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.

翻译：我们研究了在有限傅里叶曲线星座上，考虑切线空间人工噪声时的匹配译码与欧几里得失配译码。每个假设都诱导了一个具有符号相关秩一协方差的高斯分布。我们推导了任意符号对之间的精确欧几里得成对错误，以及双边切线正交符号对在匹配译码下的精确高斯期望表示。对于均匀偶数星座，欧几里得方法在所有偏移类别上提供了显式的距离谱和符号错误界；匹配方法在对径符号对上是精确的，并通过蒙特卡洛方法在全码本水平上进行数值基准测试。通过孤立切线空间人工噪声的检测理论后果，这些结果在解析上阐明了噪声分数和星座密度如何影响失配行为；保密率的影响需要额外的信道和对抗模型建模。