Prerequisites: sufficiency in calculus, probability theory, linear algebra, and digital communication theory.

Course Content.

Introduction: examples of statistical reasoning (2 hours).

Rudiments of Multivariate Normal Theory (9 hours). Solution to assigned problems (6 hours).

Estimation Theory: Classical vs Bayesian Parameter Estimators. How to measure the performance of an estimator. Cramer-Rao bounds. Estimation of non random parameters (22 hours). Solution to assigned problems (12 hours).

Estimation of random parameters: MMSE estimation, linear MMSE estimation. Discrete-Time Kalman Filter. Extended Kalman Filter. Applications of Kalman Filter to tracking (9 hours). Solution to assigned problems (4 hours).

Applications to communication theory (8 hours).

Detection Theory: Neyman-Pearson Lemma, Testing of composite binary hypotheses, UMP tests, Constant False Alarm Rate property; Bayes detectors (4 hours). Solution to assigned problems (5 hours).

Overview.

This is a course in estimation and detection theory; it is aimed at providing principles and tools to solve problems in signal processing, radar, sonar, and communication. It will also serve as the necessary prerequisite for more advanced courses in communication engineering.

Learning Outcomes.

Knowledge and understanding

After the course the student should understand the following aspects of estimation and detection theory

*classical and Bayesian approaches to estimation; strategies to solve binary hypotheses tests (Neyman-Pearson, GLRT).

*The Kalman filter and the extended Kalman filter and their use to solve simplified tracking problems.

*Synchronization techniques of digital receivers (phase recovery circuits and frequency recovery circuits) starting from first principles (estimation theory).

Applying knowledge and understanding

After the course the student should be able to

*formulate and solve parameter estimation problems and derive corresponding Cramer-Rao lower bounds.

*Formulate and solve detection problems resorting to the optimum (i.e., Neyman-Pearson test or UMP test) if possible or to a suboptimum one (GLRT).

*Evaluate the performance parameters and discuss complexity issues associated with different solutions.

Making judgements

Students should acquire the ability to compare pros and cons of different approaches to the solution of a specific problem through examples and problems.

Communication

The ability to communicate on technical topics should be acquired by discussing in a rigorous way not only concepts and tools of detection and estimation theory, but also the adopted solution to a specific problem.

Learning skills

Selected problems will be proposed that require elaborating on introduced concepts and methods, also with the help of selected readings suggested by the instructor (from the list of references). Identifying solutions to non trivial problems will be  important to be ready for autonomous lifelong learning.

Examination.

Written exam. The exam consists of two cascaded parts (maximum overall duration: two hours and a half):

the first part is closed book (suggested duration 50 minutes); the student is asked to illustrate two theoretical topics; it is aimed to verify to what extent the student has gained knowledge and understanding of the selected topics of the course and is able to communicate about his/her understanding (the maximum score for illustrating each topic is typically 5/30);

the second part, that starts when the student has completed the first part, is open book and requires solving  two (or three) problems; it is aimed to determine to what extent the student has: 1) the ability to identify and use data to formulate responses to well-defined problems, 2) problem solving abilities and the capacity to integrate different concepts and tools (the maximum score for the solution of each problem is typically 10/30 or 6-7/30 if the second part of the exam requires solving three problems).

Office Hours: by appointment; contact the instructor by email or at the end of class meetings.

Statistical Signal Processing - Master degree (LM) in Communication Engineering and Electronic Technologies (Fall semester)

Overview.

This is a course in estimation and detection theory; it is aimed at providing principles and tools to solve problems in signal processing, radar, sonar, and communication. It will also serve as the necessary prerequisite for more advanced courses in communication engineering.

Learning Outcomes.

Knowledge and understanding

After the course the student should understand the following aspects of estimation and detection theory

*classical and Bayesian approaches to estimation; strategies to solve binary hypotheses tests (Neyman-Pearson, GLRT).

*The Kalman filter and the extended Kalman filter and their use to solve simplified tracking problems.

*Synchronization techniques of digital receivers (phase recovery circuits and frequency recovery circuits) starting from first principles (estimation theory).

Applying knowledge and understanding

After the course the student should  be able to

*formulate and solve parameter estimation problems and derive corresponding Cramer-Rao lower bounds.

*Formulate and solve detection problems resorting to the optimum (i.e., Neyman-Pearson test or UMP test) if possible or to a suboptimum one (GLRT).

*Evaluate the performance parameters and discuss complexity issues associated with different solutions.

Making judgements

Students should acquire the ability to compare pros and cons of different approaches to the solution of a specific problem through examples and problems.

Communication

The ability to communicate on technical topics should be acquired by discussing in a rigorous way not only concepts and tools of detection and estimation theory, but also the adopted solution to a specific problem.

Learning skills

Selected problems will be proposed that require elaborating on introduced concepts and methods, also with the help of selected readings suggested by the instructor (from the list of references). Identifying solutions to non trivial problems will be  important to be ready for autonomous lifelong learning.

Course Content.

Introduction: examples of statistical reasoning (2 hours).

Rudiments of Multivariate Normal Theory (9 hours). Solution to assigned problems (6 hours).

Estimation Theory: Classical vs Bayesian Parameter Estimators. How to measure the performance of an estimator. Cramer-Rao bounds. Estimation of non random parameters (22 hours). Solution to assigned problems (12 hours).

Estimation of random parameters: MMSE estimation, linear MMSE estimation. Discrete-Time Kalman Filter. Extended Kalman Filter. Applications of Kalman Filter to tracking (9 hours). Solution to assigned problems (4 hours).

Applications to communication theory (8 hours).

Detection Theory: Neyman-Pearson Lemma, Testing of composite binary hypotheses, UMP tests, Constant False Alarm Rate property; Bayes detectors (4 hours). Solution to assigned problems (5 hours).

Prerequisites: sufficiency in calculus, probability theory, linear algebra, digital communication theory.

Examination.

Written exam. The exam consists of two cascaded parts (maximum overall duration: two hours and a half):

the first part is closed book (suggested duration 50 minutes); the student is asked to illustrate two theoretical topics; it is aimed to verify to what extent the student has gained knowledge and understanding of the selected topics of the course and is able to communicate about his/her understanding (the maximum score for illustrating each topic is typically 5/30);

the second part, that starts when the student has completed the first part, is open book and requires solving  two (or three) problems; it is aimed to determine to what extent the student has: 1) the ability to identify and use data to formulate responses to well-defined problems, 2) problem solving abilities and the capacity to integrate different concepts and tools (the maximum score for the solution of each problem is typically 10/30 or 6-7/30 if the second part of the exam requires solving three problems).

Office Hours: By appointment; contact the instructor by email or at the end of class meetings.

References.

[1] Handouts (in progress).

[2] L. L. Scharf, ``Statistical Signal Processing: Detection, Estimation, and Time Series Analysis,’’ Addison-Wesley, 1991.

[3] H. L. Van Trees, ``Detection, Estimation and Modulation Theory,’’ Part. 1, John Wiley & Sons, 1968.

[4] H. L. Van Trees, ``Optimum Array Processing. Part. 4 of Detection, Estimation, and Modulation Theory," John Wiley & Sons, 2002.

[5] S. M. Kay: ``Fundamentals of Statistical Signal Processing: Estimation Theory,’’ Volume I, Prentice-Hall, 1993.

[6] S. M. Kay: ``Fundamentals of Statistical Signal Processing: Detection Theory,’’ Volume II, Prentice-Hall, 1998.

[7] Y. Bar-Shalom, T. E. Fortmann, ``Tracking and Data Association, Academic Press’’, 1988.

[8] Y. Bar-Shalom, X., Rong Li, T. Kirubarajan, ``Estimation with Applications to Tracking and Navigation. Theory Algorithms and Software,'' John Wiley & Sons, 2001.

[9] U. Mengali, A. N. D’Andrea: ``Synchronization Techniques for Digital Receivers,’’ Plenum Press, 1997.

[10] H. Meyr, M. Moeneclaey, S. A. Fechtel: ``Digital Communication Receivers. Synchronization, Channel Estimation and Signal Processing,'' John Wiley & Sons, 1998.

[1] Handouts (in progress).

[2] L. L. Scharf, ``Statistical Signal Processing: Detection, Estimation, and Time Series Analysis,’’ Addison-Wesley, 1991.

[3] H. L. Van Trees, ``Detection, Estimation and Modulation Theory,’’ Part. 1, John Wiley & Sons, 1968.

[4] H. L. Van Trees, ``Optimum Array Processing. Part. 4 of Detection, Estimation, and Modulation Theory," John Wiley & Sons, 2002.

[5] S. M. Kay: ``Fundamentals of Statistical Signal Processing: Estimation Theory,’’ Volume I, Prentice-Hall, 1993.

[6] S. M. Kay: ``Fundamentals of Statistical Signal Processing: Detection Theory,’’ Volume II, Prentice-Hall, 1998.

[7] Y. Bar-Shalom, T. E. Fortmann, ``Tracking and Data Association, Academic Press’’, 1988.

[8] Y. Bar-Shalom, X., Rong Li, T. Kirubarajan, ``Estimation with Applications to Tracking and Navigation. Theory Algorithms and Software,'' John Wiley & Sons, 2001.

[9] U. Mengali, A. N. D’Andrea: ``Synchronization Techniques for Digital Receivers,’’ Plenum Press, 1997.

[10] H. Meyr, M. Moeneclaey, S. A. Fechtel: ``Digital Communication Receivers. Synchronization, Channel Estimation and Signal Processing,'' John Wiley & Sons, 1998.