Int. J. Communications, Network and System Sciences, 2009, 2, 845-851
doi:10.4236/ijcns.2009.29098 Published Online December 2009 (http://www.SciRP.org/journal/ijcns/).
Copyright © 2009 SciRes. IJCNS
845
Frequency-Domain Receivers for Rate-1 Space-Time
Block Codes
Mário Marques da Silva1,2,3, Rui Dinis1,4, Américo M. C. Correia1,5
1Instituto de Telecomunicações, Lisbon, Portugal
2Centro de Estudos de Sistem as de Informação e Tecnol o gias Informáticas, Portu g al
3Universidade Autónoma de Lisboa, Lisboa, Portugal
4Universidade Nova, Lisboa, Portugal
5Instituto Superior de Ciências do Traba lho e da Empresa, Instituto Universidade de Lisboa , Lisboa, Portugal
E-mail: marques.silva@ieee.org, rdinis@netcabo.pt, americo.correia@iscte.pt
Received September 24, 2009; revised October 28, 2009; accepted November 30, 2009
Abstract
This paper considers iterative frequency-domain receivers for block transmission techniques with rate-1
Space Time Block Coding (STBC) for two and four transmit antennas using both Orthogonal Frequency Di-
vision Multiplexing (OFDM) and Single-Carrier (SC) schemes. The proposed receiver includes an interfer-
ence canceller which enhances the performance of the non-orthogonal STBC scheme with 4 transmit anten-
nas, allowing performances close to those of orthogonal codes. Our performance results show that combining
STBC with block transmission techniques allows excellent performances.
Keywords: SC-FDE, Turbo Equalization, STBC, OFDM
1. Introduction
Block transmission techniques, with appropriate cyclic
prefixes and employing FDE techniques (Frequency-
Domain Equalization), have been shown to be suitable
for high data rate transmission over severely time-dis-
persive channels [1,2]. OFDM (Orthogonal Frequency
Division Multiplexing) is the most popular modulation
based on this technique.
Single Carrier modulation using FDE is an alternative
approach based on this principle. As with OFDM, the
data blocks are preceded by a cyclic prefix, long enough
to cope with the overall channel length. Due to the lower
envelope fluctuations of the transmitted signals, and im-
plicitly a lower PMEPR (Peak-to-Mean Envelope Power
Ratio), Single Carrier – Frequency Domain Equalization
(SC-FDE) schemes (also named as Single Carrier-Fre-
quency Domain Multiple Access (SC-FDMA) are espe-
cially interesting for the uplink transmission (i.e., the
transmission from the mobile terminal to the base station)
[1,2].
OFDM transmission technique has been selected for
the downlink of Long Term Evolution (LTE) in Release
8 of Third Generation Partnership Project (3GPP), as
opposed to WCDMA which is the air interface technique
that has been selected by European Telecommunications
Standard Institute (ETSI) for UMTS. Moreover, SC-FDE
technique has been selected for the uplink of LTE in Re-
lease 8 of 3GPP, to be deployed in 2010.
A promising Iterative Block–Decision Feedback
Equalization technique (IB-DFE) for SC-FDE was pro-
posed in [3] and extended to other scenarios in [4] and
[5]. These IB-DFE receivers can be regarded as iterative
DFE receivers where the feedforward and the feedback
operations are implemented in the frequency domain,
enhancing the performance as compared to non-iterative
methods [3–5].
Transmit Diversity (TD) techniques are particularly
interesting for fading channels where it is difficult to
have multiple receive antennas (as in conventional re-
ceiver diversity schemes). A possible scenario is the
downlink transmission where the base station uses sev-
eral transmittal antennas and the mobile terminal has a
single one [6,7].
The application of Alamouti like transmit diversity in
OFDM schemes is more-or-less straightforward [8].
With respect to SC-FDE schemes, [9] proposed a way of
combining it with a linear FDE. This technique was ex-
tended to SC-FDE with IB-DFE in [10].
In this paper, we consider transmit diversity schemes
for both OFDM and SC-FDE schemes, specifically the
STBC with two [6,7] and four antennas [11,12]. The
same concept can be used in STBC based Multiple Input
Multiple Output (MIMO) schemes by adopting receive
M. M. da SILVA ET AL.
Copyright © 2009 SciRes. IJCNS
846
diversity. For OFDM schemes we consider conventional
receiver and for SC-FDE schemes we consider IB-DFE
receivers. For non-orthogonal codes (i.e., with more than
two transmit antennas), we also consider iterative re-
ceivers with cancellation of the residual interference (for
SC schemes with IB-DFE receivers, this means a negli-
gible increase on the receiver complexity).
This paper is organized as follows. The system con-
sidered in this paper is introduced in Section 2 and Sec-
tion 3 describes the proposed iterative receiver structure
for SC-FDE systems with transmit diversity. A set of
performance results is presented in Section 4 and Section
5 contains the conclusions of this paper.
2. System Characterization
2.1. Space Time Block Coding for Two Antennas
We consider block transmission schemes and the lth
transmitted block has the form
 
1
,
G
N
lnlTS
nN
s
tshtnT


(1)
with Ts denoting the symbol duration, NG denoting the
number of samples at the cyclic prefix and hT(t) is the
adopted pulse shaping filter. For a single transmit an-
tenna system, the signal Sl(t) is transmitted over a
time-dispersive channel and the signal at the receiver
input is sampled and the cyclic prefix is removed, lead-
ing to the time-domain block

,; 0,1,...,1
nl
yn N
,
which is then subject to the frequency domain equaliza-
tion. For SC-FDE schemes the lth time-domain block to
be transmitted is
,; 0,1,...,1
nl
sn N
, where Sn, l is the
nth data symbol, selected from a given constellation (e.g.,
a QPSK constellation) under an appropriate mapping rule
(it is assumed that ,,nlNnl
ss

, ,1,...,1
GG
nNN );
the frequency-domain blocks associated with the data are
,,
; 0,1,...,1; 0,1,...,1
kl nl
SkN DFTsnN
. For OFDM
schemes, the data symbols are transmitted in the fre-
quency domain, i.e., Sk, l are selected according to an
appropriate constellation. At the output of the FDE we
have the samples
2
*
,,, ,klkl klkl
AYH H

. In the
OFDM case this equalization process is simply accom-
plished through *
,,,klkl kl
AYH
.
If we employ Alamouti’s transmit diversity we need
some processing at the transmitter. The Alamouti’s cod-
ing can be implemented either in the time domain or in
the frequency domain. In this paper we consider time-
domain coding, although the extension to frequency do-
main coding is straightforward. By considering the Space
Time Block Coding with two transmit antennas, the
time-domain blocks to be transmitted by the mth antenna
(m = 1 or 2) are

,;0,1,..., 1
m
nl
sn N
, with



1
,2 1,2 1
2*
,2 1,2
1
,2 ,2
2*
,2,21
nl nl
nl nl
nl nl
nl nl
sa
s
a
sa
sa

(2)
Considering the matrix-vector representation, this is
equivalent to

,1, 2
,1,2 **
,2 ,1
nn
nnn
aa
aa
A (3)
Assuming that the cyclic prefix is longer than the
overall channel impulse response of each channel, the lth
frequency-domain block after the FDE block (i.e., the
DFT of the lth received time-domain block, after remov-
ing the cyclic prefix) is
,,
;0,1,..., 1;0,1,..., 1
nl kl
ynN IDFTYkN
 ,
with

112 2
,,,,, ,klklklklklkl
YSHSHN 
(4)
where


,,
;0,1,..., 1;0,1,..., 1
mm
kl nl
HkN DFThnN
 
denotes the channel frequency response for the kth sub-
carrier and the mth transmit antenna (the channel is as-
sumed invariant in the frame) and Nk, l is the fre-
quency-domain block channel noise for that subcarrier
and the lth block. Assuming, for now, the conventional
linear FDE for SC schemes, the Alamouti’s post-proc-
essing for two antennas (denoted in this paper STBC2)
comes,
 
 
1* 2
*(2)
,2 1,2 1,,2,
1* 2
*(2)
,2,2,,2 1,
klklklkl klk
klkl klklklk
AYHYH
AYHYH







(5)
where
,,
, 0,1...,, 0,1...,
km nm
A
kNDFTanNand
where
 
1
22
12
(2)
,,kklkl
HH



 




. This leads to

2(2)
,2 ,2,,2
1
0,1
Mmeq
kljkljkl kklj
m
AAHN j
 

. In addition,
we define22
,,2
/
klk l j
EN ES
 
 
 
. ,
eq
kl
N denotes the
equivalent noise for detection purposes, with

2
22(2)
,,
1
2
Mm
eq
klNkl k
m
EN H






 

, and with
2
2
,2
Nkl
EN
.
The Alamouti’s post-processing for OFDM signals is
the same as defined in (5) but without multiplying by the
(2)
k
component.
M. M. da SILVA ET AL.
Copyright © 2009 SciRes. IJCNS
847
2.2. Space Time Block Coding for Four Antennas
Using unspecified complex valued modulation, such an
improvement is possible only for the two antenna
scheme. Higher schemes with 4 and 8 antennas with
code rate one exists only in the case of binary transmis-
sion [13]. The proposed STBC4 scheme has M=4 trans-
mit antennas, presenting a code rate one. The symbol
construction can be generally written as [11–12]

 
 
*
, 1,2,3,4
,1,4*
,3,4, 1,2
nn
n
nn




AA
AAA
(6)
where

,3,4n
Ais the same as

,1,2n
A, by replacing the sub-
scripts 1 by 3 and 2 by 4. Similarly to (2), considering
the Space Time Block Coding with four transmit anten-
nas, the time-domain blocks to be transmitted by the mth
antenna (m = 1, 2, 3 or 4) are

,;0,1,..., 1
m
nl
sn N
, with









1111
,4 3,4 3,4 2,4 2,41,41,4
222
** *
,43,4 2,4 2,43,41,4
333
***
,43 ,41,42 ,4,41,43
444
,43,4,42,4 1,4 1,4
nlnlnlnl nlnlnl
nlnlnlnl nlnl
nlnlnlnl nlnl
nlnlnlnl nlnl
sasasa s
sasasa
sa sas a
sasasa
 

 


 

 



,4
2*
,4,4 1
3*
,4,4 2
4
,4,4 3
nl
nl nl
nl nl
nl nl
a
sa
sa
sa


(7)
The lth frequency-domain block after the FDE block
(i.e., the DFT of the lth received time-domain block, af-
ter removing the cyclic prefix) is
,;0,1,..., 1
nl
yn N
,; 0,1,...,1
kl
IDFT YkN
, with
  
11 22 33 44
,,,,,,,,, ,klkl klklklklklklklkl
YSHSHSHSHN  
(8)
Assuming, for now, the conventional SC-FDE decod-
ing (i.e., no IB-DFE receiver), the post-processing STBC
for four antennas (M=4) comes,
 

 
1*234*
** (4)
,43,43,,42,,4 1,,4,
Re
2
,4 3,,4,4 3
1
1*23
**
,4 2,4 2,,4 3,,4,
k lk lklk lklk lklklklk
Desired Symbolsidual Interference
Mmeq
klklk klkl
m
klklklklklklkl
AYHYHYHYH
AH CAN
AYHYHYH
 

 











4* (4)
,4 1,
2
,4 2,,41,4 2
1
1* 234*
** (4)
,4 1,41,,4,,43,,42,
2
,4 1,,42,41
1
1*
,4,4,,4 1
kl klk
Mmeq
klklk klkl
m
k lk lklklklk lklk lklk
Mmeq
klklk klkl
m
klklklkl
YH
AHCAN
AYHYHYHYH
AHCAN
AYHY












 

234*
** (4)
,,42,,43,
2
,4,,4 3,4
1
kl kl klklklk
Mmeq
klklk klkl
m
HYHYH
AHCAN


 


(9)
with

1
2
(4)
,
1
Mm
kkl
m
H





, where is defined as  
above (j=1,2,3,4), and where
 
1* 423*
,, ,,
2Re
kklklklkl
CHHHH

2
,
1
Mm
kl
m
H




which stands for the residual interference
coefficient generated in the STBC decoding process. In
the following we will show how we can remove this re-
sidual interference.
3. Receiver Design
In this section we describe an IB-DFE receiver for Space
Time Block Coding with four antennas considering
SC-FDE signals. The frequency-domain block at the
output of the receiver is

,4 ;0,1,...,1
i
klj
Ak N

, with

 
4
1234
**
,43,43,,42,,41,,4,
e
1
,4,,4 3
STBCdecodingplus IBDFEfeedforward
iiiii
klklklklklkl klklkl
Cancellation ofrsidualinterferenceIBDFEfeedback
iii
kkl klkl
AYFYFYFYF
CABA
 

 



 
 


1234
**
,42,42,,43,,4,,4 1,
1
,4 1,,42
12 3 4
**
,4 1,4 1,,4,,43,,42,
1
,42,,4 1
,4
iiiii
klklklklklkl klklkl
iii
kkl klkl
iiiii
k lklklk lklklklklkl
iii
kkl klkl
i
kl
AYFYFYFYF
CAB A
AYFYFYFYF
CABA
AY
 

 







 
123 4
**
,4,,4 1,,42,,43,
1
,4 3,,4
iii i
klklkl klklklklkl
iii
kklklkl
FYFYFYF
CABA



(10)
where CK is as defined for (9). The feedforward coeffi-
cients are

,; 0,1,...,1;1,2,...,
im
kl
FkNm M and the
feedback coefficients are

,; 0,1,...,1
i
kl
Bk N
. The
block


11
,4 ,4
; 0,1,...,1; 0,1,...,1
ii
nlj nlj
An NDFTan N


 
, and
denotes the DFT transform of the data estimates
associated to the previous iteration, i.e., the Hard
Decisions associated to the time-domain block at the
output of


11
,4 ,4
;0,1,..., 1;0,1,...,1
ii
nlj klj
anN IDFTAkN


 
.

1
,4 ; 0,1,...,1;0,1,2,3
i
klj
Ak Nj
 denotes the average
signal conditioned to the FDE output for the previous
iteration

1
,4 ;0,1,...,1
i
nlj
an N
from (19). It is worth
noting that since

,4
i
klj
A
presents residual interference,
the detection of

,4
i
klj
A
should be accompanied by the
detection of

,4
i
klp
A
(with p=3-j) to allow the cancella-
tion of the residual interference generated in the STBC4
M. M. da SILVA ET AL.
Copyright © 2009 SciRes. IJCNS
848
decoding process.
In case of a SISO system, (10) takes the form

1
,,, ,,
iiii
klkl klkl kl
AYFBA

, i.e., there is a single branch (there
is no STBC4 decoding) and there is no cancellation of
the residual interference. In case of STBC2 (two transmit
antennas), there is no residual interference component.
To further improve performance with STBC4 the re-
sidual interference to be subtracted (which is a function
of the estimate of the symbol that generates interference),
we consider an Iterative Interference Cancellation (IIC)
that can be implemented as follows:
1) Compute
 
,4
iq
klj
A
using (10) without cancelling the
residual interference.
2) Based on
 
,4
iq
klj
A
from i., compute

,4
iq
klp
A
after
cancelling the corresponding residual interference.
3) Based on

,4
iq
klp
A
from ii., compute

1
,4
iq
klj
A
after
cancelling the residual interference (

,4
i
kklp
CA
).
4) Repeat steps ii. and iii. iteratively to improve the
accuracy of

,4
i
klp
A
(cancellation of the residual interfer-
ence), which will finally be used to improve the accuracy
of

,4
i
klj
A
.
It can be shown that the optimum feedback coeffi-
cients are described by [3–4].
It can be shown that the optimum feedback coeffi-
cients are described by [3–4].
 
,,,
1
1
M
iimm
klkl kl
m
BFH

(11)
and the feedforward coefficients are given by
 



 
,
,22
1
,
1
1
m
im kl
kl M
imi
lkll
m
Q
F
H





(12)
with
 
*
,,
mm
kl kl
QH for m=1 or 4 and
 
,,
mm
kl kl
QH for m=2
or 3. In the particular case of SISO we only have m=1
(with M=1) and *
,,kl kl
QH. In case of STBC of order
two (i.e., STBC2), we have
 
*
,,
mm
kl kl
QH for m=1 and
 
,,
mm
kl kl
QH for m=2. The parameter

i
l
is defined as
 
1
,,
10
1MN
iimm
lklkl
mk
FH
N

 (13)
and the correlation factor

1
4
i
lj
is defined as


1*
,4,4
1
42
,4
ˆi
nljnlj
i
lj
nlj
Ea a
Ea






(14)
It can be shown that, for the QPSK modulation, the
correlation coefficient is given by [14]
 

1
4,4,4
0
1
2
N
iIiQi
ljnljnlj
n
N



(15)
(

4
i
lj
is almost independent of l for large values of N,
provided that

,
m
kl
H
is constant for the frame duration),
as
 
 
,4
,4
tanh 2
tanh 2
Ii
Ii n
nlj
Qi
Qi n
nlj
L
L








(16)
The LLRs (Log Likelihood Ratios) of the ”in-phase
bit” and the ”quadrature bit”, associated to

,4
Ii
nlj
a
and

,4
Qi
nlj
a
, respectively, are given by
 
 
,4
2
,4
2
2
2
IiIi
nnlj
i
Qi Qi
nnlj
i
La
La
(17)
respectively, with
 
1
22
2
,4,4 ,4,4 ,4
0
11
ˆ
22
N
iii
iljnlj nljnljnlj
n
Ea aa a
N
 

 



(18)
(as with

4
i
lj
, 2
,4ilj
is almost independent of l for
large values of N, provided that

,
m
kl
H
remains constant
for the frame duration).
The conditional average values associated with the
data symbols are given by
  
,4 ,4
,4 tanh tanh
22
Ii Qi
nlj nlj
i
nlj
LL
aj






(19)
Therefore, the several symbols of order jth (j=0,1,2,3)
that comprise the STBC4 block need to be decoded in-
dependently by the IB-DFE receiver, with the exception
of the symbol estimates that originate the residual inter-
ference generated in the STBC4 decoding process, as
shown in (10). The IB-DFE with soft decisions described
above does not need to perform the channel decoding in
the feedback loop. As an alternative, we can define a
Turbo FDE that employs the channel decoder outputs,
instead of the uncoded “soft decisions” in the feedback
loop of the IB-DFE. The main difference between
IB-DFE with soft decisions and the Turbo FDE is in the
decision device: in the first case the decision device is a
symbol-by-symbol soft-decision (for QPSK constellation
this corresponds to the hyperbolic tangent, as in (19));
M. M. da SILVA ET AL.
Copyright © 2009 SciRes. IJCNS
849
for the Turbo FDE a Soft-In, Soft-Out channel decoder is
employed in the feedback loop. The Soft-In, Soft-Out
block, that can be implemented as defined in [15], pro-
vides the LLRs of both the “information bits” and
the ”coded bits”. The input of the Soft-In, Soft-Out block
are LLRs of the ”coded bits” at the FDE output, given by
(17) and (18).
The receiver for OFDM schemes with STBC2 is
straightforward. For OFDM schemes with STBC4, (10)
also applies with the difference that there is no feedback
component, and the feedforward component only have
the numerator of (12). It is worth noting that these STBC
schemes can easily be extended to multiple receive an-
tennas.
4. Performance Results
In this section we present a set of performance results
concerning the proposed receivers, for both SC-FDE and
OFDM schemes with two and four-antenna STBC
schemes. We consider both Bit Error Rate (BER) and
Block Error Rate (BLER) performances, which are ex-
pressed as a function of Eb / N0, where N0 is the one-sided
power spectral density of the noise and Eb is the energy
of the transmitted bits (i.e., the degradation due to the
useless power spent on the cyclic prefix is not included).
Each block has N = 256 symbols selected from a
QPSK constellation under a Gray mapping rule (similar
results were observed for other values of N, provided that
N >> 1). The pulse shaping filter is raised cosine with
roll-off 0.1. The results shown in this paper considers the
Pedestrian A propagation environment [16].
The channel is assumed to be invariant during the
block. The duration of the useful part of the blocks (N
symbols) is 1μs and the cyclic prefix has duration
0.125μs. For SC-FDE systems we considered the IB-
DFE receiver with soft decisions and the Turbo FDE,
both with five iterations. Beyond this number the per-
formance improvement was almost negligible.
Linear power amplification is considered at the trans-
mitter and perfect synchronization is assumed at the re-
ceiver. The channel encoder is a convolutional code with
generators 1+D2+D3+D5+D6 and 1+D+D2+D3+D6, and
the coded bits associated to a given block are interleaved
and mapped into the constellation points.
Figure 1 considers uncoded BER results for the SC-
FDE and a linear FDE receiver (i.e., just the first itera-
tion of the IB-DFE receiver) versus the IB-DFE receiver
with soft decisions (i.e., without channel decoding in the
feedback loop), in this case with five iterations. Clearly,
the increased diversity due to STBC schemes leads to
significant performance improvements relatively to the
SISO case. From this figure, it is also clear that the
IB-DFE performs always better than the linear FDE re-
ceiver. It can also be observed that the STBC4 with the
linear FDE receiver performs very badly, due to the re-
sidual interference (generated in the STBC4 decoding
process). However, when we add the IB-DFE with soft
decisions to the STBC4, we have a significant perform-
ance improvement, namely due to the ability to mitigate
the residual interference. It is worth noting that, with the
IB-DFE receiver, the STBC4 achieves a performance
improvement over the STBC2. It happens because the
proposed receiver cancels the interference generated in
the STBC4 decoding process. This residual interference
is, in fact, the reason why this STBC4 scheme is considered
as non-orthogonal. In this case, we have seen that the
non-orthogonality is not a reason for loss of perform-
ance.
Figure 2 concerns the coded results for the SC-FDE.
In this case, the Linear FDE and the Turbo FDE receiv-
eris considered. For the linear FDE receiver, the STBC4
performs worse than the STBC2, due to the residual in-
terference. However, for the Turbo FDE (i.e., the pro-
posed iterative frequency-domain receiver that employs
the channel decoder outputs), the STBC4 outperforms
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-4
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-3
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-2
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-1
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0
E[E
b
]/N
0
(dB )
BER
SISO FDE
STBC2 FDE
STBC4 FDE
SISO IB-DFE with soft decisions
STBC2 IB-DFE with soft decisions
STBC4 IB-DFE with soft decisions
Figure 1. Uncoded BER results for the SC-FDE.
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-6
10
-5
10
-4
10
-3
10
-2
10
-1
10
0
E[E
b
]/N
0
(dB)
BE
R
SISO FDE
STBC2 FDE
STBC4 FDE
SISO Turbo FDE
STBC2 Turbo FDE
STBC4 Turbo FDE
Figure 2. Coded BER results for the SC-FDE.
M. M. da SILVA ET AL.
Copyright © 2009 SciRes. IJCNS
850
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-6
10
-5
10
-4
10
-3
10
-2
10
-1
10
0
E[E
b
]/N
0
(dB )
BER
SI SO Turbo FDE
STBC2 Turbo FDE
STBC4 Turbo FDE (w/ res idual i nt erf c anc e l)
SI SO OFDM
STBC2 OFDM
STBC4 OFDM (w/ res idual int erf cancel)
Figure 3. Coded BER for SC-FDE and OFDM.
the STBC2 (and the SISO, as expected). This is a conse-
quence of the additional diversity order and the effective
residual interference cancellation inherent to the pro-
posed receiver. Therefore, although using a higher num-
ber of antennas leads to an increase in the system com-
plexity, its advantage is clear as long as the proposed
iterative receiver is adopted.
Figure 3 shows a performance comparison between
SC-FDE and OFDM when channel coding is considered
(it is well-know that uncoded performances are very poor
for OFDM schemes). Note that the OFDM receiver for
the STBC4 also includes a residual interference canceller,
similar to the one included and described in the IB-DFE
that was considered for the SC-FDE STBC4. The pro-
posed Turbo FDE receiver for SC-FDE signals allows
similar or better performance than coded OFDM signals
for the STBC schemes considered. However, OFDM
technique presents much more demanding requirements
in terms of PMEPR, as compared to SC-FDE technique.
Figure 4 shows the uncoded BER performance of
STBC4 with and without residual interference cancella-
tion for both SC-FDE (in this case the IB-DFE receiver
is considered) and OFDM. From this figure it is seen that,
when the residual interference cancellation is considered,
SC-FDE with the proposed iterative receiver achieves
better results than those achieved with OFDM. Moreover,
when we focus on the results without the residual inter-
ference cancellation, it is clear the much better results
achieved with the SC-FDE due to the inherent ability of
the iterative frequency domain SC-FDE receiver to can-
cel generic interference. In this case, SC-FDE without
the residual interference cancellation achieves approxi-
mately the same performance than that achieved with the
OFDM scheme with the interference cancelled. Finally,
it is noticeable the very bad performance obtained with
the OFDM technique when the residual interference is
not cancelled.
Figure 5 shows the coded BER performance of
STBC4 with and without residual interference cancella-
tion for both SC-FDE and OFDM. From this figure it is
observed that, when the residual interference cancellation
is considered, SC-FDE with the proposed iterative re-
ceiver (i.e., the Turbo FDE receiver) achieves similar
results to those achieved with OFDM. However, when
we focus on the results without the residual interference
cancellation, as before, it is clear the better results
achieved with the SC-FDE, for higher values of 0
/
b
EN,
due to the inherent ability of the iterative frequency domain
receiver (Turbo FDE) to cancel generic interference. Figure
6 presents results similar to Figure 3, but in terms of
BLER, instead of the BER. As before, for the same di-
versity order, SC-FDE schemes achieve similar results as
those obtained with the OFDM. The BLER results confirm
the advantage of the STBC4 over lower diversity orders.
5. Conclusions
In this paper we considered iterative frequency-do main
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0
E[E
b
]/N
0
(dB)
BER
IB-DFE with soft decisions (w/ residual interf cancel)
I B-DFE with s oft dec ision (w/out residual interf c anc el)
OFDM (w/ res idual interf c ancel)
OFDM (w/out res idual int erf c anc el)
Figure 4. Uncoded BER performance for STBC4 (w/ and
w/out residual interference cancellation).
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10-6
10-5
10-4
10-3
10-2
10-1
100
E[E
b
]/N
0
(dB )
BER
OFDM (w/ res idual int erf c anc el)
OFDM (w/ out res idual int erf c anc el)
Turbo FDE (w/ res idual int erf c anc el)
Turbo FDE (w/ out res idual int erf c anc el)
Figure 5. Coded BER performance for STBC4 (w/ and
w/out residual interference cancellation).
M. M. da SILVA ET AL.
Copyright © 2009 SciRes. IJCNS
851
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-4
10
-3
10
-2
10
-1
10
0
E[E
b
]/N
0
(dB )
BLER
S ISO Tu rbo FDE
S TB C2 Tu r b o FDE
STBC4 Turbo FDE (w/ res idual int erf c anc el)
SISO OFDM
STBC2 OFDM
STBC4 OFDM (w/ res idual int erf c anc el)
Figure 6. Coded BLER for SC-FDE and OFDM
receivers for SC-FDE technique with code rate-1 STBC
using two or four transmit antennas. OFDM technique
was also considered in system description and perform-
ance results.
Since our STBC with 4 transmit antennas is not or-
thogonal, our receiver includes the cancellation of the
residual interference.
The proposed Turbo FDE receiver for SC-FDE signals
allows similar or better performance than coded OFDM
signals with the same diversity order. However, OFDM
technique presents much more demanding requirements
in terms of PMEPR, as compared to SC-FDE technique,
limiting its applicability. In this sense, SC-FDE is a good
alternative to OFDM transmission technique, especially
for the uplink.
It was shown that the best overall performance is
achieved with STBC4 schemes, as long as the receiver
includes the described residual interference cancellation
system. It is worth noting that by adding N order receive
diversity (N receive antennas instead of a single one), the
proposed SC-FDE STBC4 receiver keeps being valid and
the system can be seen as a 4×N MIMO system.
6. Acknowledgements
This work was supported by the Portuguese Foundation
for the Science and Technology (FCT).
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