The 3 rd MCM of COST 289 : TU Košice , October 30 - 31 , 2003

The 3rd MCM of COST 289: TU Košice, October 30-31, 2003

Technical University of Košice, Slovakia

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THE PIECE-WISE LINEARMICROSTATISTIC

MULTI-USER RECEIVER

Dušan Kocur, Jana Čížová, Stanislav Marchevský

Department of Electronics and Multimedial CommunicationsTechnical University of Košice

Park Komenskeho 13 , 041 20 KošiceSlovak Republic

e-mail: [email protected]

CONTENT

• multi-user detection receiver (MUD),• motivation for new MUD design, • single-channel conventional microstatistic filter

(CMF),• multi-channel CMF (M-CMF): structure,• M-CMF: design procedure,• microstatistic MUD (MSF-MUD),• computer experiments,• conclusions.



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1. MULTI-USER DETECTION RECEIVER (MUD)

• MUD refers to the process of demodulating one or more user data streams from a non-orthogonal multiplex based on knowledge on spreading codes (signature sequence), timing, phases and received amplitudes of all users,

• optimum receiver: makes decisions by selecting the transmitted sequence to minimize the sequence error probability (maximum likelihood sequence detection, ML).



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( )r t

MF-1

MF-2

MF-M

BMF (1) ( )y n

(2) ( )y n

( ) ( )My n

VITERBI

DECISION

ALGORITHM

1ˆ [ ]b n

2ˆ [ ]b n

ˆ [ ]Mb n

BiT

Fig. 1. Base-band optimum receiver

bank of matched filters MF-k: the k-th matched filter



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• high performance gains of optimum receiver: achieved at the cost of extremely high degree of complexity,

• solution: suboptimum receivers,• suboptimum receiver principle: mostly replacing

Viterbi decision algorithm with a reduced complexity algorithm.

2. MOTIVATION FOR NEW MUD DEVELOPMENT



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• suboptimum receiver examples:

BMF receivers, decorrelating MUD receivers (D-MUD), minimum mean square error MUD receivers

(MMSE-MUD), non-linear single-stage MUD receivers (NSS-

MUD); e.g neural network or Volterra filter based MUD receivers,

non-linear multi-stage MUD receivers: serial or parallel interference cancellation (SIC, PIC receivers), etc.



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• NSS-MUD principle: the output of the NSS-MUD is taken as the sign of the multi-channel non-linear transformation of the outputs of the BMF,

• basic idea for a new NSS-MUD design: application of M-CMF in order to do the multi-channel non-linear transformation of the outputs of the BMF.

WHY TO DO IT?



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• boundary of decision regions:

optimum receiver: non-linear, suboptimum receivers: approximation of

boundary of decision region of optimum receiver,

linear suboptimum receivers: linear approximation (e.g. BMF receiver , MMSE-MUD, D-MUD),

non-linear suboptimum receivers: non-linear approximation.



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• intention: to design of the receiver with piece-wise linear approximation of boundary of the decision region,

• why (1): this approximation should provide better results than that of linear approximation,

• why (2): this approximation should provide less complex implementation than that of non-linear suboptimum receiver.



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3. SINGLE-CHANNEL CONVENTIONAL MICROSTATISTIC FILTER (CMF)



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• minimum mean-square non-linear estimator, • the desired signal (filter output) is given by a

linear combination of signal samples obtained by a threshold decomposition of the input signal of the filter,

• CMF: the piece-wise linear system,• CMF structure (Fig.2): threshold decomposer (TD)

+ multi-channel Wiener filter (M-WF) + constant term.

Fig. 2. CMF

TD( )y n

( ) ( )Ly n

(1) ( )y n

( 1) ( )y n

( ) ( )Ly n

M-WF

(0) ( )h nˆ( )d n

M-WF output is given by a linear combination of its input signal samples

Constant term: necessary to get the unbiased estimation



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Fig. 3. Threshold decomposer

TD( )y n

( ) ( )Ly n

(1) ( )y n

( 1) ( )y n

( ) ( )Ly n

1 1L Ll l l l

TD threshold values:

Threshold decomposition for positive samples:

1( )

1 1

1

( )0

( ) ( ) ( )

( )

ji

j j j

j j j

y n lfor

y n y n l for l y n l

forl l l y n

(1)



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Fig. 4. Threshold decomposition. Example

2

1

1

2

2

2

2

L

l

l

l

l

Threshold values:

(2) ( )y n

(1) ( )y n

( 1) ( )y n

( 2) ( )y n

( )y n

n



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4. MULTI-CHANNEL CONVENTIONAL MICROSTATISTIC FILTER (M-CMF)



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• minimum mean-square non-linear estimator, • the estimations of the desired signals (filter

outputs) are given by linear combinations of signal samples obtained by the threshold decomposition of the input signals of the filter.

( , ) ( )M Ly n

( ) ( )My n( , ) ( )M Ly n

TDM

(2, ) ( )Ly n

TD2

(2) ( )y n(2, ) ( )Ly n

(1, ) ( )Ly n

TD1

(1) ( )y n

(1, ) ( )Ly n

M-WF1

(1,0) ( )h n

(1)ˆ ( )d n

M-WF2

(2,0) ( )h n

(2)ˆ ( )d n

M-WFM

( ,0) ( )Mh n

( )ˆ ( )Md n

MULTI-CHANNEL

CONVENTIONAL

MICROSTATISTIC

FILTER

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Fig. 5. M-CMF

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

5. OPTIMUM TIME-INVARIANT M-CMF DESIGN

• M-CMF responses for :1,2, ,k M

Assumptions: • the input and desired signals are stationary

random processes (time-invariant filter design), • threshold values of TDs are fixed, known in

advance.

(2)



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• estimation error:( ) ( )ˆ( ) ( ) ( )k k

ke n d n d n

22 ( ) ( )ˆ( ( )) ( ) ( ) ( )k kk kMSE n E e n E d n d n

H

2( )( ( )) ( ) 2 ( ) ( ) ( ) ( ) ( )k T Tk k k k kMSE n E d n n n n n n

H H P H R H

( )( ) ( ) ( ) ( ) ( ) ( )T kkn E n n n E d n n R Y Y P Y

(3)

(4)

(5)

(6)



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• mean-square estimation error:

• because of the constant threshold values, there is the only extreme of the mean-square error represented by the global minimum given by:

1( ) ( ) ( )optkk n n nH R P

• minimum mean-square error:

2( )

2( ) 1

( ( )) ( ) ( ) ( )

( ) ( ) ( ) ( )

opt Topt kkk k

opt T optkk k

MSE n E d n n n

E d n n n n

H H P

H R H

(7)

(8)



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6. MICROSTATISTIC MULTI-USER DETECTION RECEIVER (MSF-MUD)

• MSF-MUD (Fig.6) is obtained from the optimum receiver by replacing the Viterbi decision algorithm with the M-CMF,

• output of MSF-MUD is taken as the sign of the non-linear transformation of the output of the BMF due to the M-CMF,

• MSF-MUD is MMSE piece-wise linear receiver,• design: the same approaches as for the optimum

linear MMSE-MUD.



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Fig. 6. MSF-MUD

MF-1

MF-2

MF-M

BMF (1) ( )y n

(2) ( )y n

( ) ( )My n

( )r tM-CMF

(1)ˆ ( )d n

(2)ˆ ( )d n

( )ˆ ( )Md n

1ˆ [ ]b n

2ˆ [ ]b n

ˆ [ ]Mb n

BiT



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7. COMPUTER EXPERIMENTS

a) Two experiments.b) M=2 user base-band synchronous CDMA

transmission system.c) Signature waveforms: Gold sequences with the

period of seven chips.d) Input signal to the receiver: the sum of

antipodally modulated signature waveforms embedded in AWGN.

e) Receivers: optimum receiver, BMF receiver, D-MUD, MMSE-MUD and MSF-MUD.



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f) Training sequence: 3000 information bits.g) Training sequence application: estimation of

( ) ( ).kn and nR P

h) M-CMF:L=2, N=0, threshold values were set experimentally.

i) Performance index: bit error rate (BER) vs. information signal energy per bit to noise power spectral density (Eb/No).



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Fig. 7. Results of the 1st experiment for the 1st user

The power of the signal at the input of the receiver produced by all users at the input of the receiver was the same.

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Fig. 8. Results of the 2nd experiment for the 1st user

The power of the signal at the input of the receiver produced by the first user was ten times smaller than that of the second user,

(i.e. performance properties at near-far effect) .

8. CONCLUSIONS

a) The time-invariant M-CMF was introduced.b) MSF-MUD receiver structure based on M-CMF

has been proposed.c) Experiment 1 (Fig.7): all receivers applied in our

experiments can provide almost the same results.

d) Experiment 2 (Fig.8): the optimum receiver: the best results, the MSF-MUD outperforms clearly the linear MUD receivers.



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e) The simple computer simulation has shown that the MSF-MUD could outperform the other tested linear MUD receivers.

f) These results were achieved at the expense of the higher computational complexity of the MSF-MUD.

MSF-MUD IS A PROMISING SUBOPTIMUM CDMA RECEIVERS



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THANK YOU VERY MUCH

FOR YOUR ATTENTION



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Documents

The 3 rd MCM of COST 289 : TU Košice , October 30 - 31 , 2003