Injecting artificial noise (AN) along the tangent space of a curved constellation makes each transmitted symbol induce a Gaussian observation with a symbol-dependent rank-one covariance, so the matched maximum-likelihood (ML) decoder differs from the Euclidean nearest-neighbor decoder by a single rank-one correction per candidate. We develop a baseband-demapper realization of this correction for the Fourier-curve constellation and instantiate a regular $(3,6)$ low-density parity-check (LDPC)-coded link at $(k,M){=}(20,64)$. Against four baselines (Euclidean-mismatched, flat-constellation isotropic-AN, no-AN, and same-spectral-efficiency narrowband), the matched decoder extends the BLER${=}10^{-1}$ operating range by approximately $5$\,dB over the Euclidean-mismatched counterpart on the same tangent-AN transmitter, at a cost of $2kM$ additional multiply-accumulate operations per symbol ($+50\%/+100\%$ under residual/template-correlation accounting) and a $20$\,KB constellation--tangent lookup table ($10$\,KB incremental over a Euclidean template-only LUT). A bit-interleaved coded-modulation achievable-rate (BICM-AIR) computation supports the same matched-metric advantage at the tested labeling and max-log demapper, indicating that the BLER gain is not merely an artifact of this particular LDPC simulation, and a Woodbury extension generalizes the rank-one correction to per-tone Ricean fading. In the tested Monte-Carlo runs, a design-aware bounded-search eavesdropper without the phase-key shows no successful LDPC decoding at any tested $k\in\{2,8,20\}$ within a $B{=}10^{3}$ non-code-aided search budget; code-aided, multi-frame, and known-preamble attacks are left to follow-up work. LUT quantization down to $6$ bits yields no measurable coded-BLER degradation at the tested operating points.

翻译：沿曲线星座切空间注入人工噪声后，每个发送符号会诱导出具有符号相关秩一协方差的高斯观测，因此匹配的最大似然解码器与欧氏近邻解码器的差异仅在于每个候选符号需进行单次秩一修正。我们针对傅里叶曲线星座开发了该修正的基带解映射器实现，并在$(k,M){=}(20,64)$参数下实例化了一个规则$(3,6)$低密度奇偶校验码链路。与四种基线（欧氏失配、平坦星座各向异性人工噪声、无人工噪声以及相同频谱效率窄带）相比，基于相同切空间人工噪声发射机的匹配解码器在BLER${=}10^{-1}$工作点将欧氏失配方案的运行范围扩展约$5$\,dB，其代价为每个符号增加$2kM$次乘累加运算（残差/模板相关计算模式下分别增加$+50\%/+100\%$）以及$20$\,KB的星座-切空间查找表（相比纯欧氏模板查找表增量$10$\,KB）。比特交织编码调制可达速率计算支持在测试的标签映射与最大对数解映射器下观察到相同的匹配度量优势，表明该BLER增益并非特定LDPC仿真的人为产物，而伍德伯里扩展则可将该秩一修正推广至每音调莱斯衰落场景。在蒙特卡洛仿真中，未持有相位密钥的感知受限边界搜索窃听者在$B{=}10^{3}$非编码辅助搜索预算内，对任何测试的$k\in\{2,8,20\}$均未能成功完成LDPC解码；编码辅助、多帧及已知前导攻击则留待后续研究。查找表量化至$6$比特时，在测试工作点未观察到可测量的编码BLER性能退化。