Pilot assisted channel estimation for MC-CDMA signal transmission using overlap FDE

Abstract

Recently, multi-carrier code division multiple access (MC-CDMA) has been attracting much attention as a broadband wireless access technique for the next generation mobile communications systems. Frequency-domain equalization (FDE) based on the minimum mean square error (MMSE) criterion can take advantage of the channel frequency-selectivity and improve the average bit error rate (BER) performance due to frequency-diversity gain. However, conventional MC-CDMA requires the insertion of guard interval (GI) and this reduces the transmission efficiency. Overlap FDE technique has been proposed that requires no GI insertion. Recently, we showed that MC-CDMA using overlap FDE can provide almost the same BER performance as the conventional MC-CDMA downlink using the GI insertion. However, our previous work assumed the ideal channel estimation. In this paper, we propose a pilot assisted channel estimation technique suitable for MC-CDMA downlink using overlap FDE and evaluate the BER performance by computer simulation.

Full text

Page 1

Pilot Assisted Channel Estimation for MC-CDMA
Signal Transmission Using Overlap FDE
Hiromichi TOMEBA† Kazuki TAKEDA† 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, kazuki, 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 as a broadband
wireless access technique for the next generation mobile
communications systems. Frequency-domain equalization (FDE)
based on the minimum mean square error (MMSE) criterion can
take advantage of the channel frequency-selectivity and improve
the average bit error rate (BER) performance due to frequency-
diversity gain. However, conventional MC-CDMA requires the
insertion of guard interval (GI) and this reduces the transmission
efficiency. Overlap FDE technique has been proposed that
requires no GI insertion. Recently, we showed that MC-CDMA
using overlap FDE can provide almost the same BER
performance as the conventional MC-CDMA downlink using the
GI insertion. However, our previous work assumed the ideal
channel estimation. In this paper, we propose a pilot assisted
channel estimation technique suitable for MC-CDMA downlink
using overlap FDE and evaluate the BER performance by
computer simulation.
Keywords-component; Frequency-selective fading channel, overlap
FDE, Channel estimation, MC-CDMA.
I.INTRODUCTION
Broadband data services are demanded in the next
generation mobile communication systems. However, the
broadband channel is composed of many propagation paths
having different time delays, thereby resulting in severe
frequency-selective channel; the transmission performance
degrades due to severe inter-symbol interference (ISI) [1, 2].
Recently, multicarrier-code division multiple access (MC-
CDMA), which uses a number of low rate orthogonal
subcarriers to reduce the ISI resulting from frequency-
selective channel, has been attracting much attention [3-5]. A
good bit error rate (BER) performance can be achieved by
using frequency-domain equalization based on minimum
mean square error criterion (MMSE-FDE) [5].
The conventional MC-CDMA requires the insertion of
guard interval (GI) to make the received signal to be a circular
convolution of the transmit signal and the channel impulse
response. However, the GI insertion reduces the transmission
efficiency. Recently, an FDE technique that requires no GI
insertion, called overlap FDE, was proposed for the single-
carrier transmission [6, 7]. The overlap FDE can also be
applied to MC-CDMA. We have shown [8, 9] that overlap
FDE can provide almost the same BER performance as that of
MC-CDMA using the conventional FDE with GI insertion.
However, our previous work assumed the ideal channel
estimation. In this paper, we propose a pilot assisted channel
estimation technique suitable for MC-CDMA downlink using
overlap FDE, and evaluate its BER performance by computer
simulation.
The remainder of this paper is organized as follows. Sect. II
describes the transmission system model of MC-CDMA
downlink using the overlap FDE. The proposed channel
estimation technique is present in Sect. III. In Sect. IV, the
average BER performance is evaluated by computer
simulation. Sect. V offers some conclusions.
II.TRANSMIT SYSTEM MODEL
Figure 1 illustrates the transmitter and receiver structure for
MC-CDMA downlink with overlap FDE. Throughout the
paper, sample-spaced discrete-time signal representation is
used.
A. Received signal representation
At the transmitter, U data symbol sequences {du(i);
i=0~(Nc/SF?1)},
u=0~(U?1),
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. A sum of U
chip streams is multiplied by a scrambling sequence cscr(t). To
generate the MC-CDMA signal block with Nc subcarriers, Nc-
point inverse fast Fourier transform (IFFT) having Tc as the
sampling period is applied. In the conventional MC-CDMA
transmitter, the guard interval (GI) is inserted to the transmit
signal. However, overlap FDE requires no GI insertion,
thereby, improving the transmission efficiency.
The MC-CDMA chip stream is transmitted over a
frequency-selective fading channel and is received at a
receiver. We assume a sample-spaced L-path frequency-
selective block fading channel. The complex-valued path gain
and time delay of the l-th propagation path are denoted by hl
and τl, respectively. The channel impulse response h(τ) is
given by
?
=
0
l
The received MC-CDMA chip stream is divided into a
sequence of M (<Nc)-chip blocks. For performing FDE on the
m-th chip block, we pick up the MC-CDMA chip stream over a
time interval of t=(m?1/2)Nc+M/2~(m+1/2)Nc+M/2?1, which
can be expressed as
2
)(
0
SF
l
=
, t=(m?1/2)Nc+M/2~(m+1/2)Nc+M/2?1,
to be transmitted are
−
−=
1
)?? ( ?) ? (
h
L
llh
. (1)
)( ?)(?)mod)?((
1
ttNtsh
P
tr
L
?
cll
++−=
−
(2)
where P is the average received signal power and s(t) is the
MC-CDMA chip stream. η(t) is the additive white Gaussian
noise (AWGN) with zero mean and variance 2N0/Tc with N0
being the single-sided power spectrum density. s(t) can be
expressed, using the equivalent low-pass representation, as
1-4244-2424-5/08/$20.00 ©2008 IEEEICCS 2008
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?
=
m
∞
−∞
−=
cm
mNtsts
)()( (3)
with
?
?
?
?
?
−=
??
?
,
?
??
?
?
=?
−
=
otherwise0
) 1(~0,?2exp)(
)(
1
0
c
c
N
k
m
m
Nt
N
t
kjkS
ts
c
, (4)
where
??
?
=
u
−
??
?
?
??
?
?
+=
1
0
/)mod()()(
U
c
uu scrm
SF
N
mSFkd SFkckckS
, (5)
and ?x? is the largest integer smaller than or equal to x. μ(t) is
the inter-block interference (IBI), which is given by
?
=
?
lm
where u0(t) is the unit step function.
B. Overlap FDE
r(t) is decomposed by Nc-point FFT into Nc frequency
components {R(k); k=0~(Nc?1)}. R(k) is given by
1
)(
2/ ) 2/ 1(
kkSkH
Π+Ν+=
where
?
??
?
?
+−=
2/) 2/ 1(
MNmt
c
c
N
−
−
?
?
?
?
?
−−−−
−
?
=
1
0
00
1
t
))?()()}(mod)((
)
u
mod)?(({
s
)(?
L
l
lc
clml
tutN
Ntsh
t
, (6)
)()()(
~
)(
?2exp)(
12/) 2/ 1
+
(
k
N
t
kjtr
N
kR
MN
?
m
MNmt
cc
c
c
??
?
?
??
?
?−=
−+
+−=
, (7)
?
?
?
?
?
?
?
??
?
?
?
?
?
??
?
?
??
?
?−=Π
??
?
?
??
?
?−=Ν
??
?
?
??
?
?−=
??
?
?
?−=
?
)2
?
) 2
?
=
l
−++
+−=
−++
+−=
−++
−
12/) 2 / 1(
2/ / 1(
12/)2 / 1(
2// 1(
12/)2/ 1(
1
0
?2exp)( ?
1
)(
?2 exp)(?
1
)(
?2 exp)(
1
)(
~
S
?
N
?2 exp
2
SF
)(
MNm
MNmt
cc
MNm
MNmt
cc
MNm
c
L
c
l
l
c
c
c
c
c
N
t
kjt
N
k
N
t
kjt
N
k
N
t
kjtsk
kjh
P
kH
. (8)
One-tap FDE is performed on
~
kRkR
=
)()()(
kw
. (9)
We use the MMSE-FDE weight that minimizes the mean
square error (MSE) ε between
S
]| )(
)(| [?
kSkRE
−=
,
)(
~k
and

)(
~kR
. ε is defined as

~
~
2
(10)
where E[·] represents the expectation operation. MMSE-FDE
weight w(k) can be obtained by solving
some manipulations, we obtain the following MMSE-FDE
weight w(k):
)(
)(
σ
+
kHU
where σ2 is the variance of the IBI plus noise power.
The Nc-point IFFT is applied to {
obtain the equalized
Nc-chip
t=(m+1/2)M?Nc/2~(m+1/2)M+Nc/2?1}. In order to suppress
the IBI, we only pick up its center part of M chips, {
t=mM~((m+1)M?1)}, and store it into the buffer.
The resulting sequence of equalized M-chip blocks is the
equalized MC-CDMA chip stream. For MC-CDMA
demodulation, Nc-point FFT is applied to decompose the m-th
MC-CDMA chip block )(
{ tr
; t=mNc~((m+1)Nc?1)} into Nc
subcarrier components {
Rm
descrambling and despreading, the sequence of decision
variable, {)(
du
; i=0~(Nc/SF−1)}, associated with {du(i);
i=0~(Nc/SF−1)} is obtained.
If M is too small, the residual IBI can be sufficiently
suppressed, but the number of FFT/IFFT operations per MC-
CDMA chip block increases [8]. In this paper, we assume
M=Nc/2.
0)(/ ?
∂=∂
kw
. After
22
2 | )(|
=
∗
kH
kw
, (11)
)(
block
~kR
; k=0~(Nc?1)} to
{)(
~tr
;
)(
~tr
;
~
)(
ˆ
k
;
k=0~(Nc?1)}. After
ˆi
III.
CHANNEL ESTIMATION
FDE requires the accurate channel estimation. We consider
the pilot-assisted channel estimation (CE) [10-15]. In Refs.
[12-15], a pilot assisted channel estimation, called PACE in
this paper, was presented for OFDM using GI insertion. If no
GI insertion is used for the pilot block similar to the overlap
FDE, the accuracy of channel estimation significantly degrades
due to the IBI from the previous data block. In Refs. [16, 17],
another channel estimation technique was presented, in which a
short pilot sequence is inserted at both ends of each data block.
The pilot sequence inserted at the end of the present data block
plays as a cyclic prefix for the pilot sequence inserted at the
beginning of next data block. Therefore, channel estimation
can be carried out without suffering from the IBI. However, the
insertion of pilot sequence results in the loss of data rate and
power.
In this paper, we propose a new channel estimation
technique that requires no GI insertion, in which a short pilot
sequence is repeated in the pilot chip block. We call this
Data
mod.
User #0
Nc-Point IFFT
Spreading
+
Nc–Point FFT
User #U-1
c0(t)
cU-1(t)
Scrambling
cscr(t)
Descrambling
cscr(t)
*
c0(t)
*
cU-1(t)
Σ
Σ
Demod.
Demod.
Transmit
data
#0
#U-1
Received
data
Overlap FDE
Despreading
*
Data
mod.
MC-CDMA demodulation
Transmitter Receiver
Nc-Point FFT
MMSE-FDE
Nc-point IFFT
Selection
M
Buffer
Nc
Channel estimation
Fig. 1. Transmitter/receiver structure of MC-CDMA downlink using overlap FDE
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channel estimation technique as cyclic PACE (CPACE). In the
following, we consider a short pilot sequence with a period of
Nc/2 is repeated twice in the pilot chip block.
A.Principle of CPACE
CPACE uses the time-multiplexed pilot chip block to be
periodically transmitted every N data chip blocks as shown in
Fig. 2. The pilot chip block {sp(t); t=0~(Nc?1)} is given by
))2/ mod(()(
cp
Ntats
=

The received pilot chip block {rp(t); t=0~(Nc?1)} is given by
2
)(
0
SF
l
=
. (12)
)( ?)(?))2/mod()? ((
1
ttNtah
PU
tr
L
?
cllp
++−=
−
. (13)
1)
CE using the latter half of pilot chip block
The first half of the pilot chip block, {sp(t); t=0~(Nc/2?1)},
plays a role of the cyclic prefix for the latter half of the pilot
chip block, {sp(t); t=Nc/2~(Nc?1)}. By applying Nc/2-point
FFT to {rp(t); t=Nc/2~(Nc?1)}, as shown in Fig. 3(a), the
received pilot chip block can be transformed into Nc/2
frequency components {R1(q);q=0~(Nc/2?1)} without causing
the IBI if the maximum delay time τmax of the channel is
shorter than Nc/2.
R1(q) is given by
N data blocks
) 2 ()() 2 (
2/
?2exp) 2/(
2/
1
)(
12/
0
1
qqAqHU
N
t
qjNtr
N
qR
c
?
=
N
t
c
cp
c
Π+=
??
?
?
??
?
?−+=
−
,(14)
where
?
=
t
−
??
?
?
??
?
?−=
12/
0
2/
?2exp)(
2/
1
)(
c
N
cc
N
t
qjta
N
qA
(15)
with |A(q)|2=2. The initial channel gain estimate
q=0~(Nc/2?1), is obtained as
)(/ )() 2 (
11
qAqRqH
==
However, an interpolation technique is necessary since FDE
requires Nc channel gain estimates {
Furthermore,)2 (
1
qH
is noisy. Therefore, we apply the delay
time-domain windowing technique [14] to reduce the noise
while interpolating the initial channel gain estimates {
q=0~(Nc/2?1)} to obtain {(
H
The instantaneous channel impulse response estimate
{) ? (
; τ=0~(Nc/2?1)}, can be obtained by performing Nc/2-
point IFFT on {)2 (
1
qH
; q=0~(Nc/2?1)} as
?
=
?
The channel impulse response is present only over τ=0~τmax,
while the noise due to the AWGN spreads over the entire
delay time-domain as shown in Fig. 4. To reduce the noise,
) ? (
is replaced by zeros for τ=τmax+1~(Nc?1) and an Nc-
point FFT is applied. Improved channel gain estimates
{
)(
H
; k=0~(Nc?1)} can be obtained as [14, 15]
?
=
?
??
?
?
=
0
2
? sin
c
N
.
In CPACE, the maximum delay time τmax must be known.
τmax can be estimated using the average power delay profile
{E[|) ? (
|2]; τ=0~(Nc/2?1)}. Although the actual channel
impulse response is present only over τ=0~τmax, we introduce
the threshold Lth to determine the maximum delay time as
τmax=arg max {E[|) ? (|2]?Lth}. The optimum Lth that
minimizes the BER is found by computer simulation.
2)
CE using the first half of pilot block
So far, we have described the channel estimation scheme
which uses the latter half of the pilot chip block {sp(t);
t=Nc/2~(Nc?1)}. If the maximum delay time τmax is known, we
can apply an Nc/2-point FFT to the first half of the received
pilot chip block {rp(t); t=(τmax+1)~(Nc/2+ τmax)}, as shown in
Fig. 3(b), to obtain
Nc/2
{R2(q);q=0~(Nc/2?1)} without causing IBI. R2(q) is given by
) 2 (
1
~
Hq
,
)( / )
q
2 ()2 (
~
qAqHU
Π+
. (16)
)(
1kH
; k=0~(Nc?1)}.
~
) 2 (
1
~
Hq
)
1k
; k=0~(Nc?1)}.
~
1h
~
−
??
?
?
??
?−=
1
0
11
2/
??2exp) 2 (
~
H
) ? (
~
h
c
N
q
c
N
q
jq
. (17)
~
1h
1k
?
=
q
−
?
?
?
?
?
?
?
?
?
?
?
?
?
??
?
?
??
?
?
−
−
N
−
??
?
?
??
?
?
−
?
??
?
−
N
??
?
?
??
?
?−=
12/
max
max
1
?
0
11
) 1 (?
2
?exp
?
2
?sin
)2 (
~
H
?
?2 exp) ? (
~
h
)(
max
c
N
c
c
c
qk
j
qk
qk
q
N
kjkH
τ
(18)
~
1h
~
1h
frequency components
Pilot block
One Multicarrier block
Data block
1 block
Pilot block
Fig. 2 Frame format.
0-th path
(L-1)-th path
a(t)
time
0
Nc−1
Nc/2-point FFT
Nc/2
a(t)
sp(t)
(a) FFT window for the latter half of the pilot block
0-th path
(L-1)-th path
a(t)
time
0
Nc/2+ξmax
Nc/2-point FFT
ξmax+1
a(t)
sp(t)
ξmax
(b) FFT window for the first half of the pilot block
Fig. 3 Received pilot block and FFT window timing for CE.
Channel
impulse
0
delay time
τmax
Noise
Nc/2−1
Fig. 4 Instantaneous channel impulse response.
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)()()2 (
2/
?2 exp)(
2/
1
)(
max
max
?2/
?
=
1?
2
qqAqHU
N
t
qjtr
N
qR
c
N
t
c
p
c
Π+=
??
?
?
??
?
?−=
+
+
. (19)
The initial channel gain estimate
/ )()(
22
qRqH
=
An Nc/2-point IFFT is applied to decompose {
q=0~(Nc/2?1)} into the instantaneous channel impulse
response estimate {) ? (
; τ=0~(Nc/2?1)} as
?
=
?
Replacing) ? (
by zeros for τ=τmax+1~(Nc?1) and applying an
Nc-point FFT, Nc channel gain estimates {
k=0~(Nc?1)} can be obtained. The final channel estimate is
obtained as
2/ ))()(()(
21
kHkHkH
+=

)2 (
2
)
q
~
Hq
Π
can be obtained as
)(/ )(
qAq
. (20) 2 ()(
~
HUqA
+=
)2 (
2
~
Hq
~
2 h
−
??
?
?
??
?−=
12/
0
22
2/
??2exp)2 (
~
H
) ? (
~
h
c
N
q
c
N
q
jq
. (21)
~
2 h
)(
2kH
;
. (22)
B.
Estimation of IBI plus noise power σ2
For performing MMSE-FDE, the IBI plus noise power σ2
must be known (see Eq. (11)). σ2 can be estimated as follows.
The received pilot chip block {rp(t): t=0~(Nc?1)} is
decomposed by using an Nc-point FFT into Nc subcarrier
components {Rp(k); k=0~(Nc?1)} as
1
)(
0
N
t
c
Ν+=
where
?−=
?
=
2 for)(
qk
Rp(2q+1), q=0~Nc/2?1, contains the IBI plus noise component
only. The estimate of IBI plus noise power
using
?
=
0
q
c
N
)()()()(
?2)(
1
kkkSkHU
N
t
kjtrkR
p
N
?
=
c
+
pp
c
Π
??
?
?
??
?
?−=
−
, (23)
?
?
?
+=
=
=
??
?
?
??
?
−
12for0
?2exp)(
1
)(
1
0
qkkA
N
t
kjts
N
kS
c
N
t
c
p
c
p
, q=0~Nc/2?1. (24)
2
? ˆ can be obtained
−
+=
1
|
2/
22
| ) 12 (
p
2
? ˆ
2
c
N
qR
. (25)
IV.
COMPUTER SIMULATION
The simulation condition is summarized in Table 1.
Quadrature phase shift keying (QPSK) data modulation,
Nc=256-subcarrier MC-CDMA, and a frequency-selective
Rayleigh fading channel having an L=16-path uniform power
delay profile are assumed. The normalized maximum Doppler
frequency fDTcNc is assumed to be 0.001 (this corresponds to a
mobile terminal speed of about 80 km/h for 100Msps and 5
GHz carrier-frequency).
One pilot chip block is transmitted every N=15 data blocks
(binary phase shift (BPSK) modulation is used). A partial
sequence taken from an M-sequence of 4095 bits is used as the
pilot {A(q);q=0~(Nc/2?1)}. To estimate the channel at data
chip blocks between the two pilot blocks, linear interpolation
[18] is used. For estimation of τmax, the optimum threshold
value Lth to minimize the BER was found by computer
simulation.
Table 1 Simulation condition
Data
modulation
Pilot
No. of subcarriers
Scrambling code
Spreading codes
Spreading factor
No. of users
No. of paths
Power delay profile
Data QPSK
BPSK
Nc=256
4095-chip PN
Walsh codes
SF=1, 16
U=1, 16
L=16
Uniform
τl=lΔTc,
l=0~L?1, Δ=1, 2
256 (=Nc)
MMSE
MC-CDMA
Channel
model
Time delay
Overlap FDE
FFT window size
FDE weight
1.E-04
1.E-03
1.E-02
1.E-01
5 10 15 20
Average BER
Average received Eb/N0(dB)
Ideal channel and
noise estimation
L=16-uniform profile
fDTcNc=0.001
CPACE
PACE
Ng=16
0
SF=1
SF=16
Fig. 5 BER performance with perfect knowledge of τmax.
Figure 5 shows the BER performance with CPACE as a
function of the average received Eb/N0when the maximum
delay time τmax is known. For comparison, the BER
performance is also plotted for PACE using pilot with and
without GI insertion (Ng=16) [13]. It can be seen from Fig. 5
that CPACE provides almost the same BER performance as
PACE with GI-inserted pilot. The degradation in the required
Eb/N0 for BER=10-2 from the ideal channel estimation case is
as small as 0.5 (0.6) dB when SF=1 (16) (out of which about
0.28 dB is due to the pilot insertion). On the other hand, PACE
with no GI-inserted pilot degrades the BER performance due
to the residual IBI.
Figure 6 shows that the BER performance of CPACE
when the maximum delay time τmax is estimated. It can be seen
from Fig. 6 that almost the same BER performance can be
obtained as the known τmax case.
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1.E-04
1.E-03
1.E-02
1.E-01
5 10 1520
Average BER
Average received Eb/N0(dB)
SF=1
SF=16 Ideal channel and
noise estimation
CPACE
Ideal estimation of τmax
Εstimated τmax
L=16-uniform profile
fDTcNc=0.001
Fig. 6 BER performance with estimation of τmax.
1.E-01
Overlap FDE
Conventional FDE with Ng=16
1.E-04
1.E-03
1.E-02
5101520
Average BER
Average received Eb/N0(dB)
L=16-uniform profile
Δ=1
2
fDTcNc=0.001
SF=16
Ideal channel and
noise estimation
Ideal channel and
noise estimation
Δ=1
Δ=2
Fig. 7 Comparison between overlap FDE and conventional FDE.
Figure 7 compares the BER performances of the overlap
FDE using CPACE and the conventional FDE using PACE
with Ng=16-chip GI when SF=U=16. The BER performances
are plotted with the time delay difference Δ between the paths
as a parameter. As Δ increases from 1 to 2, 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 overlap FDE
also degrades since the residual IBI gets stronger; however, the
performance degradation is much smaller than the conventional
FDE even using the channel estimation.
In the real fading channel environment, the channel
selectivity changes. Even in a weak frequency-selective
channel (e.g., Δ=1), the conventional FDE must use a fixed
length GI which is longer than the expected maximum path
time delay. On the other hand, the overlap FDE can simply
change the value of M to adapt to the changing in channel
frequency-selectivity at the cost of increased computational
complexity.
V.CONCLUSION
In this paper, we proposed a cyclic pilot assisted channel
estimation technique (CPACE) suitable for MC-CDMA using
overlap FDE. It was shown by the computer simulation that
CPACE provides a good BER performance and the
degradation of required Eb/N0 for BER=10-2 from the ideal
channel estimation case is as small as 0.6 dB.
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