contributed pap e r singlecarriermodulationwith ...kk/dtsp/tutoriaalit/benvenuto.pdf · pap e r...

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,

University of Padova, Italy (e-mail: [email protected]; [email protected]).

R. Dinis is with IT (Instituto das Telecomunicaçoes) and FCT-UNL

(Faculdade de Ciencias e Tecnologia 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 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

Benvenuto et al.: An Idea Whose Time Has ComeVAgain

70 Proceedings of the IEEE | Vol. 98, No. 1, January 2010


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

where the channel is characterized by the impulse

response hðj;iÞ‘ , ‘ ¼ 0; 1; . . . ;Nh � 1, obtained by sampling

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


Vol. 98, No. 1, January 2010 | Proceedings of the IEEE 71


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




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

Fig. 1. Generalized multicarrier transmitter (from [22]).




values are equally weighted sums of all N data symbols. Itis important to recognize that this form of DFT-precoded

OFDM signal is a SCM. The transmitter can be designed to

generate it in this FD fashion, or in the conventional TD

fashion, with serial transmission and pulse shaping.

Variations of this procedure abound for different

desired signal formats. For example, aliased copies of the

data block can be created and windowed with a square root

raised cosine window to yield a filtered waveform with agiven excess bandwidth or rolloff factor. If the initial DFT

operation is omitted, a bandlimited OFDM waveform is

produced. If the DFT is omitted and the N data symbols are

mapped to a noncontiguous set of subcarrier frequencies,

the result is an OFDMA signal. In this way, certain

frequency subbands known to contain signals from other

transmitters or to undergo severe fading, can be avoided

and efficient frequency division multiplexing of multipleuser signals is facilitated. The time-frequency-space se-

lector can distribute data-carrying components to different

transmitting antennas as well as to different frequencies in

space-frequency block coding schemes [33].

Non-contiguous mapping can also be used for DFT-

precoded signals, for example to allow in-band pilot tones

to be inserted without interfering with data, or to spread

data over a wider bandwidth to enhance frequency diver-sity. A SCM and multiple access scheme sometimes called

interleaved frequency domain multiple access (IFDMA)

[34], can be generated from Fig. 1, by mapping N DFT

outputs from each of up to U users onto N frequencies

which are spaced at intervals of U subcarriers. User uðu ¼ 0; 1; . . . U � 1Þ is assigned to the frequency set

fu; uþ U; uþ 2U; . . . ; uþ ðN � 1ÞUg. Each user thus

occupies a unique set of N frequencies in an interleavedfashion. For M > UN, the waveform corresponding to (14)

is, for the uth user,

sn;u ¼ ej2�unM

XN�1

‘¼0

gIFDMA n� ‘ M

UN

� �d‘;u;

n ¼ 0; 1; . . . ;M� 1 (15)

where

gIFDMAðnÞ ¼ ej2�UðN�1Þn

M1

M

sin �UNnM

� �sin �Un

M

� � ;n ¼ 0; 1; . . . ;M� 1: (16)

In an uplink scenario, each user transmits fsn;ug as in (15),

where fsn;ug, n ¼ �L; . . . ;�1, contains the cyclic prefix.

The waveform described by (16) has periodic peaks at

n ¼ 0; ðM=UÞ; 2ðM=UÞ; . . . ; ðU � 1ÞðM=UÞ, but in (15)

smM=U;u¼ðUN=MÞej2�ðum=UÞdm mod N;u, m¼0; 1; . . . ;UP� 1.

Thus again the low peak to average power ratio property is

preserved. It is clear that U IFDMA signals generated in theFD this way preserve their orthogonality independent of

their channels’ frequency selectivities, since they are

frequency-disjoint. Furthermore, each such signal is spread

in frequency by a factor of U, which yields a significant

frequency diversity advantage. The IFDMA waveform can

also be generated in the TD [35]. A generalization of

IFDMA is block IFDMA, where each user is assigned

multiple blocks of adjacent subcarriers and blocks belong-ing to different users are interleaved [36].

If NP pilot tones are to be inserted at frequencies

0;U; 2U; . . . ; ðNP � 1ÞU, with data-carrying tones being

displaced to make room for them, the set of frequencies

used for data is fp ¼ 1; 2; . . . ; ðU � 1Þ; ðU þ 1Þ; ðU þ 2Þ;. . . ð2U�1Þ; ð2U þ 1Þ; . . . ; ðN � 1þ NPÞg. In this case the

DFT-precoded OFDM data waveform, not including the

added pilot tones, can be shown to be [37]

sn ¼P

ðU � 1ÞNPMej�Nn

M

XN�1

‘¼0

gðn; ‘Þd‘ej�ðN�1Þ‘

N ;

n ¼ 0; 1; . . . ;M (17)

where

gðn; ‘Þ ¼sin �NP

UnM �

ðU�1Þ‘P

� �� sin � Un

M �ðU�1Þ‘

P

� �� sin ðU � 1Þ nM� ‘

P

� �� sin n

M� ‘P

� �� :

(18)

This expression is not that of a pure SCM signal. Howeveras will be seen later in Section VI, its peak to average

power ratio properties are favorable in comparison to those

of corresponding OFDM waveforms.

Fig. 2 shows the general receiver structure for

generalized multicarrier signals. The first element is a

DFT operation, followed by a selector (or sampler) if nec-

essary, and an equalizing FD filter. The linear operation

after channel equalization depends on the transmitter’sprematrix operation: detection and decoding for OFDM or

OFDMA, a correlation operation for multicarrier CDMA,

an IDFT for SCM, etc.

III . DIRECT EQUALIZATION METHODS

Various equalization structures whose parameters are

designed directly from an estimate of the channel frequency

response will be presented in this section. In particular, we

will assume that the exact channel frequency response is

available. In Section V we will consider techniques for

channel estimation. Moreover, a comparison in terms of

performance and computational complexity is given. The




computational complexity is evaluated in terms of number of

complex multiplications: for each structure we evaluate the

complexity per data symbol, while for each design methodwe evaluate the complexity per parameter computation. We

assume that a DFT of size P, implemented with FFT, requires

ðP=2Þ log2ðPÞ � P complex multiplications. A synoptic com-

parison of the various equalizers is provided in Table 1.

A. Time Domain Decision Feedback EqualizerIn a conventional TD DFE (TDDFE) no framing is

needed at the transmitter, as operations are performed on

a symbol-by-symbol basis in the TD. In particular, the

received signal frng is filtered by a feedforward filter

fgFF;‘g, ‘ ¼ ��;�� þ 1; . . . ;NFF � 1� � to obtain

zn ¼XNFF�1��

‘¼��gFF;‘rn�‘ (19)

where � is a suitable delay introduced by the feedforward

filter and channel. Detection is performed symbol bysymbol and interference on zn due to past symbols is

removed by the TD feedback filter fb‘g, ‘ ¼ 1; 2; . . . ;NFB,

applied on past detected symbols dn�‘, ‘ ¼ 1; 2; . . . ;NFB.

At the detection point the signal can be written as

~dn ¼ zn þXNFB

‘¼1

b‘dn�‘: (20)

Detection is applied on ~dn to obtain dn. In a direct design

approach, the feedforward and feedback filters are

designed by solving a linear system of equations [2], withcomplexity OðN3

FFÞ complex multiplications. Moreover,

from (19) and (20), the computational complexity of the

TDDFE is NFF þ NFB complex multiplications per data

symbol.

B. Decision Feedback Equalizer With a HybridTime-Frequency Structure

In the hybrid DFE (HDFE), the feedforward filter

operates in the FD on blocks of the received signal, while

the feedback operates in the TD [16], [38]. In order to allow

TD implementation of the feedback filter, data transmis-

sion with a PN extension [see (11)] must be considered

instead of cyclic prefix.As shown in Fig. 3, after the DFT of the received samples,

the feedforward filter, with coefficients fCpg, p ¼ 0; 1; . . . ;P� 1, is applied to yield the block signal fZpg, p ¼ 0; 1; . . . ;P� 1 with elements

Zp ¼ CpRp; p ¼ 0; 1; . . . ; P� 1: (21)

Through the IDFT, the sequence fZpg is then transformed

in the TD to provide the sequence fzng.From the detected data sequence fdng and (11), the

extended detected sequence fsng is given by

sn ¼ dn; n ¼ 0; 1; . . . ;M� 1,

pn�M; n ¼ M;Mþ 1; . . . ; P� 1.

�(22)

Fig. 2. Generalized multicarrier receiver (from [22]).

Table 1 Computational Complexity of Equalizer Structures




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.




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




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.




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

is z n, n ¼ 0; 1; . . . ; P� 1. If b

‘, ‘ ¼ 1; 2; . . . ;NFB, is the

rnðkÞ ¼

Pn‘¼0 h‘dn�‘ðkÞ þ

PL�1‘¼nþ1 h‘dMþn�‘ðk� 1Þ þ wkMþn n ¼ 0; . . . ; L� 1PL�1

‘¼0 h‘dn�‘ðkÞ þ wkMþn n ¼ L; . . . ;M� 1Pn�M‘¼0 h‘dn�‘�Mðkþ 1Þ þ

PL�1‘¼n�Mþ1 h‘dn�‘ðkÞ þ wkMþn n ¼ M; . . . ; P� 1

8><>: (36)

Fig. 5. Block partitioning of the received signal for overlap and save processing.




impulse response of the feedback filter. Then, the signal at

the output of backward HDFE is

~d

n ¼ z n þXNFB

‘¼1

b

‘ d

n�‘; n ¼ 0; 1; . . . ;M� 1 (38)

where d

n is the detected signal based on ~d

n. Initially,

d

n ¼ pLþn, n ¼ �1;�2; . . . ;�L. The BiHDFE scheme is

shown in Fig. 6. The output of the backward HDFE f ~d

ngis time reversed to obtain f~dBAC;ng. Lastly, output signals

f~dDIR;ng and f~dBAC;ng, from the HDFEs, respectively, are

processed for soft detection.In order to simplify the soft detection, we consider

arbitration [51] which implements a local maximuma posteriori criterion. In particular, the quality of the

local match between the reconstructed signal using

detected data, and the received sequence is estimated

over a window of size W around the symbol of interest. The

symbol of the detected sequence that provides a closer

match with the received sequence, is selected in thearbitration. First, a hard decision is taken on f~dDIR;ng and

f~dBAC;ng and the PN sequence is added, to obtain fsDIR;ngand fsBAC;ng, respectively. Let also indicate the recon-

structed signals at the output of the channel as

rDIR;n ¼XNh�1

‘¼0

h‘ sDIR;n�‘ (39)

rBAC;n ¼XNh�1

‘¼0

h‘ sBAC;n�‘: (40)

Note that (39) and (40) can be implemented in the FD as

sDIR;n and sBAC;n satisfy conditions on circularity. Then the

distance of the reconstructed signals from the received

signal is evaluated as

�DIR;n ¼1

W

XW=2

‘¼�W=2þ1

jrnþ‘ � rDIR;nþ‘j2 (41)

�BAC;n ¼1

W

XW=2

‘¼�W=2þ1

jrnþ‘ � rBAC;nþ‘j2: (42)

Lastly, the decision rule is as follows:

dn ¼dDIR;n if �DIR;n � �BAC;n

dBAC;n if �DIR;n > �BAC;n.

�(43)

The computational complexity of the structure of

BiHDFE is ð3P=2MÞ log2ðPÞþ2NFB�ð2=3ÞPMþ2ðW=MÞ,roughly double that of HDFE.

Filter Design: It can be shown that, according to the

minimum MSE criterion [50]

b

‘ ¼ b�‘ ; ‘ ¼ 1; 2; . . . ;NFB (44)

while

C

p ¼ C�P�p p ¼ 0; 1; . . . ; P� 1: (45)

The resulting design complexity in terms of complex

multiplications is the same as that of HDFE.

G. Iterative Equalization MethodsThere are alternative design methods which, for simple

signal processing with no matrix inversion, yield an

approximate minimum MSE solution by using classicalleast mean square (LMS) or recursive least square (RLS)

algorithms [26]. Note that for an FD linear equalizer these

iterative algorithms are fairly straightforward to use on a

per-subcarrier basis, while for a HDFE it is not simple to

force the constraint that the TD feedback filter should be

causal, and we should resort to a HDFE-NP, with two error

signals, one to update the feedforward filter and one to

update the feedback filter [26]. One problem with theseiterative methods, is that, since the update is block-based,

their convergence is very slow. Besides, they need a

training sequence. Hence, they should be used only for

tracking the optimal solution in the presence of a slowly

time varying channel.

Recently, a new iterative equalization method has been

proposed [52], [53], denoted iterative block DFE (IBDFE),

Fig. 6. The BiHDFE structure.




with the feedback working in the FD, where within eachblock, detection and design are updated in sequence. This

configuration yields best performance when it interacts with

decoding. Equations for IBDFE are given in Section IV-C for

a MIMO system (including the single antenna system as a

special case) while adaptive versions of the HDFE with noise

prediction are given in Section V-C.

IV. EXTENSIONS TO MIMO SYSTEMSAND PERFORMANCE COMPARISON

While MIMO techniques have been widely proposed andshow great promise for application in future wireless

systems, the number of MIMO implementations has up to

now been modest, mainly due to their hardware complex-

ity. In this context FD filtering in MIMO systems is an

approach to drastically simplify both filter design and

operation, as will be seen in the next subsections. How-

ever, to the general reader, who may find these parts very

technical, we suggest to go directly to Section IV-E onturbo equalization or even Section IV-F on performance

comparison for single-input single-output systems.

It is known that we can increase substantially the

capacity of a given system by employing multiple antennas

at both the transmitter and the receiver [54]. This allows

highly spectrally-efficient spatial multiplexing techniques

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.




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




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;

1; . . . ; P� 1, follows to obtain ~dði;qÞn , n ¼ 0; 1; . . . ;M� 1,

on which soft detection is performed. In particular, ~dði;qÞn is

described as the sum of the desired data signal and a

disturbance term that collects the effects of both noise and

residual interference, modeled as a complex Gaussian ran-

dom variable with zero mean and variance �ði;qÞ2SD . Hence

the a posteriori probability of detecting dði;qÞn ¼ �, where �

belongs to the constellation alphabet A, is

fdði;qÞn

ð�Þ ¼ K0e�~dði;qÞn ��ði;qÞ�� 2=�ði;qÞ2

SD ;

� 2 A; n ¼ 0; 1; . . . ;M� 1 (54)

with �ði;qÞ the gain of the desired signal and K0 a

normalization factor. The soft detected symbol in TD is

the mean of dði;qÞn , for n ¼ 0; 1; . . . M� 1,

mdði;qÞn

¼ E dði;qÞn

h i¼X�2A

�fdði;qÞn

ð�Þ: (55)

In (53) the soft detected signal in the FD, fmSði;qÞn

g, to be

used for the cancellation of other streams is the P-size DFT

of fmdði;qÞn

g, extended with the PN sequence [see (11)].

Filter and Signal Design: Again, the feedforward filters

Cði;qÞp and the feedback signals fYði;qÞp g are designed to

minimize the MSE (26), where the expectation is taken

with respect to fsði;qÞn g and fwði;qÞn g, given the observation

~dði;q�1Þn . In order to compute (26) we assume that the

conditional (i.e., given ~dði;q�1Þn ), statistics of fdði;qÞn g are

those of dði;q�1Þn .

Assuming that fdði;qÞn g are statistically independent the

variance of Sði;qÞp is given by

�Sði;qÞp

¼E Sði;qÞp � m

Sði;qÞp

��

2" #

¼XM�1

n¼0

X�2Aj�j2f

dðqÞn

ð�Þ � mdði;qÞn

�� 2: (56)

Note that (56) is independent of p.

After inserting (53) into (26) and using (56), the MSE

for the ith stream at the qth iteration is

Jði;qÞSD ¼

1

P2

XP�1

p¼0

n�2

W Cði;qÞp Cði;qÞHp þ Cði;qÞp :

�XNT

m¼1

&ðm;q�1Þp HðmÞp HðmÞHp Cði;qÞHp

þ mSði;q�1Þp

þ�Sði;qÞp

� �

� Cði;qÞp HðiÞp HðiÞHp Cði;qÞHp � 1� �þ Yði;qÞp

�� 2þ 2Re

hYði;qÞ�p m

Sði;q�1Þp

Cði;qÞp HðiÞp � 1� �io

(57)

Minimizing (57) with respect to Yði;qÞp and Cði;qÞp , we get

Yði;qÞp ¼ mSði;q�1Þp

1� Cði;qÞp HðiÞp

h i(58)




and

Cði;qÞp ¼HðiÞHp

XNT

m¼1

HðmÞp HðmÞHp þ �2W

�Sðm;q�1Þp

INR

24

35�1

: (59)

A slight enhancement of performance is obtained by

adding the constraint of a unitary gain of the useful signal,

i.e., �ði;qÞ ¼ Cði;qÞp HðiÞp ¼ 1. In this case Cði;qÞp turns out to bea scaled version of (59).

About complexity, at each iteration a IDFT and a per-

subcarrier multiplication is performed, so that for a single

input-single output system the structure complexity is

ðNIP log2ðPÞ=MÞ � ðP=MÞ þ ðP=MÞ complex multiplica-

tions, where we accounted for the (I)DFTs and we added a

P=M term to account for the various real multiplications

required for the computation of the soft signals. For thedesign, we only account for 3P complex multiplications in the

computation of channel dependent terms in (58) and (59).

D. Comparison of MIMO ReceiversThe comparison between MIMO-HDFE and LST-

HDFE can be found in [64], [75]. [75] also includes

comparisons with MIMO OFDM schemes. For an uncoded

or a high code rate system, when the channel has large

intersymbol interference components MIMO-HDFE and

LST-HDFE performance is similar. For low code rates,

LST-HDFE outperforms MIMO-HDFE. At low signal-to-

noise ratio (SNR), LST-HDFE receivers suffer more fromerror propagation; at high SNR the error propagation is

limited and LST-HDFE receivers enjoy significant perfor-

mance improvement over the MIMO-HDFE. In general

SCM yields better performance than OFDM, with a larger

advantage for high code rates.

IBDFE schemes were studied in [76]–[78]. The perfor-

mance with these schemes is excellent and can be very close

to the matched filter bound, especially for severely time-dispersive channels with rich multipath propagation.

E. Turbo Equalization, or IBDFE With CodingWhen IBDFE is integrated with coding/decoding, it

comes also under the name of turbo equalization in the

FD [71]. In this case, the data bits must be encoded, inter-

leaved and mapped into symbols before transmission. At

the receiver, the feedback part of the turbo equalization in

the FD includes deinterleaving, decoding and soft re-

encoding, as shown in Fig. 7. The equalized samples are

first demapped by a soft demapper that provides the loglikelihood ratio for each coded bit. A deinterleaver and soft

output decoder follow. The latter provides the refined log

likelihood ratio by exploiting the properties of the error

correcting code, [71], [72], [79]. Interleaving follows

together with soft mapping that provides probabilities

fdðqÞn

ð�Þ, � 2 A. The remaining blocks of Fig. 7 show

operations for filter design as for IBDFE.

For quaternary phase shift keying (QPSK) symbols withA ¼ f1 jg, soft demapping and mapping simplify as

follows. Defining the complex log likelihood ratio as

�ði;qÞn ¼ �ði;qÞR;n þ j�ði;qÞI;n , where �

ði;qÞR;n ð�

ði;qÞI;n Þ is associated to

Re½dði;qÞn � ðIm½dði;qÞn �Þ, the soft demapper yields [26]

�ði;qÞn ¼4m

dði;q�1Þn

�ði;qÞ2SD

(60)

i.e., the log likelihood ratio is proportional to the equalizer

soft output. In turn, if ði;qÞn ¼ ði;qÞR;n þ jði;qÞI;n is the complex

log likelihood ratio at the decoder output (extrinsic

information) we have

mdði;q�1Þn

¼ tanhði;qÞR;n

2

!þ j tanh

ði;qÞI;n

2

!: (61)

Fig. 7. Feedback part of turbo equalization (IBDFE with coding).




F. ComparisonWe compare the nonlinear FD equalization schemes in

two respects: performance and complexity. We consider a

single antenna scenario ðNR ¼ NT ¼ 1Þ.

Performance Comparison: In order to compare the

performance of the systems, we considered a QPSK trans-

mission on a Rayleigh fading channel having an exponen-

tial power delay profile with aroot-mean square delayspread �rms=T ¼ 2, normalized with respect to the symbol

period. The channel estimate is assumed ideal. The size of

the DFT has been set to P ¼ 128, while the PN extension

length is L ¼ 16. For TDDFE, NFF ¼ 16 and NFB ¼ 16.

Fig. 8 [52] shows the average BER as a function of the

channel average SNR for the following schemes: a) TDDFE

with possible errors in the feedback process, b) TDDFE

with ideal (ID) feedback signal (labelled TDDFE-ID),c) matched filter bound, d) HDFE and e) IBDFE with

various iterations. From Fig. 8 we note that IBDFE after

four iterations provides the lowest BER outperforming

even TDDFE-ID. HDFE has a performance close to that of

TDDFE and clearly all nonlinear structures outperform the

FD linear equalizer provided by the IBDFE at the first

iteration. In this scenario the advantage of IBDFE over

TDDFE is about 1 dB. We note that IBDFE is 2 dB awayfrom the matched filter bound for this channel.

As for ELHDFE, a fair comparison with the other

schemes should include the different data rate due to the

absence of prefixes or sequences. To this end, we evaluated

the throughput when a stop and wait automatic repeat

request (ARQ) strategy is used to retransmit the packets in

error. We assume a full-buffer condition and we neglect

the overhead time for the acknowledging [43]. Fig. 9shows the achievable throughput as a function of the

average SNR for HDFE and ELHDFE. The reference

scenario is a transmission of a signal. We assume a DFT

size of P ¼ 64 symbols, �rms=T ¼ 2 and L ¼ 16. A rate 1/2

convolutional code having generating polynomials (133_8,171_8) is used at the transmitter. We note that in this

scenario the performance loss due to the increased inter-

ference for ELHDFE is widely compensated by the

increased throughput due to the absence of extension,

yielding 30% more throughput than that of HDFE.

Computational Complexity: Although in some cases BER

improvement might not be enough to justify the adoptionof FD structures, it is important to compare the

computational complexity of the various structures to

understand the benefits of the FD approach. As a reference

scenario we consider P ¼ 256, L ¼ NFF ¼ NFB ¼ 16.

Table 1 summarizes the complexity for the equalizer

structures. It shows that HDFE, ELHDFE and IBDFE

significantly reduce the complexity by about 25% with

respect to TDDFE. Table 2 shows instead the complexityrelated to the equalizer design. We observe that the

complexity of the HDFE and of the bidirectional HDFE

design grows quadratically with the number of feedback

filter taps, while the complexity of TDDFE grows as the

third power of the filter taps. ELHDFE has a considerably

higher design complexity, as it grows with P3, since the

circularity of convolution between the transmitt signal and

the channel cannot be exploited. As mentioned, asuboptimal solution could be to design the same filter as

for HDFE, with considerably lower complexity but also an

increased intersymbol interference [42].

V. CHANNEL ESTIMATION METHODS

In order to perform channel estimation in the FD, known

blocks of training symbols, or pilot symbols, are transmittedFig. 8. BER performance of various equalizer structures

(from [52]). MF: matched filter bound.

Fig. 9. Throughput performance comparison of HDFE and

ELHDFE (from [43]).




in addition to data, as a reference for the equalizer adap-tation process at the start of transmission, and periodically

thereafter to ensure accurate adaptation to time-varying

channels. Once equalizer parameters are initially estimat-

ed with sufficient accuracy, receiver hard or soft decisions

can be used for further improving tracking accuracy and

performance, in an iterative fashion.

A. Types of Training SignalsThe traditional method of transmitting pilot symbols in

SCM is by time multiplexing them with data; training

blocks of known pseudo random data symbols (also some-

times called unique words) are interspersed at regular

intervals among longer blocks of data symbols. The pilot

blocks should be at least twice as long as the expected

maximum channel impulse response length. The pilot

block should preferably be designed to have a constantenvelope and almost flat spectrum. Constant amplitude

zero autocorrelation (CAZAC), maximal length PN se-

quences, or Chu sequences [80], have this property. It is

pointed out in [29] and in Section II-A that a periodic pilot

block (e.g., a PN extension) can replace the cyclic prefix at

the beginning of every data block, and then the receiver’s

DFT processing block consists of the data block plus the

pilot block.Fig. 10 shows the arrangement of a time multiplexed

pilot block followed by a data block, and how it can be

processed in the FD. Suppose the pilot block length is NP

time samples. Taking the DFT of the received pilot block,

and dividing by the DFT of the transmitted pilot block

gives NP uniformly-spaced estimated samples of the chan-

nel frequency response [see (62) below]. What is needed

for the equalizer design is P > NP uniformly spacedsamples of the response. So FD interpolation is necessary.

In a multiple access scenario, a single time multiplexed

pilot block may contain pilots from more than one user

signal. An efficient way to do this is to generate each user’s

pilot signal as a IFDMA waveform, orthogonal with thoseof the other users, as described in Section II-B. All such

pilot waveforms may be superimposed to form the pilot

block.

The channel impulse response or the equalizer response

could be estimated and adapted from one or more suc-

cessive time multiplexed pilot blocks by using well known

LMS or RLS TD system identification methods [81]. How-

ever for impulse responses spanning many symbol inter-vals, such TD processing, with adaptive transversal filters,

would largely nullify the signal processing complexity

reduction advantages of FD equalization. Thus, FD pro-

cessing is preferable for channel estimation and equalizer

adaptation.

Pilots can also be frequency multiplexed with data. In

this case, pilot tones displace or replace data-carrying tones

in the FD. Displacement of data tones by uniformly-spacedpilot tones is commonly used for OFDM systems. The total

bandwidth is then increased by the number of pilot-

occupied tones, or for fixed bandwidth the data payload is

reduced by the inserted pilots. Frequency multiplexed

pilots can also be used in the generalized multicarrier

context with DFT-precoded OFDM [37], [82]. In the latter

case, the resulting data-carrying signal is generally not a

pure SCM signal, as pointed out in Section II-B but it hasthe low peak to average power ratio properties of SCM

signals and its receiver structure is similar to that of pure

SCM signals.

Loss of spectral efficiency due to pilot insertion can be

avoided if data tones are replaced by regularly-spaced pilots.

This type of frequency multiplexed pilot insertion, called

FD superimposed pilot technique, has the effect of causing

periodic nulls to appear in the spectrum of the transmittedsignal (at the frequencies of the inserted pilots). Powerful

nonlinear equalization techniques such as IBDFE or turbo

equalization can mitigate the resulting received signal dis-

tortion, so that FD superimposed pilot technique systems

Fig. 10. Time multiplexed (TM) pilots, showing FD processing at the receiver (cyclic prefixes are not shown). The dash-dot contour

is the interpolated channel frequency response.




can approach to within about 1 dB the performance of pilot

tone displacement systems, while requiring no extra

bandwidth or overhead for pilots [37], [83].

Fig. 11 illustrates how pilots frequency multiplexedwith data are processed at a receiver. The NP received

subcarriers bearing pilot tones are selected, and after

division by the transmitted pilot tones, the NP samples of

the channel impulse response estimate are interpolated to

P samples. Channel estimation processing in the FD is

identical for time and frequency multiplexed pilots, after

the expansion or selection of the pilot frequencies.

Time multiplexed pilots have the advantage that theyare temporally separate from the data blocks, and therefore

they do not affect the peak to average power ratio prop-

erties of the transmitted signals. They can also be used for

purposes of timing synchronization. However, as men-

tioned below, they require their own cyclic prefix of suf-

ficient length to avoid interblock interference, thus adding

to the pilot overhead. Frequency multiplexed pilots share

the cyclic prefix with data, avoiding the extra overhead(and in the case of FD superimposed pilot technique pilots,

consume no overhead). Frequency multiplexed pilots can

also be advantageous from a system implementation per-

spective, if OFDM and SCM transmission modes coexist in

the same system. On the other hand, SCM blocks that

contain frequency multiplexed pilots have higher peak to

average power ratio than nonpilot blocks, and so these

blocks require slightly higher power backoff.The temporal spacing of pilot blocks depends on the

maximum expected Doppler frequency of the channel.

Sampling theory considerations suggest that the frequency

at which pilot blocks are transmitted should be about twice

the highest expected Doppler frequency and the spacing of

pilots in frequency should be about half of the maximum

channel coherence bandwidth (equivalent to training

block lengths of about twice the maximum impulse re-sponse length) [84].

Equalizer parameters must be adapted, or trained, by

one or a combination of the following two methods:

1) Channel estimate-based adaptation, in which the

frequency or impulse responses of the channel or

channels are estimated, along with the signal to

noise ratio, and the results are substituted in the

appropriate formula for the equalizer response ofSection III.

2) Equalizer error-based adaptation, in which equal-

izer parameters are adapted directly, by feeding

back the equalizer’s output error to an adaptation

algorithm, such as LMS or RLS [81].

B. Channel Estimate-Based Adaptation: Pilot-BasedChannel Estimation

For indirect adaptation from pilot training, the channel

frequency response at a set of equally-spaced pilot fre-

quencies p0 2 P, during the training block is estimated as

Hp0 ¼Rp0

Tp0; p0 2 P (62)

where Rp0 is the P-size DFT of the channel output due to

the pilot at frequency p0. Tp0 is the pilot at that frequency in

the case of frequency multiplexed pilots. In the case of

time multiplexed pilots, Tp0 is the p0 component of the DFT

of the pilot training sequence. This approach to pilot-aided

channel estimation is equally applicable to OFDM and to

SCM. Most of the expressions for FD equalizer parametersin the previous section also require an estimate of the

additive white noise variance. This may be estimated in

several ways, for example by measuring the received power

spectrum at several out of band frequencies.

The number of pilot symbols NP is usually a small

fraction of the DFT size P, to keep pilot overhead low.

Interpolation in the FD is necessary to generate the esti-

mated channel frequency response at all P frequenciesneeded by the equalizer. A simple FD interpolation tech-

nique is to transform Hp0 to the TD by a NP-point inverse

DFT, pad it with P� NP zeros, and transform back to the FD

with a P-point DFT [85] to get Hp for p ¼ 0; 1; . . . ; P� 1. A

more accurate interpolation is to use a Wiener interpolation

filter designed according to the channel’s FD correlation

properties if these are known or assumed, windowing over a

set of adjacent frequencies [84], [86]. A joint or separateinterpolation in the TD is necessary to extend channel

estimates to data blocks that are not associated with pilot

blocks [84], [87], [88]. The extension to multiple transmit-

ting and receiving antennas is straightforward [88]. A

distinct set of pilots must be transmitted from each stream,

separated in time, frequency or code from those of other

users [39], [89]. Thus data-displacing pilot overhead

Fig. 11. Frequency multiplexed pilots, showing FD processing

at the receiver (cyclic prefixss are not shown). The dash-dot contour is

the interpolated channel frequency response.




increases in proportion to the number of simultaneoustransmitted signals. Equation (62) has a counterpart for

estimating the vector channel of the ith stream from its pilots

TðiÞp0 as

HðiÞp0 ¼

Rp0

TðiÞp0

; p0 2 P: (63)

Note that the use of (62) or (63) to estimate the chan-

nel for FD equalization assumes that each pilot training

sequence has its own cyclic prefix appended to it.

Otherwise, Rp0 will be corrupted by an adjacent data

block. This prefix requirement is automatically satisfied in

the case of frequency multiplexed pilots, which share the

cyclic prefix with the data blocks in which they areembedded. However the addition of a cyclic prefix to a

time multiplexed pilot block substantially increases its

effective length, and hence the total pilot overhead. For

the case where U users’ pilots are frequency multiplexed,

via IFDMA, in a common pilot block, the added overhead

per user is reduced by a factor of U. In the absence of a

time multiplexed pilot cyclic prefix, the resulting random

data-induced error in the channel response estimate mustbe reduced by averaging over many successive training

blocks. Reference [90] proposes this approach for OFDM

with pseudorandom training blocks between successive

OFDM blocks.

C. Equalizer Error-Based AdaptationThe RLS algorithm can be used to design an HDFE. We

define the errors in the TD at block k as

enðkÞ ¼ dnðkÞ � ~dnðkÞ; n ¼ 0; 1; . . . ;M� 1: (64)

Now, an RLS with respect to filter coefficients at iteration

k, fCpðkÞg and fb‘ðkÞg, yields operations with large

matrices. An alternative is to operate in the FD also forthe feedback coefficients fBpðkÞg, p ¼ 0; 1; . . . ; P� 1.

However, now the problem is how to force the causality

constraint b0ðkÞ ¼ 0. Fortunately, the HDFE-NP structure

can be a valid alternative, when the global optimization of

RLS is split into two local optimizations [26].

In fact, we define two cost functions, one that

minimizes the error at the output of the feedforward and

the other the error at the detection point. For afeedforward at iteration k, fCpðkÞg, p ¼ 0; 1; . . . ; P� 1 at

the detection point, we introduce the FD error sequences

at equalizer output

EF;pðkÞ ¼ SpðkÞ � ZpðkÞ¼ SpðkÞ � CpRpðkÞ; p¼0; 1; . . . ; P�1 (65)

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




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

decision feedback iterative channel estimation algorithms

are described in [94]. Each user transmits QPSK modu-

lation with a rate 1/2 constraint length 7 convolutional

code through an independent WINNER C2 channel with1.47 s delay spread and 50 km/h vehicular speeds,

described in [94]. The symbol rate is 40 Mbaud. DFT size is

1024 data symbols, and the frame size is 12 DFT blocks,

with two 256-symbol pilot blocks at the beginning and end

of each frame. The performance loss relative to perfect

channel state information is about 1 dB in the absence of

out of cell interference, and rises to about 2.2 dB when four

�15 dB out of cell interferers are present. The performanceloss is significantly higher if iterative channel estimation

and least squares processing are not used [94]. For single

user, single antenna transmission, the performance differ-

ence between iterative channel estimation-based channel

estimation and perfect channel state information can be

very small for the same channel conditions [37].

VI. IMPLEMENTATION ISSUES: EFFECTSOF RF HARDWARE IMPAIRMENTS

The performance of nonlinear FD equalizer can be

degraded by radio frequency hardware impairments.Here we consider the effects of nonlinear high power

amplifiers (HPAs), phase noise and frequency offset.

A. Nonlinear Power AmplifiersHPAs used in radio transmitters can cause significant

distortion to signals whose instantaneous power fluctua-

tions approach the HPA’s output saturation range. Even

small amounts of nonlinear distortion can cause undesir-

able out of band spectral components, which can interfere

with signals in adjacent frequency channels. Regulatory

agencies typically specify spectral masks, which set limits

on transmitted power spectral density. Larger amounts of

Fig. 12. Frame error rate (FER) versus average SNR per antenna for

decision feedback iterative channel estimation (DFICE) with

1 or 2 iterations, supplemented with direct least squares adaptation,

with and without out of cell interferers (OCI). Also shown for

comparison is the case of IBDFE with 4 iterations and perfect channel

state information (PCSI) (from [94]).




nonlinear distortion also cause in-band self-interference,which results in increased received BER. To comply with

spectral masks and avoid in-band nonlinear distortion, HPAs

are operated with a certain power backoffVwhich can be

defined as the ratio of maximum saturation output power to

the average output power. A large power backoff lowers HPA

efficiency and increases overall power consumption and

battery drain. It also means that a more expensive HPA, with

a higher maximum output power rating, is necessary toproduce a given average output power. Minimizing required

power backoff is thus desirable, without sacrificing BER

performance or spectral efficiency, especially for cost- and

power-sensitive user terminals [97].

SCM waveforms consist of one data symbol at a time,

transmitted in a serial fashion, whereas OFDM and

other multicarrier waveforms consist of many parallel-

transmitted data symbols. Thus SCM waveforms havelower envelope fluctuation and lower peak to average

power ratios than OFDM waveforms. This in turn implies

that they have lower required power backoff than that of

OFDM waveforms. The lower power backoff requirement

is the main reason that SCM is attractive for the uplink of

cellular systems.

Fig. 13, from [97] illustrates complementary cumula-

tive distribution functions of QPSK SCM (labeledSERMOD) and OFDMA signals for 0% and 25% square

root raised cosine rolloffs, with M ¼ 256 data symbols per

block. The 0% rolloff SCM signal is generated by the zero-

rolloff FD method of (13) and (14), followed by 5.5% raised

cosine time-windowing of the TD waveform. The 25%

rolloff SCM signal is generated by the traditional TD

method, with 25% excess bandwidth square root raised

cosine filtering of the TD waveform. The lower amplitude

range of the SCM (or DFT-precoded OFDM) signal isevident. It is also evident that excess bandwidth (25%

versus 0%) reduces the amplitude range of the SCM signal,

while having little or no effect on the OFDM signal’s

amplitude range.

Power backoff comparisons can be made by observing

and comparing the transmitted power spectral density of

various waveforms at the output of a realistically-modeled

HPA. A Rapp model [98] with a parameter p ¼ 2, is a goodapproximation to the amplitude-to-amplitude conversion

characteristic of typical moderate cost solid state power

amplifiers. The ratio of output ðVoutÞ to input ðVinÞ ampli-

tude in this model with parameter p is given by

Vout

Vin

�� ¼ 1þ Vin

Vsat

��

2p" #�1=ð2pÞ

(70)

where Vsat is the saturated output level of the amplifier.3

With p ¼ 10 or higher, the characteristic approaches that

of an ideal linear clipper, which is almost linear up to the

sharply defined saturation level. Examples of power

spectral density regrowth due to a p ¼ 2 nonlinearity for

the OFDM and SCM QPSK signals of Fig. 13 are shown in

Fig. 14(a) and (b). The greater the power backoff, the lessis the spectral regrowth at the HPA output. In Fig. 14, the

average powers of the SCM and OFDM signals being

compared (and hence their backoffs) are adjusted so that

their resulting output power spectral densities are very

similar. Fig. 14(a) shows that for the FD-generated, 0%

rolloff signals, whose complementary cumulative distribu-

tion functions are shown in Fig. 13, SCM and OFDM

require 7 dB and 9 dB backoff, respectively, for comparablemaximum spectrum sidelobe levels of about �40 dB. The

backoff for SCM is slightly decreased to about 6.3 dB for

the TD-generated signals with 25% rolloff, although the

signals’ bandwidth has increased by 25% with this rolloff

factor.

The required power backoff is significantly reduced by

up to 2 to 4 dB for a HPA with Rapp parameter p ¼ 10, that

approximates an ideal linear clipper. The ideal linearclipper characteristic p � 10, can be approached by

applying an adaptive linearization process to the HPA,

such as described in [99]. Note that SCM still has lower

required backoff than its OFDM counterpart.

The backoff requirements for QPSK block IFDMA

signals and the OFDMA with the same spectral arrange-

ment, called block equidistant frequency division multiple

access [36], with a 4-subcarrier block width, with 32 blocksspaced at 32 subcarrier intervals, are shown in Fig. 15 for

p ¼ 2 and p ¼ 10. These figures also show a spectral mask

proposed by the WINNER Project [100]. Although theFig. 13. Distribution of instantaneous power for comparable OFDMA

and SCM waveforms (SERMOD) with 0% rolloff, generated in the FD

with 5.5% raised cosine TD windowing, and with 25% rolloff generated

in the TD by square root raised cosine FD filtering.

3In this formula, the amplifier gain is normalized to unity fornotational convenience.




block IFDMA signal waveform is not exactly equivalent to

a SCM waveform, its required backoff is close to that of the

full-bandwidth case. Results presented in [97] indicate that

IFDMA has similar backoff properties to block IFDMAand full-band DFT-precoded OFDM. If DFT-precoding is

applied before the frequency components are highly ir-regularly distributed to chunks of spectrumVfor example

when frequency-adaptation is employed by a transmitter

which has knowledge of the channel it is transmitting

through [23], the peak to average power ratio properties

of the resulting waveform come close to those of OFDM,

and hence block IFDMA in this case loses its appeal [101].The power spectral density shown in Fig. 14 is for a

signal waveform which does not include frequency multi-

plexed pilots for channel estimation and synchronization.

Full-band and block IFDMA signals’ peak to average power

ratio and HPA output spectra will be affected, since

frequency multiplexed pilots essentially add another wave-form to the data waveform. As shown in [97], the presence

of pilots in the block IFDMA signal increases the backoff

required from 7.0 dB to 7.8 dB, and the difference from

block equidistant frequency division multiple access de-

creases from 1.9 dB to 1 dB. Note that only a fraction of

OFDM symbols contain pilots and need this extra backoff.

Thus the effect of frequency multiplexed pilots on the

required power backoff is minimal.It is worth noting that for the typical nonlinearities and

spectral mask requirement mentioned here, the effect of

Fig. 14.Power spectral density at output of ap ¼ 2 Rapp nonlinearity for QPSK OFDM and SCM signals with (a) 0% and (b) 25% excess bandwidth.

Fig. 15. HPA output power spectra for QPSK OFDMA and DFT-precoded OFDMA signals, corresponding to block equidistant frequency division

multiple access (B-EFDMA) and block IFDMA (B-IFDMA) respectively, with a block width of 4 and with 40 MHz nominal bandwidth.

(a) HPA has Rapp model nonlinearity with parameter p ¼ 2; (b) HPA has Rapp model nonlinearity with parameter p ¼ 10.




nonlinear distortion on the system error probability per-formance is negligible [97].

B. Phase Noise and Frequency OffsetThe effect of noise and other small imperfections on

oscillators used in up- and down-converters leads to phase

noise and frequency offsets. The effect on an ideal complex

baseband signal sðtÞ is to convert it to sðtÞej2��ðtÞ, where

�ðtÞ ¼ �f tþ �ðtÞ=2�, and where the frequency offset is

�f and the phase noise is �ðtÞ=2�. �f is normally a small

fraction of the carrier frequency fc, and �ðtÞ=2� can be

modeled as a Brownian motion (Wiener) noise process,with a Lorentzian power spectral density whose variance

is ct, where

c � f3 dB

�f 2c

(71)

where f3 dB is the 3 dB frequency of the phase noise power

spectral density [102]. TD multiplication of a factor such as

ej2��ðtÞ is equivalent to a convolution in the FD. Thus phase

noise and frequency offset cause intersubcarrier (and

therefore intersymbol) interference to OFDM waveforms

[17]. Phase noise mitigation techniques at the receiver for

OFDM are therefore relatively complex, and can involve

something like transversal filtering in the FD [103].On the other hand, assuming the bandlimiting input

receiver filter length is much shorter than the variations of

�ðtÞ, the effect of the factor ej2��ðtÞ on received SCM

signals is essentially a slowly varying modulation on the

detected data symbols, which is easily and robustly tracked

and compensated by decision-directed phase locked loop

(PLL) techniques, after frequency or TD equalization

[104]. Thus the symbol rate-sampled TD signal at theequalizer output can be modeled as

~dn ¼ snej�n þ w0n ¼ snej2� nT�fþPn

‘¼1"‘ð Þ þ w0n (72)

for n ¼ 0; 1; . . . ; P� 1, where f"‘g are the Gaussian

Brownian motion increments of the phase noise process

and w0n is the noise (and interference) term at the equalizer

output.

The time-varying phase process f�ng can be trackedwith a second order soft decision directed PLL, which uses

log likelihood ratio information from a turbo equalizer

[105]. For QPSK, the PLL update at the nth data symbol

period is, (�i ¼ 0 for i � 0): (see equation at bottom of

page) where tR;n and tI;n are defined as:

tR;n ¼R;n

2þ I;n

2þ 2

ffiffiffi2p

�2w0

Re r�nej�nþ�4

(74)

tI;n ¼R;n

2� I;n

2þ 2

ffiffiffi2p

�2w0

Re r�nej�n��4

(75)

�1 and �2 are PLL constants, designed for stability and PLLbandwidth, and R;n and I;n are, respectively, the log

likelihood ratio of the real and imaginary parts of the

decoder output and �2w0 is the variance of w0n.

Fig. 16 presents the BER achieved for QPSK versus

Eb=N0 for this method of compensation, used together with

turbo equalization of Section IV-E and low density parity

check code (LDPC) coding [105]. The code used here is a

regular (3,6) LDPC code with a 504 � 1008 parity checkmatrix. The number of iterations in the LDPC decoder and

the number of iterations in the turbo equalizer are 4. The

code block length is 1008. The DFT length is also 1008.

The bandwidth is 40 MHz and the channel is the WINNER

C2 channel. �f PT ¼ 0:1 represents a relatively large fre-

quency offset: 10% of the subcarrier spacing. The value of

�2 ¼ 0:001 corresponds to a phase noise power spectral

density bandwidth of about 6.4 KHz. These represent verysevere degrees of frequency offset and phase noise, but the

compensation approach results in a performance loss of

only about 1 to 1.5 dB.

�n ¼ �n�1 þ �1ð�n�1 � �n�2Þ þ �2

Im r�n�1ej�n�1þ�4� �

sinhðtR;n�1Þ þ Im r�n�1ej�n�1��4� �

sinhðtI;n�1ÞcoshðtR;n�1Þ þ coshðtI;n�1Þ

(73)

Fig. 16. Phase noise and frequency offset compensation,

QPSK (from [105]). �f ¼ Pf.




Signals such as IFDMA, in which multiple independentusers are frequency-interleaved will experience multiuser

interference from phase noise and frequency offset, just as

adjacent subcarriers in OFDM experience intersubcarrier

interference. This is explored further in [106] and [107].

VII. PERFORMANCE COMPARISONS OFSINGLE CARRIER WITH OFDM

As pointed out previously, single carrier or DFT-precoded

OFDM systems have radio frequency hardware implemen-

tation advantages over OFDM, which are especially impor-

tant for uplink transmission from low-power, low-cost user

wireless terminals to base stations. On the other hand,

OFDM and its variants are well-suited for downlink trans-

mission, especially when base station transmitters can

exploit channel state information to optimize frequencyresources allocated to user terminal receivers. If we neglect

the implementation advantages of SCM and the adaptive

frequency assignment advantages of OFDM, how do their

bit- or frame-error rate performances compare?

The answer depends on the system and channel param-

eters under which they are being compared. Asymptotic

information theory-based studies [108], [109] indicate that

they have similar performance, with SCM being slightlybetter for high code rates and OFDM being slightly better

for low code rates. Simulation comparisons, such as [110]

support this finding with some qualifications: high code

rate and high SNR, with Viterbi-decoded convolutional

codes favor SCM, while the use of more powerful turbo

codes gives OFDM a slight performance advantage over

linearly equalized SCM. Evidently OFDM combined with

powerful low rate coding and decoding is better able toexploit the diversity that arises from frequency selectivity.

On the other hand, at high code rates with only moderately

powerful codes (or for uncoded systems without spatial

diversity), OFDM is very vulnerable to dips in the channel

frequency response.

When SCM with frequency domain equalization is

aided by FD nonlinear equalizers, its BER performance

improves markedly, and it can come very close to the per-formance of comparable OFDM systems [16], [38]. When

FD iterative or turbo equalization is employed, SCM’s

performance improves further, to the point where it can

exceed that of OFDM for both ideal channel knowledge and

for iterative channel estimation [82].

For MIMO systems, SCM with FD nonlinear equal-

ization can equal or exceed the performance of OFDM

systems with Viterbi decoding of convolutional codes [75].

However [111] shows that for a highly dispersive channel(uniform power delay profile) and a powerful, rate 1/2

turbo code, 2 � 2 and 4 � 4 MIMO OFDM with iterative

space-time decoding can slightly out-perform comparable

MIMO SCM systems with the same code and with turbo

equalization.

In summary, error rate performance of SCM systems may

be slightly better or slightly worse than that of comparable

OFDM systems, depending on channels, code parameters,equalization techniques, spatial diversity and multiuser

interference. However the differences are not large, espe-

cially when each system’s coding, equalization, multiuser

detection and channel estimation techniques are optimized.

VIII . CONCLUSION

In this paper we provided an overview of nonlinear fre-

quency domain equalization techniques for SCM transmis-sions. The main advantage of the frequency domain

approach is a reduced complexity with respect to time

domain implementations, due to its efficient implementa-

tion by means of FFTs. On the other hand, nonlinear

equalization can be implemented fully in the frequency

domain only by iterative techniques and with the burden of

a reduced bandwidth efficiency due to the use of PN

extension. Still, when compared to OFDM which has thesame spectral efficiency, SCM systems with frequency

domain equalization have the advantage of a lower peak to

average power ratio while still retaining good performance

and the convenience of resource allocation by DFT-precoded

OFDM or single carrier frequency domain multiple access.

Frequency domain nonlinear equalization techniques can be

extended to multiantenna systems, as shown in this paper,

with a wide range of configurations for a flexible use ofspace, time and frequency dimensions. The importance of

SCM transmissions with FD equalization is confirmed by

being under consideration in various standards, the most

recent being 3GPP-LTE and LTE-Advanced. h

Acknowledgment

We gratefully acknowledge the contributions, in recent

years, of our students and other research colleagues to our

understanding of this topic and to many of the results that

appear in this paper: Gunther Auer, Amir Banihashemi,

Federico Boccardi, Giambattista Carnevale, Florence

Danilo-Lemoine, Reza Kalbasi, Chan-Tong Lam, Benjamin

Ng, Maryam Sabbaghian, Fayyaz Siddiqui, Filippo Tosato,

Krzysztof Wesoaowski.

RE FERENCES

[1] S. Qureshi, BAdaptive equalization,[Proc. IEEE, vol. 37, pp. 1340–1387, Sep. 1985.

[2] J. G. Proakis, Digital Communications.New York: McGraw Hill, 1994.

[3] J. A. C. Bingham, BMulticarrier modulationfor data transmission: An idea whose time

has come,[ IEEE Trans. Commun., vol. 28,pp. 5–14, May 1990.

[4] G. Stuber, J. Barry, S. McLaughlin, Y. Li,M. Ingram, and T. Pratt, BBroadbandMIMO-OFDM wireless communications,[Proc. IEEE, vol. 92, pp. 611–640, Feb. 2004.

[5] M. Sternad, T. Ottosson, T. Ahlen,A. Svensson, and A. Brunstrom, BTowardssystems beyond 3G based on adaptiveOFDMA transmission,[ Proc. IEEE, vol. 95,pp. 2432–2455, Dec. 2007.

[6] M. Doelz, E. Heald, and D. Martin, BBinarydata transmission techniques for linear




systems,[ Proc. IRE, vol. 45, pp. 656–661,May 1957.

[7] M. Zimmerman and A. Kirsch, BTheAN/GSC-10 (KATHRYN) variable rate datamodem for HF radio,[ IEEE Trans. Commun.Technol., vol. COM-15, pp. 197–203,Apr. 1967.

[8] J. Holsinger, BDigital communication overfixed time-continuous channels withmemoryVWith special application totelephone channels,[ Ph.D. thesis, Dept. ofElectrical Engineering, M.I.T., Oct. 1964.

[9] R. Chang, BSynthesis of band-limitedorthogonal signals for multichannel datatransmission,[ Bell Sys. Tech. J., vol. 45,pp. 1775–1796, Apr. 1966.

[10] S. Weinstein and P. Ebert, BDatatransmission by frequency-divisionmultiplexing using the discrete fouriertransform,[ IEEE Trans. Commun., vol. 19,pp. 628–634, Jan. 1971.

[11] T. Walzman and M. Schwartz, BAutomaticequalization using the discrete frequencydomain,[ IEEE Trans. Inf. Theory, vol. 19,pp. 59–68, Jan. 1973.

[12] H. Sari, G. Karam, and I. Jeanclaude,BChannel equalization and carriersnchronization in OFDM systems,[ in Proc.Int. Tirrenia Workshop Digital Commun.,Tirrenia, Italy, Sep. 1993.

[13] H. Sari, G. Karam, and I. Jeanclaude,BFrequency-domain equalization of mobileradio and terrestrial broadcast channels,[ inProc. Conf. Global Commun. (GLOBECOM),San Francisco, CA, Nov./Dec. 1994, pp. 1–5.

[14] H. Sari, G. Karam, and I. Jeanclaude,BTransmission techniques for digitalterrestrial TV broadcasting,[ IEEE Commun.Mag., vol. 33, pp. 100–109, Feb. 1995.

[15] M. Clark, BAdaptive frequency-domainequalization and diversity combining forbroadband wireless communications,[IEEE J. Sel. Areas Commun., vol. 16,pp. 1385–1395, Oct. 1998.

[16] N. Benvenuto and S. Tomasin, BOn thecomparison between OFDM and singlecarrier modulation with a DFE using afrequency domain feedforward filter,[ IEEETrans. Commun., vol. 50, pp. 947–955,Jun. 2002.

[17] T. Pollet, M. v. Bladel, and M. Moeneclaey,BBER sensitivity of OFDM systems to carrierfrequency offset and Wiener phase noise,[IEEE Trans. Commun., vol. 43, pp. 191–193,Feb.–Apr. 1995.

[18] G. Carron, R. Ness, L. Deneire, L. v. Perre,and M. Engels, BComparison of twomodulation techniques using frequencydomain processing for in-house networks,[IEEE Trans. Consum. Electron., vol. 47,pp. 63–72, Feb. 2001.

[19] E. Dahlman, S. Parkvall, J. Skold, andP. Beming, 3G EvolutionVHSPA and LTE forMobile Broadband. Oxford, U.K.:Academic, 2007.

[20] Z. Wang and G. Giannakis, BWirelessmulticarrier communicationsVWhereFourier meets Shannon,[ IEEE Signal Process.Mag., vol. 17, pp. 29–48, May 2000.

[21] D. Falconer, R. Dinis, T. Matsumoto, M. Ran,A. Springer, and P. Zhu, WWRF/WG4/Subgroup on New Air Interfaces White Paper: AMixed Single Carrier/OFDM Air Interface forFuture-Generation Cellular Wireless Systems,Aug. 2003R

[22] Wireless World Research Forum, ‘‘BroadbandFrequency Domain-Based Air Interfaces forFuture-Generation Wireless Systems,’’

WWRF Working Group 4, White Paper,Sep. 2005R

[23] IST-4-027756 WINNER II, D4.6.1,The WINNER II Air Interface: RefinedMultiple Access Concepts, Nov. 2006R

[24] 3d generation partnership project, ‘‘TechnicalSpecification Group Radio Access Network:Evolved Universal Terrestrial Radio Access(E-UTRA); Physical Channels andModulation,’’ 3GPP TS 36.211 V8.1.0,release 8, Nov. 2007R

[25] H. Myung, J. Lim, and D. Goodman, BSinglecarrier FDMA for uplink wirelesstransmission,[ IEEE Vehic. Technol.Magazine, vol. 1, pp. 30–38, Sep. 2006.

[26] N. Benvenuto and G. Cherubini, Algorithmsfor Communications Systems and TheirApplications. Chichester, U.K.: Wiley,2002.

[27] A. Stamoulis, G. B. Giannakis, andA. Scaglione, BBlock FIR decision-feedbackequalizer for filterbank precodedtransmissions with blind estimationcapabilities,[ IEEE Trans. Commun., vol. 49,pp. 69–83, Jan. 2001.

[28] A. Scaglione, G. B. Giannakis, andS. Barbarossa, BRedundant filterbankprecoders and equalizersVPart I:Unification and optimal designs, and part II:Blind channel estimation, synchronizationand direct equalization,[ IEEE Trans. SignalProcess., vol. 47, pp. 1988–2022, Jul. 1999.

[29] L. Deneire, B. Gyselinckx, and M. Engels,BTraining sequence versus cyclicprefixVA new look on single carriercommunication,[ IEEE Commun. Lett., vol. 5,pp. 292–294, Jul. 2001.

[30] R. Fischer and J. Huber, BOn the equivalenceof single- and multicarrier modulation: Anew view,[ in Proc. Int. Symp. Info. Theory(ISIT), Ulm, Germany, Jul. 1997.

[31] L. Bruhl and B. Rembold, BUnifiedspatio-temporal frequency domainequalization for multi- and single-carrierCDMA systems,[ in Proc. Vehic. Tech. Conf.(VTC) Fall, Vancouver, Canada, Oct. 2002,pp. 676–680.

[32] D. A. Wiegandt, Z. Wu, and C. Nassar, BHighthroughput, high performance OFDM viapseudo-orthogonal carrier interferometryspreading codes,[ IEEE Trans. Commun.,vol. 51, pp. 1123–1134, Jul. 2003.

[33] N. Al-Dhahir, BSingle-carrierfrequency-domain equalization forspace-time block-coded transmissions overfrequency-selective fading channels,[ IEEECommun. Lett., vol. 5, pp. 304–306,Jul. 2001.

[34] U. Sorger, I. D. Broeck, and M. Schnell,BInterleaved FDMAVA new spread-spectrum multiple-access scheme,[ in Proc.Int. Conf. Commun. (ICC), Atlanta, GA,Jun. 1998, pp. 1013–1017.

[35] C.-M. Chang and K.-C. Chen,BFrequency-domain approach to multiuserdetection in DS-CDMA communications,[IEEE Commun. Lett., vol. 4, pp. 331–333,Nov. 2000.

[36] T. Svensson, T. Frank, D. Falconer,M. Sternad, E. Costa, and A. Klein,BB-IFDMAVA power-efficient multipleaccess scheme for non-frequency-adaptivetransmission,[ in Proc. Information SocietyTechnologies (IST) Summit, Budapest,Hungary, Jul. 2007.

[37] C.-T. Lam, D. Falconer, andF. Danilo-Lemoine, BIterative frequencydomain channel estimation forDFT-precoded OFDM systems using in-band

pilots,[ IEEE J. Sel. Areas Commun., vol. 26,Feb. 2008.

[38] D. Falconer, S. L. Ariyavisitakul,A. Benyamin-Seeyar, and B. Eidson,BFrequency domain equalization forsingle-carrier broadband wireless systems,[IEEE Commun. Mag., vol. 40, pp. 58–66,Apr. 2002.

[39] J. Coon, S. Armour, M. Beach, andJ. McGeehan, BAdaptive frequency domainequalization for single carrier multiple inputmultiple output wireless transmissions,[IEEE Trans. Signal Process., vol. 53,pp. 3247–3256, Aug. 2005.

[40] A. Koppler and R. Weigel, BNoise predictiveDFE for single carrier block transmissionwith a cyclic prefix,[ in Proc. Int. OFDMWorkshop (InOWo), Hamburg, Germany,2002.

[41] Y. Zhu and K. B. Letaief, BSingle carrierfrequency domain equalization with timedomain noise prediction for widebandwireless communications,[ IEEE Trans.Wireless Commun., vol. 5, pp. 3548–3557,Dec. 2006.

[42] D. Falconer and S. L. Ariyavisitakul,BBroadband wireless using single carrier andfrequency domain equalization,[ in Proc. Int.Symp. Wireless Personal Multimedia Commun.(WPMC), Honolulu, HI, Oct. 2002.

[43] S. Tomasin, BOverlap and save frequencydomain DFE for throughput efficient singlecarrier transmission,[ in Proc. Int. Symp.Personal, Indoor and Mobile Radio Commun.(PIMRC), Berlin, Germany, Sep. 2005.

[44] N. J. Bershad and P. L. Feintuch,BA normalized frequency domain LMSadaptive algorithm,[ IEEE Trans. Acoust.,Speech, Signal Process., vol. 34, pp. 452–461,Jun. 1986.

[45] R. P. Bitmead and B. D. O. Anderson,BAdaptive frequency sampling filters,[IEEE Trans. Circuits Syst., vol. 28,pp. 524–543, Jun. 1981.

[46] C. F. N. Cowan and P. M. Grant,Adaptive Filters. Englewood Cliffs, NJ:Prentice-Hall, 1985.

[47] B. Widrow, BFundamental relationsbetween the LMS algorithm and the DFT,[IEEE Trans. Circuits Syst., vol. 34,pp. 814–820, Jul. 1987.

[48] H. Suzuki, BPerformance of a new adaptivediversity-equalization for digital mobileradio,[ IEE Elec. Lett., vol. 26, pp. 626–627,May 1990.

[49] S. Ariyavisitakul, BA decision feedbackequalizer with time-reversal structure,[IEEE J. Sel. Areas Commun., vol. 10,pp. 599–613, Apr. 1992.

[50] S. Tomasin, BEfficient bidirectional DFE fordoubly selective wireless channels,[EURASIP J. Appl. Signal Proc., vol. 2006,pp. 1–10, 2006, Article ID 70572.

[51] J. K. Nelson, A. C. Singer, U. Madhow, andC. S. McGahey, BBAD: Bidirectionalarbitrated decision-feedback equalization,[IEEE Trans. Commun., vol. 53, pp. 214–218,Feb. 2005.

[52] N. Benvenuto and S. Tomasin, BIterativedesign and detection of a DFE in thefrequency domain,[ IEEE Trans. Commun.,vol. 53, pp. 1867–1875, Nov. 2005.

[53] N. Benvenuto and S. Tomasin, BBlockiterative DFE for single carrier modulation,[IEE Elec. Letters, vol. 38, pp. 1144–1145,Sep. 2002.

[54] G. Foschini, BLayered-space-timearchitecture for wireless communication in a




fading enviroment when usingmulti-element antennas,[ Bell Labs Tech J.,pp. 41–59, Autumn, 1996.

[55] G. J. Foschini and M. J. Gans, BOn limits ofwireless communications in fadingenvironments when using multipleantennas,[ Wireless Personal Commun., vol. 6,pp. 315–335, Mar. 1998.

[56] P. W. Wolniasky, G. J. Foschini,G. D. Golden, and R. A. Valenzuela,BV-BLAST: An architecture for realizing veryhigh rates over rich-scattering wirelesschannel,[ in Proc. Int. Symp. Signals, Syst.Electron. (ISSSE), Pisa, Italy, Oct. 1998,pp. 295–300.

[57] G. Foschini, D. Chizhik, M. Gans,C. Papadias, and R. Valenzuela, BAnalysisand performance of some basic space-timearchitecture,[ IEEE J. Sel. Areas Commun.,vol. 21, pp. 303–320, Apr. 2003.

[58] J. Winters, J. Salz, and R. Gitlin,BThe capacity of wireless communicationsystems can be substantialy increased by theuse of antenna diversity,[ in Proc. Int. Conf.Universal Personal Commun. (ICUPC), Dallas,TX, Sep./Oct. 1992, pp. 02.01/1–02.01/5.

[59] S. Sfar, R. Murch, and K. Letaief, BLayeredspace-time multiuser detection over wirelessuplink systems,[ IEEE Trans. WirelessCommun., vol. 2, pp. 653–668, Jul. 2003.

[60] C. Tidestav, M. Sternad, and A. Ahlen,BReuse within a cellVInterference rejectionor multiuser detection?’’ IEEE Trans.Commun., vol. 47, pp. 1511–1522, Oct. 1999.

[61] N. Al-Dhahir and A. H. Sayed, BThefinite-length multi-input multi-outputMMSE-DFE,[ IEEE Trans. Signal Process.,vol. 48, pp. 2921–2936, Oct. 2000.

[62] A. Lozano and C. Papadias, BLayeredspace-time receiver for frequency-selectivewireless channels,[ IEEE Trans. Commun.,vol. 50, pp. 65–73, Jan. 2002.

[63] J. Tubbax, L. Vanderperre, S. Donnay, andM. Engels, BSingle-carrier communicationsusing decision-feedback equalization formultiple antennas,[ in Proc. Int. Conf.Commun. (ICC), Helsinki, Finland,May 2003, vol. 4, pp. 2321–2325.

[64] R. Kalbasi, R. Dinis, D. Falconer, andA. Banihashemi, BHybrid time-frequencylayered space-time receivers for severetime-dispersive channels,[ in Proc. SignalProcessing Advances in Wireless Commun.(SPAWC) Workshop, Lisbon, Portugal,Jul. 2004.

[65] F. Pancaldi and G. M. Vitetta,BFrequency-domain equalization forspace-time block-coded systems,[ IEEETrans. Wireless Commun., vol. 4,pp. 2907–2916, Nov. 2005.

[66] A. Papasakellariou, BOverview ofinterference cancellation for CDMA wirelesssystems,[ in Proc. Int. Conf. Info. Tech. Codingand Computing (ITCC), Las Vegas, NV,Mar. 2000, pp. 86–90.

[67] N. Benvenuto, F. Boccardi, and G. Carnevale,BFrequency domain realization of space-timereceivers in dispersive wireless channels,[IEEE Trans. Signal Process., vol. 55,pp. 313–326, Jan. 2007.

[68] T. Abe and T. Matsumoto, BSpace-time turboequalization in frequency-selective MIMOchannels,[ IEEE Trans. Veh. Technol., vol. 52,pp. 469–475, May 2003.

[69] T. Abe, S. Tomisato, and T. Matsumoto,BA MIMO turbo equalizer forfrequency-selective channels with unknowninterference,[ IEEE Trans. Veh. Technol.,vol. 52, pp. 476–482, May 2003.

[70] S. Tomasin and N. Benvenuto,BFrequency-domain interferencecancellation and non-linear equalizationfor CDMA systems,[ IEEE Trans. WirelessCommun., vol. 4, pp. 2329–2339, Sep. 2005.

[71] M. Tuchler and J. Hagenauer, BTurboequalization using frequency domainequalizers,[ in Proc. Allerton Conf.,Monticello, IL, Oct. 2000.

[72] M. Tuchler, A. Singer, and R. Koetter,BMinimum mean squared error equalizationusing a priori information,[ IEEE Trans.Commun., vol. 50, pp. 673–683, Mar. 2002.

[73] R. Dinis, A. Gusmao, and N. Esteves,BIterative block-dfe techniques forsingle-carrier-based broadbandcommunications with transmit/receive spacediversity,[ in Proc. Int. Symp. WirelessCommun. Sys. (ISWCS), Port Louis,Mauritius, Sep. 2004.

[74] S. Alamouti, BA simple transmit diversitytechnique for wireless communications,[IEEE J. Sel. Areas Commun., vol. 16,pp. 1451–1458, Oct. 1998.

[75] R. Kalbasi, D. Falconer, A. Banihashemi, andR. Dinis, BA comparison of frequencydomain block MIMO transmission systems,[IEEE Trans. Veh. Technol., vol. 58,pp. 165–175, Jan. 2009.

[76] R. Kalbasi, R. Dinis, D. Falconer, andA. Banihashemi, BLayered space-timereceivers for single-carrier transmission withiterative frequency-domain equalization,[ inProc. Vehic. Tech. Conf. (VTC) Spring, Milan,Italy, May 2004.

[77] R. Kalbasi, R. Dinis, D. Falconer, andA. Banihashemi, BAn iterativefrequency-domain layered space-timereceiver for SDMA systems with singlecarrier transmission,[ in Proc. Int. Conf. onAcoustics, Speech, and Signal Processing(ICASSP), Montreal, Canada, May 2004.

[78] R. Dinis, R. Kalbasi, D. Falconer, andA. Banihashemi, BIterative layeredspace-time receivers for single-carriertransmission over severe time-dispersivechannels,[ IEEE Commun. Lett., vol. 8,pp. 579–581, Sep. 2004.

[79] M. Tuchler and J. Hagenauer, BLinear timeand frequency domain turbo equalization,[in Proc. Vehic. Tech. Conf. (VTC) Fall,Atlantic City, NJ, Oct. 2001, pp. 1449–1453.

[80] D. Chu, BPolyphase codes with good periodiccorrelation properties,[ IEEE Trans. Inf.Theory, vol. 18, pp. 531–532, Jul. 1972.

[81] S. Haykin, Adaptive Filter Theory, 3rd ed.Englewood Cliffs, NJ: Prentice-Hall, 1996.

[82] G. Auer, F. Danilo-Lemoine, D. Falconer,and C.-T. Lam, BDesign of time andfrequency domain pilots for generalizedmulticarrier systems,[ in Proc. Int. Conf.Commun. (ICC), Glasgow, U.K., Jun. 2007.

[83] R. Dinis, C.-T. Lam, and D. Falconer, BJointfrequency-domain equalization and channelestimation using superimposed pilots,[ inProc. Wireless Commun. and Networking Conf.(WCNC), Las Vegas, NV, Apr. 2008.

[84] P. Hoher, S. Kaiser, and P. Robertson,BPilot symbol-aided channel estimation intime and frequency,[ in Proc. CTMC WithinGLOBECOM, Phoenix, AZ, Nov. 1997,pp. 90–96.

[85] L. Deneire, P. Vandenameele, L. v. Perre,B. Gyselinckx, and M. Engels, BA lowcomplexity ML channel estimator forOFDM,[ in Proc. Int. Conf. Commun. (ICC),Helsinki, Finland, Jun. 2001.

[86] Y. Li, BPilot-symbol-aided channelestimation for OFDM in wireless systems,[

IEEE Trans. Veh. Technol., vol. 49,pp. 1207–1215, Jul. 2000.

[87] Y. Li, J. Leonard, J. Cimini, andN. R. Sollenberger, BRobust channelestimation for OFDM systems with rapiddispersive fading channels,[ IEEE Trans.

Commun., vol. 46, pp. 902–915, Jun. 1998.

[88] G. Auer, BChannel estimation for OFDMsystems with multiple transmit antennas byfiltering in time and frequency,[ in Proc.Vehic. Tech. Conf. (VTC) Fall, Orlando, FL,Oct. 2003.

[89] F. Siddiqui, F. Danilo-Lemoine, andD. Falconer, BOn interference in uplinkSDMA SC-FDE system,[ in Proc. Conf.Communication Networks and ServicesResearch (CNSR), Fredericton, Canada,May 2007.

[90] M. Muck, M. de Courville, and P. Duhamel,BA pseudo random postfix OFDMmodulatorVSemi-blind channel estimationand equalization,[ IEEE Trans. Signal Process.,vol. 54, pp. 1005–1017, Mar. 2006.

[91] F. Sanzi, S. Jelting, and J. Speidel,BA comparative study of iterative channelestimators for mobile OFDM systems,[IEEE Trans. Wireless Commun., vol. 2,pp. 849–859, Sep. 2003.

[92] J. Bonnet and G. Auer, BOptimized iterativechannel estimation for OFDM,[ in Proc.Vehic. Tech. Conf. (VTC) Fall, Montreal,Canada, Sep. 2006.

[93] C.-T. Lam, D. Falconer, andF. Danilo-Lemoine, BA low complexityfrequency domain iterative decision-directedchannel estimation technique for singlecarrier systems,[ in Proc. Vehic. Tech. Conf.(VTC) Spring, Dublin, Ireland, Apr. 2007.

[94] F. Siddiqui, F. Danilo-Lemoine, andD. Falconer, BPIC-assisted IBDFE-basediterative spatial channel estimation withintra- and inter-cell interference in SC-FDEsystems,[ in Proc. Vehic. Tech. Conf. (VTC)Fall, Baltimore, MD, Oct. 2007.

[95] IST-4-027756 WINNER II, D4.7.2,‘‘Interference Avoidance Concepts,’’Jun. 2007.

[96] J. Andrews, W. Choi, and R. W. Heath, Jr.,BOvercoming interference in spatialmultiplexing MIMO cellular networks,[IEEE Trans. Wireless Commun., vol. 14,pp. 95–104, Dec. 2007.

[97] F. Danilo-Lemoine, D. Falconer, C.-T. Lam,M. Sabbaghian, and K. Wesoaowski, BPowerbackoff reduction techniques for generalizedmulticarrier waveforms,[ EURASIP J. onWireless Commun. and Net., Special Issue onMulticarrier Systems, Article ID 437801,13 Pages, vol. 2008, Nov. 2007.

[98] C. Rapp, BEffects of HPA nonlinearity on a4DPSK/OFDM signal for a digital soundbroadcasting system,[ in Proc. Eur. Conf.Satellite Commun., Liege, France, Oct. 1991,pp. 179–184.

[99] K. Wesoaowski and J. Pochmara, BEfficientalgorithm for adjustment of adaptivepredistorter in OFDM transmitter,[ in Proc.Vehic. Tech. Conf. (VTC) Fall, Atlantic City,NJ, Oct. 2001.

[100] IST-2003-507581, ‘‘WINNER D2.5 DuplexArrangements for Future Broadband RadioInterface,’’ Oct. 2004.

[101] IST-2003-507581, ‘‘WINNER D2.2Feasibility of Multi-BandwidthTransmissions,’’ Oct. 2004.

[102] A. Demir, A. Mehrotra, and J. Roychowdhury,BPhase noise in oscillators: A unifying theoryand numerical methods for characterization,[




IEEE Trans. Circuits Syst., vol. 47,pp. 655–674, May 2000.

[103] D. Petrovic, W. Rave, and G. Fettweis,BEffects of phase noise on OFDM systemswith and without PLL: Characterization andcompensation,[ IEEE Trans. Commun.,vol. 55, pp. 1607–1616, Aug. 2007.

[104] D. D. Falconer, BJointly adaptive equalizationand carrier recovery in two dimensionaldigital communication systems,[ Bell SystemTech. J., pp. 317–334, Mar. 1976.

[105] M. Sabbaghian and D. Falconer, BJoint turbofrequency domain equalization and carriersynchronization,[ IEEE Trans. WirelessCommun., vol. 7, pp. 204–212, Jan. 2008.

[106] R. Dinis, C. Lam, and D. Falconer, BOn theimpact of phase noise and frequency offseton block transmission CDMA schemes,[ in

Proc. Int. Symp. Wireless Commun. Sys.(ISCWS), Port Louis, Mauritius, Sep. 2004.

[107] R. Dinis, C. Lam, and D. Falconer, BCarriersynchronisation requirements for CDMAsystems with frequency-domain orthogonalsignature sequences,[ in Proc. Int. Symp.Spread Spectrum Tech. and Applications(ISSSTA), Sydney, Australia, Sep. 2004.

[108] N. Zervos and I. Kalet, BOptimized decisionfeedback equalization versus optimizedorthogonal frequency division multiplexingfor high speed transmission over the localcable network,[ in Proc. Int. Conf.Commun. (ICC), Boston, MA, Jun. 1989,pp. 1080–1085.

[109] V. Aue, G. P. Fettweis, and R. Valenzuela,BA comparison of performance of linearlyequalized single carrier and coded OFDM

over frequency selective fading channelsusing the random coding technique,[ in Proc.Int. Conf. Commun. (ICC), Atlanta, GA,Jun. 1998.

[110] L. Ye and A. Burr, BFrequency diversitycomparison of coded SC-FDE and OFDM ondifferent channels,[ in Proc. Int. Symp.Personal, Indoor and Mobile Radio Commun.(PIMRC), Athens, Greece, Sep. 2007.

[111] M. Yee, M. Sandell, and Y. Sun,BComparison study of single-carrier andmulti-carrier modulation using iterativebased receiver for MIMO system,[ in Proc.Vehic. Tech. Conf. (VTC) Spring, Milan, Italy,May 2004, pp. 1275–1279.

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.




contributed pap e r singlecarriermodulationwith ...kk/dtsp/tutoriaalit/benvenuto.pdf · pap e r...

Documents