1. 0 Presenter: Chun-Hsien Peng ( 彭俊賢 ) Advisor: Prof. Chong-Yung Chi ( 祁忠勇 教授 ) Institute of Communications Engineering & Department of Electrical Engineering National Tsing Hua University Hsinchu, Taiwan 30013, R.O.C. E-mail: d905610@oz.nthu.edu.tw Blind Beamforming for Multiuser OFDM Systems by Kurtosis Maximization Based on Subcarrier Averaging

2. 1 2. MIMO Models for Beamforming of Multiuser OFDM Systems 1. Introduction 3. Post-FFT Fourier Beamformer by Subcarrier Averaging OUTLINE 4. Blind Post-FFT KMBFA by Subcarrier Averaging 5. Simulation Results 6. Conclusions and Future Researches KMBFA: Kurtosis Maximization Beamforming Algorithm

3. 2 f1f1 f3f3 f5f5 f4f4 f6f6 f2f2 f1f1 f7f7 CCI CCI: CCI: Co-channel Interference ISI: ISI: Intersymbol Interference (due to Multipath) 1. Introduction (Noise) (Multipath channel) (Multipath channel) ISI, MAI,CCI  Wireless communication problems: ISI, MAI, and CCI suppression in cellular wireless communication systems MAI: MAI: Multiple Access Interference (Caused by Multiple Users) in a Cell MAI ISI pre-FFT post-FFT beamfoming receiverscombating CCI, MAI and ISI A multiuser OFDM system with antenna arrays such as the pre-FFT and post-FFT beamfoming receivers have been considered for combating CCI, MAI and ISI in the receiver design.

4. 3 2. MIMO Models for Beamforming of Multiuser OFDM Systems  Transmitter for “Quasi-synchronous” Multiuser OFDM Systems : data sequence of user : number of subcarriers : length of guard interval (GI) approximately Gaussian (by Central Limit Theorem)

5. 4 (Received signals) (Transmitted signals) (Noise vector) 1 2 time delay DOA path gain where ( steering vector) Baseband discrete-time received signal: : total number of paths (or DOAs) associated with user : ( ) total number of paths (or DOAs) of all the users : number of receive antennas DOA: Direction of Arrival

6. 5 Some general assumptions : (A1) are i.i.d. QPSK symbol sequences (i.e., for each k is a random variable with uniform probability mass function over the sample space ), and is statistically independent of for. Non-Gaussian process QPSK: Quadriphase-shift Keying : identity matrix (A4) is zero-mean white Gaussian with and statistically independent of 's. i.i.d.: Independent Identically Distributed (A3) Quasi-synchronous OFDM Systems (A2), for all ;, and L is known. number of receive antennas total number of paths of all the users

7. 6  Pre-FFT Beamforming Structure (Pre-FFT BFS) [18,19] [18] M. Okada and S. Komaki, “Pre-DFT combining space diversity assisted COFDM,” IEEE Trans. Vehicular Technology, vol. 50, pp. 487-496, Mar. 2001. [19] Z. Lei and F.P.S. Chin, “Post and pre-FFT beamforming in an OFDM system,” IEEE 59th Vehicular Technology Conference, vol. 1, Milan, Italy, May 17-19, 2004, pp. 39-43.

8. 7  MIMO Model for Pre-FFT BFS ( DOA matrix) full column rank with by Assumption(A2) approximately Gaussian (by Central Limit Theorem) (A2), for all ;

9. 8 Remarks: MIMO Model: By Assumptions (A1) and (A3), one can observe that for each fixed n is a zero-mean L × 1 random vector with all the L random components being mutually statistically independent with. SOS based blind beamforming algorithms can be applied, but HOS based blind beamforming algorithms are not applicable because is approximately a Gaussian vector process. Each column of the mixing matrix A only comprise the energy from a single path. Though beamforming algorithms using SOS can be applied to extract each source, their performance is limited due to lack of path diversity. (A1) are i.i.d. QPSK symbol sequences (i.e., for each k is a random variable with uniform probability mass function over the sample space ), and is statistically independent of for. (A3)

10. 9  Post-FFT BFS [19,20] [19] Z. Lei and F.P.S. Chin, “Post and pre-FFT beamforming in an OFDM system,” IEEE 59th Vehicular Technology Conference, vol. 1, Milan, Italy, May 17-19, 2004, pp. 39-43. [20] D. Bartolome and A. I. Perez-Neira, “MMSE techniques for space diversity receivers in OFDM-based wireless LANs,” IEEE J. Sel. Areas Commun., vol. 21, pp. 151-160, Feb. 2003. KMBFA: Kurtosis Maximization Beamforming Algorithm

11. 10  MIMO Model for Post-FFT BFS After the processes of the removal of GI, S/P conversion, N -point FFT operation, and P/S conversion at each receive antenna, the MIMO model for each subcarrier k of the post-FFT BFS can be established as follows: ( vector) ( matrix) full column rank and

12. 11 Remarks: Each column of the mixing matrix comprises multipath energy implying a path diversity gain in the estimation of each source can be foreseen. MIMO Model: All the components 's (QPSK signals) of the P × 1 random input vector are zero-mean non-Gaussian mutually statistically independent with. However, a set of N estimators is needed each for one subcarrier k because of for all for all k j. This leads to high computational complexity. ( vector)

13. 12 Theoretically, the nonblind MMSE beamformer associated with post-FFT BFS is optimum and performs much better than that associated with pre-FFT BFS owing to lack of path diversity for the latter. However, the latter only needs one OFDM pilot block for the estimation of channel matrix, but the former may need many pilots to accurately estimate the channel matrix (and thus needs many OFDM blocks provided over which the channel is static) [19,20,21]. Remarks: [19] Z. Lei and F.P.S. Chin, “Post and pre-FFT beamforming in an OFDM system,” IEEE 59th Vehicular Technology Conference, vol. 1, Milan, Italy, May 17-19, 2004, pp. 39-43. [20] D. Bartolome and A. I. Perez-Neira, “MMSE techniques for space diversity receivers in OFDM-based wireless LANs,” IEEE J. Sel. Areas Commun., vol. 21, pp. 151-160, Feb. 2003. [21] M. Budsabathon, Y. Hara, and S. Hara, “Optimum beamforming for pre-FFT OFDM adaptive antenna array,” IEEE Trans. Vehicular Technology, vol. 53, pp. 945-955, Jul. 2004. Blind algorithms associated with post-FFT BFS using HOS (such as FKMA) are applicable to the estimation of, but in general, they also require many OFDM data blocks with the assumption that the channel is static over these OFDM data blocks, and, again, a set of N estimators is needed.

14. 13 GOAL To design a block-by-block blind beamforming algorithm which is exactly the same for all the subcarriers, and attains “maximum multipath diversity gain” in the meantime.

15. 14 Time Delays 3. Post-FFT Fourier Beamformer by Subcarrier Averaging L × 1 vector where L p × 1 vector DOAs Path gains Notations:

16. 15 Alternative form for : (correlated sources) where zero-mean wide-sense non-Gaussian stationary process by treating k as a time index

17. 16 In spite of,, which implies that all the components of become “uncorrelated” by subcarrier averaging. Lemma 1. Under the assumptions (A1) and (A3), it can be shown that, where denotes “convergence in probability” as. NOTE Subcarrier average of

18. 17 Let be a beamformer (a spatial filter) with the input being. Its output is then where Post-FFT beamformer: for sufficiently large where.

19. 18 For finite Q, the output of spatial filter is then where Under the noise-free assumption, and the assumptions (A1) through (A3), the r th column of A can be estimated by input- output cross-correlation (IOCC) as follows: Channel of interest Bias and

20. 19 (magnitude of the normalized cross correlation between and and ). A “blind performance index” for post-FFT beamformer: is an estimate of and is an estimate of implying that the better the estimation accuracy of both and, the larger the value of. NOTE

21. 20 4. Blind Post-FFT KMBFA by Subcarrier Averaging Proposed Blind Post-FFT KMBFA TDEC: Time Delay Estimation and Compensation KMBFA: Kurtosis Maximization Beamforming Algorithm at the th stage Source Extraction Using Hybrid- - TDEC Classification Deflation Update through BMRC No Yes Update by ?

22. 21  Kurtosis Maximization Based on Subcarrier Averaging Let us define the kurtosis of by subcarrier averaging as follows: By Lemma 1, it can be easily shown that Lemma 1. =1 0 (may depend on i for other modulations such as BPSK signals)

23. 22 The objective function to be maximized for the design of the beamformer : “magnitude of normalized kurtosis” of Maximization ?

24. 23 (A5) if, where are distinct integers. (A6) if, where are distinct integers. (A7) and if and Theorem 1: Under the assumptions (A1) through (A3), (A5) through (A7), and the noise-free assumption, attains maximum, and where is an unknown constant, and is an unknown integer. Assumptions:

25. 24 No Compute at the th iteration Yes Super -expo Algorithm (SEA) nential ? To the th iteration Update through a gradient type optimization algorithm such that ( matrix)  Post-FFT by Subcarrier Averaging

26. 25 Remarks: Empirically, we find that the proposed iterative post-FFT also shares the fast convergence and guaranteed convergence advantages of the conventional FKMA. An initial condition is needed to initialize the proposed post-FFT. For finite N and finite SNR, The proposed post-FFT may fail to extract the sources when any of the assumptions (A5), (A6) and (A7) are not satisfied, while the probability of the event that violation of any of the three assumptions occurs depends on values of (length of GI) and (number of paths of each user).

27. 26 The proposed post-FFT is also applicable to the case of BPSK symbol sequence. Three Extra Assumptions (A8) (A9) (A10) if and if and Therefore, the proposed post-FFT may fail to extract a source with higher probability for the BPSK case than for the QPSK case due to the above three extra assumptions required. (for the QPSK case) ×

28. 27 At th stage:  Multistage Source Extraction Assume that and, are the source estimate and the associated channel estimate obtained at stage. which basically corresponds to the MIMO signal with all the contributions from removed. Cancellation (or Deflation Processing)... Source Extraction Using Hybrid- - Deflation

29. 28 Initial Condition: Post-FFT beamformer where (Output) (Channel estimate)... Source Extraction Using Hybrid- - Deflation

30. 29 Post-FFT : initialized by (Output of ) (Channel estimate)... Source Extraction Using Hybrid- - Deflation Hybrid- - :

31. 30 where is an unknown constant,, Remark: unknown time delay The proposed blind Hybrid- - performs well only with Assumptions (A1) through (A4) required, and it is applicable to both the BPSK case and the QPSK case.

32. 31  Time Delay Estimation and Compensation (TDEC) at the th stage Source Extraction Using Hybrid- - TDEC Classification Deflation Update through BMRC No Yes Update by ? unknown time delay

33. 32 where The unknown time delay in the extracted source can be estimated also by subcarrier averaging

34. 33 Update by  Classification and BMRC at the th stage Source Extraction Using Hybrid- - TDEC Classification Deflation Update through BMRC No Yes ? BMRC: Blind Maximum Ratio Combining

35. 34  Correlated Sources Assume that is a cluster of correlated sources impinging on the receiver antenna array where : path gain of each correlated signal in the cluster : DOA of each correlated signal in the cluster MIMO signal models replaced by

36. 35 Remarks: The proposed post-FFT KMBFA is able to accurately estimate the associated source signal as long as is sufficiently large, implying its robustness to correlated signals. On the other hand, the Capon's MV beamformer is incapable of extracting the associated source regardless of the value of because is no longer a steering vector of a certain DOA required by the Capon's MV beamformer.

37. 36 5. Simulation Results  Parameters Used: Consider a four-user ( ) OFDM system with, and. 's: zero-mean, i.i.d. BPSK (or QPSK) signals used with : i.i.d. zero-mean Gaussian with. Input SNR: performance index: average symbol error rate (SER)

38. 37 Multipath Channel Parameters  Example 1 (Environment without Correlated Sources): Fifty sets of time delay parameters were generated randomly. For each set of time delay parameters, fifty sets of data were generated.

39. 38 (a) QPSK signals ( ) post-FFT KMBFA if post-FFT is used ( ) post-FFT KMBFA if post-FFT Beamformer is used ( ) post-FFT KMBFA if Hybrid- - is used (b) BPSK signals INPUT SNR (dB)

40. 39 (b) (a) BPSK signals QPSK signals INPUT SNR (dB)

41. 40 's are all distinct DOAs 's ( ) were generated randomly  Example 2 (Environment with Correlated Sources): Multipath Channel Parameters total number of correlated sources of a cluster

42. 41 (b) (a) BPSK signals QPSK signals INPUT SNR (dB)

43. 42 6. Conclusions and Future Researches Under Assumptions (A1) through (A4), we have presented a block-by-block processing algorithm based on subcarrier averaging, namely the post-FFT KMBFA, for the estimation of symbol sequences of all the active users of an OFDM system. It is also a multistage blind beamforming algorithm consisting of source extraction using the proposed blind Hybrid- -, TDEC processing, classification and BMRC processing at each stage. The proposed blind Hybrid- -, which is the kernel of the proposed post-FFT KMBFA, is also a selection scheme by the performance of two blind beamformers, the post-FFT and the post-FFT beamformer, using subcarrier averages of one OFDM block. Moreover, as the conventional FKMA, the post-FFT supported by Theorem 1 is also a computationally fast source extraction algorithm.  Conclusions

44. 43 Some simulation results were provided to support that the proposed post-FFT KMBFA performs well no matter whether correlated sources are present or not, and its performance is close to the “optimal” nonblind MMSE beamformer associated with the post-FFT BFS, in addition to a performance comparison of some existing beamformers The results of this chapter have been partly presented at IEEE ISPACS'05 (Hong Kong, Dec. 13-16, 2005), co-authored by Chun-Hsien Peng, C.-C. Lin, Y.-H. Lin, and C.-Y. Chi, and have been submitted to IEEE Trans. Signal Processing for publication, co-authored by Chun-Hsien Peng, K.-C. Huang, C.-Y. Chi, and W.-K. Ma. ISPACS: Intelligent Signal Processing and Communication Systems

45. 44 We considered the uplink of a multiuser OFDM system under the scenario of multiple distinct DOAs for each user, and a flat fading channel for each DOA. The extension of the proposed blind beamforming algorithm to more general scenarios is a worthwhile research. The feasibility of other digital symbols such as 16-QAM is a future research in addition to the estimation of L. Subcarrier averaging may open a door for efficient post-FFT blind beamforming algorithms of multiuser OFDM systems using one OFDM block.  Future Researches

46. 45 Thank you very much

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