Adaptive and Array Signal Processing, Part 1 - Interaktive Studienpläne der TU Ilmenau

After completing this module, the students are able to understand the fundamental concepts of adaptive filters and array signal processing. These concepts include the mathematical background, in particular concepts and "tricks" that can be used for the derivation of new research results. Furthermore, they range from adaptive temporal and spatial filters to (multi-dimensional) high-resolution parameter estimation techniques and tensor-based signal processing concepts. The students have a deep understanding of these universal (timeless) principles that are applicable in several research areas and disciplines.

The students are enabled to read and understand current research publications in the areas of adaptive filters and array signal processing. They are able use these concepts and results for their own research and understand the presentations about these topics at international conferences. Furthermore, they are able to read and understand current IEEE journal and conference publications in this area. Moreover, they have been enabled to develop new research ideas and results that build on this published "state-of-the-art."

1Introduction
- 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  
- Correlation matrices 2.3Linear 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  
- Error-performance surface 
- MMSE (minimum mean-squared error) 
- Canonical form of the error-performance surface 
- 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
3.5 Least Mean Square (LMS) Algorithm 
3.6 Recursive Least Squares (RLS) Algorithm

4 High-Resolution Parameter Estimation  
- Data model (DOA estimation)  
- Eigendecomposition of the spatial correlation matrix at the receive array  
- Subspace estimates  
- Estimation of the model order
4.1 Spectral MUSIC 
- DOA estimation  
- Example: uniform linear array (ULA) 
- Root-MUSIC for ULAs 
- Periodogram 
- MVDR spatial spectrum estimation (review)
4.2 Standard ESPRIT 
- Selection matrices 
- Shift invariance property
4.3 Signal Reconstruction 
- LS solution 
- MVDR / BLUE solution  
- Wiener solution (MMSE solution) 
- Antenna patterns 
4.4 Spatial smoothing

Skript, Overheadprojektor, Beamer Script, projector

• T. Kaiser, A. Bourdoux, H. Boche, Smart Antennas State of The Art.
  
• Hindawi Publishing Corporation, 2005.
• A. H. Sayed, Fundamentals of Adaptive Filtering.
  John Wiley & Sons, Inc., New York, NY, 2003.
• T. K. Moon and W. C. Stirling, Mathematical Methods and Algorithms for Signal Processing.
  Prentice-Hall, 2000.
• S. Haykin and M. Moher, Modern Wireless Communications.
  Pearson Education, Inc., 2005.
• S. Haykin, Adaptive Filter Theory.
  Prentice-Hall, 4th edition, 2002.
• A. Paulraj, R. Nabar, and D. Gore, Introduction to Space-Time Wireless Communications.
  Cambridge University Press, 2003.
• H. L. V. Trees, Optimum Array Processing.
  John Wiley & Sons, Inc., New York, NY, 2002.
• M. Haardt, Efficient One-, Two-, and Multidimensional High-Resolution Array Signal Processing.
  Shaker Verlag GmbH, 1996, ISBN: 978-3-8265-2220-8.
• G. Strang, Linear Algebra and Its Applications.
  Thomson Brooks/Cole Cengage learning.
• G. Strang, Introduction to Linear Algebra.
  Wellesley - Cambridge Press, Fifth Edition.
• L. L. Scharf, Statistical Signal Processing.
  Addison-Wesley Publishing Co., 1991.
• S. M. Kay, Fundamentals of Statistical Signal Processing, Estimation Theory.
  Prentice-Hall, Englewood Cliffs, N.J., 1993.
• M. Haardt, M. Pesavento, F. Roemer, and M. N. El Korso, Subspace methods and exploitation of special array structures.
  in Academic Press Library in Signal Processing: Volume 3 - Array and Statistical Signal Processing (A. M. Zoubir, M. Viberg, R. Chellappa, and S. Theodoridis, eds.), vol. 3, pp. 651 - 717, Elsevier Ltd., 2014, Chapter 15, ISBN 978-0-12-411597-2 ISBN: 978-3-8265-2220-8.