049029 - Advanced seminar in signal processing and communications



Under construction! Last update 11-Feb-07


Instructor: Prof. Yonina Eldar

Teaching assistant: Ami Wiesel

Time and location: Sundays 14:30-16:30, Meyer 354



The course will focus on the theory and applications of modern convex optimization methods in signal processing and wireless communications. The main objective is to introduce the available state of the art optimization tools, and to learn how to utilize them. We will discuss various estimation, detection and design problems, using newly developed optimization tools and illustrate recent successes in applying these techniques to solving core problems in signal processing and communications. We will discuss several standard mathematical tricks that can be used in order to convert a variety of problems into standard form which can be efficiently solved. In more difficult problems, we will show how convex optimization tools can be used in order to obtain relaxations and tractable suboptimal solutions.



We will NOT treat the numerical solutions for the resulting optimization problems. For those who are interested, this is addressed in course EE-46197. Nonetheless, we do not assume any prior knowledge in convex optimization theory and EE-46197 is NOT a prerequisite.


Presentation and grading:

Each student will prepare one of the lectures below based on the links to the reading material and present it to the class (please contact Ami to be assigned a topic). The presentation should be written in Powerpoint using the blends.ppt design template. Please do not change the fonts or the template. The presentation should be divided into three parts: the optimization topic, the application and a 20 minutes discussion / future work / conclusions section. A Powerpoint file with the slides should be sent to Ami at least a week before the actual presentation. The grade will be based on the presentation and the discussion that follows it.


Background material: Luo, Luo and Yu, Palomar et al.


Tentative syllabus:

Review of basic convex optimization

Reading assignment:

Convex Optimization by S. Boyd and L. Vandenberghe, Cambridge University Press 2003

Week 1 (Udi Pfeffer)

Convex sets and convex functions

Reading assignment: Chapters 2-3 in Convex Optimization

Presentations: sets, functions.

Week 2 (Michal Lahav)

Convex optimization theory / duality

Reading assignment: Chapters 4-5 in Convex Optimization

Presentations: problems, duality.

Week 3 (Guest lecture by Dori Peleg on Sunday 15:30-17:30 in room 1061 Meyer)

Optimization topic: Short review on numerical optimization methods (+SOCP and SDP)

Reading assignment: Chapters 9-11 in Convex Optimization, Vandenberghe et al, Lobo et al

Applications in signal processing

Week 4 (Evgeniy Braginskiy)

Optimization topic: SOCP and Robust optimization

Application: Robust least squares

Reading assignment: Lobo et al, El Ghaoui & Lebret, Changrasekran et al

Presentations: socp, rls.

Week 5 (Erez Menzly)

Optimization topic: SDP

Application: Minimax / regret estimation

Reading assignment: Vandenberghe et al, Eldar et al, Eldar et al, Eldar et al

Presentations: sdp, minimax.

Week 6 (Zvika Ben Haim)

Application: Improved Cramer Rao bounds

Reading assignment: Eldar

Presentations: CRLB.

Week 7 (Slava Chernoi)

Optimization topic: Hidden convexity & SDP relaxation

Application: ML detection in MIMO channels

Reading assignment: Beck & Eldar, Ma et al, Wiesel et al, Sidiropoulos et al

Presentations: SDP1, SDP2.

Week 8 (Erez Sabbag)

Optimization topic: Primal/Dual decomposition

Application: Network utility maximization

Reading assignment: Boyd et al, Palomar et al

Presentations: Decomposition, Decomposition2.

Applications in communications

Week 9 (David Zelikovski)

Application: Multiuser beamforming design

Reading assignment: Bengtsson & Otterstern, Visotsky & Madow, Schubert and Boche, Wiesel et al

Presentation: beamforming

Week 10 (Tamar Shoham)

Optimization topic: Geometric programming

Application: Power control

Presentation: gp

Reading assignment: Boyd et al, Chiang et al

Week 11 (Amos Schreibman)

Application: Adaptive filtering and equalization

Reading assignment: Vandenberghe et al, Davidson et al, Davidson et al

Presentation: FIR

Week 12 (Eyal Feigenbaum)

Application: Iterative Water filling

Reading assignment: Yu et al, Yu et al, Jindal et al

Presentation: IWF

Week 13 (Alina Maor) Will take place 12:30-14:30, Feb 11 in Meyer 354

Optimization topic: Majorization

Application: Joint receiver/transmitter design

Presentation: Majorization

Reading assignment: Palomar et al

Week 14 (Tomer Michaeli) Will take place 14:30-16:30, Feb 11 in Meyer 354

Optimization topic: Analysis of SDP relaxation

Reading assignment: Jalden et al, Kisialiou et al

Presentation: SDR



Additional projects


1) Tightness of SDP relaxation Pataki, Beck, Nemirovski et al, Z. Q. Luo

2) Zero duality in nonconvex optimization problems Wei Yu