Blind Channel Estimation in OFDM Systems by Relying on the Gaussian Assumption of the Input

1. Blind Channel Estimation in OFDM Systems byRelying on the Gaussian Assumption of the Input ISSPIT 2009Ajman University of Science & Technology, UAE Presented by: Ahmed Abdul Quadeer Dec. 15, 2009

2. Outline 2 • Introduction • Techniques for channel estimation • MLE of the channel IR using Gaussian assumption on the transmitted data • Proposed approaches for channel estimation: • Blind approach using Genetic algorithm • Semi-blind approach using Steepest Descent algorithm • Simulation Results • Conclusion

3. Importance of OFDM Need for Channel Estimation Introduction 3

4. Importance of OFDM 4 High spectral efficiency. High data transmission rates. Robust to multi-path fading. Simple implementation of receiver. Used in WIMAX and 4G wireless systems.

5. Need for Channel Estimation 5 Transmitter Channel Receiver Y = H ʘ X X H X = Y ./ H

6. Methods based on Approach Methods based on Constraints Techniques for channel estimation 6

7. Methods based on Approach 7 Training-based: Pilots sent with data symbols Blind: Natural constraints used Semi-Blind: Combination of pilots and constraints

8. Methods based on Constraints 8 • Channel Constraints • Finite delay spread • Frequency correlation • Time correlation • Transmit/Receive (spatial) correlation • Data Constraints • Finite alphabet • Channel coding • Pilots • Cyclic prefix • Gaussian assumption on data

9. Gaussian assumption on the transmitted data MLE of the channel IR Plot of Likelihood Function vs Channel Taps MLE of the channel IR using Gaussian assumption on the transmitted data 9

10. Gaussian Assumption On The Transmitted Data 10 Time domain transmitted data assumed Gaussian  large weighted sum of i.i.d random variables

11. Distribution of Transmitted Data 11

12. MLE of the Channel IR 12 (Gaussian input) + (Gaussian Noise)  Gaussian Output Likelihood function should be uni-modal to pursue a completely blind approach

13. Plot of Likelihood Function vs Channel Taps N = 64, L = 2, σn2 = 0.1 N = 64, L = 2, σn2 = 0.1 (Top view) 13

14. Blind approach using Genetic algorithm Semi-blind approach using Steepest Descent algorithm Proposed approaches for channel estimation 14

15. Blind Approach: GeneticAlgorithm 15 • Stochastic search algorithm • Finds the best solution based on natural selection and evolution. • Reproduction operators: • Crossover: Method of combining the features of parent to form two offspring (BLX – α algorithm) • Mutation: Arbitrary gene of a selected offspring is altered to prevent premature convergence/local minima (Non-uniform mutation)

16. Semi-blind Approach: SD Algorithm 16 • Semi-Blind approach using Steepest Descent (SD) algorithm • Needs an initial estimate close to optimum • Requires Gradient of likelihood function w.r.t. the channel IR

17. Evaluating Gradient of Likelihood Function w.r.t Channel IR 17 Chain rule used Gradient of Likelihood function w.r.t. channel IR given by

18. Simulation Results 18

19. Simulation Parameters 19 Number of sub-carriers, N = 64 Cyclic prefix length, L = 8 Channel length = 9 Modulation scheme: BPSK/16QAM Number of iterations = 20 Number of pilots = 6

20. Genetic Algorithm Parameters • Population size: 100 • Number of generation: 50 • Cross-over scheme: BLX – α (α = 0.5) • Cross-over probability: 0.8 • Mutation scheme: Non-uniform • Mutation probability: 0.08 • Number of elite chromosomes: 5

21. BER vs SNR Comparison for BPSK Modulated Data 21

22. BER vs SNR Comparison for 16QAM Modulated Data 22

23. Conclusion 23

24. Conclusion 24 Gaussian assumption on the transmitted data  Channel Estimation by maximizing likelihood function Likelihood function multi-modal  Blind approach extremely challenging Blind approach using Genetic algorithm Semi-blind approach using Steepest Descent algorithm

25. Questions Thank You 25

26. Extra Slides 26

27. System Overview 27 Input Bits Modulator IFFT Cyclic Prefix Channel Output Bits Demodulator Channel Estimation FFT Cyclic Prefix Removal Transmitter Receiver

28. Approach Gaussian Assumption on Transmitted Data Distribution of Transmitted Data MLE of the Channel IR Plot of Likelihood Function vs Channel Taps Semi-blind Approach Evaluating Gradient of Likelihood function w.r.t Channel IR Computational Complexity Simulation Results Channel Centered Blind Estimation 28

29. Computational Complexity 29 • Gradient and Likelihood function involve two matrix operations, size (N+L) x (N+L) • Block matrix calculations used for reducing the computational complexity

30. Reduction in Complexity 30 • Consider the practical scenario of HIPERLAN/2 with N=1024 and L=128 • Matrix operation reduction • Size (N+L) x (N+L)  Size L x L + N-point FFT • Size 1152 x 1152  Size 128 x 128 + 1024-point FFT

31. Constraints used 31 • Data Constraints: • Gaussian assumption (on transmitted data), • Cyclic Prefix and • Pilots • Channel Constraints: • Finite delay spread and • Frequency correlation

32. OFDM Receiver Requirements • Time variant channels • Reduce training overhead • Avoid latency • Reduce complexity and storage requirements • Special channel conditions • Zeros on FFT grid of channel IR • Time variation within the OFDM symbol