Objectives

This course provides a solid foundation in statistical signal processing and advanced physical layer communication techniques, with a strong emphasis on theory and practical application. Students begin by exploring core concepts in estimation and detection theory, including properties of estimators, maximum likelihood and Bayesian approaches, and decision-making under uncertainty. The course then focuses on advanced communication techniques, examining how signals are transmitted and received over various channel models. Topics include equalization strategies for handling inter-symbol interference, multi-carrier systems like OFDM, and synchronization and channel estimation challenges. Additionally, the course covers diversity techniques and multi-antenna systems, exploring how methods like MIMO and beamforming enhance communication reliability and performance in fading environments. Practical experience is emphasized through programming assignments using MATLAB and/or Python, enabling students to simulate and analyze real-world systems. By the end of the course, students will be equipped to understand, apply, and critically assess signal processing methods in communication contexts, and will be prepared for further study or research in the field.

Prerequisite:  Basic knowledge of calculus, linear algebra, probability theory, signal theory, and digital communications.

Final Exam: Oral exam. Typically two or three open questions.

Classroom code (2025-2026):    TBD

Lessons:    TBD

Contents 

• Part 1 - Statistical Signal Processing  (30 hours)

  • Estimation Theory (20 hours)

    • Properties of estimators: unbiasedness, efficiency, consistency. 

    • Minimum Variance Unbiased Estimation. Cramer-Rao lower bound. 

    • Linear models. Sufficient statistics. Maximum Likelihood estimation. Least squares. 

    • Bayesian Estimation, Linear MMSE estimation. 

    • Application to carrier phase and symbol timing estimation in communications.

• Detection Theory (10 hours)

  • Neyman-Pearson Theorem. Minimum Probability of Error. Bayes Risk. Multiple Hypothesis Testing.

  • Detection of deterministic signals: Matched filters. 

  • Detection of random signals: The Estimator-Correlator.

• Part 2 - Advanced Physical Layer Communications (30 hours)

  • Equalization and multi-carrier systems (18 hours)

    • Channels as LTI and LTV systems. Examples of channel models.

    • Optimal receivers for channels with ISI and AWGN, Maximum likelihood sequence estimation. 

    • Block transmission systems, symbol detection, guard intervals, linear equalization (zero forcing, MMSE, adaptive LMS). 

    • Orthogonal frequency division multiplexing (OFDM): Modulation and demodulation, cyclic prefix, digital implementation using Discrete Fourier Transform. Synchronization issues. Channel Estimation.

  • Diversity and multi-antenna communications (12 hours)

    • Wireless channels: Shadowing, multipath fading. SISO and MIMO channels.

    • The effect of Fading. Outage Probability. Average Probability of Error. Receiver and Transmitter diversity. 

    • Multi-antenna communications, MIMO symbol detection, Multiplexing gain, MIMO beamforming, Multiplexing-Diversity trade-off.

Textbooks and resources:

[1]  Slides, notes, and codes

[2] Kay, Steven M. Fundamentals of statistical signal processing: estimation theory. Prentice-Hall, Inc., 1993.

[3] Kay, Steven M. Fundamentals of statistical signal processing: detection theory. Prentice-Hall, Inc., 1998.

[4] Proakis, John G., and Masoud Salehi. Digital communications. McGraw-hill, 2008.

[5] Goldsmith, Andrea. Wireless communications. Cambridge university press, 2005.