  Studying superpartner production together with a hard initial state radiation
(ISR) jet has been a useful strategy for searches of supersymmetry with a
compressed spectrum at the Large Hadron Collider (LHC). In the case of the top
squark (stop), the ratio of the missing transverse momentum from the lightest
neutralinos and the ISR momentum, defined as $\bar{R}_M$, turns out to be an
effective variable to distinguish the signal from the backgrounds. It has
helped to exclude the stop mass below 590 GeV along the top corridor where
$m_{\tilde{t}} - m_{\tilde{\chi}_1^0} \approx m_t$. On the other hand, the
current experimental limit is still rather weak in the $W$ corridor where
$m_{\tilde{t}} - m_{\tilde{\chi}_1^0} \approx m_W +m_b$. In this work we extend
this strategy to the parameter region around the $W$ corridor by considering
the one lepton final state. In this case the kinematic constraints are
insufficient to completely determine the neutrino momentum which is required to
calculate $\bar{R}_M$. However, the minimum value of $\bar{R}_M$ consistent
with the kinematic constraints still provides a useful discriminating variable,
allowing the exclusion reach of the stop mass to be extended to $\sim 550$ GeV
based on the current 36 fb$^{-1}$ LHC data. The same method can also be applied
to the chargino search with $m_{\tilde{\chi}_1^\pm} -m_{\tilde{\chi}_1^0}
\approx m_W$ because the analysis does not rely on $b$ jets. If no excess is
present in the current data, a chargino mass of 300 GeV along the $W$ corridor
can be excluded, beyond the limit obtained from the multilepton search.
