In this paper, we consider the uplink transmission in multicarrier code-division multiple-access (MC-CDMA) systems. As other multicarrier signals, MC-CDMA signals have high envelope fluctuations and a high peak-to-mean envelope power ratio (PMEPR), which leads to amplification difficulties. This is particularly important for the uplink transmission, since an efficient low-cost power amplification is desirable at the mobile terminals (MTs). Moreover, the transmission over time-dispersive channels destroys the orthogonality between spreading codes, which might lead to significant multiple-access interference levels. To reduce the envelope fluctuations of the transmitted signals, while maintaining the spectral efficiency, the MC-CDMA signal associated to each MT is submitted to a clipping device, followed by a frequency-domain filtering operation. However, the nonlinear distortion effects can be high when an MC-CDMA transmitter with reduced envelope fluctuations is intended (e.g., a small clipping level and/or when successive clipping and filtering operations are employed). In this paper, we define an iterative receiver that jointly performs a turbo multiuser detection and the estimation and cancellation of the nonlinear distortion effects. Our performance results show that the proposed receiver structure allows good performances, very close to the linear receiver ones, even for high system load and/or when a PMEPR as low as 1.7 dB is intended for each MT

Dinis, Rui

Silva, Paulo

IEEE Transactions on Vehicular Technology

In this paper, we consider the uplink transmission in
multicarrier code-division multiple-access (MC-CDMA) systems.
As other multicarrier signals, MC-CDMA signals have high envelope
fluctuations and a high peak-to-mean envelope power ratio
(PMEPR), which leads to amplification difficulties. This is particularly
important for the uplink transmission, since an efficient
low-cost power amplification is desirable at the mobile terminals
(MTs). Moreover, the transmission over time-dispersive channels
destroys the orthogonality between spreading codes, which might
lead to significant multiple-access interference levels. To reduce
the envelope fluctuations of the transmitted signals, while maintaining
the spectral efficiency, the MC-CDMA signal associated to
each MT is submitted to a clipping device, followed by a frequencydomain
filtering operation. However, the nonlinear distortion effects
can be high when an MC-CDMA transmitter with reduced
envelope fluctuations is intended (e.g., a small clipping level and/or
when successive clipping and filtering operations are employed).
In this paper, we define an iterative receiver that jointly performs
a turbo multiuser detection and the estimation and cancellation
of the nonlinear distortion effects. Our performance results show
that the proposed receiver structure allows good performances,
very close to the linear receiver ones, even for high system load
and/or when a PMEPR as low as 1.7 dB is intended for each MT

Camões - Repositório Institucional da Universidade Autónoma de Lisboa

2288 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 58, NO. 5, JUNE 2009Joint Turbo Equalization and Multiuser Detection ofMC-CDMA Signals With Low Envelope FluctuationsPaulo Silva and Rui Dinis, Member, IEEEAbstract—In this paper, we consider the uplink transmission inmulticarrier code-division multiple-access (MC-CDMA) systems.As other multicarrier signals, MC-CDMA signals have high enve-lope fluctuations and a high peak-to-mean envelope power ratio(PMEPR), which leads to amplification difficulties. This is par-ticularly important for the uplink transmission, since an efficientlow-cost power amplification is desirable at the mobile terminals(MTs). Moreover, the transmission over time-dispersive channelsdestroys the orthogonality between spreading codes, which mightlead to significant multiple-access interference levels. To reducethe envelope fluctuations of the transmitted signals, while main-taining the spectral efficiency, the MC-CDMA signal associated toeach MT is submitted to a clipping device, followed by a frequency-domain filtering operation. However, the nonlinear distortion ef-fects can be high when an MC-CDMA transmitter with reducedenvelope fluctuations is intended (e.g., a small clipping level and/orwhen successive clipping and filtering operations are employed).In this paper, we define an iterative receiver that jointly performsa turbo multiuser detection and the estimation and cancellationof the nonlinear distortion effects. Our performance results showthat the proposed receiver structure allows good performances,very close to the linear receiver ones, even for high system loadand/or when a PMEPR as low as 1.7 dB is intended for each MT.Index Terms—Multicarrier code-division multiple access (MC-CDMA), multiuser detection (MUD), nonlinear distortion, turboequalization.I. INTRODUCTIONMULTICARRIER code-division multiple-access (MC-CDMA) schemes combine an orthogonal frequency-division multiplexing (OFDM) modulation [1] with acode-division multiple-access (CDMA) scheme [2]. Spread-ing is performed in the frequency domain, and MC-CDMAschemes are promising candidates for future broadband wire-less systems. Since the transmission over time-dispersive chan-nels destroys the orthogonality between spreading codes, afrequency-domain equalizer (FDE) optimized under an MMSEcriterion is usually employed at the receiver [3], [4]. Since anManuscript received June 6, 2008; revised October 14, 2008. First publishedNovember 25, 2008; current version published May 11, 2009. This workwas supported in part by the Fundação para a Ciência e Tecnologia underpluriannual funding, U-BOAT Project PTDC/EEA-TEL/67066/2006, and theFCT/POCI 2010 research Grant SFRH/BD/24520/2005). The review of thispaper was coordinated by Dr. C. Cozzo.P. Silva is with the Escola Superior de Tecnologia, University of Algarve,8005-139 Faro, Portugal, and also with the Instituto de Telecomunicações,Instituto Superior Técnico, Technical University of Lisbon, 1049-001 Lisbon,Portugal (e-mail: psilva@ualg.pt).R. Dinis is with the Instituto de Telecomunicações, Instituto SuperiorTécnico, Technical University of Lisbon, 1049-001 Lisbon, Portugal (e-mail:rdinis@ist.utl.pt).Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.Digital Object Identifier 10.1109/TVT.2008.2010051MMSE FDE does not perform an ideal channel inversion, weare not able to fully orthogonalize the different spreading codes,which can lead to severe interference levels, particularly forfully loaded systems and/or when different powers are assignedto different spreading codes. To improve the performance,several receivers that perform turbo multiuser detection (MUD)were proposed [5]–[7]. In [5], the use of soft information forinterference cancellation is exploited in MC-CDMA systems.An iterative semiblind receiver for coded MC-CDMA systems,able to deal with intracell and intercell interference, is proposedin [6]. A novel low-complexity parallel interference cancella-tion (PIC) receiver for turbo coded MC-CDMA systems is alsoinvestigated in [7]. A promising iterative receiver for multicodeMC-CDMA signals was proposed in [8], based on the iterativeblock decision-feedback equalizer (IB-DFE) concept [9]–[11],allowing significant performance improvements, particularlyfor fully loaded systems and high spreading factors.As with other multicarrier schemes, MC-CDMA signalshave strong envelope fluctuations and high peak-to-mean en-velope power ratio (PMEPR) values, which lead to amplifi-cation difficulties. For this reason, it is desirable to reducethe envelope fluctuations of the transmitted signals. This isparticularly important for the uplink transmission, since anefficient low-cost power amplification is desirable at the mobileterminal (MT). Several techniques have been recommendedfor reducing the envelope fluctuations of multicarrier signals[12]–[15]. A promising approach is to employ clipping tech-niques, combined with a frequency-domain filtering operationso as to reduce the envelope fluctuations of the transmitted sig-nals while maintaining the spectral occupation of conventionalschemes [15]. By repeating the clipping and filtering (C&F)procedure, we can further reduce the PMEPR of the transmittedsignals. However, the nonlinear distortion effects can be severewhen a transmission with very low PMEPR values is intended[15], [16]. By using iterative receivers with estimation andcancellation of nonlinear distortion effects, we can significantlyimprove the performance in the presence of strong nonlineardistortion effects [17]–[19]. However, for low SNRs, the errordecisions might lead to error propagation effects, since errorsin the estimation of nonlinear distortion effects can precludeits cancellation. This is particularly serious for high systemload and/or when we decrease the clipping level to furtherreduce the PMEPR of the transmitted signals [19]. In [16], anenhanced receiver structure for the downlink transmission ofMC-CDMA has been considered, where an iterative estimationand cancellation of nonlinear distortion effects is carried out.In this paper, we consider the uplink transmission inMC-CDMA systems. We modify the approach in [19] so as to0018-9545/$25.00 © 2009 IEEESILVA AND DINIS: JOINT TURBO EQUALIZATION AND MULTIUSER DETECTION OF MC-CDMA SIGNALS WITH LOW ENVELOPE FLUCTUATIONS 2289cope with its major limitations, namely, the poor performancein the presence of severely nonlinear distortion effects and/or atlow SNRs, the envelope fluctuation regrowth after the filteringoperation, and the limitations of using the soft decisions valuesto obtain an estimate of the nonlinear distortion effects. Toallow an efficient power amplification, the PMEPR-reducingtechniques in [15] are adopted by each MT, which can berepeated several times. The base station (BS) has several receiveantennas, so as to reduce the transmit power requirements ofeach MT. To avoid error propagation effects in the typicalregion of operation, we use channel decoder outputs in thefeedback loop, in a turbolike fashion (a similar approach wasproposed for OFDM schemes [20]). We define an iterativereceiver that jointly performs a turbo MUD and the estimationand cancellation of nonlinear distortion effects, for each iter-ation, that are inherent to the transmitted signals. To improvethe performance at low SNRs, we consider a threshold-basedcancellation.This paper is organized as follows: The linear transmitter andreceiver structures are described in Section II. In Section III,we describe the nonlinear transmitter and receiver structuresproposed in this paper. Implementation complexity issues arediscussed in Section IV. Section V presents a set of perfor-mance results, and Section VI is concerned with the conclusionsof the paper.Throughout this paper, we will employ the following no-tation: bold letters A denote matrices or vectors; IN denotesthe N × N identity matrix; 0N×M denotes the N × M zeromatrix; (·)T , (·)∗, (·)H , and diag(·) denote the transpose, con-jugate, Hermitian, and diagonal matrices, respectively; [A]n,mdenotes the element of line n and column m of matrix A.x mod y is the remainder of division of x by y, and δk,k′ = 1if k = k′ and 0 otherwise.II. LINEAR TRANSMITTER AND RECEIVER STRUCTURESIn this paper, we consider the uplink transmission in MC-CDMA systems employing frequency-domain spreading. Thefrequency-domain block to be transmitted by the pth MT is{Sk,p; k = 0, 1, . . . , N − 1}, where N = KM , with K denot-ing the spreading factor and M being the number of datasymbols for that MT. The frequency-domain symbols aregiven by Sk,p = ξpCk,pAk mod M,p, where ξp is an appropriateweighting coefficient that accounts for the propagation losses,and {Ak,p; k = 0, 1, . . . , M − 1} is the block of data symbolsassociated to the pth MT, assumed to be selected from a givenconstellation (in fact, different constellations could be selectedfor different data symbols, as when loading techniques areemployed; in that case, the power associated to different datasymbols is not necessarily the same). {Ck,p; k = 0, 1, . . . , N −1} is the corresponding spreading sequence1 (a pseudorandomspreading is assumed, with Ck,p belonging to a QPSK constel-lation; without loss of generality, it is assumed that |Ck,p| = 1).1This corresponds to uniformly spreading the chips associated to a givensymbol within the transmission band, i.e., to employing a rectangular inter-leaver with dimensions K × M .As usual, it is assumed that the length of the cyclic prefix(CP) is higher than the length of the overall channel impulseresponse. We will assume that the BS has L receive antennasand the received time-domain block associated to the lth diver-sity branch, after discarding the samples associated to the CP,is {y(l)n ;n = 0, 1, . . . , N − 1}. The corresponding frequency-domain block {Y (l)k ; k = 0, 1, . . . , N − 1} [i.e., the length-N discrete Fourier transform (DFT) of the block {y(l)n ;n =0, 1, . . . , N − 1}] isY(l)k =P∑p=1Sk,pHCh(l)k,p + N(l)k=P∑p=1Ak mod M,pCk,pξpHCh(l)k,p + N(l)k=P∑p=1Ak mod M,pH(l)k,p + N(l)k (1)with HCh(l)k,p denoting the channel frequency response betweenthe pth MT and the lth diversity branch at the kth subcar-rier, N (l)k being the corresponding channel noise, and H(l)k,p =ξpHCh(l)k,p Ck,p. To detect the kth symbol of the pth MT, wewill use the set of subcarriers Ψk = {k, k + M, . . . , k + (K −1)M}.By definingY(k)=[Y(1)(k) · · · Y(L)(k)]T , withY(l)(k)=[Y (l)k · · · Y(l)k+(K−1)M ] denoting the line vector with thereceived samples associated to the set of frequencies Ψk for thelth antenna, and A(k) = [Ak mod M,1 · · · Ak mod M,P ]T ,we haveY(k) = HT (k)A(k) + N(k) (2)where N(k) = [N(1)(k) · · · N(L)(k)]T , with N(l)(k) =[N (l)k · · · N(l)k+(K−1)M ] denoting the line vector with thenoise samples associated to the set of frequencies Ψk for the lthantenna. In (2), H(k) is the P × KL overall channel frequencyresponse matrix associated to A(k), i.e.,H(k)=[H(1)(k) · · · H(L)(k)]=[H1(k) · · · HP (k)]T(3)whereH(l)(k) =⎡⎢⎢⎣H(l)k,1 · · · H(l)k+(K−1)M,1......H(l)k,P · · · H(l)k+(K−1)M,P⎤⎥⎥⎦ (4)is a P × K matrix with lines associated to the different MTsand columns associated to the set of frequencies Ψk for the lthantenna, andHp(k) =[H(1)k,p · · · H(1)k+(K−1)M,p· · · H(L)k,p · · · H(L)k+(K−1)M,p]T(5)is a column vector associated to the pth MT.

English

Joint Turbo Equalization and Multiuser Detection of MC-CDMA Signals with Low Envelope Fluctuations,

Universidade do Algarve

Joint turbo equalization and multiuser detection of MC-CDMA signals with low envelope fluctuations

P. Silva

R. Dinis

Crossref

Joint Turbo Equalization and Multiuser Detection of MC-CDMA Signals With Low Envelope Fluctuations

Sapientia

Repositório Institucional da Universidade Autónoma de Lisboa

2288 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 58, NO. 5, JUNE 2009
Joint Turbo Equalization and Multiuser Detection of
MC-CDMA Signals With Low Envelope Fluctuations
Paulo Silva and Rui Dinis, Member, IEEE
Abstract—In this paper, we consider the uplink transmission in
multicarrier code-division multiple-access (MC-CDMA) systems.
As other multicarrier signals, MC-CDMA signals have high enve-
lope fluctuations and a high peak-to-mean envelope power ratio
(PMEPR), which leads to amplification difficulties. This is par-
ticularly important for the uplink transmission, since an efficient
low-cost power amplification is desirable at the mobile terminals
(MTs). Moreover, the transmission over time-dispersive channels
destroys the orthogonality between spreading codes, which might
lead to significant multiple-access interference levels. To reduce
the envelope fluctuations of the transmitted signals, while main-
taining the spectral efficiency, the MC-CDMA signal associated to
each MT is submitted to a clipping device, followed by a frequency-
domain filtering operation. However, the nonlinear distortion ef-
fects can be high when an MC-CDMA transmitter with reduced
envelope fluctuations is intended (e.g., a small clipping level and/or
when successive clipping and filtering operations are employed).
In this paper, we define an iterative receiver that jointly performs
a turbo multiuser detection and the estimation and cancellation
of the nonlinear distortion effects. Our performance results show
that the proposed receiver structure allows good performances,
very close to the linear receiver ones, even for high system load
and/or when a PMEPR as low as 1.7 dB is intended for each MT.
Index Terms—Multicarrier code-division multiple access (MC-
CDMA), multiuser detection (MUD), nonlinear distortion, turbo
equalization.
I. INTRODUCTION
MULTICARRIER code-division multiple-access (MC-CDMA) schemes combine an orthogonal frequency-
division multiplexing (OFDM) modulation [1] with a
code-division multiple-access (CDMA) scheme [2]. Spread-
ing is performed in the frequency domain, and MC-CDMA
schemes are promising candidates for future broadband wire-
less systems. Since the transmission over time-dispersive chan-
nels destroys the orthogonality between spreading codes, a
frequency-domain equalizer (FDE) optimized under an MMSE
criterion is usually employed at the receiver [3], [4]. Since an
Manuscript received June 6, 2008; revised October 14, 2008. First published
November 25, 2008; current version published May 11, 2009. This work
was supported in part by the Fundação para a Ciência e Tecnologia under
pluriannual funding, U-BOAT Project PTDC/EEA-TEL/67066/2006, and the
FCT/POCI 2010 research Grant SFRH/BD/24520/2005). The review of this
paper was coordinated by Dr. C. Cozzo.
P. Silva is with the Escola Superior de Tecnologia, University of Algarve,
8005-139 Faro, Portugal, and also with the Instituto de Telecomunicações,
Instituto Superior Técnico, Technical University of Lisbon, 1049-001 Lisbon,
Portugal (e-mail: psilva@ualg.pt).
R. Dinis is with the Instituto de Telecomunicações, Instituto Superior
Técnico, Technical University of Lisbon, 1049-001 Lisbon, Portugal (e-mail:
rdinis@ist.utl.pt).
Color versions of one or more of the figures in this paper are available online
at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TVT.2008.2010051
MMSE FDE does not perform an ideal channel inversion, we
are not able to fully orthogonalize the different spreading codes,
which can lead to severe interference levels, particularly for
fully loaded systems and/or when different powers are assigned
to different spreading codes. To improve the performance,
several receivers that perform turbo multiuser detection (MUD)
were proposed [5]–[7]. In [5], the use of soft information for
interference cancellation is exploited in MC-CDMA systems.
An iterative semiblind receiver for coded MC-CDMA systems,
able to deal with intracell and intercell interference, is proposed
in [6]. A novel low-complexity parallel interference cancella-
tion (PIC) receiver for turbo coded MC-CDMA systems is also
investigated in [7]. A promising iterative receiver for multicode
MC-CDMA signals was proposed in [8], based on the iterative
block decision-feedback equalizer (IB-DFE) concept [9]–[11],
allowing significant performance improvements, particularly
for fully loaded systems and high spreading factors.
As with other multicarrier schemes, MC-CDMA signals
have strong envelope fluctuations and high peak-to-mean en-
velope power ratio (PMEPR) values, which lead to amplifi-
cation difficulties. For this reason, it is desirable to reduce
the envelope fluctuations of the transmitted signals. This is
particularly important for the uplink transmission, since an
efficient low-cost power amplification is desirable at the mobile
terminal (MT). Several techniques have been recommended
for reducing the envelope fluctuations of multicarrier signals
[12]–[15]. A promising approach is to employ clipping tech-
niques, combined with a frequency-domain filtering operation
so as to reduce the envelope fluctuations of the transmitted sig-
nals while maintaining the spectral occupation of conventional
schemes [15]. By repeating the clipping and filtering (C&F)
procedure, we can further reduce the PMEPR of the transmitted
signals. However, the nonlinear distortion effects can be severe
when a transmission with very low PMEPR values is intended
[15], [16]. By using iterative receivers with estimation and
cancellation of nonlinear distortion effects, we can significantly
improve the performance in the presence of strong nonlinear
distortion effects [17]–[19]. However, for low SNRs, the error
decisions might lead to error propagation effects, since errors
in the estimation of nonlinear distortion effects can preclude
its cancellation. This is particularly serious for high system
load and/or when we decrease the clipping level to further
reduce the PMEPR of the transmitted signals [19]. In [16], an
enhanced receiver structure for the downlink transmission of
MC-CDMA has been considered, where an iterative estimation
and cancellation of nonlinear distortion effects is carried out.
In this paper, we consider the uplink transmission in
MC-CDMA systems. We modify the approach in [19] so as to
0018-9545/$25.00 © 2009 IEEE
SILVA AND DINIS: JOINT TURBO EQUALIZATION AND MULTIUSER DETECTION OF MC-CDMA SIGNALS WITH LOW ENVELOPE FLUCTUATIONS 2289
cope with its major limitations, namely, the poor performance
in the presence of severely nonlinear distortion effects and/or at
low SNRs, the envelope fluctuation regrowth after the filtering
operation, and the limitations of using the soft decisions values
to obtain an estimate of the nonlinear distortion effects. To
allow an efficient power amplification, the PMEPR-reducing
techniques in [15] are adopted by each MT, which can be
repeated several times. The base station (BS) has several receive
antennas, so as to reduce the transmit power requirements of
each MT. To avoid error propagation effects in the typical
region of operation, we use channel decoder outputs in the
feedback loop, in a turbolike fashion (a similar approach was
proposed for OFDM schemes [20]). We define an iterative
receiver that jointly performs a turbo MUD and the estimation
and cancellation of nonlinear distortion effects, for each iter-
ation, that are inherent to the transmitted signals. To improve
the performance at low SNRs, we consider a threshold-based
cancellation.
This paper is organized as follows: The linear transmitter and
receiver structures are described in Section II. In Section III,
we describe the nonlinear transmitter and receiver structures
proposed in this paper. Implementation complexity issues are
discussed in Section IV. Section V presents a set of perfor-
mance results, and Section VI is concerned with the conclusions
of the paper.
Throughout this paper, we will employ the following no-
tation: bold letters A denote matrices or vectors; IN denotes
the N ×N identity matrix; 0N×M denotes the N ×M zero
matrix; (·)T , (·)∗, (·)H , and diag(·) denote the transpose, con-
jugate, Hermitian, and diagonal matrices, respectively; [A]n,m
denotes the element of line n and column m of matrix A.
x mod y is the remainder of division of x by y, and δk,k′ = 1
if k = k′ and 0 otherwise.
II. LINEAR TRANSMITTER AND RECEIVER STRUCTURES
In this paper, we consider the uplink transmission in MC-
CDMA systems employing frequency-domain spreading. The
frequency-domain block to be transmitted by the pth MT is
{Sk,p; k = 0, 1, . . . , N − 1}, where N = KM , with K denot-
ing the spreading factor and M being the number of data
symbols for that MT. The frequency-domain symbols are
given by Sk,p = ξpCk,pAk mod M,p, where ξp is an appropriate
weighting coefficient that accounts for the propagation losses,
and {Ak,p; k = 0, 1, . . . ,M − 1} is the block of data symbols
associated to the pth MT, assumed to be selected from a given
constellation (in fact, different constellations could be selected
for different data symbols, as when loading techniques are
employed; in that case, the power associated to different data
symbols is not necessarily the same). {Ck,p; k = 0, 1, . . . , N −
1} is the corresponding spreading sequence1 (a pseudorandom
spreading is assumed, with Ck,p belonging to a QPSK constel-
lation; without loss of generality, it is assumed that |Ck,p| = 1).
1This corresponds to uniformly spreading the chips associated to a given
symbol within the transmission band, i.e., to employing a rectangular inter-
leaver with dimensions K ×M .
As usual, it is assumed that the length of the cyclic prefix
(CP) is higher than the length of the overall channel impulse
response. We will assume that the BS has L receive antennas
and the received time-domain block associated to the lth diver-
sity branch, after discarding the samples associated to the CP,
is {y(l)n ;n = 0, 1, . . . , N − 1}. The corresponding frequency-
domain block {Y (l)k ; k = 0, 1, . . . , N − 1} [i.e., the length-
N discrete Fourier transform (DFT) of the block {y(l)n ;n =
0, 1, . . . , N − 1}] is
Y
(l)
k =
P∑
p=1
Sk,pH
Ch(l)
k,p + N
(l)
k
=
P∑
p=1
Ak mod M,pCk,pξpH
Ch(l)
k,p + N
(l)
k
=
P∑
p=1
Ak mod M,pH
(l)
k,p + N
(l)
k (1)
with HCh(l)k,p denoting the channel frequency response between
the pth MT and the lth diversity branch at the kth subcar-
rier, N (l)k being the corresponding channel noise, and H
(l)
k,p =
ξpH
Ch(l)
k,p Ck,p. To detect the kth symbol of the pth MT, we
will use the set of subcarriers Ψk = {k, k + M, . . . , k + (K −
1)M}.
By definingY(k)=[Y(1)(k) · · · Y(L)(k)]T , withY(l)(k)=
[Y (l)k · · · Y (l)k+(K−1)M ] denoting the line vector with the
received samples associated to the set of frequencies Ψk for the
lth antenna, and A(k) = [Ak mod M,1 · · · Ak mod M,P ]T ,
we have
Y(k) = HT (k)A(k) + N(k) (2)
where N(k) = [N(1)(k) · · · N(L)(k)]T , with N(l)(k) =
[N (l)k · · · N (l)k+(K−1)M ] denoting the line vector with the
noise samples associated to the set of frequencies Ψk for the lth
antenna. In (2), H(k) is the P ×KL overall channel frequency
response matrix associated to A(k), i.e.,
H(k)=
[
H(1)(k) · · · H(L)(k)
]
=[H1(k) · · · HP (k)]T
(3)
where
H(l)(k) =
⎡
⎢⎢⎣
H
(l)
k,1 · · · H(l)k+(K−1)M,1
.
.
.
.
.
.
H
(l)
k,P · · · H(l)k+(K−1)M,P
⎤
⎥⎥⎦ (4)
is a P ×K matrix with lines associated to the different MTs
and columns associated to the set of frequencies Ψk for the lth
antenna, and
Hp(k) =
[
H
(1)
k,p · · · H(1)k+(K−1)M,p
· · · H(L)k,p · · · H(L)k+(K−1)M,p
]T
(5)
is a column vector associated to the pth MT.


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Joint turbo equalization and multiuser detection of MC-CDMA signals with low envelope fluctuations

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Repositório Institucional da Universidade Autónoma de Lisboa