UNIK9910 – Random Matrix Theory for Wireless Communications
Schedule, syllabus and examination date
Course content
The asymptotic behavior of the eigenvalues of large random matrices has been extensively studied since the fifties. One of the first related result was the work of Eugene Wigner in 1955 who remarked that the eigenvalue distribution of a standard Gaussian hermitian matrix converges to a deterministic probability distribution called the semi-circular law when the dimensions of the matrix converge to + ∞. Since that time, the study of the eigenvalue distribution of random matrices has triggered numerous works, in the theoretical physics as well as probability theory communities.
In the communication field, the introduction of random matrices can be dated to 1997. In order to analyze system dependent parameters, researchers relied mainly on exhaustive simulations to determine the performance of communication systems. Random matrices were however discovered to be an efficient tool for performance analysis and system design. In particular, the self-averaging effect of random matrices was shown to be able to capture the parameters of interest of communication schemes. The results led to very active research in many fields such as, just to name a few:
- (MC)-CDMA systems with large spreading factors and large number of users
- MIMO systems with large number of transmit and receive antennas
- Design of multi-stage detectors
- Channel modelling of communication systems
- Ad hoc networks with a great number of nodes
Learning outcome
The course is intended to give a comprehensive overview of random matrices and their application to the analysis and design of communication systems. As communication systems become more and more complex, the course should provide the students with appropriate mathematical tools to cope with the analysis and design of suited schemes.
Admission
PhD candidates from the University of Oslo should apply for classes and register for examinations through Studentweb.
If a course has limited intake capacity, priority will be given to PhD candidates who follow an individual education plan where this particular course is included. Some national researchers’ schools may have specific rules for ranking applicants for courses with limited intake capacity.
PhD candidates who have been admitted to another higher education institution must apply for a position as a visiting student within a given deadline.
Prerequisites
Formal prerequisite knowledge
No obligatory prerequisites beyond the minimum requirements for entrance to higher education in Norway.
Teaching
2 hrs. lectures and 1 hr. exercise pr week. Compulsory problem solving.
- Course: Overview and Historical development.
- Course: Probability and convergence measures review.
- Course: Basic Results on Random Matrix Theory
- Course: Stieltjes Transform Method.
- Course: Results on Unitary Random Matrix Theory
- Course: Asymptotic analysis of (MC)-CDMA systems
- Course: Asymptotic Analysis of MIMO systems
- Course: Asymptotic design of receivers
- Course: Random matrices and open topics in telecommunications
Access to teaching
A student who has completed compulsory instruction and coursework and has had these approved, is not entitled to repeat that instruction and coursework. A student who has been admitted to a course, but who has not completed compulsory instruction and coursework or had these approved, is entitled to repeat that instruction and coursework, depending on available capacity.
Examination
Examinations in the theoretical syllabus are judged as pass or fail, where the award of a pass denotes that a high standard has been attained.
Examination support material
No examination support material is allowed.
Grading scale
Grades are awarded on a scale from A to F, where A is the best grade and F is a fail. Read more about the grading system.
Explanations and appeals
Resit an examination
If the candidate does not pass one of the courses in the training component, it can not be retaken until the following semester at the earliest. The Department arranges the new examination.
Special examination arrangements
Application form, deadline and requirements for special examination arrangements.