# APPLIED MATHEMATICS FOR COMMUNICATION SYSTEMS - 2023/4

Module code: EEEM062

## Module Overview

Expected prior / parallel learning: We expect you to ideally have some background in arithmetic, algebra, complex numbers, integration, and differentiation to follow this module.  Besides, you will find it helpful to have some knowledge about linear systems, linear algebra and stochastic processes for following.

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.

EEEM017: Complementary with EEEM062, since EEEM017 covers other fundamental aspects of communication system design like data rate. Maths taught in EEEM062, i.e. probability, is useful to understand the theory behind data rate taught in EEEM017.

EEEM018: EEEM062 provides link level knowledge of communication system that complements well with the system level knowledge taught in advanced wireless communication technologies

EEEM061 - Advanced 5G Wireless Technologies. Maths taught in EEEM062, i.e. linear algebra and matrix, is useful to understand the theory behind massive multiple-input multiple output communication system (part of 5G system) taught in EEEM061. Similarly, Fourier analysis aught in EEEM062, is useful to understand the theory behind orthogonal frequency division multiplexing (part of 5G system) taught in EEEM061.

EEE1032 and EEE2035: Similarities of mathematic topics cover in 1st and 2nd years (e.g. Fourier analysis, Probability, Algebra), but adapted here to communications to provide a level-playing field for students directly coming for a MSc and who do not necessarily already have acquired this background knowledge.

### Module provider

Computer Science and Electronic Eng

HELIOT Fabien (CS & EE)

### 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

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, sinus cardinal function, Discrete Fourier transform and its properties

ELEMENTS OF DETECTION AND ESTIMATION THEORY WITH APPLICATIONS IN RECEIVER PROCESSING

Detection methods for single and multi-antenna systems – Probability of detection error, matched filter, h linear detection methods (e.g., zero forcing detection, minimum mean square error detection), 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 2HR INVIGILATED (CLOSED BOOK) EXAM 80

N/A

## Assessment Strategy

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

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

• Matlab IT lab-based coursework assignment

• 2-hour (closed book and invigilated) written examination at the end of the module teaching during the examination week

Formative assessment and feedback

In this module, you 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;

• during the revision lecture, through discussion and problem-solving exercises;

• through the graded coursework assignment;

## Module aims

• The aim of this module is to introduce some of the most fundamental mathematical concepts and tools used for the analysis and design of digital communication systems as well as to introduce techniques and methodologies that are used in for designing state-of-the-art digital communication receivers
• To develop your digital capabilities by teaching you Matlab, a programming and numeric computing platform used by millions of engineers and scientists around the world to analyze data, develop algorithms, and create models;
• Improve your employability by making you acquainted to the basic building blocks of a communication system (signal, transceiver, detection, estimation) and how to model/simulate it in Matlab;
• Nurture your resourcefulness and resilience through scaffold teaching and group works
• Enhance your global and cultural capabilities by encouraging you to exchange and work with your peers, especially through the Matlab lab and group coursework.
• The module also aims to provide opportunities for students to learn about the Surrey Pillars listed below

## Learning outcomes

 Ref Attributes Developed 001 Define and understand basic concepts in matrix analysis, signals and systems, random processes, specialised math functions and properties of Fourier transform K M1 002 Analyse the mathematical concepts with the help of computer software programs with respect to practical digital communication systems KCT M2, M3 003 Explain and compare/contrast various choices for designing basic building blocks in a digital receiver CPT M4, M5, M16, M17 004 Apply the provided mathematical tools for the design of digital receiver modules. KPT M2, M5, M12

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 you to the concepts, methodologies, and mathematical tools of the course and to provide you with pointers that can further be used for deepening your learning experiences. Recorded lectures and practical lab sessions are the two main vehicles for delivering the strategy. Recorded lectures are designed to provide you with the fundamental knowledge about the several topics of this module. Whereas practical sessions are designed to support and further this knowledge via practical implementation in Matlab. This will help with your digital capabilities and employability. The practical lab sessions are complemented by a group coursework assignment. The group work will help with your resourcefullness and cultural capability. In order to increase the effectiveness of our teaching and your learning  experience, feedback on your learning will be provided, through class discussions (Q&A), lab/tutorial questions, coursework evaluation, and office hours .Additional learning material is also added on SurreyLearn to further help with your learning experience.

Learning and teaching methods include the following.

• Recorded lectures

• Live Lecture

• Live Tutorial sessions

• Live Supervised Matlab IT lab/Q&A sessions on recorded lecture

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

• Office hours, at least one hour every week

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.