An Improved MMSE-MUD Algorithm for MAI Hui LI :1st
Weiting GAO :2nd
School of Electronics
School of Electronics
School of Electronics
Information
Information
Information
Northwestern Polytechnical
Northwestern Polytechnical
Northwestern Polytechnical
University
University
University
Xian
China.
Xian
[email protected]
Mengying REN :3rd
China.
Xian
[email protected]
Abstract˖Multiple access interference˄MAI˅and related Near-far Problem˄FNP˅,limit the development of the Code Division Multiple Access˄CDMA˅system. The classic Minimum Mean Square Error-MUD˄MMSE-MUD˅algorithm can effectively suppress MAI. But too much error will be introduced into the approximate estimation and its computation complexity is too high. To solve this problem, this paper presents an improved MMSE-MUD algorithm. This improved algorithm significantly reduced the error been introduced into approximate estimation and computational complexity. Also has excellent convergence and BER performance. The simulation results show the effectiveness of this improved MMSE-MUD algorithm.
China.
[email protected]
e (σ ) · nk (σ ) = lim§¨ k Ek ¸¹ σ → 0©
(2)
C. Near-far Resistance (NFR): AME of all users’ energy in the worst case:
η k , j = inf η k
(3)
E j [i ]> 0 ( i , j ) ≠ ( 0, k )
Keywords˖MAI,MUD,MMSE-MUD,FNP
where, η k , j is NFR to i-Bit of k-user’s.
I. INTRODCUTION DS-CDMA system is a multiple access methods. This approach support high transfer rates and improve the bandwidth utilization [1]. But MAI,ISI due to channel and spreading code in not entirely a result of orthogonal and FNP due to the suppression of strong signal to weak signal for different users’ power[2]. All of these severely limit the development of CDMA system. MUD technology is designed to study how to effectively restore the original information loaded by signals of the users with there are MAI,ISI and FNP[3] .
received by i-Bit of the j-user’s. III. IMPROVED MMSE-MUD ALGORITHM A. Classic MMSE-MUD Algorithm [5] Assuming a DS-CDMA system. The basic idea of MMSE-MUD is to find the estimator of a random variable W based on observation value Z .Common method of the estimation theory is in order to find a transformation function
∧
Assuming the case of noise variance for k users’ is σ in Additive White Gaussian Noise˄AWGN˅channel. There are three performance standards of MUD[4] as follows: 2
∧
b k = sgn(ckT y ) to be the estimate of the k-user’s emission characters, where y is match filter output vector as: y = RAb + Z .
A. Bit Error Rat (BER):
ek (σ )
σ2
)
(1)
MMSE-MUD is designed to find a linear transformation ck of any user to minimize MSE between the transmit signal bk and the estimate of the k-user’s, as follows:
B. Asymptotic Multi-user Efficiency (AME): The standard to measure the influence of BER to the desired users’ by the interference users’. Defined as the limits of multi-user efficiency within the high SIR:
978-1-4244-9763-8/11/$26.00 ©2011 IEEE
∧
W(Z ) to make the mean square error of
E[(W − W ( Z ))2 ] minimum. View of linear estimation: Make a linear transformation ck of k users in the channel, as
II. PERFORMANCE STANDARDS OF MUD
Pk (σ ) = Q(
E j [i ] is energy
ck
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{
= arg min E ( bk − c k
ck , y
)} 2
(4)
received signal r is as follows:
Output decision is bˆk = sgn( ck , y ) .For all K users, this
~
problem is change to find a K × K matrix C = [c1 ,..., cK ] to make the error cost function under the sense of mean square minimum, as: T
T
ٛ
ªΛs ... 0 º H ªUs º « . »» « H » R = U...UH = [Us Un ] « . U «¬0 ... Λn »¼ ¬« n ¼»
(5)
+ C E { yy T }C T
error vector covariance matrix is as follows: cov(b − Cy ) = [ I + σ −2 ARA]−1 _
_
where, Λ s = diag (λ1䯸...䯸
(6)
+ (C − C )( RA 2 R + σ −2 R )(C − C )T
λk ) contains K
(13)
largest Eigen
value in descending order of matrix R. And Λ n = σ I N − K 2
_
where, C = A [ R + σ A ] . −1
−2 −1
2
2
contains N - K mini-mum eigenvector σ ,at the same time 2
T
For min{ x } = min{tr ( xx )} ,so that:
min J ( C ) = min{tr[cov ( b − Cy )]} d
tr[cov ( b − Cy )] = 0
Set as: dC MMSE-MUD is as follows:
U s = [u1䯸...䯸 uK ] contains the features of Λ s corresponding to the amount of orthogonal, U n = [u K +1䯸...䯸 u N ] contains the features of Λ n corresponding to the amount, and expand
(7)
to be the signal subspace.
, so the ultimately derived
Set
C MMSE = A−1 ( R + σ 2 A−2 )−1
multiuser detector weight vector as ck ( k = 1䯸 2䯸...䯸 K ) ,filter output vector is y ,set 1-user as desired user, desired user’s output decision
(8)
∧
MMSE-MUD output decision is as follows: ∧
b k = sgn(
where,
(12)
Eigen value decomposition of R is as follows:
T
co v( b − C y ) = E { b b } − E { b y } − C E { yb }
ٛ~
R = E[rr H ] = S A2 S H + σ 2 I N
A1
AK
linear
T
is b1 = sgn(c1 y ) .The improved MMSE-MUD is as follows:
1 ([ R + σ 2 A−2 ]−1 y )) Ak
σ2 σ2 σ 2 A−2 = diag{ 2 䯸...䯸 2 }
the
ٛ~T ~ٛ
ٛ~
~
ٛ
~
ٛ
⋅ U s YC ( M )−1 U sH S k
. Optimal solution where, C (M ) =
meet the minimum cost function J ( C ) = E{ b − Cy } is 2
as follows:
C opt = [ R + σ 2 A−2 ]−1
−1
ٛ~H ~ٛ
C k new = [ S k U s YC ( M ) U s Sk ]−1
(9)
M
¦α n −1
M −n
(14)
r (n )r (n ) ( M is the number of H
individual user real-time transmission of date, (10)
~H
α (0 ≤ α ≤ 1)
~
is the forgetting factor, Y (M ) = U s C (M )U s .
B. The System Model of the Improved Linear MMSE-MUD algorithm
Because this improved algorithm determine U s = [u1䯸...䯸 uK ] without
As in a multi-channel DS-CDMA system with K users. Vector model of DS-CDMA baseband signal reception[6] [7] is as follows:
Λ s ,so this improved algorithm does not need to estimate signal Eigen value matrix Λ s in the detection process.
䱊
ٛ
r = S Ab + σ n 䱊
ٛ
䱊
matrix
Thus reduce the errors introduced. Then reduce the algorithm complexity and improve algorithm performance.
(11)
䱊
S = [ sٛ1 ,..., sٛk ] is the normalized spreading code vector of k-user’s Sk =[sk,1, sk,2,..., sk,L ] , hk =[sk,1, sk,2,..., sk,L ] Where,
only need to Eigen value
IV. SIMLATION A. The Detection of SIR, Convergence and the Interference Suppression In an AEGN background synchronization multipath channel DS-CDMA system[9].Set the multipath number P = 3 , source adapts 2 PSK signal, spread spectrum
䱊
sٛk =Sk hk , , A = diag ( A12䯸...䯸 AK2 ) . L is multi-channel
number, n is AWGN plural vector. Covariance matrix of
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gain N = 31 ,spreading sequence adapts GOLD sequence, modulation scheme BPSK , the sampling rate equal to the chip rate. Output SIR in the nth iteration is defined as follows: ~
SIR =
1 N0
N0
¦ n0 =1
C 1H ( n ) s 1 ~
C 1H ( n ) s k
2
B. Detection of Algorithm Accuracy In Figure3 and Figure4:As under the same background noise, all levels of judgment error probability of the improved algorithm attenuate fast with the increase of SNR and completely disappear before the completion of detection. But the all judgment error probability changes of original algorithm is always unstable. This shows the improved algorithm has a higher detection accuracy.
2
+ C 1H ( n )
2
(15)
1 ˅ :Set the 1-user in channel as the desired user, SNR = 20dB .In Figure1:The improve algorithm has a better SRI performance. SNR of the improved algorithm is significantly higher than the original algorithm when iteration number is greater than400.This shows the improved algorithm has more interference suppression.
Fig.3 Error probability decay of the improved algorithm
Fig.1
Detection of SIR performance
2):In Figure2:The changes of user residual energy to the improved algorithm is close to zero of theoretical value when the iteration number is greater than 1000 in same background noise. But changes of original algorithm is always unstable and essentially higher than 0.2dB.This shows the improved algorithm has a faster convergence rate.
Fig.4 Error probability decay of the original algorithm C. Detection of BER performance
Fig.2
Set an AWGN background DS-CDMA system with users number of K(K=10). Each user sends a message symbol in every simulation step (1s), make spread spectrum processing on the information symbol of these 10 users by 10 m sequences( P = 31 ). Then merge the sum and add AWGN. Make dispreading processing on the information symbol by the same 10 m sequences at the receiving end and the sending end. Then make integral and decision processing. Ultimately, complete recovery 10 users’ symbol. The send symbol transmission time is equal to the send number of symbol.
Detection of residual energy
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In Figure5: The improved algorithm has a better BER performance when the power of users’ disordered arrangement. In Figure6: The improved algorithm also has a better BER performance when users’ power is according to the ascending to arrangement.
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2008.01. Li XˈFan H. Direct Blind Multiuser Detection for CDMA in Multipath
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without Channel Estimation [J]. IEEE Transactions on Signal Processingˈ2001ˈ49(1)˖63-73. Steven M.Kayˊ Fundamentals of Statistical Signal Processing Volume
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I˖Estimation Theory and Volume II˖Detection Theory[M]ˊPublishing House of Electronics industryˈ2003 Georgios B.GiannakisˈYingbo HuaˊSignal Proccessing Advances in
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on Improved Subspace Track Algorithm [J]. Journal of Northwester Polytechnical Universityˈ2008ˈ26(1): 53-56. ˄In Chinese˅ William HˊTranterˈKˊSam ShanmuganˈTheodore SˊRappaportˈ
[9]
Kurt LˊKosbarˊPrinciples of Communication Systems Simulation with Wireless Applications [M]ˊChina Machine Pressˈ2005 Hui LiˈJue WangˈHongmei Yu. Accelerated Subspace Tracking
Fig.5 Detection of BER performance1
Method and Its Applications to Multiuser Systems [J]. CNKI˖SUN˖ DZXU.0.2007-12-026. ˄In Chinese˅
Fig.6 Detection of BER performance 2 V.CONCLUSIONS This paper put forward a new kind of improved MMSE-MUD algorithm based on the original MMSE-MUD algorithm. The improved MMSE-MUD algorithm has better advantages than the original algorithm not only in performance of SIR and BER, and also in the convergence performance of algorithm, the detection accuracy and the interference suppression. So this improved algorithm is an effective algorithm. THANKS A. China Aerospace Science and Technology Corporation Aerospace Science and Technology Innovation Fund(NO. &$6& ) funded project. B .2010 Graduate Student of Northwestern Polytechnical University Venture Seed Fund (NO.= ) funded project.
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