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