  Here, we consider a classically scale-invariant extension of the Standard
Model (SM) with two-component dark matter (DM) candidates, including a Dirac
spinor and a scalar DM. We probe the parameter space of the model, constrained
by relic density and direct detection, and investigate the generation of
gravitational waves (GWs) produced by an electroweak first-order phase
transition (EFOPT). The analysis demonstrates that there are points in the
parameter space, leading to a detectable GW spectrum arising from the
first-order phase transition, which is also consistent with the DM relic
abundance and direct detection bounds. These GWs could be observed by
forthcoming space-based interferometers such as the Big Bang Observer (BBO),
Decihertz Interferometer Gravitational-wave Observatory (DECIGO), and
Ultimate-DECIGO (UDECIGO).
