  We study the properties of the stochastic gravitational wave background
(SGWB) resulting from the mergers of primordial black holes (PBH) that formed
from the collapse of sub-horizon regions in the early universe. We adopt a
model-independent approach, where we parameterize the fraction $f_H$ of the
wavelength of the perturbation mode in units of the horizon radius when the
patch starts to gravitationally collapse. Assuming a monochromatic spectrum of
isocurvature perturbations and spherically-symmetric density perturbations, we
investigate the isotropic SGWB energy density and angular power spectrum at
various frequencies, PBH masses, and horizon size fractions. The key effect of
sub-horizon formation is a change in the PBH mass function and formation
redshift, which, in turn, affects gravitational wave (GW) observables. We find
that sub-horizon PBH formation in general enhances the isotropic SGWB energy
density and the absolute angular power spectrum. However, the quasi-monotonic
increases in both quantities as $f_H$ decreases cease when the chirp mass of
the binary PBHs reaches a mass threshold determined by the frequency of
observation; the isotropic SGWB energy density spectrum significantly drops
above the corresponding cutoff frequency.
