  We consider the edge statistics of large dimensional deformed rectangular
matrices of the form $Y_t=Y+\sqrt{t}X,$ where $Y$ is a $p \times n$
deterministic signal matrix whose rank is comparable to $n$, $X$ is a $p\times
n$ random noise matrix with centered i.i.d. entries with variance $n^{-1}$, and
$t>0$ gives the noise level. This model is referred to as the
interference-plus-noise matrix in the study of massive multiple-input
multiple-output (MIMO) system, which belongs to the category of the so-called
signal-plus-noise model. For the case $t=1$, the spectral statistics of this
model have been studied to a certain extent in the literature. In this paper,
we study the singular value and singular vector statistics of $Y_t$ around the
right-most edge of the singular value spectrum in the harder regime
$n^{-2/3}\ll t \ll 1$. This regime is harder than the $t=1$ case, because on
one hand, the edge behavior of the empirical spectral distribution (ESD) of
$YY^\top$ has a strong effect on the edge statistics of $Y_tY_t^\top$ since
$t\ll 1$ is "small", while on the other hand, the edge statistics of $Y_t$ is
also not merely a perturbation of those of $Y$ since $t\gg n^{-2/3}$ is
"large". Under certain regularity assumptions on $Y,$ we prove the edge
universality, eigenvalues rigidity and eigenvector delocalization for the
matrices $Y_tY_t^\top$ and $Y_t^\top Y_t$. These results can be used to
estimate and infer the massive MIMO system. To prove the main results, we
analyze the edge behavior of the asymptotic ESD for $Y_tY_t^\top$, and
establish some sharp local laws on the resolvent of $Y_tY_t^\top$. These
results can be of independent interest, and used as useful inputs for many
other problems regarding the spectral statistics of $Y_t$.
