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: xiao_gao_123@hotmail.com; lh@nwpu.edu.cn

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: xiao_gao_123@hotmail.com.

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

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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