Spiral-Based Waveforms for Spectrum-Efficient Communication
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Existing intra-symbol amplitude modulation-based communication methods are inefficient in minimizing spectrum usage, as they rely on exponentials which are not optimal for this purpose.
Innovation Solution
The use of non-periodic functions such as piecewise cubic polynomials and the Archimedes Spiral function to generate spiral-based symbol waveforms that reduce spectrum usage, including techniques like spline interpolation with 'Not-a-Knot' and 'Zero Derivative' end conditions, and linear amplitude variation.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If exponential functions are used for intra-symbol amplitude modulation, then signal modulation is achieved, but spectrum usage efficiency deteriorates
Solution Approach 1:
The patent changes the mathematical function type from exponential to piecewise cubic polynomial with specific boundary conditions (zero first and second derivatives at endpoints). This parameter change in the amplitude variation function fundamentally alters the spectral characteristics, reducing out-of-band emissions and improving spectrum efficiency while maintaining communication performance
Solution Approach 2:
The amplitude variation is divided into multiple segments using piecewise cubic polynomials, where each segment is optimized to have smooth transitions with zero derivatives at boundaries. This segmentation approach allows precise control over the amplitude profile to minimize spectral leakage while maintaining signal integrity
2Quantity of substance
If smooth amplitude variations are implemented to reduce spectrum usage, then bandwidth efficiency improves, but waveform complexity increases
Solution Approach 1:
The patent specifies particular parameter constraints for the cubic polynomial coefficients by imposing zero first and second derivative conditions at the boundaries. These parameter constraints simplify the mathematical formulation and enable efficient computation while achieving the desired smooth amplitude variations that reduce spectral leakage
Data Source
AI summary
Methods for communicating are disclosed. A method includes obtaining at least one input communication symbol selected from a set of communication symbols, converting the at least one input communication symbol into at least one transmittable waveform using at least one defined spiral waveform function, and transmitting the at least one transmittable waveform over a communication channel. Example spiral waveform functions include spline-based piecewise functions and Archimedes spiral functions.