Machine Learning Applications
in Electromagnetics and
Antenna Array Processing
Contents
Preface
Acknowledgments
1 Linear Support Vector Machines
1.1 Introduction
1.2 Learning Machines
1.2.1 The Structure of a Learning Machine
1.2.2 Learning Criteria
1.2.3 Algorithms
1.2.4 Example
1.2.5 Dual Representations and Dual Solutions
1.3 Empirical Risk and Structural Risk
1.4 Support Vector Machines for Classification
1.4.1 The SVC Criterion
1.4.2 Support Vector Machine Optimization
1.5 Support Vector Machines for Regression
1.5.1 The ν Support Vector Regression
References
2 Linear Gaussian Processes
2.1 Introduction
2.2 The Bayes’ Rule
2.2.1 Computing the Probability of an Event Conditional to Another
2.2.2 Definition of Conditional Probabilities
2.2.3 The Bayes’ Rule and the Marginalization Operation
2.2.4 Independency and Conditional Independency
2.3 Bayesian Inference in a Linear Estimator
2.4 Linear Regression with Gaussian Processes
2.4.1 Parameter Posterior
2.5 Predictive Posterior Derivation
2.6 Dual Representation of the Predictive Posterior
2.6.1 Derivation of the Dual Solution
2.6.2 Interpretation of the Variance Term
2.7 Inference over the Likelihood Parameter
2.8 Multitask Gaussian Processes
References
3
Kernels for Signal and Array Processing
3.1 Introduction
3.2 Kernel Fundamentals and Theory
3.2.1 Motivation for RKHS
3.2.2 The Kernel Trick
3.2.3 Some Dot Product Properties
3.2.4 Their Use for Kernel Construction
3.2.5 Kernel Eigenanalysis
3.2.6 Complex RKHS and Complex Kernels
3.3 Kernel Machine Learning
3.3.1 Kernel Machines and Regularization
3.3.2 The Importance of the Bias Kernel
3.3.3 Kernel Support Vector Machines
3.3.4 Kernel Gaussian Processes
3.4 Kernel Framework for Estimating Signal Models
3.4.1 Primal Signal Models
3.4.2 RKHS Signal Models
3.4.3 Dual Signal Models
References
4 The Basic Concepts of Deep Learning
4.1 Introduction
4.2 Feedforward Neural Networks
4.2.1 Structure of a Feedforward Neural Network
4.2.2 Training Criteria and Activation Functions
4.2.3 ReLU for Hidden Units
4.2.4 Training with the BP Algorithm
4.3 Manifold Learning and Embedding Spaces
4.3.1 Manifolds, Embeddings, and Algorithms
4.3.2 Autoencoders
4.3.3 Deep Belief Networks
References
5 Deep Learning Structures
5.1 Introduction
5.2 Stacked Autoencoders
5.3 Convolutional Neural Networks
5.4 Recurrent Neural Networks
5.4.1 Basic Recurrent Neural Network
5.4.2 Training a Recurrent Neural Network
5.4.3 Long Short-Term Memory Network
5.5 Variational Autoencoders
References
6
Direction of Arrival Estimation
6.1 Introduction
6.2 Fundamentals of DOA Estimation
6.3 Conventional DOA Estimation
6.3.1 Subspace Methods
6.3.2 Rotational Invariance Technique
6.4 Statistical Learning Methods
6.4.1 Steering Field Sampling
6.4.2 Support Vector Machine MuSiC
6.5 Neural Networks for Direction of Arrival
6.5.1 Feature Extraction
6.5.2 Backpropagation Neural Network
6.5.3 Forward-Propagation Neural Network
6.5.4 Autoencoder Framework for DOA Estimation with Array Imperfections
6.5.5 Deep Learning for DOA Estimation with Random Arrays
References
7 Beamforming
7.1 Introduction
7.2 Fundamentals of Beamforming
7.2.1 Analog Beamforming
7.2.2 Digital Beamforming/Precoding
7.2.3 Hybrid Beamforming
7.3 Conventional Beamforming
7.3.1 Beamforming with Spatial Reference
7.3.2 Beamforming with Temporal Reference
7.4 Support Vector Machine Beamformer
7.5 Beamforming with Kernels
7.5.1 Kernel Array Processors with Temporal Reference
7.5.2 Kernel Array Processor with Spatial Reference
7.6 RBF NN Beamformer
7.7 Hybrid Beamforming with Q-Learning
References
8 Computational Electromagnetics
8.1 Introduction
8.2 Finite-Difference Time Domain
8.2.1 Deep Learning Approach
8.3 Finite-Difference Frequency Domain
8.3.1 Deep Learning Approach
8.4 Finite Element Method
8.4.1 Deep Learning Approach
8.5 Inverse Scattering
8.5.1 Nonlinear Electromagnetic Inverse Scattering Using DeepNIS
References
9 Reconfigurable Antennas and Cognitive Radio
9.1 Introduction
9.2 Basic Cognitive Radio Architecture
9.3 Reconfiguration Mechanisms in Reconfigurable Antennas
9.4 Examples
9.4.1 Reconfigurable Fractal Antennas
9.4.2 Pattern Reconfigurable Microstrip Antenna
9.4.3 Star Reconfigurable Antenna
9.4.4 Reconfigurable Wideband Antenna
9.4.5 Frequency Reconfigurable Antenna
9.5 Machine Learning Implementation on Hardware
9.6 Conclusion
References
About the Authors
Index