ee563 convex optimization - module 8 · 2020-07-14 · convex optimization. outline •sum-rate...
TRANSCRIPT
![Page 1: EE563 Convex Optimization - Module 8 · 2020-07-14 · Convex Optimization. Outline •Sum-Rate Maximization Problem in Communications •Solution utilizing KKT Conditions Section](https://reader034.vdocument.in/reader034/viewer/2022050220/5f65f44f0c00d526000b35b3/html5/thumbnails/1.jpg)
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
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Outline
• Sum-Rate Maximization Problem in Communications
• Solution utilizing KKT Conditions
Section 5.5.3, Example 5.2
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Recap - Karush-Kuhn-Tucker (KKT) Optimality Conditions
Stationarity
Primal Feasibility
Dual Feasibility
Complementary Slackness
Assumption:
Primal Optimization problem
Lagrange Dual Problem:
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Sum Rate Maximization Problem in Communications
Model:
Transmitter
Problem:
![Page 5: EE563 Convex Optimization - Module 8 · 2020-07-14 · Convex Optimization. Outline •Sum-Rate Maximization Problem in Communications •Solution utilizing KKT Conditions Section](https://reader034.vdocument.in/reader034/viewer/2022050220/5f65f44f0c00d526000b35b3/html5/thumbnails/5.jpg)
Problem Formulation:
Sum Rate Maximization Problem in Communications
![Page 6: EE563 Convex Optimization - Module 8 · 2020-07-14 · Convex Optimization. Outline •Sum-Rate Maximization Problem in Communications •Solution utilizing KKT Conditions Section](https://reader034.vdocument.in/reader034/viewer/2022050220/5f65f44f0c00d526000b35b3/html5/thumbnails/6.jpg)
Problem Formulation
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Optimization Problem
Primal Feasibility Dual Feasibility
![Page 8: EE563 Convex Optimization - Module 8 · 2020-07-14 · Convex Optimization. Outline •Sum-Rate Maximization Problem in Communications •Solution utilizing KKT Conditions Section](https://reader034.vdocument.in/reader034/viewer/2022050220/5f65f44f0c00d526000b35b3/html5/thumbnails/8.jpg)
Optimization Problem
Stationarity
![Page 9: EE563 Convex Optimization - Module 8 · 2020-07-14 · Convex Optimization. Outline •Sum-Rate Maximization Problem in Communications •Solution utilizing KKT Conditions Section](https://reader034.vdocument.in/reader034/viewer/2022050220/5f65f44f0c00d526000b35b3/html5/thumbnails/9.jpg)
Optimization Problem
Complementary Slackness
![Page 10: EE563 Convex Optimization - Module 8 · 2020-07-14 · Convex Optimization. Outline •Sum-Rate Maximization Problem in Communications •Solution utilizing KKT Conditions Section](https://reader034.vdocument.in/reader034/viewer/2022050220/5f65f44f0c00d526000b35b3/html5/thumbnails/10.jpg)
Optimization Problem
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Water-filling Interpretation
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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)