  Coherent propagation of two interacting particles in $1d$ weak random
potential is considered. An accurate estimate of the matrix element of
interaction in the basis of localized states leads to mapping onto the relevant
matrix model. This mapping allows to clarify the mechanism of enhancement of
the localization length which turns out to be rather different from the one
considered in the literature. Although the existence of enhancement is
transparent, an analytical solution of the matrix model was found only for very
short samples. For a more realistic situation numerical simulations were
performed. The result of these simulations is consistent with l_{2}/l_1 \sim
l_1^{\gamma} , where $l_1$ and $l_2$ are the single and two particle
localization lengths and the exponent $\gamma$ depends on the strength of the
interaction. In particular, in the limit of strong particle-particle
interaction there is no enhancement of the coherent propagation at all ($l_{2}
\approx l_1$).
