Published data from long-term observations of a strip of sky at declination \delta \sim 5 ^ { \circ } carried out at 7.6 cm on the RATAN-600 radio telescope are used to estimate some statistical properties of radio sources . Limits on the sensitivity of the survey due to noise imposed by background sources , which dominates the radiometer sensitivity , are refined . The vast majority of noise due to background sources is associated with known radio sources ( for example , from the NVSS with a detection threshold of 2.3 mJy ) with normal steep spectra ( \alpha = 0.7 - 0.8 ,S \propto \nu ^ { - \alpha } ) , which have also been detected in new deep surveys at decimeter wavelengths . When all such objects are removed from the observational data , this leaves another noise component that is observed to be roughly identical in independent groups of observations . We suggest this represents a new population of radio sources that are not present in known catalogs at the 0.6 mJy level at 7.6 cm . The studied redshift dependence of the number of steep-spectrum objects shows that the sensitivity of our survey is sufficient to detect powerful FRII radio sources at any redshift , right to the epoch of formation of the first galaxies . The inferred new population is most likely associated with low-luminosity objects at redshifts z < 1 . In spite of the appearance of new means of carrying out direct studies of distant galaxies , searches for objects with very high redshifts among steep and ultra-steep spectrum radio sources remains an effective method for studying the early Universe .