  We use cosmological hydrodynamic simulations to study the gravitational wave
(GW) signals from high-redshift binary black holes (BBHs) formed by dynamical
capture (ex-situ formation channel). We in particular focus on BHs originating
from the first generation of massive, metal-poor, so-called Population~III
(Pop~III) stars. An alternative (in-situ) formation pathway arises in Pop~III
binary stars, whose GW signature has been intensively studied. In our
optimistic model, we predict a local GW event rate density for ex-situ BBHs
(formed at z>4) of ~0.04 /(yr Gpc^3). This is comparable to or even higher than
the conservative predictions of the rate density for in-situ BBHs ~0.01-0.1
/(yr Gpc^3), indicating that the ex-situ formation channel may be as important
as the in-situ one for producing GW events. We also evaluate the detectability
of our simulated GW events for selected planned GW instruments, such as the
Einstein Telescope (ET). For instance, we find the all-sky detection rate with
signal-to-noise ratios above 10 to be <100 per year for the xylophone
configuration of ET. However, our results are highly sensitive to the sub-grid
models for BBH identification and evolution, such that the GW event efficiency
(rate) is reduced by a factor of 4 (20) in the pessimistic case. The ex-situ
channel of Pop III BBHs deserves further investigation with better modeling of
the environments around Pop III-seeded BHs.
