  The HIRFL-CSR external-target experiment (CEE) under construction is expected
to provide novel opportunities to the studies of the thermodynamic properties,
namely the equation of state of nuclear matter (nEOS) with heavy ion collisions
at a few hundreds MeV/u beam energies. Based on Geant 4 packages, the fast
simulations of the detector responses to the collision events generated using
transport model are conducted. The overall performance of CEE, including
spatial resolution of hits, momentum resolution of tracks and particle
identification ability has been investigated. Various observables proposed to
probe the nEOS, such as the production of light clusters, $\rm t/^3He$ yield
ratio, the radial flow, $\pi^{-}/\pi^{+}$ yield ratio and the neutral kaon
yields, have been reconstructed. The feasibility of studying nEOS beyond the
saturation density via the aforementioned observables to be measured with CEE
has been demonstrated.
