**ELE 539A: Optimization of Communication Systems**

**Current Offering: Spring 2009. Updates on lecture notes will take place during the semester. Most of the lecture notes now were 2008 version.**

**Related website on ****research activites and papers ****about nonlinear optimization of communication systems at Princeton**

**This is the sixth offering of the course at Princeton, and the content has been updated and expanded compared to the last five offerings. New lecture notes will be posted here between February and April, 2009. Current version of lecture notes may contain TYPOS and still LACKING many graphs and background materials I write on blackboard during lectures.**

**I would like to acknowledge funding support from the National Science Foundation Combined Research and Curriculum Development Grant joint with Steven Low (Caltech). We thank Stephen Boyd (Stanford) for many of the course materials on convex optimization, and Tom Luo (U. Minnesota), Wei Yu (U. Toronto), Jennifer Rexford (Princeton), Daniel Palomar (Princeton), Pablo Parrilo (MIT), Asuman Ozdaglar (MIT), and Raphael Cendrillon (Queensland U.) for contributing materials to some of the lecture notes.**

**Course Information and Schedule. 2007 Version**

**Lecture Note 1A (Overview: Communication Systems and Optimization Mentality)**

**Lecture Note 1B (Convex Sets and Convex Functions)**

**Lecture Note 2 (Convex Optimization and Lagrange Duality)**

**Lecture Note 3A (Linear Programming)**

**Lecture Note 3B (Network Flow Problem)**

**Lecture Note 4 (Geometric Programming and Applications)**

**Lecture Note 5 (Gradient and Distributed Algorithms)**

**Lecture Note 6 (TCP Congestion Control)**

**Lecture Note 8-9 (Layering As Optimization Decomposition)**

**Lecture Note 10 (Guest Lecture: Internet Routing Optimization)**

**Lecture Note 11 (Guest Lecture: Link-State Routing Protocols)**

**Lecture Note 12 (DSL Spectrum Management)**

**Lecture Note 14 (Wireless Network Power Control)**

**Lecture Note 15 (SDP and Detection and Estimation)**

**Lecture Note 16 (Nonconvex Optimization)**

**Lecture Note 17 (Stochastic Network Optimization)**

**Lecture Note 18 (Interior Point Algorithms)**

**Content:** Study how key problems in communication systems, both point-to-point and networked systems, can be formulated and solved as various forms of linear or nonlinear optimization problems. Introduce the tools of linear and convex optimization and Lagrange duality. Study both theoretical properties and computational algorithms of the optimization methodology, through specific applications to the analysis and design of communication systems.

Major problems in communication systems covered in the course: information theory problems, detection and estimation problems, decoding and equalization algorithms, beamforming in multiple antenna systems, network resource allocation, wireless network power control and multiple access, optical network provisioning and protection, network utility maximization in wired and wireless networks, network flow problems, IP routing, TCP congestion control, layering as optimization decomposition.

Major optimization techniques covered in the course: linear programming, nonlinear convex optimization, SOS method for nonconvex optimization, Lagrange duality and KKT optimality condition, gradient algorithm, Newton's method, interior point algorithm, quadratic programming, geometric programming, semidefinite programming, multi-objective Pareto optimization, robust optimization, dynamic programming.

**Assignments:** Four sets of homework assignments. One take-home midterm. One individual final project where each student either conducts original research or implements existing algorithms.

**Prerequisite:** Basic understanding of digital communication, stochastic systems, and advanced calculus. Previous exposure to linear programming will help but is not needed.