Аннотация:The Gravitational antenna OGRAN is the setup having a combination of acoustical and optical principles of gravitational wave detection. At present the antenna OGRAN is installed in underground facilities of the Baksan Neutrino Observatory of INR RAS. Using this instrument, a long time observation of the gravity gradient background is planned in parallel with neutrino events monitoring at the neutrino telescope setup (BUST), having the goal of a joint search for collapsing stars – relativistic transient events in our Galaxy and close halo region with radius ~ 100 Kpc. Extension of the zone of detectable sources requires an instrument with enhanced sensitivity. For the OGRAN antenna it could be achieved in particular using its cryogenic version with cooled solid body GW detector. The unavoidable noise background for the OGRAN setup is composed by the two natural sources of fluctuations: thermal noise of the acoustical bar and photon noise of the optical read out. Effectiveness of these sources depends on the key parameters of the setup such as mechanical losses, temperature, optical power, cavity finesse. Numerical calculation shown that at temperatures 50 – 100 K, the optical read out has the low noise factor, i.e., it is practically an “ideal registration system” without an additive noise. Тhe receiver bandwidth is several tens of Hz, and the amplitude spectral noise density hmin is only few times larger than the level of potential sensitivity with ideal registration system hmin pot ~10^{-21} Нz^{-1/2}