An MCMC approach to extracting the global 21-cm signal during the cosmic dawn from sky-averaged radio observations

Efforts are being made to observe the 21-cm signal from the 'cosmic dawn' using sky-averaged observations with individual radio dipoles. In this paper, we develop a model of the observations accounting for the 21-cm signal, foregrounds and several major instrumental effects. Given this model, we apply Markov Chain Monte Carlo techniques to demonstrate the ability of these instruments to separate the 21-cm signal from foregrounds and quantify their ability to constrain properties of the first galaxies. For concreteness, we investigate observations between 40 and 120 MHz with the proposed Dark Ages Radio Explorer mission in lunar orbit, showing its potential for science return.