  In many particle physics models, domain wall can form during the phase
transition process after discrete symmetry breaking. We study the scenario
within a complex singlet extended Standard Model framework, where a strongly
first order phase transition can occur depending on the hidden scalar mass and
the mixing between the extra heavy Higgs and the SM Higgs mass. The
gravitational wave spectrum is of a typical two-peak shape, the amplitude and
the peak from the strongly first order phase transition is able to be probed by
the future space-based interferometers, and the one locates around the peak
from the domain wall decay is far beyond the capability of the current PTA, and
future SKA.
