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Probability Theory
Introduction to Probability Theory
Set Theory
Probability Definition
Bayes’ Theorem
Random Variable
Real Scalar Gaussian Random Variable
Functions of A Random Variable
Generating Random Variables from a Uniform Distribution
Methods to Compute PDF of Functions of A Single RV
Tail Probability
Central Limit Theorem
Multiple Random Variables
Distributions with Two Random Variables
Real Gaussian Random Vector
Complex Random Variables
Zero Mean Complex Circularly Symmetric Gaussian (ZMCCSG) RV
Standard Complex Gaussian Vector
Stochastic Process
Example: White Noise Process
Example: Band-Limited White Gaussian Noise Process
Communications Theory
Introduction to Communication Theory
Detection and Estimation Theory
Fundamentals of Detection Theory
MAP and ML Criteria
Bayes Criterion
MiniMax Criterion
Neyman-Pearson Criterion
Tutorial: Differentiable Communication Systems Using Sionna
Perfomance Comaprison
Fundamentals of Estimation Theory
Parameter Estimation
Unbiased Estimates
Estimators Based on Sufficient Statistics
Minimum Variance Estimaties
Consistent Estimates
Bayes Estimation
Minimum Mean Squared Error (MMSE) Estimation
Maximum a Posteriori (MAP) Estimation
Maximum Likelihood (ML) Estimation
Comparison of Estimators
Signal Representation
Equivalent Baseband Signal Model
Equivalent Baseband Channel Model
Equivalent Baseband Noise Model
Discrete System and Equivalent Discrete Model
Orthonormal Expansions
Karhunen-Loève (KL) Expansion
Vector and Multi-Hypothesis Detection
Detection Problem with Multiple Samples
Criteria for Multiple Sample Detection of Binary Hypotheses
Example: Antipodal Signal Detection using Multiple Samples
Example: Detection with Real Additive Gaussian Noise
The Optimum Digital Detector in Additive Gaussian Noise
Optimum Digital Detector – Alternative Representation
Filtering Alternatives
Continuous Signals with White Gaussian Noise
Perfomance of Binary Receivers in AWGN
Example 5.5
Detection of Signals with Random Parameters
Composite Hypothesis Testing
Unknown Phase
Unknown Amplitude
Unknown Frequency
Unknown Delay
Rician Random Variable
Estimation of Specific Parameters
Parameter Estimation in White Gaussian Noise
Amplitude Estimation in the Coherent Case with AWGN
Amplitude Estimation in the Noncoherent Case with AWGN
Phase Estimation in AWGN
Time Delay Estimation in AWGN
Frequency Estimation in AWGN
Simultaneous Parameter Estimation in AWGN
ML Estimation for a Discrete Linear Observation Model
MAP Estimation for a Discrete Linear Observation Model
Sequential Parameter Estimation
Index
