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 joaopaulo.dacosta@ene.unb.br

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

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

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

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

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

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

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

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

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

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

= 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

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