  The inner part of dense clusters of primordial black holes is an active
environment where multiple scattering processes take place. Some of them give
rise from time to time to bounded pairs, and the rest ends up with a single
scattering event. The former eventually evolves to a binary black hole (BBH)
emitting periodic gravitational waves (GWs), while the latter with a short
distance, called close hyperbolic encounters (CHE), emits a strong GW burst. We
make the first calculation of the stochastic GW background originating from
unresolved CHE sources. Unlike the case for BBH, the low-frequency tail of the
SGWB from CHE is sensitive to the redshift dependence of the event rate, which
could help distinguish the astrophysical from the primordial black hole
contributions. We find that there is a chance that CHE can be tested by
third-generation ground-based GW detectors such as Einstein Telescope and
Cosmic Explorer.
