  This paper offers a model for incoherent scatter signal spectra without
averaging the received signal over sounding runs (realizations). The model is
based on the existent theory of radio waves single scattering from the medium
dielectric permittivity irregularities, and on the existing kinetic theory of
the plasma thermal irregularities. The proposed model is obtained for the case
of monostatic sounding. The model shows that the main contribution to the
received signal is made by ion-acoustic waves caused by certain spatial
harmonics of the ions number phase density. The model explains the width and
form of the signal spectrum by macroscopic characteristics of the medium, and
its fine 'peaked' structure by characteristics of the ions number phase
density. The notion of the weight volume is introduced to define the domain of
wave vectors and velocities in the spatial spectrum of the ions number phase
density which makes the main contribution to the formation of the scattered
signal. This weight volume depends on the antenna pattern, the form of the
sounding signal, and on the time window of spectral processing, as well as on
ionospheric plasma macroscopic parameters: electron and ion temperatures, ion
composition, and the drift velocity. Within the context of additional
assumption about the ions number phase density, the proposed model was tested
by the data from the Irkutsk incoherent scatter radar. The test showed a good
fit of the model to experiment.
