Beschreibung
Detecting the global 21-cm signal from Cosmic Dawn and the Epoch of Reionization requires extremely precise calibration, since instrumental systematics can easily mimic or obscure the cosmological signal. In this work, we investigate the numerical stability of the Bayesian calibration pipeline used by the REACH experiment, which models receiver noise using the noise wave formalism. We identify a strong degeneracy between two noise wave components that leads to ill-conditioned and non-reproducible calibration solutions. Using singular value decomposition, we trace the origin of this instability and introduce a physically motivated mitigation strategy: fixing or independently estimating the noise source temperature before refitting the remaining noise wave parameters. Tests on mock data show that this approach produces stable, reproducible calibration solutions while preserving calibration quality. Although developed for REACH, the degeneracy arises from the structure of the noise wave model itself, making the method relevant for future global 21-cm experiments seeking robust constraints on early-Universe cosmology.