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Blind Channel Estimation in OFDM Systems by Relying on the Gaussian Assumption of the Input
ISSPIT Ajman University of Science & Technology, UAE Presented by: Ahmed Abdul Quadeer Dec. 15, 2009
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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
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Introduction 3 Importance of OFDM Need for Channel Estimation
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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.
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Need for Channel Estimation
5 Transmitter Channel Receiver Y = H ʘ X X H X = Y ./ H
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Techniques for channel estimation
6 Methods based on Approach Methods based on Constraints
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Methods based on Approach
7 Training-based: Pilots sent with data symbols Blind: Natural constraints used Semi-Blind: Combination of pilots and constraints
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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
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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
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Gaussian Assumption On The Transmitted Data
10 Time domain transmitted data assumed Gaussian large weighted sum of i.i.d random variables
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Distribution of Transmitted Data
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MLE of the Channel IR 12 (Gaussian input) + (Gaussian Noise) Gaussian Output Likelihood function should be uni-modal to pursue a completely blind approach
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Plot of Likelihood Function vs Channel Taps
13 N = 64, L = 2, σn2 = 0.1 N = 64, L = 2, σn2 = 0.1 (Top view)
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Proposed approaches for channel estimation
14 Blind approach using Genetic algorithm Semi-blind approach using Steepest Descent algorithm
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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)
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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
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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
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Simulation Results 18
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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
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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
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BER vs SNR Comparison for BPSK Modulated Data
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BER vs SNR Comparison for 16QAM Modulated Data
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Conclusion 23
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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
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Thank You 25 Questions
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Extra Slides 26
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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
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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
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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
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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 point FFT
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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
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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
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