Constellation Shaping With Functional Fitting for Higher-Order QAM
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Solution Overview
Problem
Current wireless communication systems using higher-order quadrature amplitude modulation (QAM) schemes have fixed constellations with equal probability, limiting channel capacity improvement and transmission rates.
Innovation Solution
Implementing piecewise polynomial approximations to shape constellations dynamically, allowing for unequal probability distribution of symbol sequences to enhance transmission efficiency.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If fixed constellations with equal probability are used in higher-order QAM schemes, then implementation simplicity is maintained, but channel capacity and transmission rates are limited
Solution Approach 1:
The constellation shaping process is segmented into multiple stages: generating candidate symbol sequences, calculating metrics for each sequence, sorting sequences by metric values, and selecting the top N sequences. This segmentation transforms the complex problem of optimal constellation shaping into manageable discrete steps that can be implemented efficiently
Solution Approach 2:
The system dynamically adjusts the probability distribution of symbol sequences based on calculated metrics rather than using fixed equal probability. The selection of top N sequences creates a dynamic, adaptive constellation that optimizes channel capacity while maintaining implementability through algorithmic control
2Productivity
If dynamic constellation shaping is implemented to improve transmission rates, then channel capacity increases, but computational complexity increases
Solution Approach 1:
Candidate symbol sequences are generated in advance before transmission. The metrics for these sequences are pre-calculated and stored, allowing the receiver to efficiently decode without performing complex real-time calculations. This preliminary action shifts computational burden to the transmission phase where results can be cached
Solution Approach 2:
Instead of performing complex optimization calculations at the receiver, the system uses pre-computed metric values and stored sequence information. The receiver copies and matches incoming signals against pre-established candidate sequences, dramatically reducing processing complexity while maintaining optimal transmission rates
Data Source
AI summary
A wireless communication device configured with approximation schemes utilizing functional fitting in constellation shaping is disclosed. The device is configured to obtain subintervals over which to form piecewise polynomial approximations of a plurality of terms, obtain, utilizing the piecewise polynomial approximations of the plurality of terms, an approximation of a total number of first symbol sequences over a first alphabet having a first alphabet size, each respective symbol sequence of the total number of first symbol sequences having a first symbol sequence length and a first symbol sequence energy, obtain a bit sequence having a bit sequence length, encode the bit sequence, utilizing the approximation of the total number of first symbol sequences, to a second symbol sequence over a second alphabet having a second alphabet size, the second symbol sequence having a second symbol sequence length and a second symbol sequence energy, and transmit the second symbol sequence.