Joint use of Overlap FDE and STTD for MC-CDMA Downlink Transmission

Abstract

Recently, multi-carrier code division multiple access (MC-CDMA) has been attracting much attention for the next generation mobile communications systems. Using frequency-domain equalization based on minimum mean square error criterion (MMSE-FDE), the frequency diversity effect can be obtained and improved bit error rate (BER) performance can be obtained. Antenna diversity is an effective technique to further improve the BER performance. Space-time transmit diversity (STTD) is suitable for the downlink transmission. Recently, overlap FDE that requires no guard interval (GI) insertion are presented. Combining STTD decoding and overlap FDE is not straightforward. In this paper, we propose STTD decoding for the MC-CDMA transmission using overlap FDE and then, its BER performance is evaluated by computer simulation.

Full text

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Joint use of Overlap FDE and STTD for MC-CDMA Downlink Transmission
Hiromichi TOMEBA† Kazuaki TAKEDA† and Fumiyuki ADACHI‡
Dept. of Electrical and Communication Engineering, Graduate School of Engineering, Tohoku University
6-6-05 Aza-Aoba, Aramaki, Aoba-ku, Sendai, 980-8579 Japan
E-mail: †{tomeba, takeda}@mobile.ecei.tohoku.ac.jp, ‡adachi@ecei.tohoku.ac.jp
Abstract— Recently, multi-carrier code division multiple access
(MC-CDMA) has been attracting much attention for the next
generation mobile communications systems. Using frequency-
domain equalization based on minimum mean square error
criterion (MMSE-FDE), the frequency diversity effect can be
obtained and improved bit error rate (BER) performance can be
obtained. Antenna diversity is an effective technique to further
improve the BER performance. Space-time transmit diversity
(STTD) is suitable for the downlink transmission. Recently,
overlap FDE that requires no guard interval (GI) insertion are
presented. Combining STTD decoding and overlap FDE is not
straightforward. In this paper, we propose STTD decoding for
the MC-CDMA transmission using overlap FDE and then, its
BER performance is evaluated by computer simulation.
Keywords-component; Frequency-selective fading channel, overlap
FDE, STTD, MC-CDMA.
I.
INTRODUCTION
Broadband data services are demanded in the next
generation mobile communication systems. However, the
broadband mobile channel is composed of many propagation
paths with different time delays, producing severe frequency-
selective fading which significantly degrades the transmission
performance [1, 2]. Recently, multi-carrier code division
multiple access (MC-CDMA), which uses a number of lower-
rate orthogonal subcarriers, has been attracting much attention
[3-5]. A good bit error rate (BER) performance can be
achieved by using frequency-domain equalization (FDE)
based on minimum mean square error (MMSE) criterion [5].
The conventional FDE requires the insertion of guard interval
(GI) to avoid the inter-block interference (IBI); however, the
GI insertion reduces the transmission efficiency. Recently, an
overlap FDE technique was proposed for the single-carrier
transmission [6, 7]. The overlap FDE requires no GI insertion.
We have shown that overlap MMSE-FDE can obtain almost
the same BER performance as the conventional MMSE-FDE
using GI insertion [8].
Antenna diversity is known as an effective technique to
improve the BER performance in a severe frequency-selective
fading channel, [1, 2]. Transmit antenna diversity is attractive
for the downlink transmission because the complexity problem
of a mobile terminal can be alleviated [9-11]. It was shown
[12, 13] that the joint use of the conventional FDE and space-
time transmit diversity (STTD) can significantly improve the
BER performance of multi-carrier transmission. In [12, 13],
joint FDE and STTD decoding is applied to each subcarrier
component. However, when overlap FDE is used for MC-
CDMA, each frequency component obtained by fast Fourier
transform (FFT) doesn’t correspond to subcarrier component
of the MC-CDMA signal. Therefore, the conventional STTD
decoding cannot directly be applied to MC-CDMA using
overlap FDE. In this paper, we propose STTD decoding for
MC-CDMA transmission with overlap FDE.
The remainder of this paper is organized as follows. Sect. II
describes the transmission system model of MC-CDMA using
proposed STTD decoding for overlap FDE. In Sect. III, the
average BER performance in a frequency-selective Rayleigh
fading channel is evaluated by computer simulation. Sect. IV
offers some conclusions.
II.
TRANSMIT SYSTEM MODEL
In this paper, the downlink transmission is considered.
Figure 1 illustrates the transmitter and receiver structure for
MC-CDMA with overlap FDE and two-antenna STTD.
Throughout the paper, sample-spaced discrete-time signal
representation is used.
A. Transmit signal
At the transmitter, U data symbol sequences {du(i)}
u=0~(U−1) are respectively spread by orthogonal spreading
codes {cu(t); t=0~(SF−1)}, u=0~(U−1), to obtain the multi-
code chip sequence, where SF denotes the spreading factor,
and further multiplied by a scrambling sequence cscr(t). To
generate the MC-CDMA signal with Nc subcarriers, Nc-point
IFFT is applied. The k-th subcarrier components {S2m(k);
k=0~(Nc−1)} of the 2m-th MC-CDMA signal is expressed as

∑
=
u

−






+=
1
0
2
2/)mod()(
2
SF
)(
U
c
uuscrm
SF
N
mSF kd SFkckc
P
kS
, (1)
where P is the transmit power per code and x is the largest
integer smaller than or equal to x.
For STTD encoding, two consecutive MC-CDMA signals
{S2m(k), S2m+1(k)} are encoded into two signal blocks as shown
in Fig. 2(a) Nc-point inverse FFT (IFFT) is applied to generate
the STTD encoded MC-CDMA signals to be transmitted from
two antennas. Nc-point IFFT is first applied to generate the
two consecutive MC-CDMA signal blocks {s2m(t), s2m+1(t);
t=0~(Nc−1)}:

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Nc–Point IFFT
Nc–Point IFFT
Data
mod.
User #0
Nc–Point IFFT
Nc–Point IFFT
Spreading
+
User #U-1
c0(t)
cU-1(t)
ScramblingScrambling
cscr(t)cscr(t)
Transmit
data
Data
mod.
Transmitter
STTD encoding
2Nc–Point FFT
FDE
2Nc–Point IFFT
Nc–Point FFT
Nc–Point FFT
Descrambling
cscr(t)
*
c0(t)
*
cU-1(t)
*
Σ Σ
Σ Σ
Demod.
Demod.
#0
#U-1
Received
data
Overlap-FDE
Despreading
MC-CDMA demodulation
Nc
Receiver
For 0-th transmit antenna
STTD decoding
For 1-th transmit antenna
S/P

Fig. 1 Transmitter/receiver structure of MC-CDMA with joint overlap FDE and STTD.

S2m(k)
−S2m+1(k)
IFFT for antenna 0
S2m(k)S2m+1(k)
time
The k-th subcarrier component
STTD encoding
IFFT for antenna 1
*
S2m+1(k)S2m(k)
*

(a) Frequency-domain
s2m(t)s2m+1(t)
time
Time-domain MC-CDMA signal
STTD encoding
s2m(t)
−s2m+1(Nc− t)
for antenna 0
for antenna 1
*
s2m+1(t)
s2m(Nc− t)
*

(b) Time-domain
Fig. 2 STTD encoding [12].
r2m(t)
s2m+1(t)
s2m(t)
time
02Nc−1
Nc
s2m+3(t)
r2m+1(t)
3Nc−1
s2m+2(t)
−s2m−1(Nc−t)
*
s2m−2(Nc−t)
**
s2m−2(Nc−t)
−s2m+1(Nc−t)
*
−s2m+1(Nc−t)
*
s2m(Nc−t)s2m(Nc−t)
**
From 0-th Tx
antenna
From 1-th Tx
antenna

Fig. 3 Received signal.













=






=
∑
=
k
∑
=
k
−
++
−
1
0
1212
1
0
22
π2exp)()(
π2exp)()(
c
c
N
c
mm
N
c
mm
N
k
tjkSts
N
k
tjkSts
(2)
STTD encoding can also be done in the time-domain as
shown in Fig. 2(b). STTD encoded MC-CDMA signal blocks
are transmitted from two transmit antennas without inserting
the GI. Note that the transmit power must be reduced by half
in order to keep the total transmit power the same as the non
diversity case.
B. Received signal
We assume a sample-spaced L-path frequency-selective
block fading channel. The complex-valued path gain between
the n-th transmit antenna (n=0, 1) and the receive antenna and
time delay of the l-th propagation path are denoted by hn,l and
τl, respectively. The channel impulse response hn(t) is
expressed as
∑
=
l
−
−=
1
0
,
)τ( δ
l
)(
L
lnn
thth
. (3)
The received signal)(trat the receiver is expressed as
)( η)τ()(
1
0
1
0
,
ttshtr
L
ln
lnln
+−=∑∑
=
−
=
, (4)
where η(t) is the additive white Gaussian noise (AWGN)
process with zero mean and variance 2N0/Tc with N0 being the
single-sided power spectrum density (Tc is the FFT/IFFT
sampling period).
)(tsn
is
representation of STTD encoded MC-CDMA signal.
the equivalent low-pass
C. Overlap FDE
The 2Nc-sample received signal block containing s2m(t) in
its center is denoted by r2m(t). For STTD decoding, two signal
blocks {r2m(t), r2m+1(t)} are necessary. 2Nc-point FFT is
applied to decompose the received signal blocks {r2m(t),
r2m+1(t)} into 2Nc frequency components {R2m(q), R2m+1(q);
q=0~(2Nc−1)}, which are given as












−=





−=
∑
=
t
∑
=
t
−
++
−
12
0
1212
12
0
22
2
π2 exp)(
2
1
N
)(
2
π2 exp)(
2
1
N
)(
c
c
N
c
m
c
m
N
c
m
c
m
N
t
qjtrqR
N
t
qjtrqR
, (5)
STTD decoding for the conventional FDE with GI insertion
is very simple and S2m(k) and S2m+1(k) can be easily recovered
from R2m(k) and R2m+1(k) as (see in Appendix A)




−=
+=
∗∗
0
+
∗
1
+
∗∗
1
+
∗
0
)] ()([)()()(
ˆ
)] ()([)()()(
ˆ
12212
1222
kwkRkwkRkS
kwkRkwkRkS
mmm
mmm
. (6)
On the other hand, when overlap FDE is used, since the
FFT window size is extended to 2Nc samples as shown in Fig.
3, S2m(k) and S2m+1(k) cannot be directly recovered from
R2m(q) and R2m+1(q) (see Appendix B). It is understood from
Eq. (6) that the conventional frequency-domain STTD
decoding can be performed using the addition, subtraction and
conjugate operations on
{
2
Rm
)()(
012
kwkRm
+
,
)}()(
112
kwkRm
+
FDE, {R2m(q), R2m+1(q)} are multiplied by the FDE weight
{wn(k); n=0, 1)} as
~
22 ,
qwqRqR
nmmn
)()(
0
kwk
∗
,
)()(
12
kwkRm
∗
,
∗∗
. To get them for the overlap



=
=
∗
n
++
∗
)()()(
~
R
)()()(
1212 ,n
qwqRq
mm
, (7)
The overlap MMSE-FDE weight is given by
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12
1
0
2
)2/(| )q(|
)(
)(
−
=
+
=
∑
n
σ
PH
SF
U
qH
qw
n
n
n
, (8)
where
∑
=
l
−





−=
1
0
,
2
τ
N
π2exp)(
L
c
l
lnn
qjhqH
, (9)
and 2σ2 is the variance of the IBI plus noise. After FDE, 2Nc-
point IFFT is applied to {
(
,
R
mn
)
~
q
; q=0~(2Nc−1)} as













=






=
∑
=
q
∑
=
q
−
++
−
12
0
1 2 ,n1 2 ,n
r
12
0
2 ,n 2 ,n
r
2
π2 exp)(
~
R
)(
~
2
π2 exp)(
~
R
)(
~
c
c
N
c
mm
N
c
mm
N
q
tjqt
N
q
tjqt
. (10)
Then, the central Nc samples of time-domain equalized
output is picked up to suppress the residual IBI. The resulting
output can be expressed as
~
)(
2 ,2 ,cmnmn
Ntrts




+=
+
(
=
++
) 2/
~
)(
~
) 2/(
~
s
1 2 ,n1 2 ,ncmm
Ntrt
, (11)
D. STTD decoding
Nc-point FFT is applied to
the frequency-domain signals
)}
k
(
~
s
~
S
),
),
(
(
~
s
~
S
{
{
1 2 ,n 2 ,n
t
(
t
k
mm
+
to transform
)}
as
12 ,n2 ,nmm
+












−=





−=
∑
=
t
∑
=
t
−
++
−
1
0
12 ,
n
1 2 ,
n
1
0
2 ,
n
2 ,
n
π2 exp)(
~
s
1
)(
~
S
π2exp)(
~
s
1
)(
~
S
c
c
N
c
m
c
m
N
c
m
c
m
N
t
kjt
N
k
N
t
kjt
N
k
. (12)
STTD decoding is carried out as
~
)(
ˆ
2 , 02
SkS
m



−=
+=
∗
++
∗
+
)(
~
S)(
~
S)(
ˆ
)(
~
S)(
12 , 02 , 112
12 , 1
kkkS
kk
mmm
mm
. (13)
After STTD decoding, the descrambling and despreading are
carried out to recover the transmitted data. Note that above
STTD decoding can also be implemented in the time-domain
as




−−=
−+=
∗
++
∗
+
)(
~
s)(
~
2 , 1
s)(
ˆ
s
)(
~
s)(
~
s)(
ˆ
s
12 , 012
1 2 , 12 , 02
tNtt
tNtt
cmmm
cmmm
. (14)
III. SIMULATION RESULTS
The simulation conditions are summarized in Table 1. We
assumed an L-path frequency-selective block Rayleigh fading
channel having an exponential power delay profile with decay
factor α dB with sample-spaced path delays τl= ∆l with
l=0~(L−1) for ∆=1~3. Ideal channel estimation is also
assumed. For comparison, the BER performance of MC-
CDMA transmission with the conventional FDE using GI
insertion of Ng=16 samples [13] is also presented.

Table 1 Simulation conditions
Data modulation
No. of subcarriers
Scrambling code
Spreading codes
Spreading factor
No. of users
No. of transmit antennas
No. of paths
QPSK
Nc=256
4095-chip PN
Walsh codes
SF=1, 16
U=1, 16
Nt=1, 2
L=16
Exponential with
decay factor
α=0 and 6 (dB)
τl=∆l, l=0~L−1
∆=1, 2, 3
512 (=2Nc)
MC-CDMA
Power delay profile
Channel
model
Time delay
FFT window size
Overlap FDE
FDE weight
MMSE
Ideal Channel estimation

Figure 4 shows the average BER performance using
proposed STTD decoding for overlap FDE as a function of
the average received Eb/N0 (=0.5(PNcTc/N0)) for ∆=1 and
α=0dB. The frequency block-interleaver is used to take
advantage of the channel frequency-selectivity. The proposed
STTD decoding for overlap FDE gives almost the same BER
performance as the conventional STTD. However, since
overlap FDE cannot perfectly suppress the IBI, the BER
performance of STTD decoding for overlap FDE is slightly
worse than the conventional STTD in high average Eb/N0
region. The performance degradation for BER=10-3 is as small
as 1.2 (0.8) dB from the conventional STTD when SF=1 (16).
Figure 5 shows the BER performances of OFDM
(SF=U=1) with the delay time difference ∆ as a parameter for
α=0 and 6dB. In the case of α=0dB, as ∆ increases from 1 to
2, 3, the BER performance of the conventional FDE
significantly degrades due to the IBI caused by delayed paths
whose time delays exceed the GI length. The BER
performance of proposed STTD decoding for overlap FDE
also degrades since the residual IBI increases; however, the
performance degradation is much smaller. On the other hand,
in the case of α=6dB, the IBI is reduced and therefore the
proposed STTD decoding for overlap FDE provides almost
the same BER performance as the conventional STTD. The
results show that conventional STTD must use the longer GI
than maximum path delay time even if in a weak frequency-
selective channel (e.g., α=6dB) since the BER performance of
conventional STTD without longer GI significantly degrades
when the channel frequency-selectivity becomes severe (i.e.,
α=0dB). On the other hand, the BER performance
degradation of proposed STTD decoding is much smaller
even if the channel frequency-selectivity becomes severe.
This indicates that the proposed STTD decoding for overlap
FDE is robust against the changing of channel frequency-
selectivity compared to the conventional STTD.
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1.E-04
1.E-03
1.E-02
Average BER
1.E-01
510
Average received Eb/N 0 (dB)
152025
L=16 uniform
SF=U=1(OFDM)
Proposed STTD decoding
Conventional (Ng=16)
Conventional (Ng=16)
Proposed STTD decoding
Without STTD
With STTD

(a) OFDM (SF=1)
1.E-04
1.E-03
1.E-02
Average BER
1.E-01
5 1015 20
Average received Eb/N 0 (dB)
Without STTD
With STTD
L=16 uniform
SF=U=16
Proposed STTD decoding
Conventional (Ng=16)
Conventional (Ng=16)
Proposed STTD decoding

(b) MC-CDMA (SF=16)
Fig. 4 Average BER performance.
IV. CONCLUSION
In this paper, we proposed STTD decoding for STTD encoded
MC-CDMA with overlap FDE. Its BER performance in a
frequency-selective Rayleigh fading channel was evaluated by
computer simulation. It was shown that a BER performance
close to that with GI insertion can be achieved even though
the GI is not inserted. The BER performance with overlap
FDE degrades due to increased IBI as the time delay
difference increases; however,
performance with proposed STTD decoding is close to that of
MC-CDMA system with GI insertion.
the achievable BER
1.E-04
1.E-03
1.E-02
Average BER
1.E-01
510 15 2025
Average received Eb/N 0 (dB)
∆=1
2
3
L=16 α=0dB
SF=U=1(OFDM)
Nt=2
Proposed STTD decoding
Conventional (Ng=16)
Conventional (Ng=16)
Proposed STTD decoding

(a) α=0dB
1.E-04 1.E-04
1.E-031.E-03
1.E-02
Average BER
1.E-011.E-01
5510 101515 20202525
Average received Eb/N 0 (dB)
Average received Eb/N 0 (dB)
1.E-02
Average BER
L=16 α=6dB
SF=U=1(OFDM)
Nt=2
∆=1
2
3
Proposed STTD decoding
Conventional (Ng=16)
Conventional (Ng=16)
Proposed STTD decoding

(b) α=6dB
Fig. 5 Impact of ∆ for OFDM.
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APPENDIX A: CONVENTIONAL STTD DECODING
In the conventional FDE and STTD decoding [12, 13], at
the receiver side, after the removal of GI from the
superimposed received two consecutive MC-CDMA signals,
Nc-point FFT is applied to decompose them into Nc subcarrier
components each. The k-th subcarrier components of the 2m-
and (2m+1)-th received MC-CDMA signal are given by



Π+−=
Π++=
+
∗
2
+
∗
2
+
+
)()()()()()(
)()()()()()(
1210112
2121202
kkSkHkSkHkR
kkSkHkSkHkR
mmmm
mmmm
,(A1)
where Π2m(k) and Π2m+1(k) are the noise components.
Frequency-domain STTD decoding is carried out as [13]



−=
+=
∗
2
+
∗
1
+
∗
2
+
∗
0
)()()()()(
ˆ
)()()()()(
ˆ
01212
1122
kwkRkwkRkS
kwkRkwkRkS
mmm
mmm
. (A2)
After STTD decoding, descrambling and dispreading is
applied to obtain the decision variable.
APPENDIX B: SIGNAL REPRESENTATIONS
For the proposed STTD decoding for overlap FDE, we
apply 2Nc-point FFT to two received signal block {r2m(t),
r2m+1(t)}, which can be expressed as







++−=
++−=
∑∑
=
0n
∑∑
=
1
++
−
=
++
−
=
1212
1
0
2mod12 ,n,12
1
0
22
1
0
2mod2 ,n,2
)(η)(ν))τ (()(
)(η)(ν))τ(()(
mm
L
l
Nlmlnm
n
mm
L
l
Nlmlnm
tttyhtr
tttyhtr
c
c
, (B1)
where {yn,m(t), n=0, 1} is the desired signal block of 2Nc
samples, νm(t) is the IBI component and ηm(t) is the noise
component. yn,m(t) and νm(t) are given as





−=−

−−
−=
t
−
−
N
=+−
) 2/
−
s
=
∗
2
+
∗
2
−
12~2/3)),

2/3((
12/3~2/,(
12/~0
N
)),2/((
)(
1
2
1
2 , 0
y
c
(B1a)
1
cccm
cccm
s
cccm
t
m
NNNtN
tN
NtNtNs
t

N
,





−=−−
−
1
=−
−
N
=+
) 2/
−
N
=
∗
2
+
(
∗
2
−
2~2/3, ))2/3(
12/3~2/,(
2/~0
N
,)) 2/((
)(
12
2
2 , 1
y
cc
,
~
cc

t
m
cccm
cccm
m
N
(B1b)
−
/
c
N
NtN

tNs
tts
NtNts
t






−=−
−
1
=−−−
s
=+
=
+
∗
2
+
(
+
2~2/3,) 2/3
123~2/)),2/((
12/0,) 2/(
)(
22
1
t
2
12 , 0
y
cccm
cccm
ccm
s
m
NtN
NNtNtN
NtNs
t

(
, (B1c)
1





−=−
−
1
=−
) 2/
−
N
−
s
−
N
=+
N
=
+
∗
2
+
+
2~2/3,3(
12/3~2/,))2/((
2/~0,) 2/
)(
32
12
1 2 , 1
y
cccm
ccccm
ccm
s
m
NNtt
NtNt
NtNts
t
,
−
(B1d)
∑∑
=
0
n
−
=
−






−
−
(t
−×

−
)}
−
t
=
11
0
00
2 ,
n
2
u
2 ,
)t
,
2
τ(({
)}τ()τ({
)(ν
L
l
l
lmlmnl
u
n
m
tytyh
t
, ( B2a)
∑∑
=
0
n
−
=
+−
+





−−×
−−
)}
=
11
0
00
1 2 ,
n
1
u
2 ,
)t
,
12
τ({
)}τ()τ({
)(ν
L
l
l
lmlmnl
u
n
m
tytyh
t
,( B2b)
where u0(t)(=1 (0) for t≥0 (t<0)) is the unit step function. 2Nc
frequency components {R2m(q), R2m+1(q); q=0~(2Nc−1)} of
{r2m(t), r2m+1(t)} are given by






Π+Ν+=
Π+Ν+=
++
=
++
=
1
∑
n
∑
n
)()()()()(
)()()()()(
1212
0
12 ,n12
22
1
0
2 ,n2
qqqYqHqR
qqqYqHqR
mmmnm
mmmnm
, (B3)
where















−=Π





−=Ν





−=
∑
=
t
∑
=
t
∑
=
t
−
−
−
1
0
1
0
1
0
,,
π2exp)(η
2
1
N
)(
π2exp)(ν
2
1
N
)(
π2exp)(
2
1
N
)(
c
c
c
N
c
m
c
m
N
c
m
c
m
N
c
mn
c
mn
N
t
qjtq
N
t
qjtq
N
t
qjtyqY
. (B4)
MMSE-FDE is carried out as Eq. (7). The MMSE weights
{wn(k); n=0, 1)} minimizes the mean square error (MSE)
between
)(
2 ,
qY
mn
and
)(
2 ,
qR
mn
as
~
| [minarg )(
2 ,
)}({
qw
n
~
]| )q()(
2
2 ,
n
YqREqw
mmnn
−=
. (B5)
1524