  Discs around young planets, so-called circumplanetary discs (CPDs), are
essential for planet growth, satellite formation, and planet detection. We
study the millimetre and centimetre emission from accreting CPDs by using the
simple $\alpha$ disc model. We find that it is easier to detect CPDs at shorter
radio wavelengths (e.g. $\lambda\lesssim$ 1 mm). For example, if the system is
140 pc away from us, deep observations (e.g. 5 hours) at ALMA Band 7 (0.87 mm)
are sensitive to as small as 0.03 lunar mass of dust in CPDs. If the CPD is
around a Jupiter mass planet 20 AU away from the host star and has
$\alpha\lesssim 0.001$, ALMA can detect this disc when it accretes faster than
$10^{-10} M_{\odot}/yr$. ALMA can also detect the "minimum mass sub-nebulae"
disc if such a disc exists around a young planet in YSOs. However, to
distinguish the embedded compact CPD from the circumstellar disc material, we
should observe circumstellar discs with large gaps/cavities using the highest
resolution possible. We also calculate the CPD fluxes at VLA bands, and discuss
the possibility of detecting radio emission from jets/winds launched in CPDs.
Finally we argue that, if the radial drift of dust particles is considered, the
drifting timescale for millimetre dust in CPDs can be extremely short. It only
takes 10$^2$-10$^{3}$ years for CPDs to lose millimetre dust. Thus, for CPDs to
be detectable at radio wavelengths, mm-sized dust in CPDs needs to be
replenished continuously, or the disc has a significant fraction of
micron-sized dust or a high gas surface density so that the particle drifting
timescale is long, or the radial drift is prevented by other means (e.g.
pressure traps).
