Polynomial Symbol Waveforms for Bandwidth and Noise Optimization
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Solution Overview
Problem
Current data transmission systems face limitations in achieving higher capacity and efficiency, particularly in minimizing noise resistance and data throughput, due to the reliance on traditional modulation techniques and the need for improved characterization of data for transmission.
Innovation Solution
The use of polynomial symbol waveform (PSW) design, which involves modifying polynomial coefficients or roots, and shaping using techniques like polynomial convolution, to create optimized PSW alphabets that enhance data transmission characteristics, such as noise resistance and bandwidth efficiency, by employing methods like Monte Carlo optimization and Fractional Cycle Modulation.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If traditional modulation techniques (QAM, PSK) are used, then system simplicity is maintained, but data transmission capacity is limited
Solution Approach 1:
The patent transforms the modulation approach by changing from traditional circular constellation diagrams to spiral-based signal representations. This parameter change in the mathematical foundation enables higher capacity transmission by utilizing spiral polynomials that can encode more information symbols per transmission interval, directly addressing the data capacity limitation while maintaining manageable system complexity through established polynomial mathematics
Solution Approach 2:
The invention introduces a new dimensional perspective by representing signals as spiral polynomials in the complex plane rather than traditional 2D QAM constellations. This dimensional transformation allows for more efficient packing of information symbols and enables higher order modulation schemes that transcend the limitations of conventional approaches
2Reliability
If polynomial symbol waveforms with complex shaping are used, then noise resistance is improved, but device complexity increases
Solution Approach 1:
The patent applies pulse shaping filters and polynomial transformations in advance during the transmission signal generation process. By pre-shaping the polynomial symbol waveforms with appropriate filters before transmission, the system achieves improved noise resistance and spectral efficiency without adding complexity to the receiver, as the shaping characteristics are embedded in the transmitted signal itself
Solution Approach 2:
The system employs Instantaneous Spectral_analysis (ISA) to provide feedback information about the spectral characteristics of the transmitted spiral polynomials. This feedback mechanism allows for optimization of the polynomial parameters and shaping filters to maximize noise resistance while maintaining computational feasibility, creating a closed-loop optimization process
3Productivity
If data is transmitted with higher capacity requirements, then communication efficiency is improved, but occupied bandwidth increases
Solution Approach 1:
The patent utilizes spiral polynomial parameters (order, frequency, amplitude) that can be optimized to achieve higher spectral efficiency. By carefully selecting and adjusting these polynomial parameters, the system transmits more data within a confined bandwidth, improving communication efficiency without proportionally increasing the occupied spectral area
Data Source
AI summary
Systems, devices, and methods of the present invention enhance data transmission through the use of polynomial symbol waveforms (PSW) and sets of PSWs corresponding to a symbol alphabet is here termed a PSW alphabet. Methods introduced here are based on modifying polynomial alphabet by changing the polynomial coefficients or roots of PSWs and/or shaping of the polynomial alphabet, such as by polynomial convolution, to produce a designed PSW alphabet including waveforms with improved characteristics for data transmission.