Matched and Euclidean-Mismatched Decoding on Fourier-Curve Constellations with Tangent Noise
This work provides theoretical insights for communication systems using artificial noise, but the secrecy-rate implications require further modeling, making it an incremental contribution.
The paper derives exact Euclidean pairwise error expressions and matched decoding representations for Fourier-curve constellations with tangent-space artificial noise, providing explicit distance spectra and symbol-error bounds for uniform even constellations. The results analytically clarify how noise fraction and constellation density affect mismatch behavior.
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.