Geometric Signal Constellations for Closing the Shannon Capacity Gap
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Existing communication systems utilize constellations that leave a significant gap to the theoretical Shannon Gaussian capacity, limiting the achievable capacity and efficiency of digital transmission systems.
Innovation Solution
The development of unequally spaced geometrically shaped constellations that optimize capacity measures such as parallel decode (PD) and joint capacity, using techniques like LDPC and Turbo codes, to reduce or eliminate the gap to Gaussian channel capacity.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If conventional constellations that maximize minimum distance (dmin) are used, then reliability is improved, but capacity is limited and falls short of Shannon Gaussian capacity
Solution Approach 1:
The patent transforms the constellation design from equal-spacing to unequal-spacing by changing the positional parameters of constellation points. This parameter change allows the system to move from dmin-optimized constellations to capacity-optimized constellations, achieving up to 100% capacity increase while maintaining reliability through capacity-optimized point distributions.
Solution Approach 2:
The patent introduces asymmetry in constellation point spacing, moving away from symmetric equal-spacing designs. The unequal-spacing geometric constellations create asymmetric distributions that better match the Gaussian channel capacity requirements, allowing points to be positioned at optimal locations rather than uniform intervals.
2Ease of manufacture
If equal-spacing constellations are used, then manufacturing simplicity is maintained, but capacity efficiency is reduced due to gap from Shannon limit
Solution Approach 1:
The patent changes the spacing parameters from uniform to non-uniform distributions. This parameter transformation enables the constellation to achieve capacity-optimized performance while the overall geometric structure remains implementable through standard modulation techniques.
Solution Approach 2:
The patent extends constellation design from one-dimensional equal-spacing to multi-dimensional geometric arrangements. By utilizing additional spatial dimensions and non-linear geometric transformations, the system achieves higher capacity efficiency while maintaining practical implementability.
3Reliability
If dmin-maximized constellations are used, then robustness against noise is improved, but power efficiency is reduced requiring higher power for same capacity
Solution Approach 1:
The patent optimizes the positional parameters of constellation points to maximize capacity rather than minimum distance. This parameter optimization redistributes power efficiency across the constellation, allowing lower average transmission power for the same capacity by positioning points at capacity-optimized locations rather than dmin-optimized locations.
Solution Approach 2:
The patent applies different spacing characteristics to different regions of the constellation. Instead of uniform spacing, local variations in point density and spacing are introduced to optimize capacity and power efficiency, with inner points and outer points having different spacing characteristics tailored to their respective roles in capacity transmission.
Data Source
AI summary
Communication systems are described that use signal constellations, which have unequally spaced (i.e. ‘geometrically’ shaped) points. In many embodiments, the communication systems use specific geometric constellations that are capacity optimized at a specific SNR. In addition, ranges within which the constellation points of a capacity optimized constellation can be perturbed and are still likely to achieve a given percentage of the optimal capacity increase compared to a constellation that maximizes dmin, are also described. Capacity measures that are used in the selection of the location of constellation points include, but are not limited to, parallel decode (PD) capacity and joint capacity.