  We introduce a new representation of an integer spin $S$ via bosonic
operators which is useful in describing the paramagnetic phase and transitions
to magnetically ordered phases in magnetic systems with large single-ion
easy-plane anisotropy $D$. Considering the exchange interaction between spins
as a perturbation and using the diagram technique we derive the elementary
excitation spectrum and the ground state energy in the third order of the
perturbation theory. In the special case of S=1 we obtain these expressions
also using simpler spin representations some of which were introduced before.
Comparison with results of previous numerical studies of 2D systems with S=1
demonstrates that our approach works better than other analytical methods
applied before for such systems. We apply our results for the elementary
excitation spectrum analysis obtained experimentally in $\rm NiCl_2$-$\rm
4SC(NH_2)_2$ (DTN). It is demonstrated that a set of model parameters (exchange
constants and $D$) which has been used for DTN so far describes badly the
experimentally obtained spectrum. A new set of parameters is proposed using
which we fit the spectrum and values of two critical fields of DTN.
