Table Of ContentMachine Learning Applications
in Electromagnetics and
Antenna Array Processing
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ForalistingofrecenttitlesintheArtechHouseElectromagneticsSeries,
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Machine Learning Applications
in Electromagnetics and
Antenna Array Processing
Manel Martínez-Ramón
Arjun Gupta
José Luis Rojo-Álvarez
Christos Christodoulou
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ISBN13:978-1-63081-775-6
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Contents
Preface xi
Acknowledgments xiii
1 LinearSupportVectorMachines 1
1.1 Introduction 1
1.2 LearningMachines 2
1.2.1 TheStructureofaLearningMachine 3
1.2.2 LearningCriteria 4
1.2.3 Algorithms 6
1.2.4 Example 8
1.2.5 DualRepresentationsandDualSolutions 8
1.3 EmpiricalRiskandStructuralRisk 12
1.4 SupportVectorMachinesforClassification 16
1.4.1 TheSVCCriterion 16
1.4.2 SupportVectorMachineOptimization 20
1.5 SupportVectorMachinesforRegression 27
1.5.1 Theν SupportVectorRegression 29
References 32
v
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vi MachineLearningApplicationsinElectromagneticsandAntennaArrayProcessing
2 LinearGaussianProcesses 35
2.1 Introduction 35
2.2 TheBayes’Rule 36
2.2.1 ComputingtheProbabilityofanEvent
ConditionaltoAnother 37
2.2.2 DefinitionofConditionalProbabilities 38
2.2.3 TheBayes’RuleandtheMarginalization
Operation 38
2.2.4 IndependencyandConditional
Independency 39
2.3 BayesianInferenceinaLinearEstimator 40
2.4 LinearRegressionwithGaussianProcesses 41
2.4.1 ParameterPosterior 42
2.5 PredictivePosteriorDerivation 44
2.6 DualRepresentationofthePredictivePosterior 46
2.6.1 DerivationoftheDualSolution 46
2.6.2 InterpretationoftheVarianceTerm 49
2.7 InferenceovertheLikelihoodParameter 53
2.8 MultitaskGaussianProcesses 56
References 58
3 KernelsforSignalandArrayProcessing 61
3.1 Introduction 61
3.2 KernelFundamentalsandTheory 62
3.2.1 MotivationforRKHS 63
3.2.2 TheKernelTrick 68
3.2.3 SomeDotProductProperties 71
3.2.4 TheirUseforKernelConstruction 76
3.2.5 KernelEigenanalysis 80
3.2.6 ComplexRKHSandComplexKernels 89
3.3 KernelMachineLearning 91
3.3.1 KernelMachinesandRegularization 92
3.3.2 TheImportanceoftheBiasKernel 96
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Contents vii
3.3.3 KernelSupportVectorMachines 100
3.3.4 KernelGaussianProcesses 106
3.4 KernelFrameworkforEstimatingSignalModels 108
3.4.1 PrimalSignalModels 110
3.4.2 RKHSSignalModels 113
3.4.3 DualSignalModels 116
References 118
4 TheBasicConceptsofDeepLearning 121
4.1 Introduction 121
4.2 FeedforwardNeuralNetworks 123
4.2.1 StructureofaFeedforwardNeural
Network 123
4.2.2 TrainingCriteriaandActivationFunctions 126
4.2.3 ReLUforHiddenUnits 131
4.2.4 TrainingwiththeBPAlgorithm 132
4.3 ManifoldLearningandEmbeddingSpaces 141
4.3.1 Manifolds,Embeddings,andAlgorithms 143
4.3.2 Autoencoders 147
4.3.3 DeepBeliefNetworks 158
References 163
5 DeepLearningStructures 167
5.1 Introduction 167
5.2 StackedAutoencoders 168
5.3 ConvolutionalNeuralNetworks 175
5.4 RecurrentNeuralNetworks 183
5.4.1 BasicRecurrentNeuralNetwork 183
5.4.2 TrainingaRecurrentNeuralNetwork 184
5.4.3 LongShort-TermMemoryNetwork 186
5.5 VariationalAutoencoders 188
References 193
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viii MachineLearningApplicationsinElectromagneticsandAntennaArrayProcessing
6 DirectionofArrivalEstimation 195
6.1 Introduction 195
6.2 FundamentalsofDOAEstimation 197
6.3 ConventionalDOAEstimation 202
6.3.1 SubspaceMethods 202
6.3.2 RotationalInvarianceTechnique 204
6.4 StatisticalLearningMethods 206
6.4.1 SteeringFieldSampling 206
6.4.2 SupportVectorMachineMuSiC 213
6.5 NeuralNetworksforDirectionofArrival 217
6.5.1 FeatureExtraction 217
6.5.2 BackpropagationNeuralNetwork 219
6.5.3 Forward-PropagationNeuralNetwork 222
6.5.4 AutoencoderFrameworkforDOA
EstimationwithArrayImperfections 226
6.5.5 DeepLearningforDOAEstimationwith
RandomArrays 230
References 235
7 Beamforming 239
7.1 Introduction 239
7.2 FundamentalsofBeamforming 240
7.2.1 AnalogBeamforming 240
7.2.2 DigitalBeamforming/Precoding 241
7.2.3 HybridBeamforming 243
7.3 ConventionalBeamforming 246
7.3.1 BeamformingwithSpatialReference 246
7.3.2 BeamformingwithTemporalReference 249
7.4 SupportVectorMachineBeamformer 250
7.5 BeamformingwithKernels 254
7.5.1 KernelArrayProcessorswithTemporal
Reference 254
7.5.2 KernelArrayProcessorwithSpatialReference 256
7.6 RBFNNBeamformer 260
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Contents ix
7.7 HybridBeamformingwithQ-Learning 262
References 267
8 ComputationalElectromagnetics 271
8.1 Introduction 271
8.2 Finite-DifferenceTimeDomain 272
8.2.1 DeepLearningApproach 273
8.3 Finite-DifferenceFrequencyDomain 280
8.3.1 DeepLearningApproach 283
8.4 FiniteElementMethod 286
8.4.1 DeepLearningApproach 287
8.5 InverseScattering 290
8.5.1 NonlinearElectromagneticInverse
ScatteringUsingDeepNIS 292
References 295
9 ReconfigurableAntennasand
CognitiveRadio 297
9.1 Introduction 297
9.2 BasicCognitiveRadioArchitecture 298
9.3 ReconfigurationMechanismsinReconfigurable
Antennas 299
9.4 Examples 299
9.4.1 ReconfigurableFractalAntennas 300
9.4.2 PatternReconfigurableMicrostripAntenna 304
9.4.3 StarReconfigurableAntenna 307
9.4.4 ReconfigurableWidebandAntenna 309
9.4.5 FrequencyReconfigurableAntenna 312
9.5 MachineLearningImplementationonHardware 315
9.6 Conclusion 316
References 316
AbouttheAuthors 319
Index 321
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