High-redshift quasars at $z \geq 3$ -- I. Radio spectra
  We present the radio properties of optically selected quasars with $z\geq3$.
The complete sample consists of 102 quasars with a flux density level
$S_{1.4}\geq100$ mJy in a declination range -35$^{\circ}$ $\leq$ Dec $\leq$
+49$^{\circ}$. The observations were obtained in 2017-2020 using the radio
telescope RATAN-600. We measured flux densities at six frequencies 1.2, 2.3,
4.7, 8.2, 11.2, and 22 GHz quasi-simultaneously with uncertainties of 9-31 %.
The detection rate is 100, 89, and 46 % at 4.7, 11.2, and 22 GHz, respectively.
We have analysed the averaged radio spectra of the quasars based on the RATAN
and literature data. We classify 46 % of radio spectra as peaked-spectrum, 24 %
as flat, and none as ultra-steep spectra ($\alpha\leq-1.1$). The multifrequency
data reveal that a peaked spectral shape (PS) is a common feature for bright
high-redshift quasars. This indicates the dominance of bright compact core
emission and the insignificant contribution of extended optically thin
kpc-scale components in observed radio spectra. Using these new radio data, the
radio loudness $\log~R$ was estimated for 71 objects with a median value of
3.5, showing that the majority of the quasars are highly radio-loud with
$\log~R>2.5$. We have not found any significant correlation between $z$ and
$\alpha$. Several new megahertz-peaked spectrum (MPS) and gigahertz-peaked
spectrum (GPS) candidates are suggested. Further studies of their variability
and additional low-frequency observations are needed to classify them
precisely.
