1. Estimation Techniques for High Resolution and Multi-Dimensional Array Signal Processing EMS Group – Fh IIS and TU IL Electronic Measurements and Signal Processing Group (EMS) LASP – UnB Laboratory of Array Signal Processing
Prof. João Paulo C. Lustosa da Costa

2. Content of the intensive course (1)
Introduction to multi-channel systems
Mathematical background
High resolution array signal processing
Model order selection
Beamforming
Direction of arrival (DOA) estimation
Signal reconstruction via pseudo inverse
Prewhitening
Independent component analysis (ICA) for instantaneous mixtures
ICA for convolutive mixtures 2 2

3. Content of the intensive course (1)
Introduction to multi-channel systems
Mathematical background
High resolution array signal processing
Model order selection
Beamforming
Direction of arrival (DOA) estimation
Signal reconstruction via pseudo inverse
Prewhitening
Independent component analysis (ICA) for instantaneous mixtures
ICA for convolutive mixtures 3 3

4. Introduction to multichannel systems (1)
Standard (Matrix) Array Signal Processing
Four gains: array gain, diversity gain, spatial multiplexing gain and interference reduction gain RX TX
Array gain: 3 for each side
Diversity gain: same information for each path
Spatial multiplexing gain: different information for each path 4

5. Introduction to multichannel systems (2)
Standard (Matrix) Array Signal Processing
Four gains: array gain, diversity gain, spatial multiplexing gain and interference reduction gain RX TX
Array gain: 3 for each side
Diversity gain: same information for each path
Spatial multiplexing gain: different information for each path 5

6. Introduction to multichannel systems (3)
Standard (Matrix) Array Signal Processing
Four gains: array gain, diversity gain, spatial multiplexing gain and interference reduction gain RX TX
Interferer 6

7. Introduction to multichannel systems (4)
Standard (Matrix) Array Signal Processing
Four gains: array gain, diversity gain, spatial multiplexing gain and interference reduction gain RX TX
Interferer 7

8. Introduction to multichannel systems (5)
MIMO Channel Model
Direction of Departure (DOD)
Transmit array: 1-D or 2-D
Direction of Arrival (DOA)
Receive array: 1-D or 2-D
Frequency
Delay
Time
Doppler shift 8

9. Introduction to multichannel systems (6)
Multi-dimensional array signal processing
Dimensions depend on the type of application
MIMO
Received data: two spatial dimensions, frequency and time
Channel: 4 spatial dimensions, frequency and time
Microphone array
Received data: one spatial dimension and time
After Time Frequency Analysis
Space, time and frequency
EEG (similarly as microphone array)
Psychometrics
Chemistry
Food industry 9

10. Introduction to multichannel systems (7)
Multi-dimensional array signal processing
Advantages: increased identifiability, separation without imposing additional constraints and improved accuracy (tensor gain) m1 m2 1 1 1 2 1 3 2 1 2 2 2 3
RX: Uniform
Rectangular Array (URA) 3 1 3 2 3 3 n 1 2 3
9 x 3 matrix: maximum rank is 3.
Solve maximum 3 sources! 10

11. Rectangular Array (URA)
Introduction to multichannel systems (8)
Multi-dimensional array signal processing
Advantages: increased identifiability, separation without imposing additional constraints and improved accuracy (tensor gain) m1 1 2 3 n 1 2 3 m2 1 2 3
RX: Uniform
Rectangular Array (URA)
3 x 3 x 3 tensor: maximum rank is 5.
Solve maximum 5 sources!
J. B. Kruskal. Rank, decomposition, and uniqueness for 3-way and N-way arrays. Multiway Data Analysis, pages 7–18, 1989 11

12. = Introduction to multichannel systems (9) + +
Multi-dimensional array signal processing
Advantages: increased identifiability, separation without imposing additional constraints and improved accuracy (tensor gain)
For matrix model, nonrealistic assumptions such as orthogonality (PCA) or independence (ICA) should be done.
For tensor model, separation is unique up to scalar and permutation ambiguities. = + + 12

13. Introduction to multichannel systems (10)
Multi-dimensional array signal processing
Advantages: increased identifiability, separation without imposing additional constraints and improved accuracy (tensor gain)
Array interpolation due to imperfections
Application of tensor based techniques
Estimation of number of sources d
also known as model order selection
multi-dimensional schemes: better accuracy
Prewhitening schemes
multi-dimensional schemes: better accuracy and lower complexity
Parameter estimation
Drastic reduction of computational complexity
Multidimensional searches are decomposed into several one dimensional searches 13