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Adaptive Filters Spring 2015 CSE 623

Adaptive Filters CSE 623 Spring 2015

Course Information

DEPARTMENT & PROGRAM:   Electrical Engineering, Masters in Wireless Communications

              

COURSE CODE-COURSE NAME: EE-623 Adaptive Filters.                                                 CR: 3

 

COURSE DESCRIPTION:

 

Students attending this lecture should learn the basics of adaptive filters. To achieve this, necessary algorithms will be derived and applied to problems arising in speech and audio processing. The algorithms comprise Wiener filtering, linear prediction, and adaptive schemes such as the NLMS algorithm, affine projection, and the RLS algorithm. For applications from speech and audio processing we use noise and reverberation reduction, echo cancellation, and beamforming.

 

 

PREREQUISITE:          EE-771 Stochastic Processes

 

 

CO-REQUISITE:           None

 

TEXT AND MATERIALS:

Textbook

ADAPTIVE FILTERS THEORY AND APPLICATIONS

Second Edition, Behrouz Farhang-Boroujeny, University of Utah, USA

 

References Material:

  1. Adaptive Filters by Ali H.Sayed, 2008
  2. Adaptive Filter Theory by Simon Haykin, 2002
  3. Adaptive Filtering Algorithms and Practical Implementation Fourth Edition by Paulo S. R. Diniz

 

RELEVANT PROGRAM LEARNING OUTCOME:

The course is designed so that students will achieve the PLO/s:

  1. Design/Development of Solution: Design solution for complex Networks problems and design Networks/Systems, components or processes that meets specified needs with appropriate consideration for public health and safety, cultural societal and environmental considerations.
  2. Investigation: Conduct investigation into complex problems using research based methods including design experiments, analysis and interpretation of data, and synthesis of information to provide valid conclusions.

 

Course Objectives:

The aim of the course is to introduce techniques in adaptive signal processing and adaptive filter theory with applications on related fields. Also the objective of this course is to provide the mathematical framework for an understanding of adaptive statistical signal processing, where the goal is to extract information from noisy or corrupted data, where the properties of the signal and/or the interference are partially unknown or change with time. The basic tools of vector spaces and discrete-time stochastic processes are reviewed and applied to the methods of Wiener filtering and least-squares filtering. Various types of adaptive filters will be introduced and their properties will be studied, specifically convergence, tracking, robustness and computational complexity. Applications will mainly be addressed through student MATLAB based projects.

 

Course Learning Outcomes:

This course treats adaptive signal processing algorithms for extracting relevant information from noisy signals. The emphasis is on recursive, model based estimation methods for signals and systems whose properties change in time. Applications in, for example, communications, control and medicine are discussed.

Upon successful completion of the course, the student will be able to:

 

  1. Identify applications in which it would be possible to use the different adaptive filtering approaches. Analyze the accuracy and determine advantages and disadvantages of each method.

 

  1. Design and apply optimal minimum mean square estimators and in particular linear estimators. To understand and compute their expected performance and verify it. Design, implement and apply Wiener filters (FIR, non-causal, causal) and evaluate their performance. Design, implement and apply LMS and RLS filters for given applications.

 

  1. Use a combination of theory and software implementations to solve adaptive signal problems.  Use the theoretical understanding to do troubleshooting, e.g., in cases the observed performance is not as expected.

 

  1. Report the solution and results from the application of the adaptive filtering techniques to given problems. Implement and apply LMS and RLS filters for given applications.

 

 

PRACTICAL APPLICATIONS

The practical applications of this course are as follows

  1. System identification
  2. Linear predictor
  3. Inverse modeling
  4. Jammer suppression
  5. Adaptive notch filter
  6. Noise canceller
  7. Echo cancellation
  8. Voice echo canceller
  9. Data echo canceller
  10. Multiple-input multiple-output (MIMO) echo cancellation
  11. Adaptive feedback cancellation in hearing aids
  12. Fetal monitoring, cancelling of maternal ECG during labor

 

 

LECTURE PLAN:

Instruction                         70%

Discussion                         10%

Project                               10%

Exercises/Tutorial              10%

COURSE TARGETS

 

Module No.

CLO No.

Teaching Methodology

Assessment Methodology

Learning Domain with Level

I, II, IV, XIII

1

Lecture, Discussion

Quiz, Assignment, Exam

C1

III, V, VI, X,

2

Lecture, Discussion

Quiz, Assignment, Exam

C3

VII, VIII, IX, XI

3

Lecture, Discussion, Presentation

Quiz, Assignment, Exam

C2

 XII, XIV, XV

4

Lecture, Discussion, Presentation

Quiz, Assignment, Exam

C3

 

ASSESMENT:

Assignments          10%

Quizzes                 15%

OHT Exam            30%

Project                   15%

Final Exam            30%

_____________________________

Total                      100%

Course Contents

Module

Topic

Reference

Week/Lecture

 

I.

   

1.  Introduction

1.1 Linear Filters

1.2 Adaptive Filters

1.3 Adaptive Filter Structures

1.4 Adaptation Approaches

             1.4.1 Approach Based on Wiener Filter Theory

1.4.2 Method of Least-Squares

1.5 Real and Complex Forms of Adaptive Filters

 

 

Chapter 1

 

 

 

 

 

 

    

       1/1-2

 

 

 

 

 

 

II.

1.6 Applications

1.6.1 Modeling

1.6.2 Inverse Modeling

1.6.3 Linear Prediction

1.6.4 Interference Cancellation

 

  Chapter 1

2/3-4

III.

3 Wiener Filters

3.1 Mean-Squared Error Criterion

3.2 Wiener Filter – Transversal, Real-Valued Case

3.3 Principle of Orthogonality

3.4 Normalized Performance Function

3.5 Extension to Complex-Valued Case

3.6 Unconstrained Wiener Filters

3.6.1 Performance Function

3.6.2 Optimum Transfer Function

3.6.3 Modeling

3.6.4 Inverse Modeling

3.6.5 Noise Cancellation

 

Chapter 3

3/5-6

IV.

4 Eigenanalysis and Performance Surface

4.1 Eigenvalues and Eigenvectors

4.2 Properties of Eigenvalues and Eigenvectors

4.3 Performance Surface

Chapter 4

4/7-8

 

V.

 

 

 

 

 

 

VI.

 

 

 

 

 

 

 

 

 

 

 

 

VII.

 

 

 

 

 

 

 

 

 

 

 

 

 

VIII.

 

 

 

 

 

 

 

 

 

 

 

IX.

 

 

 

 

 

 

 

 

 

 

X.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

XI.

 

 

 

 

 

 

 

XII.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

XIII.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

XIV.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

XV.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

XVI.

 

5 Search Methods

5.1 Method of Steepest Descent

5.2 Learning Curve

5.3 Effect of Eigenvalue Spread

5.4 Newton’s Method

5.5 An Alternative Interpretation of Newton’s Algorithm

        

6 LMS Algorithm

6.1 Derivation of LMS Algorithm

6.2 Average Tap-Weight Behavior of the LMS Algorithm

6.3 MSE Behavior of the LMS Algorithm

6.3.1 Learning Curve

6.3.2 Weight-Error Correlation Matrix

6.3.3 Excess MSE and Misadjustment

6.3.4 Stability

6.3.5 The Effect of Initial Values of Tap Weights on the Transient  Behavior

          

6 LMS Algorithm

6.5 Simplified LMS Algorithms

6.6 Normalized LMS Algorithm

6.7 Affine Projection LMS Algorithm

6.8 Variable Step-Size LMS Algorithm

6.9 LMS Algorithm for Complex-Valued Signals

6.10 Beamforming (Revisited)

6.11 Linearly Constrained LMS Algorithm

6.11.1 Statement of the Problem and Its Optimal Solution

6.11.2 Update Equations

          

 

9 Subband Adaptive Filters

9.1 DFT Filter Banks

9.1.1 Weighted Overlap–Add Method for Realization of DFT Analysis Filter Banks

9.1.2 Weighted Overlap–Add Method for Realization of DFT Synthesis Filter Banks

9.2 Complementary Filter Banks

9.3 Subband Adaptive Filter Structures

9.4 Selection of Analysis and Synthesis Filters

9.5 Computational Complexity

9.6 Decimation Factor and Aliasing

 

 

10 IIR Adaptive Filters

10.1 Output Error Method

10.2 Equation Error Method

10.3 Case Study : IIR Adaptive Line Enhancement

10.3.1 IIR ALE Filter, W(z)

10.3.2 Performance Functions

10.3.3 Simultaneous Adaptation of s and w

10.3.4 Robust Adaptation of  w

12.5.4 Excess MSE and Misadjustment

12.5.5 Initial Transient Behavior of the RLS Algorithm

 

14 Tracking

14.1 Formulation of the Tracking Problem

14.2 Generalized Formulation of LMS Algorithm

14.3 MSE Analysis of the Generalized LMS Algorithm

14.4 Optimum Step-Size Parameters

14.5 Comparisons of Conventional Algorithms

14.6 Comparisons Based on Optimum Step-Size Parameters

14.7 VSLMS: An Algorithm with Optimum Tracking Behavior

14.7.1 Derivation of VSLMS Algorithm

14.7.2 Variations and Extensions

14.7.3 Normalization of the Parameter ρ

14.7.4 Computer Simulations

14.8 RLS Algorithm with Variable Forgetting Factor

 

 

 

16 Active Noise Control

16.1 Broadband Feedforward Single-Channel ANC

16.1.1 System Block Diagram in the Absence of the Secondary Path S1(z)

16.1.2 Filtered-X LMS Algorithm

16.1.3 Convergence Analysis

16.1.4 Adding the Secondary Path S1(z)

 

 

17 Synchronization and Equalization in Data Transmission Systems

17.1 Continuous Time Channel Model

17.2 Discrete Time Channel Model and Equalizer Structures

17.2.1 Symbol-Spaced Equalizer

17.2.2 Fractionally Spaced Equalizer

17.2.3 Decision Feedback Equalizer

17.3 Timing Recovery

17.3.1 Cost Function

17.3.2 The Optimum Timing Phase

17.3.3 Improving the Cost Function

17.3.4 Algorithms

17.3.5 Early-Late Gate Timing Recovery

17.3.6 Gradient-Based Algorithm

17.4 Equalizers Design and Performance Analysis

17.4.1 Wiener–Hopf Equation for Symbol-Spaced Equalizers

17.4.2 Numerical Examples

17.5 Adaptation Algorithms

 

 

18 Sensor Array Processing

18.1 Narrowband Sensor Arrays

18.1.1 Array Topology and Parameters

18.1.2 Signal subspace, noise subspace, and spectral factorization

18.1.3 Direction of Arrival Estimation

18.1.4 Beamforming Methods

18.2 Broadband Sensor Arrays

18.2.1 Steering

18.2.2 Beamforming Methods

18.3 Robust Beamforming

18.3.1 Soft-Constraint Minimization

18.3.2 Diagonal Loading Method

18.3.3 Methods Based on Sample Matrix Inversion

 

19 Code Division Multiple Access Systems

19.1 CDMA Signal Model

19.1.1 Chip-Spaced Users-Synchronous Model

19.1.2 Chip-Spaced Users-Asynchronous Model

19.1.3 Fractionally Spaced Model

19.2 Linear Detectors

19.2.1 Conventional Detector: The Matched Filter Detector

19.2.2 Decorrelator Detector

19.2.3 Minimum Mean-Squared Error (Optimal) Detector

19.2.4 Minimum Output Energy (Blind) Detector

19.2.5 Soft Detectors

19.3 Adaptation Methods

19.3.1 Conventional Detector

19.3.2 Decorrelator Detector

19.3.3 MMSE Detector

19.3.4 MOE Detector

19.3.5 Soft Detectors

 

20 OFDM and MIMO Communications

20.1 OFDM Communication Systems

20.1.1 The Principle of OFDM

20.1.2 Packet Structure

20.1.3 Carrier Acquisition

20.1.4 Timing Acquisition

20.1.5 Channel Estimation and Frequency Domain Equalization

20.1.6 Estimation of Rhh and Rνν

20.1.7 Carrier-Tracking Methods

20.1.8 Channel-Tracking Methods

20.2 MIMO Communication Systems

20.2.1 MIMO Channel Model

20.2.2 Transmission Techniques for Space-Diversity Gain

20.2.3 Transmission Techniques and MIMO Detectors

for Space-Multiplexing Gain

20.2.4 Channel Estimation Methods

20.3 MIMO–OFDM

 

Review Week

 

Chapter 5

 

 

 

 

 

 

Chapter 6

 

 

 

 

 

 

 

 

 

 

 

 

Chapter 6

 

 

 

 

 

 

 

 

 

 

 

 

 

Chapter 9

 

 

 

 

 

 

 

 

 

 

 

Chapter 10

 

 

 

 

 

 

 

 

 

 

Chapter 14

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Chapter 16

 

 

 

 

 

 

 

Chapter 17

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Chapter 18

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Chapter 19

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Chapter 20

 

5/9-10

 

 

 

 

 

 

6/11-12

 

 

 

 

 

 

 

 

 

 

 

 

7/13-14

 

 

 

 

 

 

 

 

 

 

 

 

 

8/15-16

 

 

 

 

 

 

 

 

 

 

 

9/17-18

 

 

 

 

 

 

 

 

 

 

10/19-20

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

11/21-22

 

 

 

 

 

 

 

12/23-24

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

13/25-26

 

 

 

 

 

 

 

 

 

 

 

 

 

 

14/27-28

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

15/29-30

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

16/31-32

 

 

 

 

 

Final Examination

 

16

Term Projects

Course Comments