Technical University of Ko šice, Slovakia

Technical University of Košice, Slovakia

Sub-Optimum MSF-MUD for CDMA Systems

Dušan Kocur, Jana Čížová, Stanislav MarchevskýDepartment of Electronics and Multimedia Communications

Faculty of Electrical Engineering and InformaticsTechnical University of Košice, Park Komenského 13, 041 20 Košice

Slovak RepublicE-mail: [email protected], [email protected], Stanislav.Marchevsky@

tuke.sk

COST 289: Antalya, July 6-8, 2004 2 of 29

1. Introduction • microstatistic multi-user receiver (MSF-MUD),

• microstatistic filter (MSF),

• threshold decomposer (TD) level estimation,

• scanning method (SC-M),

• genetic algorithm based method (GA-M),

• method of cumulative distribution function (CDF-M),

• computer experiments,

• conclusions.


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2. MSF-MUD receiver

• MSF-MUD is the promising member of the nonlinear single–stage multi-user receivers' (NSS–MUD) family,

• NSS-MUDs approximate the nonlinear boundary of the decision regions better than the linear receivers,

• the output of the NSS-MUD is taken as the sign of the nonlinear transformation of the output of a bank of the matched filters (BMF),

• the nonlinear transformation is done by multi-channel conventional microstatistic filter (M-CMF).

COST 289: Antalya, July 6-8, 2004


4 of 29COST 289: Antalya, July 6-8, 2004

Fig. 1: MSF-MUD receiver.

2. MSF-MUD receiver (cont.)


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3. M-CMF

Fig. 2: Blok diagram of the M-CMF.



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3.1 Threshold decomposer

01

,1 1

1

i ifor y n l

j

i j i i i i iy n y n l for l y n l jj j

i i i il l for l y nj jj

,

0, , 1,2, , , 1,2, ,i j i

y n l i M j LL

01

,1 1

1

i ifor y n l

j

i j i i i i iy n y n l for l y n l jj j

i i i il l for l y nj jj

,

0, , 1,2, , , 1,2, ,i j i

y n l i M j LL

l1=-0.5, l2=0.5

Fig. 3: TD input – output relations.



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4. M-CMF and MSF-MUD



M-CMF output:

MSF-MUD output: ,

where unbiased M-CMF output,

impulse responses of the Wienner filter (WF),

outputs of the TDi.

( ) ( , ) ( , )( ,0) ( , )

1 0

ˆ ( ) ( ) ( ) ( ),M L N

k i j i jk k l

i j L l

d n h n h n y n l

ˆ ˆ kkb n sign d n

( ,0) ( )kh n( , )( , ) ( )i jk lh n

( )ˆ ( ) ( ) ( ) ( ) ( ),k T Tk kd n n n n n H Y Y H

( , ) ( )i jy n

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5. The M-CMF design procedure


• minimum mean–square error criterion:

where

threshold value vector,

desired signals.

22 ( ) ( )ˆ( ( ), ) ( ) ( ) ( ) ,k k

k kMSE n E e n E d n d n H L

(1) (2) ( ) TT T M T L L L L

( ) ( )kd n


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Step 1 – threshold values estimation (SC-M, GA-M, CDF-M).

Step 2 – optimum coefficients estimation: ,

...cross–correlation vector of the desired signals and the signals at the output of the TDi,

... cross–correlation function of the signals at the output of the TDi ,

Step 3 – evaluation of the cost function of MSF-MUD (minimum BER).

1optk kn n nH R P

k nP

nR

5. The M-CMF design procedure – basic principle



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6. TD level estimation



• optimum TD levels satisfy the condition:

where

• assumptions:

0, ,MAXl J Y

( , )max ( ) .i jMAXY y n

( ) ( )2 1 1 2 1,2, , ,

Ti i ii il l l l for i M L

( ) ( )1 1 1 1 1,2, , ,i il l l and l l l for i M

( ) ( )2 2 2 2 1,2, , .i il l and l l for i M


6. TD level estimation (cont.)


Fig. 4: Histogram of the absolute values of the BMF outputs. J interval estimation.

Fig. 3: BER vs. threshold level.


6.1 Scanning method (SC-M)


• are taken from J by uniform sampling with step ,

• possible values can be find,

• the huge number of M-CMF has to be designed (usually several thousands).

ikl

l( / )round J l

Fig. 5: BER vs. Eb/No.


6.2 Genetic algorithm based method (GA-M)

• multi–dimensional and stochastic search method for non-linear optimization task,

• sophisticated scanning of interval J,

• maximum number of M-CMF design is 200.

Fig. 6: BER vs. Eb/No



6.3 Method of cumulative distribution function (CDF-M)

• application of CDF function of absolute values of outputs of BMF,

• CDF:

• only 1 M-CMF design.

Fig. 7: BER vs. Eb/No

Pr ,i ik LEVELy n l P


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7. Computer experiments

• synchronous DS–CDMA base-band transmission system in the AWGN channel,

• first 3 experiments are deal with MSF-MUD design procedure,

• next 9 experiments are deal with MSF-MUD properties.




7. Computer experiments (cont.)

Number of users 2

Number of Transmitted bits 1 000

Spreading codes Gold

Number of chips for 1 period

31

Environment AWGN

Number of threshold levels 4

Fig. 8: MSF-MUD.BER vs. Eb/No vs. different values of PLEVEL.



7. Computer experiments (cont.)Number of users 30

Number of transmitted bits

10, 100, 200, 300, 500, 1 000, 2 000, 5 000,

7 000



31

Environment AWGN

Number of threshold levels

4Fig. 8: MSF-MUD. BER vs. Eb/No vs. different length of training sequences.





Length of training sequence

300


10 000



31

Environment AWGN

Number of threshold levels

4Fig. 9: BER vs. Eb/No for MSF-MUDs,

BMF, D-MUD and MMSE-MUD.




Number of users 2


10 000



31

Environment AWGN

Near-far effect 1:1

Fig. 10: BER vs. Eb/No for MSF-MUD, BMF, D-MUD, MMSE-MUD and ML-

MUD.




Number of users 10


10 000



31

Environment AWGN

Near-far effect 1:1

Fig. 11: BER vs. Eb/No for MSF-MUD, BMF, D-MUD and MMSE-MUD.




Number of users 20


10 000



31

Environment AWGN

Near-far effect 1:1





Number of users 30


10 000



31

Environment AWGN

Near-far effect 1:1





Number of users1, 2, 5, 7, 10,

20, 30


10 000, 7 000



31

Eb/No 5 dB

Environment AWGN

Near-far effect 1:1 Fig. 14: BER vs. number of users for MSF-MUD, BMF, D-MUD and MMSE-MUD.




Number of users 2


10 000



31

Environment AWGN

Near-far effect 0.1:1

Fig. 15: BER vs. EbNo for MSF-MUD, BMF, D-MUD and MMSE-MUD.




Number of users 5


10 000



31

Environment AWGN

Near-far effect 0.1:1

Fig. 16: BER vs. EbNo for MSF-MUD, BMF, D-MUD and MMSE-MUD.





10 000



31

Eb/No 5 dB

Environment AWGN

Near-far effect {0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7,

0.8, 0.9, 1}:1 Fig. 17: BER vs. A1/A2 for MSF-MUD, BMF, D-MUD and MMSE-MUD.




Number of users 5

Number of transmitted bits 10 000



31

Environment AWGN

Near-far effect 1:1

Fig. 18: BER vs. Eb/No for MSF-MUD in synchronous and asynchronous system.

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8. CONCLUSIONS

• the design procedure of M-CMF and MSF-MUD was described.

Properties:

• comparable or lower complexity than other non-linear MUD,

• easily rearranged in adaptive or blind modifications,

• attractive and promissing for CDMA and advanced transmission systems like MC-CDMA.



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THANK YOU

FOR YOUR ATTENTION



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