  The next-generation CMB satellite missions are expected to provide robust
constraints on a wide range of cosmological parameters with unprecedented
precision. But these constraints on the parameters could weaken if we do not
attribute dark energy to a cosmological constant. The cosmological models
involving interaction between dark energy and dark matter can give rise to
comparable energy densities at the present epoch, thereby alleviating the
so-called cosmic coincidence problem. In the present paper, we perform a
forecast analysis to test the ability of the future generation high-sensitive
Cosmic Microwave Background (CMB), and Baryon Acoustic Oscillation (BAO)
experiments to constrain phenomenological interacting dark energy models. We
consider cosmic variance limited future CMB polarization experiment PICO along
with BAO information from the DESI experiment to constrain the parameters of
the interacting dark sector. Based on the stability of the cosmological
perturbations, we consider two possibilities for the interaction scenario. We
investigate the impact of both the coupling constant and the equation of state
parameter of dark energy on the CMB temperature power spectrum, matter power
spectrum, and $f\sigma_8$. We have used simulated temperature and polarization
data from PICO within the multipole ranges ($\ell = 2 - 4000$), and as
expected, we do see PICO alone produces better constraints than Planck on the
$\Lambda$CDM parameters. With the integration of the PICO and DESI missions, we
observe a significant improvement in the constraints on several cosmological
parameters, especially the equation of state parameter of dark energy. However,
we note that additional data is required to constrain a small positive coupling
constant.
