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### Lecture: Direction of Arrival (DOA) Estimation

The lecture will teach the theoretical basics required for the study of scientific publications in the field of direction of arrival estimation. Furthermore, some state of the art direction of arrival estimation techniques will be discussed.

#### Introduction

• direction of arrival estimation 

#### Linear Algebra

• matrices
• Hermitian matrices
• Singular Value Decomposition (SVD)

#### Modelling

• phasor notation
• antenna arrays
• random signals 
• normal distribution

#### Subspaces

• correlation matrix
• measurements
• correlated sources [3, 4]

#### Parametric Methods

• Maximum Likelihood Estimator (MLE)
• Deterministic Maximum Likelihood (DML) 

#### Conventional Methods

• beamforming network
• conventional beamformer 
• Capon’s beamformer (Minimum Variance Distortionless Response, MVDR) 

#### Subspace Methods

• MUltiple SIgnal Classification (MUSIC) 
• Estimation of Signal Parameters via Rotational Invariance Techniques (ESPRIT) 

#### General References for the Lecture

mathematical basics: [10, 11]

estimation theory: 

spectral analysis, array signal processing: [13-15]

Radar signal processing is an important application of direction of arrival estimation. From a mathematical perspective, direction of arrival estimation as well as range estimation and velocity estimation are spectral estimation problems.

#### General References for the Lab

digital signal processing: 

Matlab: 

### Presentations

The student shall give a talk on a given topic. As a starting point a paper will be recommended. However, the talk shall not be a mere summary of this paper. It shall rather comprise an original presentation of the theory linked to the lecture and own simulation results.

1. Pisarenko Method 
2. Stochastic Maximum Likelihood (SML) 
3. Minimum Norm Method 
4. Unitary ESPRIT 
5. Single Frequency Estimator 
6. Root MUSIC 
7. Alternating Projection Algorithm (APA) 
8. TLS ESPRIT 
9. Unitary Root MUSIC