Matched and Euclidean-Mismatched Decoding on Fourier-Curve Constellations with Tangent Noise
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arXiv
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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866913056264552448 |
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| author | Han, Bin Chen, Hao Sun, Muxia Poor, H. V. Schotten, Hans D. |
| author_facet | Han, Bin Chen, Hao Sun, Muxia Poor, H. V. Schotten, Hans D. |
| contents | We study matched and Euclidean-mismatched decoding on finite Fourier-curve constellations with tangent-space artificial noise. Each hypothesis induces a Gaussian law with symbol-dependent rank-one covariance. We derive exact Euclidean pairwise errors for arbitrary pairs and an exact Gaussian-expectation representation for matched decoding on bilaterally tangent-orthogonal pairs. For uniform even constellations, the Euclidean side yields explicit distance spectra and symbol-error bounds across all offset classes; the matched side is exact on antipodal pairs and benchmarked numerically at the full-codebook level via Monte Carlo. By isolating the detection-theoretic consequence of tangent-space artificial noise, these results clarify analytically how noise fraction and constellation density enter the mismatch behavior; secrecy-rate implications require additional channel and adversary modeling. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_14844 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Matched and Euclidean-Mismatched Decoding on Fourier-Curve Constellations with Tangent Noise Han, Bin Chen, Hao Sun, Muxia Poor, H. V. Schotten, Hans D. Information Theory Signal Processing We study matched and Euclidean-mismatched decoding on finite Fourier-curve constellations with tangent-space artificial noise. Each hypothesis induces a Gaussian law with symbol-dependent rank-one covariance. We derive exact Euclidean pairwise errors for arbitrary pairs and an exact Gaussian-expectation representation for matched decoding on bilaterally tangent-orthogonal pairs. For uniform even constellations, the Euclidean side yields explicit distance spectra and symbol-error bounds across all offset classes; the matched side is exact on antipodal pairs and benchmarked numerically at the full-codebook level via Monte Carlo. By isolating the detection-theoretic consequence of tangent-space artificial noise, these results clarify analytically how noise fraction and constellation density enter the mismatch behavior; secrecy-rate implications require additional channel and adversary modeling. |
| title | Matched and Euclidean-Mismatched Decoding on Fourier-Curve Constellations with Tangent Noise |
| topic | Information Theory Signal Processing |
| url | https://arxiv.org/abs/2604.14844 |