The cosmological reionization can be studied in the radio through the tomographic view offered by the redshifted 21-cm line and the integrated information carried out by the diffuse free-free emission, coupled to the Comptonization distortion, relevant at higher frequencies. Current predictions span a wide range of possibilities, while the recent EDGES observations disagree with the standard models and call, if confirmed, for non-standard physical processes and/or for an early population of extragalactic sources producing a remarkable background at high redshifts almost consistent with the ARCADE 2 claim of a significant excess of CMB absolute temperature at low frequency. These signatures can be observed in global signal and fluctuations, from very large to small angular scales. The observer peculiar motion with respect to a reference frame in rest with respect to the CMB produces boosting effects in various observable quantities, remarkable at low multipoles, and particularly in the dipole, with frequency spectral behaviours depending on the monopole emission spectrum. We present a novel investigation at radio frequencies, aimed at predicting the imprints expected in the redshifted 21-cm line signal and in the diffuse free-free emission plus the Comptonization distortion for several models. Furthermore, we consider the same type of signal but expected from the cosmological radio background determining the offset for 21-cm line. The combination of these signals and their relevance in the various frequency ranges are studied. This approach, linking monopole and anisotropy analyses, can be applied on wide sky coverage surveys as well as to sets of sky patches. Relying only on the quality of interfrequency and relative data calibration, it in principle by-passes the need for precise absolute calibration, a critical point of current and future radio interferometric facilities.
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