2. The 3 rd MCM of COST 289: TU Košice, October 30-31, 2003 Technical University of Košice, Slovakia 1 of 27 THE PIECE-WISE LINEAR MICROSTATISTIC MULTI-USER RECEIVER Dušan Kocur, Jana Čížová, Stanislav Marchevský Department of Electronics and Multimedial Communications Technical University of Košice Park Komenskeho 13, 041 20 Košice Slovak Republic e-mail: Dusan.Kocur@tuke.sk

3. 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. The 3 rd MCM of COST 289: TU Košice, October 30-31, 2003 Technical University of Košice, Slovakia 2 of 27

4. 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). The 3 rd MCM of COST 289: TU Košice, October 30-31, 2003 Technical University of Košice, Slovakia 3 of 27

5. MF-1 MF-2 MF-M BMF VITERBI DECISION ALGORITHM Fig. 1. Base-band optimum receiver bank of matched filtersMF-k: the k-th matched filter The 3 rd MCM of COST 289: TU Košice, October 30-31, 2003 Technical University of Košice, Slovakia 4 of 27

6. 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 The 3 rd MCM of COST 289: TU Košice, October 30-31, 2003 Technical University of Košice, Slovakia 5 of 27

7. 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. The 3 rd MCM of COST 289: TU Košice, October 30-31, 2003 Technical University of Košice, Slovakia 6 of 27

8. 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? The 3 rd MCM of COST 289: TU Košice, October 30-31, 2003 Technical University of Košice, Slovakia 7 of 27

9. 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. The 3 rd MCM of COST 289: TU Košice, October 30-31, 2003 Technical University of Košice, Slovakia 8 of 27

10. 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. The 3 rd MCM of COST 289: TU Košice, October 30-31, 2003 Technical University of Košice, Slovakia 9 of 27

11. 3. SINGLE-CHANNEL CONVENTIONAL MICROSTATISTIC FILTER (CMF) The 3 rd MCM of COST 289: TU Košice, October 30-31, 2003 Technical University of Košice, Slovakia 10 of 27 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.

12. Fig. 2. CMF TDTD M-WF M-WF output is given by a linear combination of its input signal samples Constant term: necessary to get the unbiased estimation The 3 rd MCM of COST 289: TU Košice, October 30-31, 2003 Technical University of Košice, Slovakia 11 of 27

13. Fig. 3. Threshold decomposer TDTD TD threshold values: Threshold decomposition for positive samples: (1) The 3 rd MCM of COST 289: TU Košice, October 30-31, 2003 Technical University of Košice, Slovakia 12 of 27

14. Fig. 4. Threshold decomposition. Example Threshold values: The 3 rd MCM of COST 289: TU Košice, October 30-31, 2003 Technical University of Košice, Slovakia 13 of 27

15. 4. MULTI-CHANNEL CONVENTIONAL MICROSTATISTIC FILTER (M-CMF) The 3 rd MCM of COST 289: TU Košice, October 30-31, 2003 Technical University of Košice, Slovakia 14 of 27 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.

16. TD M TD 2 TD 1 M-WF 1 M-WF 2 M-WF M MULTI-CHANNEL CONVENTIONAL MICROSTATISTIC FILTER 15 of 27 Fig. 5. M-CMF

17. 5. OPTIMUM TIME-INVARIANT M-CMF DESIGN M-CMF responses for : Assumptions: the input and desired signals are stationary random processes (time-invariant filter design), threshold values of TDs are fixed, known in advance. (2) The 3 rd MCM of COST 289: TU Košice, October 30-31, 2003 Technical University of Košice, Slovakia 16 of 27

18. estimation error: (3) (4) (5) (6) The 3 rd MCM of COST 289: TU Košice, October 30-31, 2003 Technical University of Košice, Slovakia 17 of 27 mean-square estimation error:

19. because of the constant threshold values, there is the only extreme of the mean-square error represented by the global minimum given by: minimum mean-square error: (7) (8) The 3 rd MCM of COST 289: TU Košice, October 30-31, 2003 Technical University of Košice, Slovakia 18 of 27

20. 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. The 3 rd MCM of COST 289: TU Košice, October 30-31, 2003 Technical University of Košice, Slovakia 19 of 27

21. Fig. 6. MSF-MUD MF-1 MF-2 MF-M BMF M-CMF The 3 rd MCM of COST 289: TU Košice, October 30-31, 2003 Technical University of Košice, Slovakia 20 of 27

22. 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. The 3 rd MCM of COST 289: TU Košice, October 30-31, 2003 Technical University of Košice, Slovakia 21 of 27

23. f)Training sequence: 3000 information bits. g)Training sequence application: estimation of 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 (E b /N o ). The 3 rd MCM of COST 289: TU Košice, October 30-31, 2003 Technical University of Košice, Slovakia 22 of 27

24. 23 of 27 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.

25. 24 of 27 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).

26. 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. The 3 rd MCM of COST 289: TU Košice, October 30-31, 2003 Technical University of Košice, Slovakia 25 of 27

27. 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 The 3 rd MCM of COST 289: TU Košice, October 30-31, 2003 Technical University of Košice, Slovakia 26 of 27

28. THANK YOU VERY MUCH FOR YOUR ATTENTION The 3 rd MCM of COST 289: TU Košice, October 30-31, 2003 Technical University of Košice, Slovakia 27 of 27