Adaptive & Array Signal Processing AASP

Transcrição

1 Adaptive & Array Signal Processing AASP Prof. Dr.-Ing. João Paulo C. Lustosa da Costa University of Brasília (UnB) Department of Electrical Engineering (ENE) Laboratory of Array Signal Processing PO Box 4386 Zip Code , Brasília - DF Homepage: 1

2 Lectures in English The lectures are taught in English - to familiarize the students with the linguistic requirements of a global economy, where technical discussions between international partners are usually conducted in English. In many universities AASP subject is offered in English - TU Ilmenau and TU Munich 2

3 Information about the Lecturer Academic Background Ph.D. in Electrical Engineering at TU Ilmenau in Germany in 2010 Master s in Electrical Engineering at UnB in 2006 Bachelor in Electronic Engineering at IME in 2003 Research areas Multidimensional Array Signal Processing MIMO Systems, parameter estimation, multilinear algebra, principal component analysis More information Contact (to schedule meetings) [email protected] 3

4 Research Area 1: Audio Sound Sources Localization Sound source 1 Microphone array Sound source 2 Applications: Intelligent Hearing Aid (PAI), interface between human and machine, and data processing. 4

5 Research Area 2: Telecommunications Channel Modeling Direction of Departure (DOD) Transmitter Array: 1-D or 2-D Direction of Arrival (DOA) Receiver array: 1-D or 2-D Frequency Time Delay Doppler shift 5

6 Information about the subject at Login and password thevenin 6

7 Objectives of the subject To allow the students to apply adaptive and array signal processing schemes to solve problems in different scientific fields The achievement of the objective is based on the final project and on the exam. 7

8 [1] Bibliography [2] S. Haykin, Adaptive Filter Theory, 3rd Edition, Prentice-Hall. [3] A. H. Sayed, Fundamentals of Adaptive Filtering, John Wiley and Sons, [4] M. Haardt, Efficient One-, Two- and Multidimensional High-Resolution Array Signal Processing, Shaker, [5] J. P. C. L. da Costa, Parameter Estimation Techniques for Multi- Dimensional Array Signal Processing, Shaker, [6] S. Makino, T.-W. Lee, and S. Sawada, Blind Speech Separation, Springer, [7] Slides, notes and papers suggested in this course. 8

9 Grades The final grade is given by: 50 % of the AASP project; 50 % of the written exam (probably at 11/06/2015). 9

10 AASP Project The title of the project should be informed until 24/03/2015. The students that suggest a new research theme should include a short description about the theme. only two students for each theme MATLAB should be used A preview presentation of the work at 21/04/2015 The intermediate presentation at 19/05/2015 together with a short two page abstract The final presentation at 16/06/2015 and 18/06/2015 together with a four page paper The abstract and the final written work should follow the IEEE template available at LASP homepage Include abstract, introduction, data model, technique description, simulations, and conclusions 10

11 See homepage Previous students 11

12 Motivation (1) An unlimited list of applications Radar; Sonar; Communications; Medical imaging; Chemistry; Food industry; Pharmacy; Psychometrics; Reflection seismology; EEG;

13 Stock Markets: One example of [1] Motivation (2) Information: Long Term Government Bond interest rates. Canada, USA, 6 European countries and Japan. Result: by visual inspection of the Eigenvalues (EVD). Three main components: Europe, Asia and North America. [1]: M. Loteran, Generating market risk scenarios using principal components analysis: methodological and practical considerations, in the Federal Reserve Board, March, 1997.

14 Wavelength Motivation (3) Ultraviolet-visible (UV-vis) Spectrometry [2] Radiation Non-identified substance Oxidation state samples Result: successful application of tensor calculus. In [2], the model order is estimated via the core consistency analysis (CORCONDIA) by visual inspection. [2]: K. S. Von Age, R. Bro, and P. Geladi, Multi-way analysis with applications in the chemical sciences, Wiley, Aug

15 Exam Preparation based on slides; Book S. Haykin, Adaptive Filter Theory, 3rd Edition, Prentice- Hall Solve the recommended exercicises 15

16 Content of AASP (1) 1 Introduction - Adaptive Filters - Single channel adaptive equalization (temporal filter) - Multi channel adaptive beamforming (spatial filter) 2 Mathematical Background 2.1 Calculus - Gradients - Differentiation with respect to a complex vector - Quadratic optimization with linear constraints (method of Lagrangian multipliers) 2.2 Stochastic processes - Stationary processes - Time averages - Ergodic processes

17 Content of AASP (2) - Correlation matrices 2.3 Linear algebra - Eigenvalue decomposition - Eigenfilter - Linear system of equations - Four fundamental subspaces - Singular value decomposition - Generalized inverse of a matrix - Projections - Low rank modeling 3 Adaptive Filters 3.1 Linear Optimum Filtering (Wiener Filters) - Principle of Orthogonality - Wiener-Hopf equations 17

18 Content of AASP (3) - Error-performance surface - MMSE (minimum mean-squared error) - MMSE filtering in case of linear Models 3.2 Linearly Constrained Minimum Variance Filter - LCMV beamformer - Minimum Variance Distortionless Response (MVDR) spectrum: Capon's method - LCMV beamforming with multiple linear constraints 3.3 Generalized Sidelobe Canceler 3.4 Iterative Solution of the Normal Equations - Steepest descent algorithm - Stability of the algorithm - Optimization of the step-size 18

19 Content of AASP (4) 3.5 Least Mean Square (LMS) Algorithm 3.6 Kalman filter 4 High-Resolution Parameter Estimation - Data model (DOA estimation) - Eigendecomposition of the spatial correlation matrix at RX - Subspace estimates 4.1 Estimation of the model order 4.2 Maximum Likelihood 4.3 Expectation-Maximization 4.4 Spectral MUSIC - DOA estimation - Example: uniform linear array (ULA) - MVDR spatial spectrum estimation (review) 4.5 Standard ESPRIT 19

20 Content of AASP (5) - Selection matrices - Shift invariance property 4.6 Signal Reconstruction - LS solution 4.7 Spatial smoothing 4.8 Forward-backward averaging 4.9 Instantaneous Independent Component Analysis (ICA) 4.10 Convolutive ICA 4.11 Multidimensional Extensions 20

21 Content of AASP (6) 5 Tensor-Based Signal Processing 5.1 Higher Order Singular Value Decomposition 5.2 Parallel Factor Analysis (PARAFAC) 5.3 Closed-Form PARAFAC 5.4 Examples of multidimensional extensions of matrix based schemes 21