University of Twente Student Theses
Polynomial Calculation of Quasi-Gray code labelings for Irregular Signal Constellations
Jellema, J.M. (2019) Polynomial Calculation of Quasi-Gray code labelings for Irregular Signal Constellations.
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| Abstract: | The commonly used quadrature amplitude modulation (QAM) constellation has a shaping loss of about 1.53dB compared to the Additive White Gaussian Noise (AWGN) Shannon capacity. Usage of non-square constellations can improve this. However, non-square constellations exhibit Gray-code loss due to the impossibility of perfect Gray-code labeling, on constellations which do not have an orthogonal basis. Labelings of constellations can be improved using non-linear constraint solvers, but this exhibits large computational costs for larger constellations. The Binary Switching Algorithm (BSA), which can produce very good labelings, is non deterministic. BSA is an algorithm based on hill climbing from many starting points to produce the assumed global optimum. This paper presents a rule-based algorithm based on the KD-tree algorithm. The proposed algorithm produces labelings which offer a good approximation of Gray-code labeling. Gray-code based labelings can offer undominated performance in a variety of situations. The algorithm as proposed can be seen as a method to extend the Symmetric Ultra-composite (SU) method as proposed by Wesel et al to arbitrary signal constellations. The proposed algorithm has a polynomial time complexity, namely O(n \log^2(n)). Enabling the creation of good labelings at very low computational cost. This method is applied to and optimized for the Golden Angle Modulation (GAM) constellation. This method produced better performance in uncoded situations than the labeling as created by Larsson. The method reduced the needed signal-to-noise ratio by 0.1 to 0.2dB for a Bit Error Rate (BER) of 10^-3 to 10^-6. For very low Signal-to-noise Ratio (SNR), the method also obtained better BER performance across the DVB-S2 constellation with Low-Density parity check codes error correction. |
| Item Type: | Essay (Bachelor) |
| Faculty: | EEMCS: Electrical Engineering, Mathematics and Computer Science |
| Subject: | 53 electrotechnology, 54 computer science |
| Programme: | Computer Science BSc (56964) |
| Keywords: | Golden Angle Modulation, Constellation mapping, Constellation labeling, Mutual information, KD-tree, BICM, BICM-ID, DVB-S2 |
| Link to this item: | https://purl.utwente.nl/essays/78792 |
| Export this item as: | BibTeX EndNote HTML Citation Reference Manager |
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