Motivating examples of digital communications. Spectrum availability and channels. Channel modeling base band and pass band channels. Digital modulation schemes for base band and pass band channels. Line coding, Pulse amplitude modulation, Phase modulation, CPFSK, Frequency shift keying, QAM.

Maximum Likelihood Estimation (MLE): Exact and approximate methods (EM algorithm, alternating maximization, etc.)Cramer-Rao Lower Bound (CRLB) Minimum Variance Unbiased Estimation (MVUE) Sufficient Statistics Best Linear Unbiased Estimation (BLUE) Large and Small Sample Properties of Estimators: Understanding the behavior of estimators in both large and small sample sizes Bayesian Inference and Estimation: Minimum Mean Square Error (MMSE) estimation MAP Estimation (Maximum A Posteriori Estimation)Wiener and Kalman Filtering (Sequential Bayes) Detection Theory: Likelihood Ratio Testing Bayes

Module 1: Human Values (5hrs)

Review: Linear algebra, matrix calculus, probability and statistics.