1 Block-by-Block Blind Channel Estimation Algorithm Using Subcarrier Averaging for Multi-user OFDM Systems Presenter: Teng-Han Tsai ( 蔡騰漢 ) Institute of Communications Engineering & Department of Electrical Engineering National Tsing Hua University Hsinchu, Taiwan 30013, R.O.C.

2 Outline 1. Introduction 3. MIMO Model for Post-FFT Beamforming Structure 4. Proposed Blind Channel Estimation Algorithm by Subcarrier Averaging 5. Simulation Results 6. Conclusions MUSIC: Multiple Signal Classification MVDR: Minimum Variance Distortionless Response 2. Review of MVDR beamformer and MUSIC algorithm MIMO: Multiple-input Multiple-output

3 Introduction

4 Wireless Environment : path gain of the l th path of user p : Direction of arrivals (DOA) of the l th path of user p : time delay of the l th path of user p : number of antennas : number of users user 1 user P BS : number of paths (or DOAs) associated with user p. : ( ) total number of paths (or DOAs) of all the users. MS 1 MS P L1L1 LPLP... Noise ULA (Uniform Linear Array) Tx signals Rx signals

5 (A1), are QPSK ( BPSK ) zero-mean independent identically distributed (i.i.d.) random sequences with, and is statistically independent of for. (A4) is zero-mean white Gaussian and statistically independent of, and. : identity matrix (A2) for all, Assumptions BPSK : Binary phase shift keying QPSK : Quadriphase shift keying (A3), and L is known.

6 Review of MVDR Beamformer and MUSIC Algorithm

7 Beamforming (1/3) [2][3] Interference suppression Antenna gain enhancement Spectral efficiency increase Signal separation and extraction Beamformer (Interfering signal) (Desired signal)... #1 #2 #Q#Q

8 Beamforming (2/3)   Assumptions: (M1), are wide-sense stationary random processes, and is statistically independent of for. (M2) for all, (M3) is zero-mean white Gaussian with and statistically independent of and Beamformer (source P ) (source 1) Beamformer Output... #1 #2 #Q#Q   MIMO Model path gain DOA (Direction of Arrival)

9 Beamforming (3/3) Under the assumption (M1) and (M2), as which implies the MVDR beamformer can perfectly extract the desired signal by processing.   MVDR Beamformer: subject to where : correlation matrix of : (known in advance) DOA of the path of user 1 (Desired source) Criterion: By Lagrange multiplier MVDR : Minimum Variance Distortionless Response

10 DOA Estimation - MUSIC Method (1/2)  EVD (Eigenvalue Decomposition) of Correlation matrix : where are orthonormal basis.1. 2.

11  Signal subspace is orthogonal to noise subspace : DOA Estimation - MUSIC Method (2/2) Compute MUSIC spectrum : and search for “infinitely high” spectral peaks.,, Construct projection matrix : may be found by solving for.

12 MIMO Model for Post-FFT Beamforming Structure

13 Post-FFT Beamforming Structure (1/2) …… A/D GI Removal S/P N -point FFT GI Removal S/P N -point FFT GI Removal S/P N -point FFT P/S A/D … … …… beamformer channel information at subcarrier 0 for user p N beamformers

14   MIMO model for each subcarrier k : Post-FFT Beamforming Structure (2/2) ( source vector) ( white Gaussian noise vector) ( vector ) where ( channel matrix) FFT Channel response of user p at subcarrier k

15 Proposed Blind Channel Estimation Algorithm by Subcarrier Averaging

16 where ( DOA matrix) ( source vector) MIMO Model (1/4)   MIMO Model ( white Gaussian noise vector ) ( ) full column rank by Assumption (A2) (component) re-expression

17 MIMO Model (2/4) 2. Same user but different path: 1. Different users:   Source Vector : The components of the source vector are statistically correlated. Under Assumption (A1) and Assumption (A3), check the components of the L × 1 source vector by statistical averaging : MVDR

18 MIMO Model (3/4) Under Assumption (A1) and Assumption (A3), check the components of the L × 1 source vector by subcarrier averaging : Define the subcarrier averaging of : where denotes “convergence in probability” as N. Each components of can be “de-correlated” by subcarrier averaging. MVDR

19 MIMO Model (4/4)   MVDR and MUSIC methods by subcarrier averaging: By subcarrier averaging, MVDR and MUSIC methods can be applied to post-FFT beamforming structure by processing where ( DOA matrix) ( source vector) ( white Gaussian noise vector ) ( ) full column rank by Assumption (A2) (component)

20 DOA Estimation Source Extraction Time Delay Estimation Path Gain Estimation Classification and Grouping Algorithm Procedure MUSIC MVDR Beamformer (estimate of channel matrix) (received signal vector)

21 Proposed Algorithm – DOA Estimation MUSIC method : where : projection matrix : EVD of correlation matrix EVD : eigenvalue decomposition ( MUSIC spectrum ) ( noise eigenvectors ) ( the smallest Q - L eigenvalues ) All the DOAs can be estimated by finding the L largest local maxima of S MUSIC ( θ ).

22 Proposed Algorithm – Source Extraction By and, we have MVDR beamformer and MVDR beamformer output where path gain : path gain associated with DOA and data : data associated with DOA and time delay : time delay associated with DOA and

23 Proposed Algorithm – Time Delay Estimation (1/3) Data sequence (QPSK signals): Estimate time delay : where   Estimate time delay by processing :

24 Proposed Algorithm – Time Delay Estimation (2/3) Data sequence (BPSK signals): Estimate time delay : where   Estimate time delay by processing :

25 Proposed Algorithm – Time Delay Estimation (3/3) Time compensated beamformer output associated with : where path gain : path gain associated with DOA and data : data associated with DOA and

26 Calculate for all the paths to be analyzed. Select a path and set it to be. Proposed Algorithm – Classification and Grouping Define (Step 1)   Procedures of classification and grouping: (Step 2) Extract all the paths that have and assign them as a new group. (Step 3) From the remaining paths, select another path and set it to be, where i = 2, …, P. (Step 4) Go to Step 2 until there is no more path to group. (Step 5) Finally, there will be P groups where all the paths of a group belongs to the same user. (Step 6)

27 Proposed Algorithm – Path Gain Estimation (1/9)   After Classification and Grouping: It is obtained P groups, where in each group there are Lp sequences with the same data symbol information multiplied by different coefficient: Group 1 Group P

28 Proposed Algorithm – Path Gain Estimation (2/9) Estimate path gain : The 4 solutions have the same magnitude but different phase angle. Therefore, it needs to choose one of them.   Estimate path gain by processing : Data sequence (QPSK signals):

29 Proposed Algorithm – Path Gain Estimation (3/9)   Decision of the path gain phase angle: QPSK For QPSK case: Select its corresponding path (first path) and rotate the path by its corresponding phase angle estimate. (Step 2) From the 4 phase angle solutions, select an angle, for i = 1, …, 4. (Step 1) After rotation Re Im Ambiguity phase

30 Proposed Algorithm – Path Gain Estimation (4/9)   Decision of the path gain phase angle: QPSK For QPSK case: Select another path, where l = 2, …, Lp and rotate it by its 4 possible path gain phase angles. (Step 3)

31 Proposed Algorithm – Path Gain Estimation (5/9)   Decision of the path gain phase angle: QPSK For QPSK case: Perform the inner product of the first rotated path and the four l-th rotated paths, for l= 2, …, Lp.. (Step 4) Calculate the phase angle of the four inner products, which the results will be approximated to {0, π/2, π, 3π/2}. (Step 5) Choose the path gain phase angle whose phase angle of inner product is closed to 0. (Step 6) They are in phase

32 Proposed Algorithm – Path Gain Estimation (6/9)   Decision of the path gain phase angle: QPSK For QPSK case: Go to the Step 2 until there is no more paths to rotate in the group.. (Step 7) Finally, the path gain phase angle for each path of the group will be obtain. (Step 8) Note: Note: As the proposed algorithm is a blind method, the estimated path gain has an ambiguity scalar. This value depends on the choice of the Phase angle solution in Step 1.

33 Proposed Algorithm – Path Gain Estimation (7/9) Estimate path gain : or The 2 solutions have the same magnitude but different phase angle. Therefore, it needs to choose one of them.   Estimate path gain by processing : Data sequence (BPSK signals):

34 Proposed Algorithm – Path Gain Estimation (8/9)   Decision of the path gain phase angle: BPSK For BPSK case: Select its corresponding path (first path) and rotate the path by its corresponding phase angle estimate. (Step 2) From the 2 phase angle solutions, select a solution, for i = 1, 2. (Step 1) Select another path, where l = 2, …, Lp and rotate it by its 2 possible path gain phase angles. (Step 3) Perform the inner product of the first rotated path and the four l-th rotated paths, for l= 2, …, Lp.. (Step 4) Ambiguity phase

35 Proposed Algorithm – Path Gain Estimation (9/9)   Decision of the path gain phase angle: BPSK For BPSK case: Calculate the phase angle of the four inner products, which the results will be approximated to {0, π}. (Step 5) Choose the path gain phase angle whose phase angle of inner product is closed to 0. (Step 6) Go to the Step 2 until there is no more paths to rotate in the group.. (Step 7) Finally, the path gain phase angle for each path of the group will be obtain. (Step 8) Note: Note: As the proposed algorithm is a blind method, the estimated path gain has an ambiguity scalar. This value depends on the choice of the Phase angle solution in Step 1.

36 ( ) where Proposed Algorithm – Channel Recovery   Estimate of channel matrix : P is P × P unknown permutation matrix. group index user index With the estimated DOA, time delay and path gain of each path, the channel matrix can be obtain: Note: Note: The permutation matrix P can be obtained using the information of the transmitted sources after the data sequence detection.

37 Data Sequence Detection Once the channel information and the noise power (from MUSIC) are obtained. A MMSE beamformer can be applied : Then the estimated data sequence for a user p will be: For QPSK For BPSK Ambiguity phase

38 Simulation Results

39 Performance Index   Definition of Normalized Mean Square Error (NMSE): where : estimate of channel matrix : Frobenius norm

40 Parameters Used : i.i.d. zero-mean Gaussian with.   A two-user ( P =2) OFDM system Q = 10. N g = 20 N = DOA randomly generated for all the users. Time delay randomly generated for all the users. Path gain randomly generated for all the users. Input SNR: L = 6.

41 NMSE of A

42 Symbol Error Ratio

43 Conclusions blind channel estimation algorithm by subcarrier averagingpost-FFT beamforming structure over one OFDM block  We have presented blind channel estimation algorithm by subcarrier averaging for the post-FFT beamforming structure over one OFDM block. This proposed algorithm basically includes DOA estimation using MUSIC method, source extraction using MVDR beamformer, time delay estimation and compensation, classification and grouping, path gain estimation and channel recovery.   Some simulation results were provided to support the blind beamformer designed by the proposed channel estimation algorithm, and its performance is very closed to the performance of the MMSE beamforming using perfect channel.  one OFDM blockgood performance.  The proposed channel estimation algorithm only needs one OFDM block to estimate channel with good performance.

44 References (1/3) [1] R. V. Nee and R. Prasad, OFDM for Wireless Multimedia Communications. Boston: Artech House, [2] J. C. Liberti and T. S. Rappaport, Smart Antennas for Wireless Communications: IS- 95 and Third Generation CDMA Applications. New Jersey: Prentice Hall, [4] Ralph O. Schmidt, “Multiple emitter location and signal parameter,” Proc. IEEE Trans. Antennas and Propagation, vol. AP-34, No. 3, pp , Dec [5] Shinsuke Hara, Montree Budsabathon, and Yoshitaka Hara, “A pre-FFT OFDM adaptive antenna array with eigenvector combining,” Proc. IEEE International Conference on Communication., vol. 4, pp , June [3] L. C. Godara, “ Application of antenna arrays to mobile communications, Part II: Beam-forming and direction-of-arrival considerations,” IEEE Proceeding, vol. 85, No. 8, pp , Aug [6] Ming LEI, Ping ZHANG, and Hiroshi HARADA, and Hiromitsu WAKANA, “LMS adaptive beamforming based on pre-FFT combining for ultra high-data-eate OFDM system,” Proc. IEEE 60th Vehicular Technology Conference, vol. 5, Los Angeles, California, USA, Sept , 2004, pp

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47 Thank you very much

48 Transmitter of OFDM Systems : data sequence of user : number of subcarriers : length of GI D/A & Up Converter GI Insertion S/P N -point IFFT … … P/S User p,, n : time-domain sample index k : frequency-domain sample index

49 Symbol Error Ratio (QPSK)

50 Symbol Error Ratio (BPSK)