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: Written and oral exam, done jointly with the first part of the course.

Classroom code (2025-2026):    ckdvlrx3

Lessons: The lessons will be held from Nov. 9th to Dec. 19th according to the following schedule:

• Monday 14 -16  -  Room 22

• Tuesday 9 - 12  -  Room 22

• Wednesday 11 -14  -  Room 10

• Thursday 12 - 14  -  Room 22

Contents 

• Part 1 - Statistical Signal Processing  (30 hours)

  • Estimation Theory (20 hours)

    • Properties of estimators: unbiasedness, efficiency, consistency.    [2, Ch. 2]

    • Minimum Variance Unbiased Estimation. Cramer-Rao lower bound. [2, Ch. 3] 

    • Linear models. Sufficient statistics. Best linear unbiased estimator. Maximum likelihood estimator. [2, Ch. 4-7]

    • Bayesian estimation, Linear MMSE estimation, Maximum a posteriori estimation. [2, Ch. 10, 11]

• Detection Theory (10 hours)

  • Neyman-Pearson Theorem. Minimum Probability of Error. Bayes Risk. Multiple Hypothesis Testing. [3, Ch. 3]

  • Detection of deterministic signals: Matched filters.  [3, Ch. 4]

  • Detection of random signals: The energy detector, the estimator-correlator.  [3, Ch. 5]

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

  • Equalization and multi-carrier systems (18 hours)

    • Review of basic principles of digital communications. Optimal receiver in the presence of AWGN.  [4, Ch. 3-4]

    • Channels as linear time invariant (LTI) and linear time-variant (LTV) systems. Inter-symbol interference, communications over frequency selective channels, channel equalization. [4, Ch. 9]

    • Block transmission systems, symbol detection, guard intervals. Linear equalization: Zero forcing, Minimum Mean-Square Error (MMSE).  [6, Ch. 3]

    • Orthogonal frequency division multiplexing (OFDM): Modulation and demodulation, cyclic prefix, digital implementation using Discrete Fourier Transform. Channel Estimation. Capacity of multi-carrier systems.  [6, Ch. 3]

  • Diversity and multi-antenna communications (12 hours)

    • Multipath Fading channels. Single-Input Single-Output (SISO) and Multi-Input Multi-Output (MIMO) channels. The effect of Fading. Outage Probability. Average Probability of Error. Receiver and Transmitter diversity.  [5, Ch. 7]

    • Multi-antenna communications, MIMO symbol detection, Multiplexing gain, MIMO beamforming, Multiplexing-Diversity trade-off.   [5, Ch. 10]

Textbooks and resources:

[1]  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.

[6] Barbarossa, Sergio. Multiantenna wireless communication systems. Artech House Publishers, 2005. 1-470.