Communications and Network, 2013, 5, 119-126
http://dx.doi.org/10.4236/cn.2013.53B2023 Published Online September 2013 (http://www.scirp.org/journal/cn)
One-User/One-Group Soft-Decision Aided Multiuser
Detection for 2D Spread MC DS-CDMAs
Hoang-Yang Lu, I-Hsuan Lai
Dept. of Electrical Engineering, National Taiwan Ocean University.
Email: hylu@mail.ntou.edu.tw, rockrice043@gmail.com
Received June, 2013
ABSTRACT
We consider the uplink of a multiuser, multiple-input multiple-output (MIMO), frequency-time-domain spread, multi-
carrier (MC), direct sequence code division multiple access (DS-CDMA) system. As other CDMA-like systems, the
multiple access interference (MAI) effect still exists in such an MC DS-CDMA system. To mitigate the MAI effect, we
propose user-based and group-based layered detection schemes. Specifically, to enable a trade-off between the per-
formance and the computational complexity, the schemes only use one user's/group's soft decisions for user-based/
group-based layered detection. The results of simulations demonstrate that the proposed schemes outperform existing
approaches, and th eir computatio nal complexity is modest.
Keywords: Multiuser detection, MC DS-CDMA, VBLAST, MIMO
1. Introduction
The rapidly increasing demand for better quality of ser-
vice (QoS) in wireless systems has motivated the devel-
opment of several promising approaches to improve sys-
tem capacity and transmission reliability. One promising
multiple access approach for sharing valuable bandwidth
resources is called multi-carrier (MC) direct sequence
code division multiple access (DS-CDMA) [1,2]. Re-
cently, a new MC scheme, called frequency-time-domain
(FT-domain) spread MC DS-CDMA, was proposed in
[3]. The scheme first spreads the transmitted symbol by a
time-domain (T-domain) signature code. Then, the T-
domain spreading signal is copied to each subcarrier to
be spread by a frequency-domain (F-domain) signature
code. In addition to providing the superior capacity per-
formance gain, FT-domain spread MC DS-CDMA sys-
tems have other attractive features, such as short and
low-chip-rate signature codes for realizing low-rate sig-
nal processing [4].
It has been shown that multiple-input multiple output
(MIMO) systems, which deploy multiple antennas on the
transmitter side and the receiver side, can yield a signifi-
cant performance gain for wireless communications [5].
Spatial multiplexing (SM), one of the key MIMO tech-
nologies [5], uses multiple transmit antennas in parallel
to send multiple symbols to the receiver. In particular, to
facilitate symbol detection in SM-based MIMO systems,
an effective layered detection scheme, called Vertical
Bell Laboratories Layered Space-Time (VBLAST), was
proposed in [5,6]. Because of VBLAST's efficiency and
feasibility, SM-based MIMO systems can provide high
throughput, and they have motivated a considerable
amount of research on applications and extensions of
VBLAST [7,8]. For example, Sfar et al. extended the
SM-based MIMO systems to SM-based MIMO CDMA
systems and presented a layered space-time (LAST)
MUD that detects transmitted messages symbol by sym-
bol [7]. The symbol-based LAST MUD is actually a
variant of VBLAST; however, its computational com-
plexity is very high, so it is not feasible in practice. To
reduce the compu tation al co mp lex ity, a user-b ased LAST
MUD was proposed in [8]. The mechanism is similar to
the symbol-based LAST MUD, but it performs layered
symbol detection user by user. In contrast to the sym-
bol-based LAST MUD, the user-based LAST MUD re-
duces the computational complexity at the expense of
performance degradation. Furthermore, like VBLAST,
both of the LAST MUD schemes need to rank the detec-
tion order of the residual layered signals before detecting
the symbols in each layer. Hence, they inevitably incur
an extra computational overhead and also suffer from
serious latency problems. Furthermore, the results re-
ported in [7,8] demonstrate that the performance of
MUDs degrades substantially when the length of the
signature codes decreases. To resolve the above prob-
lems, it is necessary to develop advanced layered detec-
tion schemes for such CDMA-like systems.
In this paper, our objective is to exploit the ad vantages
of FT-domain spread MC DS-CDMA and MIMO sys-
C
opyright © 2013 SciRes. CN
H.-Y. LU, I.-H. LAI
120
tems in order to provide advanced QoS in future wireless
communications. To this end, we investigate the uplink
of a multiuser MIMO FT-domain spread MC DS-CDMA
system, which is an extension of th e MIMO CDMA sys-
tem considered in [7,8]. In the proposed FT-domain
spread MC DS-CDMA system, users are also arranged in
groups; and each user is assigned a unique T-domain
signature code and shares an F-domain signature code
with users in the same group. Furthermore, like the SM
method, each user employs his/her T-domain and
F-domain signature codes to spread the multiple symbols.
The spreading signals are then transmitted in parallel
from the corresponding multiple antennas over fading
channels to the antenna array at the base station. How-
ever, the MAI effect, which is caused by the
non-orthogonality of signature codes and is the main
performance limitation, also affects the investigated MC
DS-CDMA system. To mitigate the MAI effect, we pro-
pose a one-user soft-decision aided user-based layered
(OUSDA-UL) MUD. Our approach ranks the detection
order by exploiting users' effective code correlation ma-
trices, and then performs layered symbol detection with
the assistance of the previous user's soft decisions [9].
That is the proposed OUSDA-UL scheme sequentially
detects a subset of all transmitted symbols stage by stage
(i.e. user by user). Moreover, in each stage, the soft deci-
sions for the corresponding transmitted symbols are es-
timated in parallel and collected for use in the next
stage's symbol detection operation. To further reduce the
computational complexity, we propose a one-group
soft-decision aided group- based layered (OGSDA-GL)
MUD. It estimates more transmitted symbols in parallel
than the proposed OUSDA-UL scheme; hence, its com-
putational complexity is lower. To enable a trade-off
between the system performance and computational
complexity, the two schemes only utilize one user's (or
one group's) soft decisions to facilitate
user-based/group-based layered detection. The soft
mechanisms incorporated by existing works usually en-
hance the system performance at the expense of high
computational complexity. Under the trade-off between
the performance and computational complexity, the pro-
posed schemes only return partial soft decisions (i.e.
one-user's soft-decisions or one-group's soft-decisions) to
mitigate interference in the nex t stage. Finally, the results
of extensive simulations show that the proposed MUDs
outperform existing approaches and their computational
complexity is modest.
Before discussing the system model, we introduce the
notations used throughout the paper: ,
{}E()T
, ()
H
,
and denote the expectation, the transpose, the
Hermitian, and the fast Fourier transform (FFT) opera-
tions respectively [10]; denotes the Kronecker prod-
uct operator [10]; and
()FFT
|| |||| ||
F
represent the Euclidean
norm and the Frobenius norm respectively [10]; and
M
I,
P
0, and
L
0 denote the
M
M identity matrix, the
1P
zero vector, and the zero matrix respectively.
The ranges of the indices and
LL
,, ,ilk
g
are 1
R
iM
,
1T
lM
, 1kK
, and 1
g
G
respectively. We ex-
plain
R
M
, T
M
, , and in Section II. KG
2. Signal Model
Consider a synchronous uplink multiuser MIMO FT-
domain spread MC DS-CDMA system. Each user is as-
signed a unique T-domain signature code and T
M
transmit antennas, which are deployed under the SM-
based symbol transmission method. In addition, as in [7,
8], users are organized into G groups, and users in the
same group share a unique F-domain signature code. For
ease of presentation, we assume that the number of users
in each group is K. Denote kkk kt
andf, respectively, as the T-domain
and F-domain signature codes of the kth user in the gth
group. Here, and
,1 ,
tt
2
]
gt,T
gN
=[
gg
t
,1 ,
ff
2
]
g
t
N
,
g
f
f=[
gg T
N
f
N are the processing gains of
the corresponding signature codes. Each user employs
his unique T-domain signature code to spread the T
M
binary phase shift keying (BPSK) modulated symbols.
Then, the T-domain spreading signals are copied to
f
N
sub-carriers, and spread by using the corresponding
F-domain signature code. After spreading the symbols in
the T-domain and F-domain, applying the inverse FFT
algorithm, and inserting a cyclic prefix (CP) [2], the
user's T
M
spreading signals are transmitted in parallel
by the T
M
transmit antennas over the complex-valued,
frequency selective Rayleigh fading channels to the base
station. Let
R
M
receive antennas be deployed at the
base station. For simplicity, we assume that the length of
all fading channels available to all users is equal to
[11]. In addition, the complex-valued channel coeffi-
cients between the ith receive antenna and the lth trans-
mit antenna of the kth user in the gth group are denoted
as ,,gl gl
kk
. We also assume that after re-
moving the CP and performing the FFT operation, the
signal will be received successfully. As a result, at the
base station's receiver, the corresponding
Q
{(h1),
i
(
i
)}Qh
f
f
NN
di-
agonal matrix of the F-domain channel's transfer function
is
,,
(1),
l
1
,
i
N
k
=
gl ([), T
f
hh QH0(
gl ])
Q
ii
N
g
kk
f
diag FFT;
Hence, the associative
effective F-domain signa-
ture code is
,
,=
ii
g
gl
gl k
k. Now, the signal received at
the base station's ith receive antenna can be expressed as
follows:
fHf
,
=1
=
M
Ti
gl
k
l
rc
,
=1 gl
k
gk
=1
 b
ii
,n
GK (1)
where ,,
ii
=
g
gl gl
kk k
cft
is the effective 1
ft
NN
FT-
Copyright © 2013 SciRes. CN
H.-Y. LU, I.-H. LAI 121
domain signature code between the base station's ith re-
ceive antenna and the lth transmit antenna of the kth user
in the gth group; and is the corresponding
i
n1
ft
NN
additive white Gaussian noise (AWGN) vector with each
entry
)(0, 2
. For ease of expression, we stack
the T
M
transmitted BPSK symbols of the kth user in
the gth group to form the user-based transmitted symbol
vector and then re-express
(1) as follows: ,1 ,2
=[
gg
g
kk
bb
,1
=[
ii
gkgk gk
Cc
,
, ]T
gM
kT
b
=1
=
GK
i
i
g
gk
k
rC
]
i
c
, ,
k
=1gk

,2
i
c
b
. (2)
i
nb
Here, ,gk MT is the corresponding
f
t
MT
NN user-based effective FT-domain spreading
matrix between the ith receive antenna and the kth user in
the gth group. Similarly, we can stack the K transmitted
symbol vectors
g
k
b of the gth group as a 1
T
KM
group-based transmitted symbol vector
12
,,
TT
gg
b
=
ii
gg
=[
g,bb
=1
G
g
]
T
T
g
K
b.
Then, (2) can be re-written as follows:
,
i
rCb
]
i
n (3)
where 12 g
=[
ii
ggg
i
K
CCCC is the effective associative
f
t
K
TT
b
T
M
]
T
T
G
b
1
T
GKM
NN
=[
group-based FT-domain spreading matrix
between the ith receive antenna and the gth group. Then,
by stacking the G group-based symbol vectors, ,
we can re-express (3) as follows: where
12 and 12G are the corre-
sponding transmitted symbol vector and the
effective
1,G
bb
,
i
n=
ii
rCb
]
i
Cbb =[
ii
CCC
i
f
t
NN GKT
M FT-domain spreading matrix
between the ith receive antenna and all the transmit an-
tennas. Finally, following [7,8], we use the effective
R
M
FT-domain spreading matrices, to match the
corresponding signals received by the base station's
,
i
C
R
M
receive antennas. Then, the sufficient statistics for the
received signal at the base station can be formulated as
follows:
=1
=
RH
ii
zCr=R bu,
M
i
C
(4)
where i
is the effective spatial-frequency-
=1
=MRH
i
i
RC
time (SFT) code correlation matrix; and u is the corre-
sponding complex Gaussian noise vector with )(0, 2R
.
3. The Proposed One-User-Soft-Decision
Aided User-Based Layered MUD
The proposed OUSDA -UL MUD fir st ranks the detection
order based on the users’ effective code correlation ma-
trices. Then, it utilizes the ordered results to successively
implement the corresponding user-based MMSE layered
detectors and estimate the transmitted symbols.
3.1. User-based Ordering
To avoid a large computational overhead for ranking the
detection order, the proposed OUSDA-UL MUD com-
putes the Frobenius norm [10] of the users' effective SFT
code correlation matrices and then sorts the matrices in a
descending order. For the kth user in the gth group, the
Frobenius norm is formulated as follows:
=1
||||=||||,
MRH
ii
g
F
gg
kkk
i
RCC
F
(5)
where
g
k
R is the effective SFT code correlation matrix
of the kth user in the gth group. Note that we assume the
coefficients of the user’s fading channels are fixed in a
frame and change frame by frame [5]. Hence, for each
user, (5) is computed in just one pass per frame. As a
result, the proposed scheme avoids the ordering problem
observed in [6-8], which affects VBLAST-like schemes.
In [6-8], the ordering mechanisms compute undetected
symbols stage by stage (i.e. symbol by symbol, or user
by user) by searching the maximization post signal-to-
noise-ratio outputs of the corresponding detectors. How-
ever, because the detectors for the undetected symbols
need to be computed stage by stage, the computational
complexity is usually prohibitive.
3.2. User-based Interference Cancellation and
Layered Symbol Detection
Without loss of generality, we assume that (1) after the
user-based ordering step, the indices of the detection or-
der are 12
1, 1, , , ,
kK
g
G
12
1, 1, , k
; and (2) the interference
caused by users 2
g
has been estimated pre-
cisely and removed from the received signal. Then, in
this step, we perform user-based layered symbol detec-
tion and interference cancellation (IC) to estimate the
transmitted symbols for the kth user in group g. Using
, the residual sufficient statistics of the corresponding
signal
()
1
gk
z can be formulated as
11
1
=
gg
gg
kk
kk


zRbu
1
, (6)
where 1
gk
R is the sub-block matrix obtained by re-
moving the corresponding rows and columns of the th,
th, , 1
1
2
12k
g
th users from the effective SFT code
correlation matrix R; and 1 is the corresponding
Gaussian noise vector. Then, to estimate the transmitted
symbols of the
gk
u
k
g
th user
g
k
b, we utilize the user-based
layered MMSE symbol detector with the soft decisions
of the 1k
g
th user and derive
2
11
,1
||||,
min Hg
gg
gk
kk
k
gg
kk
arg E

Wb bWz b
(7)
where
g
k
W denotes the k
th user's layered
T
DM
Copyright © 2013 SciRes. CN
H.-Y. LU, I.-H. LAI
122
MMSE symbol detector in which
=() T
DGgKM
(2)
T
K
kM ;
1
gk
b is the soft information
vector gleaned from the 1
T
M
1k
g
th user’s soft decisions.
From (7), it is clear that the proposed OUSDA-UL MUD
attempts to fully exploit the last user’s soft information
vector
1
gk
b in order to enhance the performance of the
kth user in the gth group. Using (7), and after some ma-
nipulation,
g
k
W and
1k
g
b can be formulated as fol-
lows:
1
})({EE
111 1
{{ }),
HH
gg g
gg
kk k
kk
E

z zb
1
}
T
g
k
gk
zb=(Wz (8)
and
1
1={
Hg
gg
k
kk
E
bWz
}, (9)
respectively. Furthermore, we assume that the transmit-
ted symbols and noise are mutually uncorrelated and the
transmitted symbols are BPSK modulated and i.i.d. [11].
We also assume that the transmitted symbols are BPSK
modulated because of the ease of derivation. In addition,
we assume that the transmission signals of the 1
1th,
2th, , 1k2
g
th users have been estimated exactly and
removed from z in (4). Hence, the residual sufficient sta-
tistics 1
gk
z in (6) contain the transmission signals of
the 1k
g
th, k
g
th, , and
K
Gth users. Note that, be-
cause we utilize the 1k
g
th user's soft decisions when
estimating the k
g
th user's transmitted symbols
g
k
b in
(7), 1
gk
z must contain the 1k
g
th user's transmitted
signal. Based on the above assumptions and after some
manipulations of (9) and (10), we have
11
1
{}= {}
gg
g
kk
k
EE

zRb, (10)
()
1
{}=
gk
T
g
k
gk
E
zb R
1
,
g
k
(11)
2
11 111
11
{}={}
HTH
gg ggg
gg
kk kkk
kk
EE
 
 zzRbb RR, (12)
where ,1 ,2,
111 1
ˆˆˆ
{}=[, , , ,]
TT
ggg gM
kDM
kkkTT
Ebbb
 
b0. Here,
,,
11
1
ˆ=tanh( ()),
2
gl gl
kk
bb

and ,
1
()
g
l
k
b
is the soft decision [9] for the BPSK symbol of the
th user in the gth group transmitted by the lth
transmit antenna;
(1)k()
1
gk
gk
R is the sub-block ma-
trix of the SFT code correlation matrix T
DM
1
gk
R for the kth
user of the gth gr o up; a n d
11
11
{}
{}=
T
gM
g
kT
k
T
gg MM
kk TT
MT
E
E




bb 00
bb0 II


,
M
T
(13)
where
,,
11
,
11
ˆˆ,,
[{}] =1, ,
gigj
kk
T
gij
g
kk
bb ij
Eotherwise

bb (14)
where denotes the (, th entry of matrix .
After some manipulations (described in the Appendix)
we have
,
[]
ij
X)ij X
()
111
1
=() ,
gk
Hg
gDD k
k
WIABBAR (15)
where we let 2
11
11
={ }
TH
gg
gg
kk
kk
E
1
g
k

 ARbbRR and
11
={
gg
kk
E
}
BRb . Using (15) to find 1
gk
b, (9) can be
rewritten as follows:
1
1
={
g
g
k
k
E
bYR b
1
}.
g
k
(16)
where ()
111
1
=(())
gk
H
H
g
DD k

YIABBAR. We also de-
rive the expression of the above soft decision ,
1
()
g
l
k
b
in (10). For this, we denote the th column of
l
g
k
W as
:,
[]
gl
k
W, which is the layered MMSE symbol detector for
the kth user in the gth group transmitted from the lth
transmit antenna. In addition, we let ,
1
g
l
k
b
(1)k, be the cor-
responding soft information of the th user in the
gth group, which is the lth entry of
1
gk
b in (16). Then,
we can express the corresponding output of the layered
MMSE symbol detector as follows:
,:,
11
=[],
Hg
g,
g
llg
k
k
kk
yb
Wz l
(17)
Furthermore, following [9], we regard the output of
the layered MMSE detector, ,
1
g
l
k
y, as approximately
Gaussian. Hence, the corresponding soft decision can be
represented as
,,, ,
,2
,, ,
(|=1)2
()=log= ,
(|=1)
g
lglglgl
kkk k
gl
kgl glgi
kk k
py bym
bpyb

(18)
where ,
g
i
k
m and 2,
g
i
k
are the corresponding equiva-
lent mean and variance of the layered MMSE detector's
output, expressed as
()
,,, :,
:, 1
22:,
:,:, 1
1
,
={}=[ ][],
={[] }=[][]
gk
Hg
g
gl glgll
lk
k
kkk
HH
g
gg gg
l
ll
k
kk kk
gl
k
mEyb
var

WR
Wu WRW,
where ()
:,
1
[]
gk
gl
k
R is the lth column vector of ()
1
gk
gk
R. Note
that, for the kth user in the gth group, we use (15) and (16)
to apply the T
M
layered MMSE symbol detectors
:,
[],=1 ,M
T
glT
klW concurrently. Then, we utilize the
corresponding
M
soft decisions in (18) to help detect
the T
M
symbols of the th user in the gth group.
In other words, the proposed OUSDA-UL MUD esti-
mates the
(1)k
T
M
transmitted symbols user-layer by user-
layer.
4. The Proposed One-Group-Soft-Decision
Aided Group-Based Layered MUD
To reduce the computational complexity of estimating
transmitted signals, we propose the OGSDA-GL MUD
scheme. It is similar to the OUSDA-UL MUD scheme,
but it detects transmitted symbols in a group-layer by
group-layer manner. The steps of OGSDA-GL MUD are
Copyright © 2013 SciRes. CN
H.-Y. LU, I.-H. LAI 123
detailed below.
4.1. Group-based Ordering
Similar to the OUSDA-UL MUD, the signals of the
group-layers are or d ered by usin g th e Froben iu s nor ms of
the groups’ effective SFT code correlation matrices, given
by
=1
||||=|||| ,
MRH
ii
g
Fgg
i
RCC
F
(19)
where
g
R is the gth group's effective SFT code corre-
lation matrix. Here, i
g
C is the corresponding effective
FT-domain signature matrix defined in (3).
4.2. Group-based IC and Layered Symbol
Detection
Without loss of generality, we assume that after the
group-based ordering step, the order of the indices is 1, 2,
, G. We also assume that the interference caused by
the transmitted signals of the 1st, 2nd, ,
(2)g
th
groups was estimated precisely and removed from the
received signal in (4). Then, as in (6), the sufficient sta-
tistics of the corresponding residual signal, 1
z, can be
expressed as follows:
111
=
gggg
zRbu

1
,
(20)
where 1
g
R
(2)g
is the sub-block matrix derived by remov-
ing the corresponding rows and columns of the 1st, 2nd,
, th groups from the SFT code correlation ma-
trix R; and and
11
=[, , , ]
TT
TT
gg
gG
bbb b
1
g
u
are the
associative residual symbol vector and noise vector re-
spectively. Furthermore, similar to (7)-(16) and based on
the MMSE method, the group-based layered MMSE de-
tector
g
W
1
and the corresponding soft information vec-
tor
g
b
of the th group can be expressed as (1)g
()
111
1
=() ,
g
H
gg
DD 
WIABB AR



(21)
and
()
111
111
1
=(()){ },
g
HH
ggg
g
DD E


bIABBARRb


 (22)
respectively, where we let
2
1111
={ }
H
T1
g
gg g
g
E
ARb bRR
 
} and .
11
={
gg
E

BRb
 
In addition, ;
=(2) T
DGg KM
1( 1),1( 1),2( 1),
11
{}=[{}, {}, , {},]
TT
gg ggM
KT DKM
T
EEbEbEb
 
b
0
,
,j
and
11
11
{}
{}=
T
gKMKM
gTT
T
gKMKM
gTT
KMT
E
E
bb 00
bb 0 II



(23)
where
(1)(1)
,,
12
1,
1
ˆˆ,
[{}]=1.
gg
kikj
T
gmn
g
bb klori
Eotherwise


bb (24)
Here, we let 1
=(1) T
mk Mi
and 2
=(1) T
nkM j
=1 T
M
()
,
where , and . Finally,
we assume that the outputs of the group-based layered
MMSE detectors in (21) and (22) are approximately
Gaussian [9]. Then, the soft decision, ,
12
kandk=1Ki and j
g
l
k
b
, for the
kth user in the gth group transmitted by the lth transmit
antenna can be expressed as follows:
,,, ,
,2
,, ,
(|=1)2
()=log= ,
(|=1)
g
lglglgl
kkk k
gl
kgl glgl
kk k
py bym
bpy b



(25)
where ,
g
l
k
y
, ,
g
l
k
m
, 2,
g
l
k
denote the corresponding
group-based layered MMSE detectors' output, the mean
of the output, and the noise power of the output. They
can be written as
11
,:,
=[][],
Hgg
g
lgp p
k
y
Wz b
(26)
()
,:,:
1
=[] [],
g
H,
g
lgp
g
k
m
WR

p
(27)
22:,1:,
,=[ ][],
H
g
pg gp
gl
k

WRW

(28)
respectively, where =(1) T
pk Ml
. Note that, based on
(20)-(27), the proposed OGSDA-GL MUD estimates the
T
K
M transmitted symbols of the gth group in parallel. It
also exploits the soft decisions of the gth group to help
the layered MMSE detectors estimate the transmitted
symbols of the (g1)
th group. This strategy enables the
OGSDA-GL MUD to estimate the transmitted symbols
group by group.
5. Simulation Results and Discussion
We conducted computer simulations and a complexity
analysis to assess the performance of the proposed
schemes. For ease of presentation, we assume the chan-
nels are complex-valued, frequency selective Rayleigh
fading channels, the channel length Q is 3, and the num-
ber of receive antennas,
R
M
, is 4. In addition, the user
concurrently transmits the spreading signals in parallel
from the T
M
transmit antennas over the fading chan-
nels to the base station. In the simulations and complex-
ity analysis, we compared the performance of the fol-
lowing six schemes: the linear MMSE SIC [13], the
decorrelating detector (DD) [4 ], the symbol-based LAST
MUD [7], the user-based LAST MUD [8], the proposed
OUSDA-UL MUD, and the proposed OGSDA-GL MUD.
We use a single user's performance (i.e. the performance
when the system settings are ,
=1G=1
K
, , and
) as the benchmark. Figures 1-4 show the bit er-
ror rate (BER) versus the signal to noise ratio (SNR) re-
sult of the compared schemes.
=1
T
M
=4
R
M
To assess the proposed schemes, we assume the sys-
Copyright © 2013 SciRes. CN
H.-Y. LU, I.-H. LAI
124
tem settings are as follows: the number of groups ,
the number of users in each group , and the num-
ber of transmit antennas of each user . In addition,
we consider two lengths of F-domain and T-domain sig-
nature codes: and (= . The
simulation results for the six schemes are shown in Fig-
ures 1 and 2. Interestingly, in Figure 1, the BER values
of the linear MMSE SIC, the DD, the symbol-based
LAST MUD, and the user-based LAST MUD hardly
change when the SNR 6 dB. That is, they appear to
be error-floor phenomena, which usually occur because
the receivers cannot mitigate the interference effectively
[12]. The results in Figure 1 also show the proposed
OUSDA-UL and OGSDA-GL MUDs are more robust
against the MAI effect than the other four methods;
hence, they achieve significantly better performance
gains. Next, we change the length of the T-domain sig-
nature code from 8 to 12 and leave the other system
settings the same as those in Figure 1. From the results
in Figure 3, we observe that the BER performance of the
six schemes is significantly better than that shown in
Figure 1. A possible intuitive explanation for this phe-
nomenon is that is due to a reduction in the load.
=4G
8)
t
=3K
T
M
N
=2
12,
f
(=9, =8
ft
NN
t
N
) =N
Figure 1. The BER versus the SNR with G = 4, K = 3, MT = 2,
MR = 4, Nf = 9, Nt = 8.
Figure 2. The BER versus the SNR with G = 4, K = 3, MT = 2,
MR = 4, Nf = 12, Nt = 8.
Figure 3. The BER versus the SNR with G = 4, K = 3, MT = 2,
MR = 4, Nf = 9, Nt = 12.
Figure 4. The BER versus the SNR with G = 4, K = 3, MT = 2,
MR = 4, Nf = 12, Nt = 16.
From the above observations, we conclude that increas-
ing the length of the T-domain signature code in the six
schemes is more effective in mitigating the MAI effect
than increasing the length of F-domain signature code.
Furthermore, as shown in Figure 3 the proposed OUSDA-
UL and OGSDA-GL MUDs also outperform the com-
pared schemes when the length of the T-domain signa-
ture code is changed. Overall, the OUSDA-UL MUD
achieves the best BER performance. Note that in Figures
1 and 2, the error floors of the six schemes occur when
the SNR 6 dB. This means that the power of each trans-
mitted symbol is stronger than when the SNR < 6 dB;
hence, the interference increases. Since none of the
compared schemes can eliminate the interference com-
pletely, error floors occur in such scenarios. However,
Figure 1 shows that the proposed schemes outperform
the other four schemes.
We also increase the lengths of both types of signature
Copyright © 2013 SciRes. CN
H.-Y. LU, I.-H. LAI 125
codes from to , while
maintaining the system settings shown in Figure 1. From
the results presented in Figure 4, we observe that all six
schemes perform better than in the scenarios discussed
above (i.e., Figures 1, 2, and 3). This is reasonable be-
cause increasing the lengths of the F-domain and the
T-domain signature codes individually can mitigate in-
ter-group MAI and inter-user MAI respectively. In this
scenario, the proposed OUSDA-UL MUD and OGSDA-
GL MUD achieve the best and second best performance
gains among the six compared schemes.
(=9, =8
ft
NN)(=12, =16)
ft
NN
Next, we analyze the computational complexity of the
six compared schemes. Because computing the inversion
of a matrix generally dominates the computational com-
plexity, we focus on that aspect of the schemes. For the
propos ed OUSDA-UL MUD and OG SDA-GL MUD, we
compute the corresponding complex multiplications and
additions (CMAs) needed for Equations (15) and (21).
Furthermore, approximately complex CMAs are
needed to find the inversion of a matrix. For ease
of reference, we show the expressions of the computa-
tional complexity for the six schemes in Table 1. For
example, in the scenario, the lin-
ear MMSE SIC, the decorrelating detector (DD), the
symbol-based LAST MUD, the user-based LAST MUD,
the proposed OUSDA-UL MUD, and the proposed
OGSDA-GL MUD r equire 13844, 13824 , 90000, 48672,
97344, and 43200 CMAs respectively. Therefore, the
proposed OUSDA- UL MUD needs the largest number
of CMAs among the six schemes. This is because it ex-
ploits the last user’s soft decisions to help improve the
BER performance, but the price is an increase in the
computational overhead. Meanwhile, the proposed
OGSDA-GL MUD needs fewer CMAs than the sym-
bol-based LAST MUD, but more than the user-based
LAST MUD. The linear MMSE SIC scheme requires the
second lowest amount of computation, but its BER per-
formance is the worst among the six schemes.
3
P
, T
M
PP
=2)(=4 ,=3GK
Table 1. Comparison of the computational complexity of the
proposed schemes.
MUDs Complex multiplications/additions
Linear MMSE SIC TT GKMGKM
3
)(
DD 3
)( T
GKM
Symbol-based LAST 3
1
0= )(iGKMT
T
GKM
i
User-based LAST 3
1
0= )*( TT
GK
iMiGKM
Proposed
OUSDA-UL 3
1=1=3D
K
k
G
g
Proposed
OGSDA-GL 3
1= 3D
G
g
7. Conclusions
We have investigated layered symbol detection strategies
for the uplink of a multiuser MIMO frequency-time-
domain spread MC DS-CDMA system. First, we pro-
posed a scheme called OUSDA-UL MUD, which ex-
ploits the last user's soft decisions to help mitigate the
MAI effect and improve the BER performance. Second,
to reduce the computation al complexity, we proposed the
OGSDA-GL MUD, which exploits the last group’s soft
decisions to facilitate layered symbol detection. The re-
sults of simulations and a complexity analysis demon-
strate that the proposed schemes yield better BER per-
formance gains than existing approaches, but their com-
putational overheads are modest.
8. Acknowledgements
This work was supported by National Taiwan Ocean
University of R.O.C. under contract NTOU-101-002.
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