sð2Þn ; . . . ; sðNTÞn �T is the NT-size column
vector with all streams symbols detected at instant n and
extended as in (22).
The minimum MSE feedforward coefficient vector is
[see also (30)]
CðiÞp ¼ ~EðiÞ�p HH
p
XNT
m¼1
HðmÞp HðmÞHp þ �W
�2D
2INR
" #�1
(48)
where
Hp ¼ Hð1Þp ;Hð2Þp ; . . . ;HðNTÞp
h i(49)
and ~EðiÞp ¼ ei � BðiÞp , with fBðiÞp g, p ¼ 0; 1; . . . ; P� 1 the
row vector DFT of fbðiÞ‘ g, ‘ ¼ 1; 2; . . . ;NFB, and ei ¼½0; . . . ; 0; 1; 0; . . . ; 0� denoting the ith unit row vector.
Let us define
Qp ¼ �2W INT
þ �2DHH
p Hp
h i�1
(50)
and fvðiÞn g, as the DFT of fQpg, p ¼ 0; 1; . . . ; P� 1. Let us
also define
vðiÞ ¼ vðiÞ1 ; v
ðiÞ2 ; . . . ; v
ðiÞNFB
h iT
ei (51)
AðiÞ ¼
vðiÞ0 v
ðiÞ�1 v
ðiÞ1�NFB
vðiÞ1 v
ðiÞ0 v
ðiÞ2�NFB
vðiÞ2 v
ðiÞ1 v
ðiÞ3�NFB
vðiÞNFB�1 v
ðiÞ0
266666664
377777775: (52)
The optimum vector of feedback coefficients bðiÞ ¼½bðiÞ1 ; b
ðiÞ2 ; . . . ; b
ðiÞNFB�T is the solution of the system of
equations AðiÞbðiÞ ¼ vðiÞ. Note the high complexity of theproposed solution.
B. The LST-HDFEThe LST-HDFE for detecting NT streams of data
symbols has NT successive multiple-input-single-output
HDFEs. At each stage, the best stream data block (see
comments on SIC), is selected, detected by a multiple-
input-single-output HDFE, transformed to FD, subtracted
from the received signal in the FD and the residual signal is
passed to the next step for equalization and detection ofthe next best data block.
For the sake of simplicity, we will assume that the
streams are ordered according to some criterion, with
i ¼ 1 corresponding to the best stream and i ¼ NT the
worse. We will also assume that we are detecting the ithstream (i.e., stage i) and the previous ði� 1Þ streams were
already detected and removed from the FD output signal
fRpg to obtain fRðiÞp g. Given fRðiÞp g, we apply the scalar
HDFE of Section III to yield fdðiÞn g, n ¼ 0; 1; . . . ;M� 1.
Note that for the LST-HDFE at stage i, the input of the
feedback filter consists only of the previous detected data
on the ith stream itself. In fact, each stage of LST-HDFE
(from before cancellation of previous detected streams to
detected data fdðiÞn g) is a multiple-input-single-output
HDFE, i.e., a MIMO-HDFE with NT � iþ 1 inputs andone output. The number of interfering signals is reduced
by one at each stage due to the cancellation of previous
detected streams in the front end.
C. Iterative Block DFE (IBDFE)In the IBDFE, both the feedforward and the feedback
filters are implemented in the FD [52], [53]. The equalizer
includes two parts: 1) the feedforward filter, which
partially equalizes for the interference and 2) the feedback
signal, which removes part of the residual interference. In
the IBDFE, the design of the various filter/signals and datadetection is iterated NI times.
Also in this case, as for HDFE, error propagation due to
the feedback is limited to within one block. Moreover,
feedforward and feedback operations are both realized in
the FD, while both TDDFE and HDFE include a feedback
operating in the TD. On the other hand, since detection is
performed on a per-block basis, the effectiveness of the
feedback to cancel interference is limited by the reliabilityof the detected data at the previous iteration. Indeed, the
iterative process gradually increases the reliability of the
detected data. However, if the initial detected data is
exceedingly poor, the iterative process may not be able to
effectively cancel the interference. An integration of
IBDFE with CDMA transmission has been proposed in
[70], where chip interleaving and multiuser interference
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cancellation has been considered to improve detection.Indeed, for CDMA, the use of chip interleaving provides a
significant robustness against error propagation, even with-
out the use of coding.
The following development is similar to that in [71],
[72] and to the soft decision feedback development of [52],
but is generalized to multiuser MIMO.
In a PIC approach, at each iteration q we have the DFT
component of the soft symbols fed back from the detectorfor each stream i in the FD, denoted as m
Sði;q�1Þp
, i ¼ 1;2; . . . ;NT. For the detection of stream i, we first remove
best estimate of interference to Rp from other streams and
then perform equalization. In IBDFE equalization is
performed both by the FD feedforward 1� NR row vector
filter Cði;qÞp and by the removal of the residual intersymbol
interference through the feedback signal Yði;qÞp whose
expression is determined in the following. Hence, thespace-frequency equalizer output at frequency p for stream
i at the qth iteration, is
~Sði;qÞp ¼ Cði;qÞp Rp �
XNT
m¼1;m6¼i
HðmÞp mSðm;q�1Þp
" #þ Yði;qÞp : (53)
At the first iteration ðq ¼ 1Þ, the feedback terms are zero,
and the equalizer is a linear minimum MSE equalizer. The
case where NT ¼ 1 and NR > 1 corresponds to a scenario
with receive diversity. In this case, the receiver design isstill validVnaturally, we do not need to remove the
interference between antennas in (53) and the receiver
coefficients are still given by (59). As shown in [73], a
similar approach could be employed for systems employing
Alamouti-like transmit diversity [74]. Note that for SIC we
detect streams successively for each iteration and we use
mSðm;qÞp
whenever it is available, i.e., for streams that were
already detected at each iteration.
After equalization (53), the IDFT of f~Sði;qÞp g, p ¼ 0;
and the RLS algorithm [26] can be used to determine a(iterative) solution for fCpðkÞg, p ¼ 0; 1; . . . ; P� 1, in
terms of fCpðk� 1Þg, p ¼ 0; 1; . . . ; P� 1, and other quan-
tities. Indeed, the solution is on a per subcarrier basis
and the RLS is scalar. From the FD error sequence at the
equalizer output fEF;pðkÞg, p ¼ 0; 1; . . . ; P� 1, we deter-
mine by IDFT the (block k) error sequence feF;nðkÞ ¼dnðkÞ � znðkÞg, n ¼ 0; 1; . . . ;M� 1, which will be used to
update the feedback coefficients. For a feedback filter atiteration k, fb‘ðkÞg, ‘ ¼ 1; 2; . . . ;NFB, we define the TD
error at detection point eB;nðkÞ ¼ dnðkÞ � ~dnðkÞ. As from
(31) and (32) the input signal of the feedback filter has a
component proportional to zn. Hence it is
eB;nðkÞ ¼ eF;nðkÞ �XNFB
‘¼1
b‘ðkÞeF;n�‘ðkÞ (66)
and the classical vector RLS algorithm can be used to yieldan iterative solution for fb‘ðkÞg, ‘ ¼ 1; 2; . . . ;NFB.
In this derivation, a simpler algorithm as LMS could be
used instead of the RLS at a cost of a longer convergence.
Moreover, we note that the first optimization is simply the
design of an FD linear equalizer.
D. Iterative Channel EstimationNon-perfect channel estimation degrades equalization
and bit error rate performance. It is well known that pilot-
based channel estimation can be augmented by iterative
channel estimation using fed-back hard or soft decisions
from the receiver’s detector or decoder. Combining initialchannel estimation from pilots with subsequent iterative
channel estimation can yield bit error rate performance
within about 1 dB of that achievable with perfect channel
state information for OFDM [91], [92].
Similar iterative channel estimation improvements are
available for SCM and DFT-precoded OFDM systems [37],
[93]. Again, our approach is similar to that of [68], [69],
but in the FD, instead of the TD. In its simplest form, withthe use of hard receiver decisions at the qth equalizer
iteration ðq > 1Þ in a block, whose DFT is fSðqÞp g,p ¼ 0; 1; . . . P� 1, a channel estimate is
HðqÞp ¼
Rp
SðqÞp
; p ¼ 0; 1; . . . ; P� 1: (67)
The effect of any hard decision errors is spread over all
frequencies due to the DFT operation in forming SðqÞp .
There is a potential problem with noise enhancement
at frequencies where SðqÞp has a small magnitude; this
latter problem is not encountered in OFDM counterpart
systems, in which SðqÞp is a data symbol. The noise
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enhancement problem can be alleviated by modifying(67) as follows [37], [93]:
HðqÞp ¼
Rp
SðqÞp
SðqÞp
��� ��� > �T
Hð0Þp S
ðqÞp
��� ��� � �T
8><>: (68)
where Hð0Þp is the initial channel estimate obtained from
the pilots, and �T is an empirically determined threshold.
For MIMO systems, the corresponding vector channel
estimate for the ith ði ¼ 1; 2; . . . ;NTÞ antenna at the qth
iteration is [94]
Hði;qÞp ¼
Rp�PNT
m¼1; 6¼iHðm;q�1Þp S
ðm;q�1Þp
Sði;qÞp
for Sði;qÞp
��� ��� > �T
Hði;0Þp for S
ði;qÞp
��� ��� � �T
8><>: (69)
These channel estimates may be regarded as rawchannel estimates, which can be further smoothed andfiltered over frequencies and over blocks according to the
channel frequency and time correlation characteristics
[37], [92].
Expressions (63) and (69) are applicable for uplinks of
MIMO cellular systems where there are NT in-cell users
transmitting simultaneously, with orthogonal pilots, to a
base station. Such cellular systems will usually also be
disturbed by out of cell interferers, which are users inother cells transmitting to their base stations. To avoid
excessive pilot overhead, out of cell interferers’ pilots are
necessarily orthogonal to in-cell users pilots, and thus
there will in general be interference from out of cell
interferers to pilots as well as to data. Cooperative sched-
uling or frequency reuse partitioning strategies among
adjacent base stations can be used to keep out of cell
interference levels low relative to received in-cell signalsat each base station [95], [96]. Equalizers error-based
least square or RLS adaptation, can then be used to
suppress the out of cell interference without having to
explicitly estimate the low level out of cell interferers
channels [94].
Fig. 12, from [94], illustrates the difference in
performance between perfect channel state information
and channel estimation using iterative channel estimationand equalizer error-based least squares adaptation. The
simulation scenario has two in-cell users’ signals at 0 dB
average relative power levels, received at a base station
with 4 receiving antennas. The particular IBDFE and
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ABOUT THE AUT HORS
Nevio Benvenuto (Senior Member, IEEE) received
the Laurea degree from the University of Padova,
Padova, Italy, in 1976 and the Ph.D. degree from
the University of Massachusetts, Amherst, and
1983, respectively, both in electrical engineering.
From 1983 to 1985 he was with AT&T Bell
Laboratories, Holmdel, NJ, working on signal
analysis problems. He spent the next three years
alternating between the University of Padova,
where he worked on communication systems
research, and Bell Laboratories, as a Visiting Professor. From 1987 to
1990, he was a member of the faculty at the University of Ancona. He was
a member of the faculty at the University of L’Aquila from 1994 to 1995.
Currently, he is a Professor in the Electrical Engineering Department,
University of Padova. His research interests include voice and data
communications, digital radio, and signal processing.
Prof. Benvenuto is an Editor for Modulation/Detection of the IEEE
Communications Society.
Rui Dinis (Member, IEEE) received the Ph.D.
degree from Instituto Superior Tecnico (IST),
Technical University of Lisbon, Portugal, in 2001.
He was a researcher at CAPS/IST (Centro de
Analise e Processamento de Sinais) from 1992 to
2005; from 2005 to 2008 he was researcher at
ISR/IST (Instituto de Sistemas e Robotica). From
2001 to 2008 he was a Professor at IST. In 2008 he
taught at FCT-UNL (Faculdade de Ciencias e
Tecnologia da Universidade Nova de Lisboa); in
2009 he joined the research center IT (Instituto de Telecomicaçoes). He
has been involved in several research projects in the broadband wireless
communications area. His main research interests include modulation,
equalization, and channel coding.
David Falconer (Life Fellow, IEEE) received the
B.A. Sc. degree in engineering physics from the
University of Toronto, Toronto, ON, Canada, in
1962, the S.M. and Ph.D. degrees in electrical
engineering from Massachusetts Institute of Tech-
nology (MIT), Cambridge, in 1963 and 1967
respectively, and an honorary doctorate of science
from the University of Edinburgh in 2009.
After a year as a postdoctoral fellow at the
Royal Institute of Technology, Stockholm, Sweden
he was with Bell Laboratories from 1967 to 1980 as a member of
technical staff and group supervisor. During 1976–1977 he was a visiting
professor at Linkoping University, Linkoping, Sweden. Since 1980 he has
been with Carleton University, Ottawa, Canada, where he is now
Professor Emeritus and Distinguished Research Professor in the
Department of Systems and Computer Engineering. His current research
interests center around beyond-third-generation broadband wireless
communications systems. He was Director of Carleton’s Broadband
Communications and Wireless Systems (BCWS) Centre from 2000 to
2004. He was the Chair of Working Group 4 (New Radio Interfaces, Relay-
Based Systems and Smart Antennas) of the Wireless World Research
Forum (WWRF) in 2004 and 2005.
Prof. Falconer received the 2008 Canadian award for Telecommuni-
cations Research, a 2008 IEEE Technical Committee for Wireless Com-
munications Recognition Award, and the IEEE Canada 2009 Fessenden
Award (Telecommunications). In 2009 he was awarded an honorary
Doctorate of Science from the University of Edinburgh.
Stefano Tomasin (Member, IEEE) received the
M.S. (Laurea) and Ph.D. degrees in telecommuni-
cations engineering from the University of Padova,
Italy, in 1999 and 2003, respectively.
In 2001–2002 he was visiting Philips Research
Laboratory in Eindhoven, the Netherlands, study-
ing mobile receivers for the digital terrestrial
television. In 2002 he joined University of Padova,
first as contract researcher for a national research
project and then, since 2005, as assistant profes-
sor. In the second half of 2004 he was visiting faculty at Qualcomm,
San Diego, CA, within a project on the multiuser detection for cellular
systems. In 2007 he was visiting Polytechnic University, Brooklyn, NY,
doing research on cooperative networks. His current research interests
include signal processing for wireless communications, access technol-
ogies for multiuser/multiantenna systems, and cross-layer protocol
design and evaluation.
Benvenuto et al.: An Idea Whose Time Has ComeVAgain
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