# APPLIED MATHEMATICS FOR COMMUNICATION SYSTEMS - 2022/3

Module code: EEEM062

## Module Overview

Expected prior / parallel learning:  Knowledge of linear systems, linear algebra and stochastic processes is helpful, however, this is not a fundamental requirement. Students should have some background in arithmetic, complex numbers, integration and differentiation, and matrix calculations.

Module purpose:  This module focuses on some of the fundamental mathematical concepts used in the analysis and design of modern digital communications systems and examines their application to link-level communications and receiver design.

### Module provider

Electrical and Electronic Engineering

HELIOT Fabien (Elec Elec En)

### Module cap (Maximum number of students): N/A

Independent Learning Hours: 96

Lecture Hours: 2

Tutorial Hours: 5

Laboratory Hours: 15

Guided Learning: 20

Captured Content: 12

Semester 1

None.

## Module content

Indicative content includes the following:

FUNDAMENTAL MATHEMATICAL CONCEPTS FOR COMMUNICATIONS

Matrix Analysis – Basic vector and matrix operations & manipulations, norm, rank, trace, inverse / pseudo inverse, Eigenvalues & Eigenvectors, matrix decomposition

Signals and Random Processes – Signals, energy and power of signals, useful operations on signals (time shifting, time scaling, time inversion, correlation, convolution), random variables, statistical mean and co-variance functions, Gaussian processes

Special Math Functions and Transforms – Dirac’s delta function, sinc function, Discrete Fourier transform and its properties

ELELMENTS OF DETECTION AND ESTIMATION THEORY WITH APPLICATIONS IN RECEIVER PROCESSING

Detection methods for single and multi-antenna systems – Probability of detection error, Hard linear detection methods (e.g., zero forcing detection, minimum mean square error detection), hard non-linear detection methods (e.g., Maximum-Likelihood detection and its approximations)

Synchronization techniques for multi-carrier systems – Time, Frequency and Phase synchronization

Channel Estimation Methods – Based on training symbols (Least Squares estimation, Minimum Mean Square Error estimation) or decisions

## Assessment pattern

Assessment type Unit of assessment Weighting
Coursework MATLAB BASED CODING ASSIGNMENT 20
Examination 4HR (OPEN BOOK) EXAM 80

## Alternative Assessment

Not applicable: students failing a unit of assessment resit the assessment in its original format.

## Assessment Strategy

The assessment strategy for this module is designed to allow students to show that they have achieved all the intended learning outcomes. The exam will assess their understanding on course’s material (captured content/recorded lectures) as well as their ability to apply the proper mathematical tools for solving analytical (numerical) and design problems. The exam will also assess their ability to perform simple design choices. In complement to the exam, the coursework assignment will test their abilities at modeling and evaluating the performance of simple digital communication systems.

Thus, the summative assessment for this module consists of the following.

• 4-hour (open book) written examination at the end of the module teaching during the examination week

• Matlab IT lab based coursework assignment

Formative assessment and feedback

For the module, students will receive formative assessment/feedback in the following ways.

• During supervised IT lab or tutorial sessions, through question and answer (Q&A) on recorded lectures/capture content, discussion and lab supervision

• By providing feedback to ungraded tutorial problems

• During the revision lecture, through discussion and problem solving exercise.

## Module aims

• The aim of this module is to provide an introduction to some of the most fundamental mathematical concepts and tools used for the analysis and the design of digital communication systems as well as to provide an introduction to techniques and methodologies that are used in state-of-the-art digital receiver design.

## Learning outcomes

 Attributes Developed 1 Define and understand basic concepts in matrix analysis, signals and systems, random processes, specialised math functions and properties of Fourier transform K 2 Analyse the mathematical concepts with the help of computer software programs with respect to practical digital communication systems KC 3 Explain and compare/contrast different design choices for basic building blocks in a digital receiver KC 4 Apply the provided mathematical tools for the design of digital receiver modules. KCP

Attributes Developed

C - Cognitive/analytical

K - Subject knowledge

T - Transferable skills

P - Professional/Practical skills

## Methods of Teaching / Learning

The learning and teaching strategy is designed to efficiently introduce the students to the concepts, methodologies and mathematical tools of the course and to provide them with pointers that can further use for deepening their learning experience.Recorded lectures and practical lab sessions are the two main vehicles for delivering the strategy; Recorded lectures are designed to provide fundamental knowledge about the various topics of this module, whereas practical sessions are designed to support and further this knowledge via practical implementation in Matlab. The practical lab sessions are complemented by a coursework assignment. In order to increase the effectiveness of the provided feedback to and from the students, recorded lectures  Q&A, class discussions, problem solving are used; additional learning material is also added on SurreyLearn to address learning difficulties.

Learning and teaching methods include the following.

• Recorded lectures:  10 weeks (week 1 to 10) – 12 hours (taught content equivalent to 2 hours of live lectures x 10 weeks)

• Live Lecture:  1 week (week 11) – 2 hours

• Live Tutorial sessions: 5 weeks – 5 hours (1 hour per week x 5 weeks)

• Live Supervised IT lab + recorded lecture Q&A sessions: 10 weeks – 15 hours (2 hour per week x 5 weeks + 1 hour per week x 5 weeks)

• Self/guided study from the recorded lectures and use of tutorial sheets.

Indicated Lecture Hours (which may also include seminars, tutorials, workshops and other contact time) are approximate and may include in-class tests where one or more of these are an assessment on the module. In-class tests are scheduled/organised separately to taught content and will be published on to student personal timetables, where they apply to taken modules, as soon as they are finalised by central administration. This will usually be after the initial publication of the teaching timetable for the relevant semester.