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# EQ2831 Foundations in Digital Communications 7.5 credits

The course provides the theoretical background of the methods and principles used in modern digital communication systems. Detection and modulation theoretic aspects are the main focus, i.e., a comprehensive study of hypothesis testing, Gaussian stochastic processes, concept of sufficient statistics and matched filters, and parallelism to estimation theory. The emphasis is to provide a rigorous mathematical framework, optimization criteria, and models which are suitable for digital communication problems. Further, problem solving skills in related topics should be trained. The intention is to deepen existing knowledge on digital communication rather than to broaden.

Course offerings are missing for current or upcoming semesters.
Headings with content from the Course syllabus EQ2831 (Spring 2019–) are denoted with an asterisk ( )

## Content and learning outcomes

### Course contents

·        A rigorous revisit of basic principles in digital communication,

·        Stochastic processes and stationary discrete‐time stochastic processes,

·        Binary and multi‐hypothesis testing problem, sufficient statistics

·        Parallelism to estimation theory, composite detection problem

·        Uni‐ and multivariate Gaussian distribution, complex Gaussian and circular symmetry

·        Continuous‐time stochastic processes

·        Detection in white Gaussian noise

·        Non‐coherent detection and nuisance parameters

### Intended learning outcomes

After the course the student should be able to

1. explain and derive the foundation of digital communication methods,
2. acquire and discuss results related research literature,
3. solve standard problems in detection, modulation, and estimation theory,
4. use the advanced theoretical tools to analyze and design new procedures adapted to specific problems.

## Literature and preparations

### Specific prerequisites

For single course students: 180 credits and documented proficiency in English B or equivalent

### Recommended prerequisites

Basic course on digital communications such as EQ2310 Digital Communications.

### Equipment

No information inserted

### Literature

A Foundation in Digital Communications

by A. Lapidoth.

Kompletterande litteratur:

1. Detection, Estimation, and Modulation Theory, Part I, by H. L. van Trees.
2. An Introduction to Signal Detection and Estimation, by H. V. Poor.
3. An Introduction to Statistical Communication Theory, by D. Middleton.

Om mer passande litteratur finns tillgänglig kommer kurslitteraturen kanske att ändras. Besök därför hemsidan där den slutgiltiga kurslitteraturen kommer att utannonseras innan kursstart.

## Examination and completion

If the course is discontinued, students may request to be examined during the following two academic years.

A, B, C, D, E, FX, F

### Examination

• INL1 - Homeworks, 7.5 credits, grading scale: A, B, C, D, E, FX, F

Based on recommendation from KTH’s coordinator for disabilities, the examiner will decide how to adapt an examination for students with documented disability.

The examiner may apply another examination format when re-examining individual students.

### Other requirements for final grade

To pass the course the student

1. has to hand in every homework. For each homework a minimum number of points must be achieved as well as the sum of all achieved points has to exceed a threshold, and
2. has to sign up for presentation of at least one exercise solution for every homework set and has to present successfully at least one solution in one exercise seminar. Those who did not successfully present have to do a presentation of a selected paper.

The final grade for the course will be set according to the sum of all achieved points in the homework assignments. The levels will be fixed before the course starts.

### Opportunity to complete the requirements via supplementary examination

No information inserted

### Opportunity to raise an approved grade via renewed examination

No information inserted

### Ethical approach

• All members of a group are responsible for the group's work.
• In any assessment, every student shall honestly disclose any help received and sources used.
• In an oral assessment, every student shall be able to present and answer questions about the entire assignment and solution.

## Further information

### Course room in Canvas

Registered students find further information about the implementation of the course in the course room in Canvas. A link to the course room can be found under the tab Studies in the Personal menu at the start of the course.

### Main field of study

Electrical Engineering

Second cycle