  The estimates of the background for the associate W Higgs production, which
stems from the two parton shower production. It is about 1 - 2.5 times larger
than the signal. However, this background does not depend on the rapidity
difference between the W and the $b \bar{b}$ pair, while the signal peaks when
the rapidity difference is zero. The detailed calculations for the enhanced
diagrams' contribution to this process, are presented, and it is shown that the
overlapping singularities, being important theoretically, lead to a negligible
contribution for the LHC range of energies
