Optimization of Communication Systems: Course Information

Description

Many core problems in communication systems and signal processing, such as allocating power across channels, designing beamformers, scheduling resources and estimating signals in noise, are at heart optimization problems. Many of them turn out to be convex, which makes them efficient to solve and their solutions reliable. This module teaches students to recognize these convex problems and to formulate them rigorously. Students start by learning how a mathematical optimization problem is defined. They then apply the fundamentals of convex analysis to problems drawn from communications and signal processing. They also learn to characterize optimal solutions through optimality conditions and to solve the problems using appropriate techniques and tools. No prior coursework is required. On completion, students will be able to model communication system design challenges as convex optimization problems, analyse the structure of their solutions and solve them in practice.

The main goal of the course is to teach students to recognize, formulate and solve the convex optimization problems that arise throughout communication systems and signal processing.

Intended Audience

MSc students in areas of applied mathematics, communication, control, computer sciences, networking

Course Textbook

• S. Boyd and L. Vandenberghe, Convex Optimization. Cambridge, U.K. Cambridge Univ. Press, 2004, Boyd-2004

• D. P. Bertsekas, “Convex Optimization Theory,” 1st Edition, Athena Scientific, 2009.

• G. C. Calafiore and L. E. Ghaoui, Optimization Models, Cambridge University Press, 2014, Calafiore-2014

Lectures

4 hours/week, 14 to 15 weeks

Grading

• Standard university grading applies
  

• The course evaluation consists of

  • Assignments (30%)

  • Fnal examination: 70%

Course Learning Outcomes

After finishing the course, the attendant will

• Define a mathematical optimization problem.

• Apply basics of convex analysis theory, tools, and techniques to optimization problems in communication systems and signal processing.

• Characterize optimal solution of a convex optimization problem in communication systems and signal processing.

• Solve convex optimization problems in communication systems and signal processing.

Working load

4h per Week + homework + viva sessions.

Credits

This is a 3 credit course.

Teaching and learning methodology

The lectures will be mainly based on blackboard and slides.

Prerequisites

Background in elementary analysis, linear algebra, and statistics.

Additional references

• D. P. Palomar and Y. C. Eldar, “Convex Optimization in Signal Processing and Communications,” Cambridge University Press, 2009.