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Blind Channel Estimation in OFDM Systems by
Relying on the Gaussian Assumption of the Input
ISSPIT 2009Ajman University of Science &
Technology, UAE
Dec. 15, 2009
Presented by: Ahmed Abdul Quadeer
Outline
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
2
Importance of OFDM Need for Channel Estimation
Introduction3
Importance of OFDM4
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 Estimation5
Transmitter Channel Receiver
X H Y = H ʘ X
X = Y ./ H
Methods based on Approach Methods based on Constraints
Techniques for channel estimation
6
Methods based on Approach
Training-based: Pilots sent with data symbols
Blind: Natural constraints used Semi-Blind: Combination of pilots and
constraints
7
Methods based on Constraints
Data Constraints Finite alphabet Channel coding Pilots Cyclic prefix Gaussian assumption on data
8
Channel Constraints Finite delay spread Frequency correlation Time correlation Transmit/Receive
(spatial) correlation
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
Gaussian Assumption On The Transmitted Data
Time domain transmitted data assumed Gaussian
large weighted sum of i.i.d random variables
10
Distribution of Transmitted Data 11
MLE of the Channel IR
(Gaussian input) + (Gaussian Noise) Gaussian Output
Likelihood function should be uni-modal to pursue a completely blind approach
12
Plot of Likelihood Function vs Channel Taps
N = 64, L = 2, σn2 = 0.1 N = 64, L = 2, σn
2 = 0.1 (Top view)
13
Blind approach using Genetic algorithm Semi-blind approach using Steepest Descent algorithm
Proposed approaches for channel estimation
14
15
Blind Approach: Genetic Algorithm
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
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
16
Evaluating Gradient of Likelihood Function w.r.t Channel IR
Chain rule used
Gradient of Likelihood function w.r.t. channel IR given by
17
Simulation Results18
Simulation Parameters
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
19
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
Conclusion23
Conclusion
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
24
Questions
Thank You25
Extra Slides26
System Overview
Transmitter
Receiver
Modulator
IFFTCyclic Prefix
Cyclic Prefix
RemovalFFTDemodul
ator
Channel Estimati
on
InputBits
Output
Bits
Channel
27
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
Computational Complexity
Gradient and Likelihood function involve two matrix operations, size (N+L) x (N+L)
Block matrix calculations used for reducing the computational complexity
29
Reduction in Complexity
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
30
Constraints used
Data Constraints: Gaussian assumption (on transmitted
data), Cyclic Prefix and Pilots
Channel Constraints: Finite delay spread and Frequency correlation
31
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
OFDM Receiver Requirements
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