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 values to generate transmission polynomials that can be converted into sinusoidals with continuously varying amplitudes for transmission, allowing for high spectral efficiency and robust synchronization.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If sinusoidal-based signal modulation is used for multiplexing, then the system can achieve basic signal transmission, 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 Legendre, Chebyshev, or Hermite polynomials) instead of sinusoidal carriers, the system achieves higher spectral efficiency without requiring sinusoidal orthogonality. The polynomial-based modulation allows for more flexible signal shaping and better spectral confinement.
Solution Approach 2:
The patent substitutes the traditional sinusoidal modulation mechanism with a polynomial-based modulation mechanism. Instead of using trigonometric functions to modulate signals, the system employs polynomial functions that can be orthogonally decomposed, thereby replacing the sinusoidal orthogonality requirement with polynomial orthogonality, which offers greater flexibility in spectral management.
2Reliability
If existing multiplexing techniques are used, then signal transmission is achieved, but resistance to coherent interference is reduced
Solution Approach 1:
The patent changes the signal representation parameter from sinusoidal waves to polynomial functions. Orthogonal polynomials have inherent properties that provide better resistance to coherent interference because they can be designed to have specific root distributions and energy concentrations, allowing the system to maintain reliability while improving spectral efficiency.
Solution Approach 2:
The patent employs a composite approach by combining orthogonal polynomial functions with division multiplexing techniques. This creates a hybrid modulation scheme where multiple polynomial-based subchannels are combined, providing both interference resistance through orthogonality and high spectral efficiency through efficient resource allocation.
3Loss of information
If high-degree polynomials are transmitted using traditional methods, then information capacity increases, but the system becomes prone to coherent interference
Solution Approach 1:
The patent segments the high-degree polynomial information into multiple lower-degree orthogonal polynomial subchannels. By decomposing the high-degree polynomial into a sum of orthogonal polynomial components, the system can transmit more information while each individual component remains resistant to coherent interference due to the orthogonality property.
Solution Approach 2:
The patent transforms the transmission parameter from direct high-degree polynomial modulation to orthogonal polynomial decomposition. This parameter change allows the system to maintain high information capacity through the richness of polynomial representations while avoiding coherent interference through the orthogonal structure that distributes energy across different spatial-frequency domains.
Data Source
AI summary
A method for communicating using polynomial-based signals. In such a method, a set of basis polynomial functions used to generate waveforms may be identified, wherein each of the basis polynomial functions in the set of basis polynomial functions is orthogonal to each of the other basis polynomial functions in the set of basis polynomial functions in a coordinate space. The set of basis polynomial functions may be combined into a message polynomial. The message polynomial may be convolved with a reference polynomial to produce a transmission polynomial. From the transmission polynomial, a sequence of amplitude values may be generated. Finally, a signal may be transmitted based on the sequence of amplitude values, which may be further modified based on, for example, instantaneous spectral analysis. In some embodiments, orthogonal polynomials may include Chebyshev or Cairns polynomials.