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

Outline Introduction Techniques for channel estimation 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

Introduction 3 Importance of OFDM Need for Channel Estimation

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

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

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

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

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

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

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

Distribution of Transmitted Data 11

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

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

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

Blind Approach: Genetic Algorithm 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)

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

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

Simulation Results 18

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

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

BER vs SNR Comparison for BPSK Modulated Data 21

BER vs SNR Comparison for 16QAM Modulated Data 22

Conclusion 23

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

Thank You 25 Questions

Extra Slides 26

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

Channel Centered Blind Estimation 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

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

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

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

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