  The COSINUS (Cryogenic Observatory for SIgnatures seen in Next-generation
Underground Searches) experiment aims at the detection of dark matter-induced
recoils in sodium iodide (NaI) crystals operated as scintillating cryogenic
calorimeters. The detection of both scintillation light and phonons allows
performing an event-by-event signal to background discrimination, thus
enhancing the sensitivity of the experiment. The construction of the
experimental facility is foreseen to start by 2021 at the INFN Gran Sasso
National Laboratory (LNGS) in Italy. It consists of a cryostat housing the
target crystals shielded from the external radioactivity by a water tank
acting, at the same time, as an active veto against cosmic ray-induced events.
Taking into account both environmental radioactivity and intrinsic
contamination of materials used for cryostat, shielding and infrastructure, we
performed a careful background budget estimation. The goal is to evaluate the
number of events that could mimic or interfere with signal detection while
optimising the geometry of the experimental setup. In this paper we present the
results of the detailed Monte Carlo simulations we performed, together with the
final design of the setup that minimises the residual amount of background
particles reaching the detector volume.
