Calibration Error in 21-Centimeter Global Spectrum Experiment

The redshifted 21 cm line signal is a powerful probe of the cosmic dawn and the epoch of reionization. The global spectrum can potentially be detected with a single antenna and spectrometer. However, this measurement requires an extremely accurate calibration of the instrument to facilitate the separation of the 21 cm signal from the much brighter foregrounds and possible variations in the instrument response. Understanding how the measurement errors propagate in a realistic instrument system and affect system calibration is the focus of this work. We simulate a 21 cm global spectrum observation based on the noise wave calibration scheme. We focus on how measurement errors in reflection coefficients affect the noise temperature and how typical errors impact the recovery of the 21 cm signal, especially in the frequency domain. Results show that for our example set up, a typical vector network analyzer (VNA) measurement error in the magnitude of the reflection coefficients of the antenna, receiver, and open cable, which are 0.001, 0.001, and 0.002 (linear), respectively, would result in a 200 mK deviation on the detected signal, and a typical measurement error of 0.48°, 0.78°, or 0.15° in the respective phases would cause a 40 mK deviation. The VNA measurement error can greatly affect the result of a 21 cm global spectrum experiment using this calibration technique, and such a feature could be mistaken for or be combined with the 21 cm signal.