Supervisor: Germain PHAM dpham at telecom-paris.fr
Project topics : Signal processing and Electrical engineering
Number of students: 2
Project description
Piecewise polynomial models are widely used in fields such as telecommunications, particularly to compensate for the nonlinear effects of certain RF components.
When a single polynomial is not sufficient to cover a wide range of values, composite models built "piecewisely" are used. However, these models may exhibit discontinuities at transition zones, causing performance and accuracy issues.
Key Features of This Project:
This project has a strong mathematical component but is still accessible to everyone (one only needs to know how to write polynomial equations and their derivatives). The most challenging part will be implementing the calculations in Matlab using a matrix-based approach and writing the equations in Latex.
This project is therefore aimed at individuals who are not intimidated by writing (large) systems of equations both manually and in Latex. Furthermore, a strong interest in scientific programming is necessary (you will need to construct block matrices).
Main Objectives:
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Formalize the mathematical problem of minimizing discontinuities in transition zones.
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Implement methods to construct continuous piecewise models in three cases:
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Simple polynomials (without memory).
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Memory polynomials.
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Generalized memory polynomials.
Required skills
This project requires a good knowledge of electrical engineering and mathematical tools for optimization problems.
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Mandatory
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Capacity to write heavy mathematical equations
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practical elements of
git -
Linux OS basics (usage of
terminalcommand lines)
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Optional
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Basic knowledge of Latex (for writing equations)
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Basic knowledge of Matlab
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Workplan (5 weeks)
gantt title ICS Project: OptiConti dateFormat DD/MM/YYYY excludes weekends axisFormat %e %b %y tickInterval 1week weekday monday todayMarker off section Week1 - Understand the problem and its mathematical foundation Literature review on piecewise polynomial functions: 25/02/2025, 3d Literature review on related optimization techniques: 25/02/2025, 3d Identify mathematical methods to minimize discontinuities: 27/02/2025, 2d Formalize the mathematical problem in the project context: 28/02/2025, 1d Deliverable slides - Synthesis of the literature review: milestone, 03/03/2025, 1d section Week2 - Structure computational approach + implement simple cases Define the structure of the Matlab implementation: 03/03/2025, 1d Define simple use cases: 03/03/2025, 1d Implement simple cases: 04/03/2025, 3d Deliverable slides - Synthesis of the simple case Matlab simulations: milestone, 07/03/2025, 1d section Week3+4 - Implementation for advanced polynomial cases Write the equations for memory polynomials and generalized memory polynomials: 10/03/2025, 3d Implement each case: 13/03/2025, 6d Deliverable slides - Synthesis of the advanced cases Matlab simulations: milestone, 21/03/2025, 1d section Week5 - Open source contribution Code refactoring and documentation: 24/03/2025, 2d Gitlab release: milestone, 27/03/2025, 1d Slides preparation: 24/03/2025, 2d Project defense: milestone, 28/03/2025, 1d
Location
School
Télécom Paris trains its students to innovate in today’s digital world. Its training and research cover all fields of information and communication sciences and technologies with a strong societal foundation in order to address the major challenges of the 21st century. Its offers engineering, PhD and professional degree programs, with international students accounting for 55% of its student body. Its research offers original, multidisciplinary world-class expertise in nine strategic areas: Data Science and Artificial Intelligence — Visual and Audio Computing, Interaction — Digital Trust — Innovation Regulations — Transformation of Innovative Firms — Cyber-Physical Systems — Communication Systems and Networks — Mathematics and Applications — Uses, Participation, Democratization of Innovation.
As a founding member of Institut Polytechnique de Paris and an IMT (Institut Mines-Télécom) school, Télécom Paris is a living laboratory that fosters practical solutions and applications while measuring their impact on society.
Hosting laboratory
Research team
The Circuits et Systèmes de Communication (C2S) team is internationally recognized for its ability to integrate digital intelligence into AMS and RF SoCs such as analog-to-digital converters (ADCs) or RF receivers for cognitive radio. By combining its expertise in the physical realization of the CMOS chip with its experience in signal processing and its knowledge of the other network layers for which LTCI’s skills are recognized, the group designs high-performance AMS and RF SoCs. The aim is to develop elements or "building blocks", enabling the system of connected objects to be interfaced on one side with the physical world via sensors, and on the other side with the system core via communications, in particular RF.