Matched and Euclidean-Mismatched Decoding on Fourier-Curve Constellations with Tangent Noise

TL;DR

This paper analyzes matched and mismatched decoding on Fourier-curve constellations with tangent-space noise, providing exact error formulas and insights into noise effects on decoding performance.

Contribution

It derives exact pairwise error probabilities and distance spectra for these constellations, clarifying the impact of tangent noise on decoding and secrecy-rate implications.

Findings

Exact Euclidean pairwise errors derived for arbitrary pairs.

Explicit distance spectra and error bounds for uniform even constellations.

Numerical benchmarking of matched decoding at the full-codebook level.

Abstract

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.