a blind adaptive sor/jgs iterative kalman mud algorithm ...jacobi gauss-seidel (jgs) iteration...
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A Blind Adaptive SOR/JGS Iterative Kalman MUD
Algorithm for Multiple Access Communication System
Weiting Gao and Hui Li Department of Electronic Information, Northwestern Polytechnical University, Xi’an, 710129, China
Email: [email protected]; [email protected]
Abstract—Based on the fast stable convergence characteristics
of successive over relaxation (SOR) iterative and Jacobi Gauss-
Seidel (JGS) iterative, a blind adaptive SOR/JGS iterative
Kalman multi-user detection (MUD) algorithm (SJK) is
proposed for multiple access communication system as direct
sequence spread spectrum code division multiple access (DS-
CDMA) system with multi-path fading channel. The proposed
combination of blind adaptive Kalman filtering theory, SOR
and JGS iterative method can adaptively control the selection of
relaxation parameters and damping parameter, and then
effectively deal the problem as time-varying noise statistics
estimation. Compared with traditional standard Kalman filter
(SKF), fading Kalman filter (FKF) and robust adaptive Kalman
filter (RAKF) algorithm, the proposed algorithm can effectively
estimate unknown noise statistics characteristics on-line while
conducting state filtering, totally track the time-varying channel,
minimize the detection error diffusion, and thus effectively
reduce multiple access interference (MAI). Simulation results
show that the SJK algorithm is of better detection accuracy,
convergence ability, dynamic tracking capability, and lower bit
error rate (BER) performance. Index Terms
Gauss-Seidel iterative, multiple access interference, Kalman.
I. INTRODUCTION
The Kalman filtering theory, an important method in
dynamic data processing field [1], includes multi-variable
control, optimal control, adaptive control and optimal
estimation. Because of the characteristics of real-time,
fast convergence, accuracy and anti-interference [2],
Kalman algorithm is widely used in multiple-access
communication, GPS, navigation and other dynamic
monitoring fields. In the modern wireless mobile
communication field, the multiple-access system such as
Direct Sequence spread Spectrum Code Division
Multiple Access (DS-CDMA) is a popular wireless
multiple-access communication technology. But the
Multiple Access Interference (MAI) and Far-Near
Problem (FNP) severely limit the development of
multiple-access communication system. The incomplete
orthogonal of spreading waveform is the main cause
factor of MAI, no matter the multiple access
Manuscript received October 14, 2013; revised March 21, 2014. This work was supported by the National Natural Science
Foundation of China under Grant No. 61171155), the Natural Science
Foundation of Shaanxi Province under Grant No. 2012JM8010), and the Doctorate Foundation of Northwestern Polytechnical University under
Grant No. CX201215). Corresponding author email: [email protected].
doi:10.12720/jcm.9.3.226-233
communication system is asynchronous or synchronous.
When the distance between interference user and base
station is closer than expected user, the received power of
interference user would be much larger than expected
user, then the correlation between spreading sequence
and interference user would surely be much larger than
that between spreading sequence and expected user. This
would always cause a significant increase of MAI
component in the traditional Multi-User Detection (MUD)
receiver, and it may easily cause that the expected user
signal is submerged by interference user signal. Namely,
the Bit Error Rate (BER) of MUD receiver is very
sensitive to the difference between expected user and
interference user. Based on the above situation, the
traditional MUD algorithm for DS-CDMA system such
as Matched Filter (MF) and decorrelation detection
receiver cannot effectively eliminate the impact of MAI
and FNP. This makes SKF, Fading Kalman Filter (FKF)
and Robust Adaptive Kalman Filter (RAKF) the focus of
research.
The SKF algorithm describes the multiple-access
system dynamic model by state equation, describes the
multiple-access system observation model by observation
equation, and then updates the new observational date of
state parameter by the prior estimated value of parameters.
This process completely ignores the historical
observation information, only needs the status parameter
estimates value of mobile communication user [3], so it is
easy to achieve its recursive form operation. However, in
the complex multiple-access communication environment,
the dynamic noise and the observation noise are always
uncertain, so the dynamic information provided by SKF
will be easily distorted, which leads the dynamic varying
information masked by the abnormal observation
distribution and other anomaly parameters deviation. This
would cause performance degradation and divergence.
To take full advantage of real-time communication
data, the FKF algorithm employs the fading factor to
limit the memory length of Kalman filter [4], and also
expands the prior state covariance matrix as k times as
before to reduce the utilization rate of total state multiple-
access communicative information [5]. Under the
guarantee of reliable observation quantity, FKF can
achieve the optimum filter detection results [6]. However,
the adding location uncertainty and the different structure
criterions of the fading factor always cause a significant
impact on the adaptive filtering stability and the detector
efficiency [7]. FKF algorithm is difficult to distinguish
Journal of Communications Vol. 9, No. 3, March 2014
226©2014 Engineering and Technology Publishing
Successive over relaxation iterative, Jacobi —
the communication model error and the front mobile user
state estimation error. When the error in the mobile
communication user models is too serious, k is not
enough to control the error influence [8]. This may causes
lag and weakening in suppression of state model error.
The RAKF algorithm treats the multiple-access
communication model information as a whole stuff [9].
When any signal is unusual in this model, RAKF will call
a unified adaptive factor to adjust the overall impact of
state parameters. Under normal circumstances, RAKF
will firstly assess the accuracy of the forecast information
by the least squares robust solutions for current multiple-
access communication users, then suppress the detection
error of the mobile communication system by the rational
application for forecast information. RAKF can not only
adaptively estimate the covariance matrix of carrier state
forecast vector and the observation quantity weights of
any mobile communication user, but also effectively
control the influence of parameters valuation on dynamic
mobile communication system, caused by abnormal
observation and abnormal carrier state disturbance [10].
However, RAKF requires reliable state valuation and a
large number of iterative calculations to solve the
equivalent covariance matrix of the observation noise
[11]. If the state valuation is influenced by any unusual
circumstances, it will be very difficult to obtain the
reliable equivalent covariance matrix characterizing of
the observation noise level [12].
Above-mentioned Kalman algorithms for MUD of the
multiple-access fading channel transmission always cause
convergent speed instability, lack of accuracy control and
other problems [13]. The fast stable convergence
characteristics of Successive Over-Relaxation (SOR) and
Jacobi Gauss-Seidel (JGS) iteration algorithm [14] make
it possible to achieve accurate real-time control for MUD
algorithm. The SOR algorithm can effectively control the
relaxation parameters and improve the convergence
performance of JGS algorithm [15], so it can improve the
stability of blind adaptive Kalman algorithm. The
combination of blind adaptive Kalman filtering theory,
JGS and SOR method can adaptively control the selection
of relaxation parameters and damping parameter, and
then effectively deal with time-varying noise statistics
estimation problem.
In this paper, we present a blind adaptive SOR/JGS
iterative Kalman MUD algorithm to restrict the
generation and diffusion of detection error, and then to
ensure the detection accuracy through the real-time
estimation of multiple access communication system.
II. SINGNAL MODEL MUD SYSTEM
In a discrete multi-path delay base-band channel of
DS-CDMA system with K users, the spread spectrum
code of k-user in fading channel is expressed as:
1
0
1
0
( ) ( ) ( ) ( ) ( )
{ ( )} , 0, , 1
P
k k k k kp
L
k l
d i c i g i g p c i p
c i i L p
(1)
where ( )kd i is the transmitted symbol sequence, ( )kc i is
a L-length spread spectrum code, P is the equivalent
channel response maximum order of all users, and ( )kg i
is the equivalent channel corresponding.
The ith sampling of reception base-band signal is:
1
1 0
( , ) ( ) ( , ) ( )
[( 1) / ], ( , ) ( ), 0, , 1
K R
k k kk r
k k
x n i x nL i A d r i b n r
R L P L d r i d rL i i L
(2)
where kA is the received signal amplitude, R is the
length of user symbols coherence.
Then spread spectrum secondary on the chaotic
sequence makes adding and adaptive filtering for the
spread spectrum result of each user in order, the output
signal model can be formed as:
01,
1 1
0 0
( ) ( ) ( )dt ( ) ( )
( ) ( )dt, ( ) ( ) ( )dt
KT
k k k i i ik k
i i k
T T
ik i k k k
x t r t s t A b i Ab n t
T s t s t n t T n t s t
(3)
where ik is the spread spectrum inter symbol correlation
coefficient, ( )kn t is the related output of additive white
Gauss noise (AWGN), and 1,
K
i i iki i k
Ab
is MAI.
When the energy characteristic waveform is limited to
[0, ]T , the characteristic waveform is
1
,0 ,
1/2
( ) ( )
, = / , [0, 1]
C
C
N
k k l T Cl l L L
T C C
s t s P t lT
P T T T N l N
, { } (4)
where ,k ls is the normalized spectrum sequence ( 1/ 2N ),
N is the spread spectrum processing gain, and CTP is the
CT -cycle matrix code piece.
The system sum noise ( )ke t [16] is defined as:
( ) ( ) ( )
( , ) ( )k k k ke t n t h t
e n i e nL i
(5)
where ( , )e n i is the sum sequences noise component.
( )k t is the colored noise with zero mean, and kh is the
colored noise intensity.
At the receiving terminal, the received signal obtained
from adaptive filter and BPSK modulate is equivalent as
1
1
( ) [ ( ) ( )
( )]cos( ) ( )
1, 1 , [ , ( 1) ], 1
K
k k k kKk i
k k Ck kk
k k
r t A b i s t iT
p t iT t e t
b t iT i T p
(6)
where ( )kb i is the signal transmitting symbol, kp is the
secondary spread spectrum waveform, T is the bit
interval, k is the time delay, and Ck is the adaptive
weight vector of filter unit.
Journal of Communications Vol. 9, No. 3, March 2014
227©2014 Engineering and Technology Publishing
Supposing the 1-user is the expected user, the Lth
sampling of the kth symbol period on Eq. (2) is a 1L
dimensional vector, and the initial weight vector is . So,
the output scalar of FIR transversal filter is as follows:
T1 K
1 int int
T T( ,0) ( , 1) 1 1 (0,0) 1 (0, 1)
H 2 T( ,0) ( , 1)
( ) ( ), { (0) | 0}
( ) ( ) ( ) ( )
[ | , | ] , [ | , | ]
[ ( ) ( ) ] , ( ) [ | , | ]
P P
n n L L
e L n n L
y k k
k b k k k
x x d d
E n n n e e
x
x Ad D d e
d
e e I e
(7)
where intD is the MAI interference matrix, intd is the
interfering symbol vector and ( )ke is sum noise vector.
Set a L-dimensional vector ( )nf as decision vector
for the expected user, so the linear MUD model is:
ˆ ( ) sgn( ( ), ( ) )kb n n n f x (8)
In traditional DS-CDMA system, the long spread
spectrum sequence cycle L satisfies / 1L N Q , by
replacing ( )k ks t iT by ,( ) ( )Qk i ks t iT , the
received signal energy characteristic waveform model is
1
,( ) ,[ / ]
0 [0, ]
( ) ( )Q c
N
k i k i Q N l T c
l l L L N
s t s P t lT
, ,
(9)
where ( )Qi is modi Q operation, [ ] is the end function.
The ( , )thi k element of time-shift characteristic
waveform cross-correlation matrix is defined as:
, ( ) ( ) ( )dt ( )i k i i k k ikl s t s t lT l
R (10)
if { 1,0,1}l , then ( ) 0l R , T( ) ( )l l R R .
Set r is the output vector of L-dimensional match
filter in symbol interval T , y RAb e , and the
received signal sampling rate is equal to chip rate. Thus,
the vector form of asynchronous DS-CDMA system base
band received signal model can be formed as:
T 2 T
1
T 1 T1 1
, { } , [ ]
diag[ , , ] , [ , , ]
K
k k k k
k
k kK k L
E = E
= L p p
r A b s p e ee R R pp
A A A p
(11)
where e is the covariance matrix of ( )ke t , 2 is the
noise variance, and R is a strictly upper triangular matrix.
Supposing k is the time delay of the kth user, in any
relevant transmission interval, if max{ }k T , estimating
the bit symbols of transmitted user signals, the
asynchronous multiple-access system with K users could
be equivalent to a synchronous multiple-access system
with 2 1K users. If 2 1K L and all spreading code of
the 2 1K users are linearly irrelevant, then the
calculation of asynchronous multiple-access system is
similar to synchronization multiple-access system.
III. BLIND ADAPTIVE SOR/JGS-KALMAN ALGORITHM
The JGS iteration is an established iterative method
based on the GS and Jacobi iteration scheme [17]. JGS
can improve the convergence speed of adaptive MUD
algorithm, but its global convergence performance is so
unstable, which may easily cause detection error
expansion. So the introduction of SOR is to control the
convergence performance of JGS. The SOR/JGS-MUD
method can be equivalent to solve a linear equations
model [18] as:
1 1 1 1( , , ) , ., ( , , )k k k kA x x b A x x b Ax b (12)
where A is the kth order reversible matrix, b is k-
dimensional column vector.
The SOR iteration scheme can be regarded as a
weighted average between the calculated value of GS
iterative format and the approximate solution ( )kx of Eq.
(12). Normally, the value of k is generally large [19], so
it is necessary to improve the iteration of adaptive MUD
algorithm to reduce computational complexity. Let
= ( ) A I I A , the equivalent transformation of Eq. (12)
is ( ) x I A x b . Let B I A , f b , the simple
iterative format of Eq.(12) is x Bx f . Assume the
main diagonal elements of reversible matrix ( )ij k ka A =
satisfy 0iia . Let 11=diag( , , )kka aD is the diagonal
matrix, then make dividing calculation for A as:
( ) A D D A= (13)
because x can be equivalent to 1 1= ( ) x D D A x D b ,
so the Jacobi iterative format of Eq. (12) can be formed
as:
1
1
( )
=
=
B D D A
f D b (14)
Supposing U is an upper triangular matrix, L is a
strictly lower triangular matrix, make dividing calculation
for x Bx f as B U L . So x Bx f is
equivalent as
1 1( ) ( ) x I L Ux I L f (15)
Let the GS iterative format is 1( )GS=B I L U and
1( )GS=f I L f , the linear equations solution of k-user
can be equivalent as:
( 1) ( 1) ( )k k k f x Lx Ux (16)
the basic iterative on Eq. (12) is ( 1) ( )k k x Bx f ,
seeking a vector ( 1)k
j of ( 1)k
x by parallel iterative to
replace ( )k
j for the subsequent iterative processing, the
Jacobi iterative condition of x Bx f is deduced as
J J x B x f , then the JGS iteration form of Eq. (15) is
JGS JGS x B x f . Because the main diagonal elements
of JB are constant zero, the calculation amount of Eq.
Journal of Communications Vol. 9, No. 3, March 2014
228©2014 Engineering and Technology Publishing
(16) can be reduced significantly. The JGS convergence is reached when A satisfies row (column) strictly diagonally dominant or row (column) weakly diagonally dominant and irreducible [20]. In summary, taking Jacobi
iterative matrix JB and Jf corresponding to B and f ,
respectively, and making dividing calculation for JB as
J B R L [21], setting the relaxation parameter is
when 0 , we have
1 1
1
1
[ ( ) ]
( ) [(1 ) ] ( )
( ) 0, ( )
( ) [(1 ) ]
J
J
J J
x x Lx R I x f
I L I R x I L f
Lx R I x f f I L f
B I L I R
(17)
the equivalent iterative format of SOR is expressed as
( 1) ( ) ( 1) ( )[ ( ) ]k k k kJ x x Lx R I x f (18)
The convergence of SOR iterative depends on the
choice of relaxation parameter . For arbitrary (0)x and
f in the general iterative process, when ( ) 1 B , the
iterative sequences ( ){ }kx generated by ( 1)k
x converges
to a specific value x , so:
1det det( ) det[(1 ) ] (1 )
(| det |) ( ) 1
(| det |) | 1 | | 1 | 1 0 2, ,
n
n
n
B I L I R
B B
B
(19)
Modulation
unit 1
Modulation
unit 2
Modulation
unit K
Spread spectrum 1
Spread spectrum 2
Spread spectrum K
Sum
noise 1Adaptive selection
Adaptive selection
Adaptive selection
Kalman
1
Kalman
2
Kalman
K
Damping
parameter
adaptive
adjustment
nuit
Sum
noise 2
Sum
noise K
1
2
K
b n
b n
b n
1
2
K
c i
c i
c i
1
2
/
/
/ k
S J
S J
S J
,x n i
1
2
K
1
2
ˆ
ˆ
ˆK
b n
b n
b n
Blind
adaptive
matched
filter
detection
unit
1
2
K
e t
e t
e t
,( )Qk is
r
1
2
K
r t
r t
r t
+
Fig. 1. The structure of SOR / JGS-Kalman MUD detector
When 1 , SOR can be equivalent to JGS, so a
proper is important to make SOR convergence faster
than JGS.
When the channel response appears suddenly change
or some new co-channel users added to the same channel,
it usually needs to resend the training sequence of
traditional adaptive algorithm. This may easily cause a
great waste of spectrum resources. In addition, the
random recursive calculation of traditional adaptive
MUD algorithm for multi-access communication system
has defected as slow convergence and large detection
errors. Therefore, it needs to study the blind adaptive
MUD algorithm, which uses the observational data only
and without the need for training sequences. In order to
solve divergent or low convergent stability and low
testing accuracy lead by standard Kalman detector, the
structure of SOR/JGS-Kalman detector is shown in Fig. 1.
The introduction of blind adaptive parameter selection
unit can precisely adjust the values of relaxation
parameter and damping parameter, thus simplify iteration
process. Set the initial vector for (0)
x , let Hermite matrix
H as computing approximate transfer matrix, is error
control limit parameter, so the next step approximate
solution is constructed as:
( ) ( ) ( )
( )1
( ) ( ) '( )( )
|| ( ) || , ( ) ( ( ),..., ( )) 0
k k k
knf f
F x F x F x x x
F x F x x x (20)
When the Jacobi matrix ( )'( )kF x deduced by ( )F x
at ( )kx is a nonsingular matrix, it can be expressed as
( 1) ( ) ( ) 1 ( )[ '( )] ( )k k k k x x F x F x (21)
Given initial vector (0)x , the iterative computation is
done for Eq. (21). If ( )'( )kF x is a singular matrix, we
introduce damping parameter k :
( 1) ( ) ( ) 1 ( )[ '( ) ] ( )k k k kk
x x F x I F x (22)
In the nth step iteration, we have
( ) ( | 1) ( ) ( )
( ) ( ) ( ) ( | 1) ( 1)
( | 1) ( 1) ( 1)
k k
H
k
k k
n n n n n
n n n n n n
n n n n
T
x F r
s
(23)
1
( ) ( | 1) ( )
[ ( ) ( | 1) ( ) ( 1)]
( | 1) ( 1) ( 1)
( ) [ ( ) ( )] ( | 1)
H
HR
n n n n
n n n n n
n n n n
n n n n n
K P F
F P F R
P P S
P I K F P
(24)
1 1
1
T T1
( ) (1 ) ( 1) [ ( ) ( 1)]
( ) (1 ) ( 1)
[ ( ) ( ) ( ) ( ) ( ) ( 1)]
n n k k
n
n
n d n d n n
n d n
d n n n n n n
s s
S S
K K P P
(25)
Journal of Communications Vol. 9, No. 3, March 2014
229©2014 Engineering and Technology Publishing
T1 1
H
( )T ( ) 1 ( ) ( ) ( )T1
( ) (1 ) ( 1) [ ( ) ( )
( ) ( | 1) ( )]
( ) ( )
n n
k k k k kk k k
n d n d n n
n n n n
Q Q
F P F
H H y y s H y y
(26)
1
( 1) ( ) ( )
( ) ( 1) ( )1 1
( ) ( 1) ( ) ( ) ( 1)
(1 ) / (1 ),0 1
( )
, , 1
( ) ( ),|| ||
nn
k k kk
k k k
k k k k k
d b b b
=
x x H F x
s x x s s
y F x F x x x
(27)
where (1,0) T I , Q is the received signal covariance
matrix, 1nd is the forgetting factor, and 0 H I .
IV. SIMULATION ANALYSIS
In each of the simulation step (1s), set each
communication user sends an effective information
sequence in a multi-path channel DS-CDMA system
(multi-path number 31P , users number is K), and use
m sequences (sequences number is K, 25N ) to make
independent spread spectrum and plus noise processing
[22], while make adding processing according to user's
order respectively. In this process, supposing the kth user
to be the minimum power user, every bit energy is 2 / 2kA T . All of these K users send asynchronous signal in
the S-band transmission asynchronous after double
spread spectrum processing. Then, the information
symbols are de-spread. Finally, through the integral
decision, the symbol recovery processing of these K users
(symbol number is equal to transmission time) is
completed at receiving and sending end by the same Km
sequence. The nth iterative output SIR of system is as
2 T
T
2 T 2
2 T 2 2 T
2
{ ( ) }SIR
var{ ( ) }
( ( ) )
( ( ) ) ( ) ( )
k
k
k k k
K
k k k k k
k
E n
n
A n
A n n n
c r
c r
c p
c p c c
(28)
A. Static Performance Comparison Analysis
Set difference multi-user power in the whole
communication process with no changes in the number of
users, this simulate the static environment to detect the
static SIR and Excess Output Energy (EOE) performance
of SJK, RAKF, FKF and SKF algorithm. EOE is defined
as the excess energy of transmitted user signal in order to
achieve single-user error performance for MUD
algorithm in the mobile communication system [23],
namely the more stable and rapidly for the EOE decay,
the more stable the system transmission performance is.
As shown in Fig. 2: Under the static transmission
condition, when the iteration number is greater than 400,
the SIR performance of SJK and RAKF algorithm are
significantly better than FKF and SKF algorithm.
Simultaneously, the SIR performance of SJK algorithm is
always better than RAKF algorithm. These mean the SJK
algorithm has faster convergence rate and stronger multi-
user interference inhibition ability than other three
algorithms under static transmission condition.
Fig. 2. The static SIR performance of expected user
Fig. 3. The Static EOE performance of expected user
As shown in Fig. 3: Under the static transmission
condition, when the iteration number is greater than 200,
the EOE curve of SJK algorithm is always below 0.1dB.
When the iteration number is greater than 600, the EOE
curve of SJK algorithm is always below 0.05dB and in
the subsequent process is close to the theoretical value of
0dB. The EOE curve of RAKF also achieves a stable
attenuation but basically greater than 0.1dB throughout
the transmission process. The same situation EOE curve
of FKF and SKF algorithm are both always in unstable
change and basically greater than 0.15dB, when the
iteration number is greater than 200, the EOE curve of
FKF and SKF algorithm both do not achieve a stable
attenuation, namely, FKF and SKF algorithm occur
detection error diffusion in case of no outside interference.
These mean the SJK algorithm has better convergence,
stability and interference rejection capability than other
three algorithms under static transmission condition.
B. Dynamic Performance Comparison Analysis
Set a relatively open detection environment based on
the existing static environments, namely, add a new set of
arithmetic distributed large power users when the
iteration number is 600, these added users can be
regarded as the external interference component. Then
withdraw the new added users and a set of existing users
Journal of Communications Vol. 9, No. 3, March 2014
230©2014 Engineering and Technology Publishing
when the iteration number is 1200, namely, here is a
interference range between 600 and 1200. This program
simulates the dynamic communication environment.
Fig. 4. The dynamic SIR performance of expected user
As shown in Fig. 4. When the iteration number is 600,
namely the new interference group is added to the
communication system, the SIR curve of SJK and RAKF
algorithm just appear little bit down peak and recover fast
at a very high speed before the removal of interference.
Simultaneously, the SIR performance of SJK algorithm is
always better than RAKF algorithm. But the SIR curve of
FKF and SKF algorithm appear great attenuation
volatility and even become unstable convergence after the
removal of interference. These mean the SJK algorithm
has better dynamic tracking performance than other three
algorithms under dynamic transmission condition.
Fig. 5. The dynamic EOE performance of expected user
As shown in Fig. 5. Under the dynamic transmission
condition, when there is new interference group added in
the communication system, the EOE curve of SJK just
appear a very brief fluctuation and recover attenuation
states quickly before the interference been withdrawn, the
EOE value of SJK algorithm is always below 0.05dB, and
later close to 0dB. Simultaneously, the EOE curve of
RAKF also appear a very brief fluctuation and recover
attenuation states, but appear a fluctuation after the
removal of interference, the EOE value of RAKF
algorithm is basically greater than 0.1dB throughout in
the end. The EOE of SKF appears serious divergence
after the interference brought into the system and
ultimately failed to converge. The EOE of FKF does not
appear serious divergence, but also ultimately failed to
converge. These mean the SJK algorithm has better
interference rejection capability, convergence stability
and MUD ability than other three algorithms under
dynamic transmission condition.
C. Detection Accuracy Performance Analysis
Using spreading sequence adapts GOLD sequence, set
step size of Adaptive BPSK signal source is 0.0005 ,
the sampling rate is equal to the chip rate, the difference
power value between the maximum user and the
minimum user is 6dB, the BER is defined as:
2( ) ( )k kP Q e (29)
where ( )ke is the equivalent energy of the k-th user.
Fig. 6. The static BER performance of expected user
As shown in the Fig. 6. Under the static transmission
condition, the BER values of SJK RAKF and FKF
algorithm are all below 310 , the BER values of SKF
algorithm is greater than 210 . In addition, the BER value
of SJK algorithm is significantly lower than those of
RAKF, FKF and SKF algorithm. The BER curve of
expected user by SJK algorithm declines faster than
RAKF, FKF and SKF algorithms in whole detection
process. These mean the SJK algorithm has better BER
performance and MAI rejection ability than other three
algorithms under static transmission condition.
Fig. 7. The dynamic BER performance of expected user
Journal of Communications Vol. 9, No. 3, March 2014
231©2014 Engineering and Technology Publishing
As shown in the Fig. 7. Under the dynamic
transmission condition, all curves have shown a
significant change, the BER performance of SJK is
closest to the static level. The BER values of RAKF, FKF
and SKF algorithm are all greater than 310 . The BER
curve of expected user by SJK algorithm declines faster
than RAKF, FKF and SKF algorithm in whole detection
process. These mean the SJK algorithm has better BER
performance and MAI rejection ability, namely the SJK
detector can effectively improve the detection accuracy
and inhibit MAI under dynamic transmission condition.
Fig. 8. Error mean square of SJK, RAKF, FKF and SKF algorithm
Fig. 9. The static path loss performance
Fig. 10. The dynamic path loss performance
As shown in Fig. 8. The decision error mean square
value of SJK always maintain a steady in whole
processing and close to 410 in the end. Simultaneously,
although RAKF reaches the same error level with SJK in
the later stage, but the attenuation of RAKF is slower
than the SJK. The decision error mean square of FKF
recover very slowly at a low speed and achieve
convergence in unsatisfactory an error level as value of 310 to 210 . The decision error mean square of SKF does
not achieve effective convergence in whole processing.
These mean the SJK algorithm has higher accuracy than
other three algorithms.
As shown in Fig. 9 and Fig. 10. The path loss curves
of SJK algorithm are able to remain stable, in either static
or dynamic conditions. By contrast, the same
performance of RAKF, FKF and SKF algorithm all
appear different degrees change. These mean the SJK
algorithm has higher transmission stability than other
three algorithms no matter under static or dynamic
transmission condition.
V. CONCLUSION
The SJK MUD algorithm can make full use of user
observation data and effectively real-time estimate the
statistical characteristics of time varying noise while
conducting state filtering. Because SJK algorithm
satisfies the basic conditions of adaptive multiuser
detection, namely, without having to inform the system
priori information in whole processing, so it is easier to
implement. This algorithm has characteristics as good
tracking performance, high detection accuracy, fast
convergence and stability of filtering process. Simulation
results show that, the SJK algorithm outperforms the
RAKF, FKF and SKF algorithm in term of SIR, EOE and
BER performance, detection accuracy control capability,
dynamic tracking capability, convergence and
transmission stability and path loss performance. As
shown in Fig. 4 and Fig. 5, when the new interference
group appears in the communication system, although the
dynamic SIR and EOE performance of SJK algorithm are
significantly better than RAKF, FKF and SKF algorithm,
but at the moment of iteration number is 600, the
performance curve of SJK algorithm also appear
significant change in a very short period. So the SJK has
a good global convergence, but for the situation of
mutation, the interference is still slightly deficiencies to
be improved. Therefore, the blind adaptive SOR/JGS
iterative Kalman MUD algorithm is an efficient MUD
scheme for the multiple-access communication system.
ACKNOWLEDGMENT
This work was supported in part by a grant from the
National Natural Science Foundation of China under
Grant No. 61171155), the Natural Science Foundation of
Shaanxi Province under Grant No. 2012JM8010), and the
Doctorate Foundation of Northwestern Polytechnical
University under Grant No. CX201215).
Journal of Communications Vol. 9, No. 3, March 2014
232©2014 Engineering and Technology Publishing
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Weiting Gao was born in Inner Mongolia,
China, 1984. He received a bachelor degree in
Electrical Information (EI) in 2007 from the
Northwestern Polytechnical University (NPU)
in the China, a Master degree in Circuits and
Systems (CS) in 2011 from the Northwestern
Polytechnical University (NPU) in China.
He is a Ph.D. student in Northwestern
Polytechnical University. His research interest
is the multi-user detection techniques of
wireless mobile communication system
Hui Li was born in Shaanxi, China, 1968. He
received a bachelor degree in Electrification
Professional (EP) in 1991 from the
Northwestern Polytechnical University (NPU)
in the China, a Master degree in Circuits and
Systems (CS) in 1996 from the Northwestern
Polytechnical University (NPU) in the China,
a Doctor degree in Systems Engineering (SE)
in 2006 from the Northwestern Polytechnical
University (NPU) in China.
He is a Professor. in Northwestern Polytechnical University. His
research interests are communication signal processing and radar signal
processing.
Journal of Communications Vol. 9, No. 3, March 2014
233©2014 Engineering and Technology Publishing