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| Preface and Acknowledgments | |
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| Notation and Symbols | |
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| Background Material | |
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| Random Variables | |
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| Variance of a Random Variable | |
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| Dependent Random Variables | |
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| Complex-Valued Random Variables | |
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| Vector-Valued Random Variables | |
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| Gaussian Random Vectors | |
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| Linear Algebra | |
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| Hermitian and Positive-Definite Matrices | |
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| Range Spaces and Nullspaces of Matrices | |
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| Schur Complements | |
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| Cholesky Factorization | |
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| QR Decomposition | |
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| Singular Value Decomposition | |
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| Kronecker Products | |
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| Complex Gradients | |
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| Cauchy-Riemann Conditions | |
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| Scalar Arguments | |
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| Vector Arguments | |
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| Optimal Estimation | |
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| Scalar-Valued Data | |
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| Estimation Without Observations | |
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| Estimation Given Dependent Observations | |
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| Orthogonality Principle | |
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| Gaussian Random Variables | |
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| Vector-Valued Data | |
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| Optimal Estimator in the Vector Case | |
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| Spherically Invariant Gaussian Variables | |
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| Equivalent Optimization Criterion | |
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| Summary and Notes | |
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| Problems and Computer Projects | |
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| Linear Estimation | |
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| Normal Equations | |
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| Mean-Square Error Criterion | |
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| Minimization by Differentiation | |
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| Minimization by Completion-of-Squares | |
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| Minimization of the Error Covariance Matrix | |
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| Optimal Linear Estimator | |
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| Orthogonality Principle | |
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| Design Examples | |
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| Orthogonality Condition | |
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| Existence of Solutions | |
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| Nonzero-Mean Variables | |
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| Linear Models | |
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| Estimation using Linear Relations | |
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| Application: Channel Estimation | |
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| Application: Block Data Estimation | |
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| Application: Linear Channel Equalization | |
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| Application: Multiple-Antenna Receivers | |
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| Constrained Estimation | |
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| Minimum-Variance Unbiased Estimation | |
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| Example: Mean Estimation | |
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| Application: Channel and Noise Estimation | |
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| Application: Decision Feedback Equalization | |
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| Application: Antenna Beamforming | |
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| Kalman Filter | |
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| Innovations Process | |
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| State-Space Model | |
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| Recursion for the State Estimator | |
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| Computing the Gain Matrix | |
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| Riccati Recursion | |
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| Covariance Form | |
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| Measurement and Time-Update Form | |
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| Summary and Notes | |
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| Problems and Computer Projects | |
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| Stochastic Gradient Algorithms | |
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| Steepest-Descent Technique | |
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| Linear Estimation Problem | |
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| Steepest-Descent Method | |
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| More General Cost Functions | |
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| Transient Behavior | |
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| Modes of Convergence | |
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| Optimal Step-Size | |
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| Weight-Error Vector Convergence | |
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| Time Constants | |
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| Learning Curve | |
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| Contour Curves of the Error Surface | |
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| Iteration-Dependent Step-Sizes | |
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| Newton?s Method | |
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| LMS Algorithm | |
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| Motivation | |
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| Instantaneous Approximation | |
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| Computational Cost | |
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| Least-Perturbation Property | |
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| Application: Adaptive Channel Estimation | |
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| Application: Adaptive Channel Equalization | |
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| Application: Decision-Feedback Equalization | |
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| Ensemble-Average Learning Curves | |
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| Normalized LMS Algorithm | |
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| Instantaneous Approximation | |
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| Computational Cost | |
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| Power Normalization | |
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| Least-Perturbation Property | |
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| Other LMS-Type Algorithms | |
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| Non-Blind Algorithms | |
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| Blind Algorithms | |
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| Some Properties | |
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| Affine Projection Algorithm | |
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| Instantaneous Approximation | |
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| Computational Cost | |
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| Least-Perturbation Property | |
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| Affine Projection Interpretation | |