Optimization Methods for Wireless Systems
Code: 45650Credits: 5
| Degree programme | Type | Course |
|---|---|---|
| Telecommunication Engineering | OP | 2 |
Contact lecturer
- Name :
- Gonzalo Seco Granados
- Email :
- gonzalo.seco@uab.cat
Group languages
You can consult this information at the end of the document.
Prerequisites
To have successfully completed the first-year subjects: Estimation and Detection Methods, Multichannel Signal Processing
Objectives
The course aims to provide students with an understanding of the mathematical foundations and practical optimization techniques used in the analysis and design of systems based on signal transmission and reception. Students will learn how to formulate and solve optimization problems related to resource allocation, power control, beamforming, signal design, parameter estimation, synchronization, and planning in wireless networks. The course covers both convex and non-convex optimization methods, with an emphasis on their application to 5G/6G networks, MIMO systems, and signal processing. Students will also be trained in the use of standard software packages for solving different types of optimization problems. Upon completion of the course, students will be able to analyze wireless systems, develop optimization-based solutions, and apply numerical algorithms to improve the performance, efficiency, and reliability of systems operating in real-world scenarios.
Learning outcomes
- (CA26) Select appropriate optimisation techniques to address complex engineering problems in wireless communication systems, MIMO systems, and terrestrial and satellite positioning systems.
- (CA27) Work effectively in interdisciplinary teams to implement distributed optimisation techniques in real-world scenarios, such as interference management and smart antenna design.
- (CA28) Apply specialised software packages in the resolution of optimisation problems, adapting mathematical models to the specific requirements of the software to obtain effective solutions.
- (KA25) Explain the fundamental concepts and classifications of optimisation problems, including convex, non-convex, linear, and nonlinear optimisations relevant to wireless systems.
- (KA26) Explain in detail the methods of convex optimisation, the theory of duality and the conditions of KKT and their application in wireless communications.
- (KA27) Identify the different types of optimisation problems and classify them within their standard families.
- (SA36) Formulate problems in the field of telecommunications engineering as standard optimisation problems.
- (SA37) Apply numerical optimisation methods, such as Newton's method and dual methods, to solve real-world optimization problems in 5G/6G networks and satellite systems.
- (SA38) Develop heuristic and iterative solutions for non-convex optimisation challenges, including resource allocation and localisation in wireless systems.
- (SA39) Simulate optimisation algorithms for specific problems in wireless communications, such as optimising resources in distributed networks and improving the performance of MIMO systems.
Contents
1. Introduction to Optimization
- Basic concepts: objective function, constraints, feasible sets
- Types of optimization problems: linear, nonlinear, convex, and non-convex
- Formulation of standard analysis and design cases in wireless systems as optimization problems
2. Convex Optimization
- Convex sets, convex functions, and convex problems
- Linear, quadratic and geometric programming
- Generalized inequalities and vector optimization
- Duality theory and KKT conditions
- Applications: power control in wireless networks, beamforming in MIMO systems
3. Non-convex Optimization
- Non-convex problem structures in wireless communications
- Global vs. local optima: challenges in non-convex optimization
- Integer programing
- Optimization on manifolds
- Heuristic and iterative methods: gradient descent, branch-and-bound algorithm
- Applications: resource allocation, localization and orientation estimation
4. Numerical Optimization Methods
- Iterative optimization algorithms: Newton's method, quasi-Newton methods
- Stochastic optimization and its relevance to wireless systems
- Distributed optimization techniques: ADMM, primal-dual methods
- Applications: parameter estimation in cell-free distributed massive MIMO networks
5. Case Studies and Applications
- Case studies from recent literature on optimization in 5G/6G networks
- Case studies from recent literature on optimization in satellite constellations and signals
- Real-world applications: cognitive radio, interference management, smart antenna design
Learning activities and methodology
| Title | Hours | ECTS | Learning outcomes |
|---|---|---|---|
| Type: Autonomous | |||
| Individual work of the student: practices preparation | 25 | 1 | CA26, CA28, KA25, KA27, SA37, SA38, SA39 |
| Individual work of the student: study and exercices resolution | 50 | 2 | CA26, KA25, KA26, KA27, SA36, SA38 |
| Type: Guided | |||
| Practical sessions | 12 | 0.48 | CA26, CA27, CA28, KA25, SA36, SA37, SA38, SA39 |
| Theory lectures | 25 | 1 | CA26, KA25, KA26, KA27, SA36, SA37, SA38 |
| Type: Supervised | |||
| Tutoring and doubt resolution | 7 | 0.28 | CA26, KA25, KA26, KA27, SA36, SA37, SA38 |
Classroom activities
- Theory classes: presentation of theoretical content.
- Laboratory sessions: application of the techniques presented in the theory classes to different real systems and implementation with different simulation software.
- Partial and final exams.
Autonomous activities
- Study of the theoretical and practical contents of the subject.
- Problem solving and preparation of assignments with solutions to some sets of problems.
- Exam preparation.
- Practical work: carrying out and deepening of laboratory practices.
Note: within the schedule set by the centre or degree programme, 15 minutes of one class will be reserved for students to evaluate their lecturers and their courses or modules through questionnaires.
Assessment
Continuous assessment activities
| Title | Weight | Hours | ECTS | Learning outcomes |
|---|---|---|---|---|
| Evaluation of the practical sessions | 30% | 2 | 0.08 | CA26, CA27, CA28, KA27, SA36, SA37, SA38, SA39 |
| Exam 1 | 35% | 2 | 0.08 | CA26, KA25, KA27, SA36, SA38 |
| Exam 2 | 35% | 2 | 0.08 | CA26, KA25, KA26, KA27, SA36, SA37, SA38 |
The final grade for the subject is obtained as the weighted average of the grades obtained in the continuous assessment activities.
Second-chance exam
The student has the option of taking a second-chance exam, which will be held once the face-to-face classes have ended, during the retake exam period set by the school. In the secondchance exam, the student may retake the part corresponding to exam 1, the part corresponding to exam 2, or both at the same time. In any case, the grade for the second-chance exam, whether corresponding to the retake of exam 1 or exam 2, will replace the grade that the student has obtained in the exam that is being retaken.
Once the grade for the second-chance exam has been replaced, the final grade for the subject is also obtained as the average of the grades for the exams (retaken, if applicable) and the laboratory grade.
Academic integrity and verification of authorship
The teaching staff reserves the right to call for an interview or an individual oral test of contrast when there are indications of copying or lack of authorship in an assessable activity. The impossibility of satisfactorily accrediting authorship may have effects on their qualification in accordance with current academic regulations.
Consideration of " Not Assessable"
The final grade will be " Not Assessable" only when the student does not take any exam, neither those of the continuous assessment nor the retake.
Consideration in the case of copying or plagiarism
Without prejudice to other disciplinary measures that may be deemed appropriate, and in accordance with current academic regulations, tests or reports where the student has committed irregularities, such as plagiarism, cheating, copying, allowing copying, etc., which could lead to a variation in the qualification, will be graded with a zero.
Bibliography
Boyd, S., & Vandenberghe, L. (2004). Convex Optimization. Cambridge University Press.
Bertsekas, D. P. (2016). Nonlinear Programming (3rd ed.). Athena Scientific.
Palomar, D. P., & Eldar, Y. C. (Eds.). (2010). Convex Optimization in Signal Processing and Communications. Cambridge University Press.
Boumal, N., (2023). An Introduction to Optimization on Smooth Manifolds. Cambridge University Press.
Software
The practical sessions will make use of the Matlab software.
Course groups and languages
The information provided is provisional until November 30. After this date, you will be able to consult the language of each group through this link. To access the information, you will need to enter the course CODE