Communications and Network, 2013, 5, 249-254
http://dx.doi.org/10.4236/cn.2013.53B2046 Published Online September 2013 (http://www.scirp.org/journal/cn)
Signal Detection for OFDM-IDMA Uplink over Doubly
Selective Channels*
Tao Peng1, Yue Xiao1, Shaoqian Li1, Huaqi an g S hu2, Eric Pierre Simon2
1Nation Key Lab of Sci. and Techno. On Commun. University of Electronic Sci. and Techno. of China, Chengdu, China
2IEMN Lab, TELICE Group, University of Lille, Lille, France
Received June, 2013
ABSTRACT
Orthogonal frequency division multiplexing-interleave division multiple access (OFDM-IDMA) systems may suffer
from serious inter-carrier interference (ICI) in time-and frequency-selective (doubly selective) channels. In such case,
the conventional OFDM-IDMA detection algorithm for quasi-static channels will result in significantly performance
degradation. In this paper, signal detection is investigated for OFDM-IDMA uplink over doubly selective channels.
Firstly, the impact of time-varying channels for OFDM-IDMA uplink is analyzed, which leads to the failure of the con-
ventional algorithm. Secondly, a novel iterative detection algorithm is developed based on an integrated interference
canceller, which can iteratively estimate and mitigate the ICI as well as multiple access interference (MAI) simultane-
ously. In addition, an improved detection algorithm is derived for reducing the complexity using an approximation to
the mean and variance of the in terference. Simulation results indicate that the proposed algorithm can significan tly en-
hance the system performance to the conventional case, and the improved algorithm can strike a balance between per-
formance and complexity.
Keywords: Interleave Division Multiple Access (IDMA); Orthogonal Frequency Division Multiplexing (OFDM);
Doubly Selective Channel
1. Introduction
As a kind of non-orthogonal multiple access scheme,
interleave division multiple access (IDMA) was devel-
oped by Ping et al.[1,2], in which random interleavers are
employed as the only means for user separation. In gen-
eral, IDMA outperforms conventional code division mul-
tiple access (CDMA) in terms of power and bandwidth
efficiency. The key innovation of IDMA is the introduc-
tion of low-rate channel coding, chip-level interleaving
and low-complexity multiuser detection. On the other
hand, orthogonal frequency division multiplexing (OFDM)
is an attractive transmission technique for future wireless
communication due to its high spectral efficiency and
excellent robustness to frequency-selective fading. Based
on the combination of IDMA and OFDM, OFDM-IDMA
was presented for achieving the advantages of both sys-
tems [3]. In OFDM-IDMA systems, inter-symbol inter-
ference (ISI) can be mitigated by OFDM and multiple
access interference (MAI) can be suppressed by IDMA.
Moreover, OFDM-IDMA can achieve more throughput
and reliability than conventional OFDM-CDMA and
orthogonal frequency-division multiple access (OFDMA)
[3-5].
In [3], an iterative multi-user detection scheme is de-
rived for OFDM-IDMA, where the complexity of each
user is independent of the channel length and number of
users. However, it assumes that the frequency-selective
channels are time invariant (quasi-static) within an OFDM
block. In practice, high speed movement of mobile ter-
minals will cause Doppler spread and result in time-
varying multipath fading channels [6,7]. In this case, the
channels will be time and frequency-selective (doubly
selective), in which the length of an OFDM block is
longer than th e coherent time. As a result, the time varia-
tion of doubly selective channels will destroy the or-
thogonal property among subcarriers and induce in-
ter-carrier interference (ICI), which complicates the data
detection in the receiver.
*This work was supported by the Foundation Project of National Key
Laboratory of Science and Technology on Communications under
Grant 9140C020404120C0201, National High-Tech R&D Program
of China ("863" Project under Grant number 2011AA01A105), Na-
tional Grand Special Science and Technology Project of China under
Grant No. 2010ZX03006-002-02, and the Fundamental Research
Funds for the Central Universities.
Due to this additional interference from other subcar-
riers, the conventional OFDM-IDMA detection algo-
rithm [3] will degrade the system performance severely
in the doubly selective channels. In [8-10], several inter-
carrier interference cancellation schemes were proposed
C
opyright © 2013 SciRes. CN

T. PENG ET AL.
250
for OFDMA and OFDM-CDMA in doubly selective chan-
nels. However, due to different system structure, these
schemes cannot be extended to OFDM-IDMA. Therefore,
signal detection of OFDM-IDMA uplink over doubly
selective channels becomes a challenging problem due to
the complex interference from MAI and ICI.
In order to overcome the above problems over the
doubly selective channels, signal detection for OFDM-
IDMA uplink is investigated in this paper. Firstly, the
impact of doubly selective channels for OFDM-IDMA
uplink is analyzed, which results in the failure of the
conventional algorithm. Then a new iterative detection
algorithm is developed based on an integrated interfer-
ence canceller, which considers the influence of not only
multiple users but also intercarrier interference. It can
eliminate ICI from other subcarriers as well as MAI in an
iterative way. Moreover, an improved detection algo-
rithm is also derived based on an approximation to the
mean and variance of the interference for reducing the
complexity. Finally, simulation results verify that the
proposed detection algorithm can greatly improve the
performance of the conventional one, and the improved
algorithm can achieve performance close to the proposed
one while keeping the computational complexity low.
The rest of this paper is organized as follows. Section
II introduces the system model of OFDM-IDMA uplink
adopted in this paper. In Section III, three detection algo-
rithms are presented for OFDM-IDMA uplink over dou-
bly selective channels. Simulation results are provided in
Section IV to demonstrate the effectiveness of the pro-
posed algorithms. The conclusions are drawn in Section
V.
2. System Model
2.1. Transmitter of OFDM-IDMA Uplink
The system model of OFDM-IDMA uplink with K si-
multaneous users is shown in Figure 1, where each user
communicates with the base station through independent
doubly selective channels. For the transmitter of user-k,
information data dk is first encoded and interleaved to
generate a low-rate permutated sequence Xk, which is
then fed into an inverse fast Fourier transform (IFFT)
modulator. After IFFT and cyclic prefix (CP) insertion,
the time domain transmitted signal from user-k can be
represented as
 
12
0
1
1,
NjunN
kk
ug
xnXuN ne
NN





 (1)
where N is the total number of subcarriers and Ng is the
length of CP.
2.2. Receiver of OFDM-IDMA Uplink
As illustrated in Figure 1, the OFDM-IDMA receiver
consists of one elementary signal estimator (ESE) detec-
tor and K soft-input soft-output (SISO) decoders (DECs),
which are used to solve the multiple access channel con-
straint and the coding constraint respectively. The out-
puts of ESE and DECs are the extrinsic log-likelihood
ratios (LLRs), which are updated via the interleavers and
deinterleavers iteratively. More detailed description of
OFDM-IDMA receiver can be found in [3].
3. Detection Algorithms of OFDM-IDMA
Uplink over Doubly Selective Channels
In the OFDM-IDMA receiver, since the SISO DECs are
standard a posteriori probability (APP) decoding, the
distinction between different detection algorithms lies in
the ESE detector. In what follows, three different ESE
detection algorithms will be given for OFDM-IDMA up-
link over doubly selective channels.
3.1. Impact of Doubly Selective Channels for
OFDM-IDMA
The doubly selective channel model considered in this paper
is the time-varying multipath fad ing channel with a d elay
spread L. The channel may vary within each OFDM
block, depending on the velocity of the user’s motion.
C
Decoder
(DEC)
Doubly
Selective
Channels
ESE
Detector
Transmitter for user-1
Transmitter for user-K




1ESE
eX
r
1
d
K
d
1 d

K
d

1
c1
x
K
x




1DEC
eX




1ESE
ec

 

1DEC
ec




ESE K
eX




DEC K
eX




ESE K
ec




DEC K
ec
CK
c
1

1
1


K

K

1
K


IFFT
IFFT
FFT
1
X
XK
R
1

Decoder
(DEC)
Figure 1. Transmitter and receiver structures of OFDM-IDMA uplink.

T. PENG ET AL. 251
The received signal from user-k without noise can be
described as
 
 
1
0
12
0
,
1,
L
kkk
l
N
j
un N
kk
u
rn hnlxnl
XuHnue
N









(2)
where hk(n,l) stands for the channel impulse response
(CIR) of path l at time n for user-k, and Hk(n,u) is the
channel frequency response at the uth subcarrier.
Equation (2) can be rewritten in a matrix form as
t
kk
rHX
k
w
(3)
where rk=[rk(0), rk(1),…, rk(N-1)]T, Xk=[Xk(0), Xk(1),…,
Xk(N-1)]T, and is given by (4), shown at the bottom
of the page.
t
k
H
Thus the received signal from all users can be given by
11
KK
t
kkk
kk
 

rrwHX (5)
where w is the additive white Gaussian noise (AWGN)
with zero mean and variance 2

.
After the CP removal and fast Fourier transform (FFT)
of r in (5), the received signal in the frequency domain is
as follows
1
Kt
NNkk
k
 

RFrFHX W (6)
where W is the noise in the frequency domain, and FN is
the FFT matrix defined as
NN

2
1,1, 0,1.
jmnN
Nmn emnN
 
 F (7)
Furthermore, denoting t
N
k
FH by
f
k
H in (6), the re-
ceived signal can be rewritten as
1.
Kf
kk
k


RHXW (8)
In (8),
f
k
H is the equivalent channel response matrix
of the doubly selective channel for user-k.
3.2. Conventional Detection Algorithm
In [3], the conventional detection algorithm of OFDM-
IDMA was proposed, which can effectively cancel the
MAI of quasi-static channels. When the channel is as-
sumed to be time invariant within an OFDM block, the
channel matrix
f
k
H in (8) can be simplified to a diago-
nal matrix denoted as

f
k
H
. In this case, the frequency
domain received signal (8) is simplified as


 
1,0 1
Kf
k
static k
k
Rm HmXmWmmN




(9)
For the subcarrier m of user-k, the received signal can
be rewritten as


 

 

 
''
'1,'
K
ff
kk
static kk
kkk
fMAI
kkk
RmHmXm HmXmWm
HmXm m 

 
 
 (10)
where


MAI
km
 is the total interference term with re-
spect to user-k on subcarrier-m, consisted of both MAI
and noise.
Without loss of generality, BPSK modulation and real-
valued channel coefficients are assumed for simplifying
the expression. Furthermore, the principle here can be
easily extended to other cases such as complex channels,
higher order modulations and multiple receive antennas
[3]. According to the central limit theorem,


MAI
km
 is
approximated as a Gaussian random variable with mean




MAI
k
Em  and variance . Based on
the definition of extrinsic LLRs, the output of ESE de-
tector is calculated by


MAI
k
Var m 





  



2
MAI
fstatic k
k
ESE kMAI
k
RmEm
eXmHmVar m



 (11)
where




MAI
k
Em  and can be ob-
tained by the mean and variance of Xk’(m).


MAI
k
Var m 

By the priori LLRs

D
EC k
eX feedback from the
DECs, the mean and variance of Xk(m) can be calculated
as follows


  

tanh2 ,
kDECk
EX meX m (12)
   

2
1.
kk
VarXmEX m

(13)
In the above conventional detection algorithm, the
MAI


MAI
km
 of quasi-static channels can be eliminated
effectively. However, in the doubly selective channel, the
channel matrix
f
k
H is not a diagonal matrix and the
frequency domain received signal cannot be expressed
 
 





2
21
2
21 21
0,10, 1
1, 01,11,1
1
1, 01,
0,0
11,1
kk k
jN
j
N
kk k
t
k
jN jN
NN
kk k
HHN
HHe HNe
N
HNHN eH
H
NNe














  


H




N
(4)

T. PENG ET AL.
252
simply as (9). More specifically, an additional interfer-
ence from other subcarriers will be introduced, resulting
from the time-varying characteristics of the channel.
Therefore, the performance will be degraded signifi-
cantly if the conventional algorithm is adopted in the
doubly selective chan nels.
3.3. Proposed Detection Algorithm
To alleviate this problem, a novel ESE detection algo-
rithm is proposed to enhance the system performance of
OFDM-IDMA uplink over doubly selective channels. It
takes into account the additional intercarrier interference
and utilizes an iterative soft interference canceller to
suppress the MAI and ICI jointly. With increasing itera-
tion number, the additional interference can be mitigated
and the transmitted signal of the desired user can be re-
covered gradually.
For analyzing the interference of user-k, the received
signal on s ubcarrier- m in (8) is expressed as


 
1
10
1
10,
,
,,
,.
KN f
kk
kn
KN
ff
kk kkk
knnm
fICIMAI
kkkk
RmHmnX nWm
HmmXmHmnXn m
HmmXmmm





 

 
 



MAI

 
(14)
As shown in (14), the interference term includes not
only the MAI from other users on subcarrier-m, but also
the ICI from other subcarrier-n
of all users. Compared to (10), an additional in terference
term will be appeared in the doubly selective
channels, which is neglected in the conventional algo-
rithm. This explains the performance degradation for
OFDM-IDMA uplink when using the conventional algo-
rithm. Consequently, this additional interference should
also be cancelled in the ESE detector. Based on an inte-
grated interference canceller, the output of the proposed
ESE detector can be obt a i ned by

,0 1nm nN

ICI
km




 


 




2,
proposed
ESE k
MAI ICI
kk
f
kMAI ICI
kk
eXm
Rm Em Em
Hmm VarmVarm



 
.
(15)
In the proposed detection algorithm, all the interfer-
ence included MAI and ICI can be suppressed and the
system performance can be improved. For suppressing
the additional in terference , the computation in
the proposed detection algorithm is more complicated
than the conventional one.

ICI
km

3.4. Improved Low-Complexity Detection
Algorithm
As described above, the proposed detection algorithm
can obtain more satisfied performance than the conventional
one. But the computation complexity of the mean and
variance of the interference is much higher than the con-
ventional one. In the follow, an improved detection algo-
rithm is proposed for reducing the complexity by an ap-
proximation to the mean and variance of the interference.
In the proposed algorithm, the interference


ICI
km

consists of the equivalent channel matrix
f
k
H and the
transmitted signal on other subcarriers. This indicates
that the value of the channel matrix
f
k
H will affect the
computation of the mean and variance of


Im IC
k
 . By
analyzing the property of the chann el matrix
f
k
H, it can
be found that the values of off-diagonal elements become
smaller and smaller with increasing distance to the main
diagonal elements. And when these off-diagonal ele-
ments are far from the main diagonal ones, their values
will be quite small that can be approximated to zero. As a
result, the row-m (1mN

) of the channel matrix
f
k
H
(1kK

) can be approximated by using the following
vector:

   
 
,0,,12,,,
,120
fff
kkk
f
k
HmHmmP Hmm
HmmP


 





(16)
where P is the number of elements that are not set to zero.
In this case, the interference
I
CI
k

only from P subcar-
riers needs to be calculated instead of all subcarriers in
the ESE detector.
Furthermore, by the expression in (15), the variance of
interference only affects the magnitude of the output of
ESE detector. Thus the variance of can be
neglected for reducing the computation complexity.

ICI
km

Consequently, the improved algorithm can reduce the
complexity in two aspects. Firstly, the computation com-
plexity of the mean of the interference is reduced to P/N
as the proposed algorithm by the approximation to the
channel matrix. Secondly, the computatio n complexity of
the variance o f th e in terferen ce is reducing to the same as
the conventional one.
4. Simulation Results
In this section, computer simulations are carried out to
verify the effectiveness of the proposed detection algo-
rithms over doubly selective channels. Simulations are
performed for OFDM-IDMA uplink with four users, em-
ploying BPSK modulation. A repetition code of rate-1/8
is adopted for all users, and the total number of subcarri-
ers is 128. The channel model used here is the extended
vehicular A (EVA) channel [11]. The normalized Dop-
pler frequency is denoted as fDT, where fD represents the
maximum Doppler frequency shift and T is an OFDM
symbol period. In the simulations, channel estimation is
not considered and perfect channel information is as-
sumed to be known at the receiver.
Figure 2 shows the bit-error-rate (BER) performance
of the conventional detection algorithm in the doubly

T. PENG ET AL. 253
selective channels with different velocities (i.e., corre-
spondingly fDT = 0.001, 0.01, 0.05, 0.1, and 0.2, respec-
tively). It can be found that the system performance de-
grades with the increase of users’ velocity. The perform-
ance is relatively poor at fDT =0.2 and fDT =0.1 compared
with fDT =0.01. This is because the conventional algo-
rithm doesn’t take into account the additional interfer-
ence from other subcarriers, which becomes larger with
the increase of normalized Doppler frequency.
Figure 3 depicts the BER performance results of the
proposed and conventional detection algorithms in the
doubly selective channels with different normalized
Doppler shift. From this figure, it can be found that the
proposed algorithm can enhance the performance obvi-
ously in the doubly selective channels. More specifically,
it can be found that the performance gap between the
proposed algo rithm and the convention al one is very sig-
nificant when fDT =0.2. And the performance of the pro-
posed algorithm with fDT =0.1 is very close to the per-
formance of the conventional one with fDT =0.001.
Figure 4 and Figure 5 show the BER performance of
the improved low-complexity algorithm with different
value of parameter P, where the performance of the con-
ventional and proposed algorithms is also included for
comparison. It can be observed that the performance gap
between the improved algorithm and conventional one
becomes greater with the increasing value of P. When P
= 3, at the cost of little complexity, the performance of
the improved algorithm is sig nificantly better th an that of
the conventio nal one. And while P = 17 for the improved
algorithm, the performance is almost the same as that of
the proposed one.
10-1
Eb/N0(dB)
B
E
R
10-3
010121416
10-2
1820
Conv ention al algorithm, fDT=0. 2
100
10-4
10-5 2684
Conventional algorithm, fDT=0.1
Conventiona l algorithm, fDT=0.05
Conventiona l algorithm, fDT=0.01
Conventiona l algorithm, fDT=0. 001
Figure 2. BER performance of the conventional algorithm
in the doubly selective channels with different normalized
Doppler frequency fDT.
10-1
Eb/N0(dB)
BER
10-3
01012 14161820
10-2
Conventional algorithm, fDT=0.2
100
10-4
10-5 2684
Conventional algorithm, fDT=0.1
Conventional algorithm, fDT=0.001
Proposed algorithm, fDT=0.2
Proposed algorithm, fDT=0.1
Figure 3. Performance comparison of the proposed algo-
rithm and the conventional one in the doubly selective
channels with different nor m alized Doppler frequency fDT.
10-1
Eb/N0(dB)
BER
10-3
010121416
10-2
1820
Conventional algorithm
100
10-4
10-5
2684
Proposed algorithm
Improv ed al go ri th m, P=3
Improv ed al go ri th m, P=5
Improv ed al go ri th m, P=17
Figure 4. BER performance of the improved algorithm in
the doubly selective channels (fDT =0.2) with different pa-
rameter P.
10-1
Eb/N0(dB)
BER
10-3
010121416
10-2
1820
Conventional algorithm
100
10-4
10-5 2684
Proposed alg orit hm
Impr oved algo ri thm , P=3
Impr oved algo ri thm , P=5
Impr oved algo ri thm , P=17
Figure 5. BER performance of the improved algorithm in
the doubly selective channels (fDT =0.1) with different pa-
rameter P.

T. PENG ET AL.
254
5. Conclusions
In this paper, three different detection algorithms are
derived for OFDM-IDMA uplink over doubly selective
channels. Among all the three detection algorithms, the
conventional algorithm suffers from performance loss
due to neglect of the additional interference from other
subcarriers, and the proposed algorithm delivers the best
performance but at the cost of higher complexity. And
the improved algorithm can achieve performance close to
the proposed on e but with a low co mputational co mplex-
ity. Consequently, it is optimal to adopt the improved
lower-complexity algorithm to obtain a tradeoff between
performance and complexity.
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