Duality Application: Waterfilling Method for Maximizing Sum Rate of the Communication Channel Zubair Khalid Department of Electrical Engineering School of Science and Engineering Lahore University of Management Sciences https://www.zubairkhalid.org/ee563_2020.html Convex Optimization
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Duality Application: WaterfillingMethod for Maximizing Sum Rate of
the Communication Channel
Zubair Khalid
Department of Electrical EngineeringSchool of Science and Engineering
Lahore University of Management Sciences
https://www.zubairkhalid.org/ee563_2020.html
Convex Optimization
Outline
• Sum-Rate Maximization Problem in Communications
• Solution utilizing KKT Conditions
Section 5.5.3, Example 5.2
Recap - Karush-Kuhn-Tucker (KKT) Optimality Conditions
Stationarity
Primal Feasibility
Dual Feasibility
Complementary Slackness
Assumption:
Primal Optimization problem
Lagrange Dual Problem:
Sum Rate Maximization Problem in Communications
Model:
Transmitter
Problem:
Problem Formulation:
Sum Rate Maximization Problem in Communications
Problem Formulation
Optimization Problem
Primal Feasibility Dual Feasibility
Optimization Problem
Stationarity
Optimization Problem
Complementary Slackness
Optimization Problem
Water-filling Interpretation
Feedback: Questions or Comments?
Email: [email protected]
Slides available at: https://www.zubairkhalid.org/ee563_2020.html(Let me know should you need latex source)
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