Int. J. Communications, Network and System Sciences, 2010, 3, 413-417
doi:10.4236/ijcns.2010.34053 Published Online April 2010 (http://www.SciRP.org/journal/ijcns/)
MIMO Multi Carrier Interleave Division Multiple Access
System with Multiuser Detection: Performance Results
Prabagarane Nagaradjane1, Sai N. Chandrasekaran2, Kuttathatti Srinivasan Vishvaksenan3
1Department of Electronics and Communication Engineering, SSN College of Engineering,
SSN Institutions, Chennai, India
2The University of Kansas, Kansas, USA
3Department of ECE, SSN College of Engineering, SSN Institutions, Chennai, India
Received January 6, 2010; revised February 17, 2010; accepted March 16, 2010
Abstract
This paper provides the performance analysis of multi input multi output (MIMO) Multi carrier (MC) inter-
leaver based multiple-access system with multiuser detection. Interleave-division multiple access (IDMA) is
a scheme in which users are separated by employing different interleavers instead of different signatures as
in a conventional code-division multiple-access (CDMA) scheme. The basic principle of IDMA is that the
interleaver is different for different users. Interleavers are generated independently and randomly. At the re-
ceiver, ZF, LLSE, VBLAST/ZF/MAP and VBLAST/LLSE/MAP detectors are employed. The performance
of the system is analyzed for different channel conditions using extensive simulation runs based on Monte
Carlo simulation trials. Simulation results divulge that VBLAST/LLSE/MAP detector results in significant
performance amelioration compared to other detectors as applied to MC/IDMA system.
Keywords: CDMA, Channel Capacity, Iterative Decoding, Multi-User Detection
1. Introduction
This paper presents an approach to asynchronous multi-
ple access scheme called interleave division multiple-
access (IDMA) [1] system with MIMO support. In an
IDMA scheme, different interleavers are used to distin-
guish users as against different codes in a conventional
code division multiple access (CDMA) system. In a
conventional CDMA scheme, interleavers are placed
before the spreaders and they are effective only when
used in conjunction with channel coding [2,3]. Recently,
a very interesting technique using chip-level interleavers
was addressed in [1], which aims at mitigating inter-
symbol interference (ISI) in multipath fading environ-
ments. Many papers have discussed the role of interleav-
ers in a multiple access systems [1,3]. IDMA inherits
many benefits of CDMA; in particular, path diversity and
mitigation of intra cell interference. Also all the users
employ a common spreading sequence. Recent research
on wireless communication systems has shown that using
multiple antennas at both transmitter and receiver offers
the possibility of communications at higher data rates
compared to single antenna systems [4-6]. Multi input
and multi output (MIMO) system has proved in the re-
cent past to provide very high capacity without any in-
crease in the transmission bandwidth and power. The inf-
ormation-theoretic capacity of these multiple-input mul-
tiple-output channels was shown to grow linearly with
smaller numbers of transmit and receive antennas in rich
scattering environments, and at sufficiently high signal-
to-noise (SNR) ratios [7-9]. MIMO profile in any wire-
less communication system can be realized by two
schemes namely, 1) using the classical BELL labs archi-
tecture (VBLAST–Vertical Bell Laboratories Space
Time architecture) and 2) Space Time Block Codes. And
OFDM techniques can compensate for multi-path fading
effects, which cause time dispersion, and out of band
emission of the received signal. So combining these tech-
niques with the IDMA system can result in MIMO
MC/IDMA that can offer bandwidth efficiency, space
diversity and lower speed parallel type of signal proc-
essing and interference rejection capability (ISI reduction)
in high data-rate transmission. Of late, significant pro-
gress has been made in multi-user detection for code-
division multiple-access (CDMA) systems [6]. In this
paper, we investigate the performance of the MIMO as-

414 P. NAGARADJANE ET AL.

sisted Multi Carrier interleave division multiple access
(MIMO MC/IDMA) scheme with multiuser detection.
We will show that the MIMO MC/IDMA scheme can
provide better performance with the aid of VBLAST/
LLSE/MAP [5,6] detection technique. Also this approa-
ch is independent of the number of users and gives better
performance in multipath environment. The rest of the
paper is organized as follows - the system model is pre-
sented in Section 2. Section 3 gives the gist of signal
detection techniques. Performance results will be pre-
sented in Section 4. Eventually conclusions are drawn in
Section 5.
2. System Model
In this section, we introduce the IDMA scheme with
Multi carrier modulation. The block diagram of MIMO
MC/IDMA scheme is elucidated in Figure 1. In IDMA
the interleavers are different for different users. Inter-
leavers are generated independently and randomly. Dif-
ferent interleavers separate the users and all the users
employ a common spreading sequence. Interleavers,
which are usually placed between forward error correc-
tion (FEC) coding and spreading, is used to combat fad-
ing effect in CDMA, whereas the arrangement of inter-
leaving and spreading is reversed in IDMA. Now, dif-
ferent interleavers distinguish distinct data streams. In
IDMA, encoder block may do FEC encoding and spre-
ading jointly. The spreader has no special function. In
this paper we consider a single user MIMO MC IDMA
system. Each of the synchronous user is equipped with M
transmit antennas and they communicate to a single base
station, equipped with N receive antennas. MIMO profile
is realized by using VBLAST (Vertical Bell Laboratories
Space Time architecture).
3. Symbol Detection Techniques
Considering a synchronous signal over a time variant cha-
nnel, the received signal at the time instant j is given as
min(, )
1
()() (),1,2,...,
mn k
kk
k
rjHxjnjjJ


 (1)
where Hk is the channel co-efficient for user k and {n (j)}
are samples of an AWGN process with variance =
No/2. Here perfect knowledge of the channel state in-
formation is assumed to be available at the receiver. In
each use of the MIMO channel, a vector x = (x1, x2…xM)T
of complex numbers is sent and a vector r = (r1, r
2,…,
rN)T of complex numbers is received. We assume an in-
put-output relationship of the form
2

r = Hx + n (2)
where H is a N × M matrix (N = number of transmit
antennas and M = number of receive antennas) repre-
senting the scattering effects of the channel and n = (n1,
n2,…, n
N)T is the noise vector. Throughout, we assume
that H is a random matrix with independent complex
Gaussian elements {hij} with mean 0 and unit variance,
denoted by hij ~N (0, 1). We also assume throughout that
n is i.i.d complex Gaussian random vector. The symbol
detection problem considered in this paper is the problem
of estimating the MIMO channel input vector x given the
received vector r assuming that the receiver has perfect
knowledge of H. The decision is made on a sym-
bol-by-symbol basis. The next section discusses the
various VBLAST detectors employed in our work.
S/P IFFT FFT MUD
Figure 1. MIMO MC/IDMA system.
SPREADER
dk c
k x k

P/S

-1
DESPREADER
d
k
ck k
x
ˆ

P. NAGARADJANE ET AL. 415
)
3.1. Zero-Forcing (ZF) Receiver
Zero-forcing (ZF) receiver is a low-complexity linear
detection algorithm that outputs,
ˆˆ
(xQx
Z
F
 (3)
where
ˆ
x
ZF = H+ r (4)
and H+ denotes the Moore-Penrose pseudo inverse of H,
which is a generalized inverse that exists even when H is
rank-deficient.
3.2. Linear Least Square Error Receiver (LLSE)
LLSE receiver is also a linear detection algorithm that
outputs
ˆˆ ()
L
LSE
aQa (5)
where
ˆLLSE
aWr (6)
and when H and n are gaussian, W is the weight vector
given by
1
()
oN
ρ
ρ
WHHHNI
M
M



(7)
3.3. V-BLAST Detection
The V-BLAST detection algorithm [6] is a recursive
procedure that extracts the components of the transmitted
vector x according to a certain ordering (k1, k2,…,kM) of
the elements of x, where, (k1, k2,…,kM) is a permutation
of (1,…, M). In VBLAST, this permutation depends on H
(which is known at the receiver by assumption) but not
on the received vector r. The VBLAST/ZF algorithm is a
variant of VBLAST derived from ZF rule. The algorithm
determines the order of channels to be detected, performs
nulling and computes the decision statistics. It then slices
the computed decision statistics and yields the decision
by performing cancellation with the help of decision
feedback, and finally computes the new pseudo-inverse
for the next iteration. V-BLAST/ZF may be seen as a
successive-cancellation scheme derived from the ZF
scheme discussed in the previous section. The ZF rule
creates a set of subchannels by forming
ˆ()
x
HHx Hn



(8)
The j'th such sub-channel has noise variance ||(H+)j||2
.N0
and the order selection rule prioritizes the sub-channel
with the smallest noise variance.
3.4. VBLAST/MAP Detection Algorithm
In this section, a detection algorithm for MIMO channels,
called VBLAST/MAP that combines the features of
VBLAST and MAP rules is used for symbol detection in
a MC/IDMA system. This algorithm does not use the lay-
ered structure of VBLAST, but uses a different strategy
for channel processing order, inspired by the MAP rule.
This algorithm is an extension of the well-known VBLA-
ST algorithm. This VBLAST/MAP combines the elements
of VBLAST algorithm and the maximum a-posteriori
(MAP) rule. The original VBLAST algorithm is a multi-
layer symbol detection scheme which detects symbols
transmitted at different transmit antennas successively in a
certain data-independent order. The VBLAST/ MAP algo-
rithm differs from VBLAST only in the ordering strategy
of the symbols detected. The complexity of the VBLAST/
MAP is higher than that of VBLAST; however, the per-
formance improvement is significant.
3.5. V-BLAST/ZF/MAP Detection Algorithm
Using the same notation of VBLAST algorithm, VBL-
AST/ZF/MAP algorithm may be described, as follows-
VBLAST/ZF/MAP algorithm is identical to VBLAST/
ZF except for the ordering in which symbols are detected.
Instead of selecting the next symbol to be detected accor-
ding to the rule, here the set of all probable symbol deci-
sions are ranked with respect to their a-posteriori prob-
abilities of being correct, as estimated by pij. Thus, it is
important to emphasize that pij’s are not true MAP prob-
abilities but approximations to how probable it is that sij
= xj. Note that the index permutation (k1, k2,… ,kM) pro-
duced by VBLAST/ZF/MAP depends on both H and r,
unlike VBLAST/ZF where the permutation depends only
on H. Complexity of VBLAST/ZF/MAP is increased
with respect to that of VBLAST/ZF by the computation
steps involved. One major point about complexities of
VBLAST/ZF and VBLAST/ZF/MAP is that, the former
allows pre-computation of all weighting vectors whereas
in the latter the weighting vector must be computed in
real-time since it also depends on r. This increased com-
plexity of VBLAST/ZF/MAP is justified by performance
improvements. The algorithm is summarized as follows:
Initialization 
HW1
1i (9)
Recursion
iii
r
W
y

)( ii yQ
s

}...{, 11
)|(
)|(

 


i
syf
syf
ij kkjp
As ijij
ijijij
}{
}...{
ma
x
arg
11
ij
i
i
p
kkj
k



kSx
ˆ
iiki

416 P. NAGARADJANE ET AL.
ii kki1i)H(x
ˆ
rr



1i ik
WH


1 ii (10)
3.6. V-BLAST/LLSE/MAP Detection Algorithm
This detection algorithm is akin to V-BLAST/ZF/MAP
detection except the weight vector defined by the Equa-
tion (7).
4. Performance Results
Figure 2 expounds the simulation results for an 8 × 12
MIMO MC/IDMA system employing ZF, LLSE,
VBLAST/ZF and VBLAST/LLSE detectors. The modula-
tion technique considered is 16-QAM and the Eb/N0 ranges
between -10 dB and 4 dB. The symbol error rate SER is
Figure 2. Symbol error rates (SER) of VBLAST/ZF, VBL-
AST/LLSE, ZF and LLSE receiver.
Figure 3. Symbol error rates (SER) of VBLAST/ZF/MAP
and VBLAST/ZF receiver.
Figure 4. Symbol error rates (SER) of VBLAST/ZF, VBLA-
ST/LLSE, VBLAST/ZF/MAP and VBLAST/LLSE/MAP
receiver.
calculated by performing 10,000 trials at each Eb/N0 point.
A new realization of H was chosen in each trial and for
each Eb/N0 value. The performance curves in Figure 2
show that VBLAST/LLSE provides significant improve-
ment in SER compared to ordinary VBLAST/ZF, ZF and
LLSE detector. Figure 3 elucidates the simulation results
for an 8 × 12 MIMO MC/IDMA system employing
VBLAST/ZF and VBLAST/MAP detectors. It is dis-
cerned that VBLAST/MAP outperforms VBLAST/ZF
detector. Figure 4 evinces the simulation results for an 8×
12 MIMO MC/IDMA system employing VBLAST/ZF,
VBLAST/LLSE, VBLAST/ZF/MAP and VBLAST/LLSE
/MAP receiver with 16QAM modulation. It is discerned
that VBLAST/LLSE/MAP outperforms VBLAST/ZF/
MAP detector in terms of SER performance.
5. Conclusions
In this paper a multiple access scheme for 4G wireless
communications has been considered based on interleav-
ers. Problems in two major areas have been identified in
this paper: efficient transmission technique and symbol
detection in the presence of multi stream interference. A
solution has been conceived to achieve the above. Simu-
lation results have proved that the MIMO MC/IDMA in
combination with VBLAST/LLSE/MAP multiuser de-
tector can achieve significant performance improvement
compared to ZF, LLSE, and VBLAST/ZF/MAP.
6
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P. NAGARADJANE ET AL. 417
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