Fundamental Group Modulation for Wireless Bandwidth Efficiency
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Solution Overview
Problem
Traditional digital modulation systems face limitations in bandwidth efficiency and signal strength requirements, particularly for high-density schemes like 64-QAM, and rely on complex inversion techniques to correct channel distortions, which can be inefficient and unstable, especially in mobile wireless communications.
Innovation Solution
Fundamental group modulation transmits information by encoding data sequences onto paths relative to 'holes' in a topological space, allowing direct detection in the image space, thereby improving communication stability and efficiency by preserving information about the underlying topology through channel distortions.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Quantity of substance
If traditional linear modulation systems (e.g., QPSK, 16-QAM, 64-QAM) are used to map data bits to constellation points, then bandwidth efficiency can be improved by using denser schemes like 64-QAM, but the required signal strength increases significantly and system complexity increases due to the need for complex inversion techniques to correct channel distortions
Solution Approach 1:
Instead of mapping data to constellation points and then attempting to invert channel effects through complex equalization, the patent inverts the approach by mapping data directly to closed paths (loops) in the complex plane. The receiver detects which holes are encircled by the received path, eliminating the need for traditional equalization and reducing system complexity while maintaining bandwidth efficiency
Solution Approach 2:
The patent extracts the essential topological feature (which holes are encircled by the path) from the complex channel-distorted signal. By focusing only on the topological invariant rather than the full signal waveform, the system achieves robust detection without complex inversion techniques
2Measurement precision
If traditional modulation systems attempt to correct channel distortions through mathematical inversion, then measurement precision can be improved, but reliability decreases in mobile wireless communications due to instability of inversion techniques under varying channel conditions
Solution Approach 1:
The patent inverts the traditional approach by making the transmitted signal itself topologically invariant rather than attempting to invert channel effects at the receiver. The closed paths are designed to be detectable through their topological properties (which holes they encircle), which remain stable under continuous deformation caused by channel distortions, thus improving reliability without sacrificing detection accuracy
Solution Approach 2:
The patent changes the fundamental parameter used for detection from amplitude and phase (which are sensitive to channel distortions) to topological invariants (which holes are encircled), which are invariant under continuous deformation. This parameter transformation makes the system reliable under varying channel conditions while maintaining detection precision
3Productivity
If dense bandwidth schemes like 64-QAM are used to increase data capacity, then productivity increases, but the required signal strength increases making the system more vulnerable to noise and interference
Solution Approach 1:
The patent moves from traditional 2D constellation point mapping to path-based encoding in the complex plane, utilizing the topological dimension of path encirclement. This allows multiple data bits to be encoded in the topological structure of a single closed path, achieving high data rates without requiring high signal strength, as detection depends on topological invariants rather than precise amplitude and phase measurements
Data Source
AI summary
Embodiments of a system and method for providing fundamental group modulation are generally described herein. In some embodiments, a trajectory mapper is arranged to receive a modulation symbol sequence. A signal trajectory sample memory is arranged to store a representation of signal trajectories for a topological space having a set of predetermined removed regions therein. The trajectory mapper accesses the signal trajectory sample memory to select a signal trajectory relative to the set of predetermined removed regions in the topological space based on the received modulation symbol sequence and produces a sequence of in-phase (I) and quadrature (Q) sample values at a specified sample rate in response to the selected signal trajectory, the I and Q sample values serving as a basis for an amplified radio frequency signal.