Spiral Polynomial Division Multiplexing for Spectral Efficiency
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Solution Overview
Problem
Existing multiplexing techniques in wireless communication rely on sinusoidal-based signal modulation, which limits spectral efficiency and requires sinusoidal orthogonality, making them less efficient in handling high-degree polynomials and prone to coherent interference.
Innovation Solution
The implementation of spiral polynomial division multiplexing (SPDM) using orthogonal polynomial functions, such as Chebyshev or Cairns polynomials, which modulate amplitude rather than sinusoids, allowing for high spectral efficiency and robust synchronization without the need for sinusoidal orthogonality.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If sinusoidal-based signal modulation is used for multiplexing, then the system can maintain traditional modulation compatibility, but spectral efficiency is limited and sinusoidal orthogonality is required
Solution Approach 1:
The patent changes the fundamental parameter of signal modulation from sinusoidal functions to polynomial functions. By using orthogonal polynomials (such as Chebyshev or Legendre polynomials) as the basis for signal representation, the system achieves higher spectral efficiency and eliminates the requirement for sinusoidal orthogonality, while maintaining the ability to represent and transmit arbitrary signals through polynomial approximation.
2Stability of the object's composition
If sinusoidal-based multiplexing is used, then existing communication frameworks can be maintained, but the system becomes prone to coherent interference and less efficient at handling high-degree polynomials
Solution Approach 1:
The patent substitutes the mathematical foundation of signal processing from trigonometric functions to polynomial functions. This replacement creates a new signal representation framework where orthogonal polynomials serve as basis functions, providing inherent resistance to coherent interference through their orthogonality properties and enabling efficient handling of high-degree polynomial signals that arise in modern communication systems.
3Productivity
If polynomial-based modulation is implemented, then spectral efficiency and interference resistance improve, but the complexity of signal processing increases
Solution Approach 1:
The patent segments the signal processing task into distinct polynomial-based operations: signal representation using orthogonal polynomial basis functions, multiplexing through polynomial addition, and demultiplexing through projection onto orthogonal basis functions. This segmentation allows each operation to leverage the mathematical properties of orthogonal polynomials, simplifying the overall processing while maintaining high spectral efficiency.
Data Source
AI summary
Systems, devices, methods, and computer readable medium for transmitting data using polynomials and instantaneous spectral analysis. In and/or prior to the transmitter, a signal may be formed by fitting the data with a Taylor series polynomial, which is projected onto Cairns series functions. The Cairns series functions are converted into Cairns exponential functions, which are combined based on frequency information to produce the set of sinusoidals with continuously time-varying amplitude, each of the sinusoidals having a different frequency.