  Support recovery of sparse signals from noisy measurements with orthogonal
matching pursuit (OMP) has been extensively studied in the literature. In this
paper, we show that for any $K$-sparse signal $\x$, if the sensing matrix $\A$
satisfies the restricted isometry property (RIP) of order $K + 1$ with
restricted isometry constant (RIC) $\delta_{K+1} < 1/\sqrt {K+1}$, then under
some constraint on the minimum magnitude of the nonzero elements of $\x$, the
OMP algorithm exactly recovers the support of $\x$ from the measurements
$\y=\A\x+\v$ in $K$ iterations, where $\v$ is the noise vector. This condition
is sharp in terms of $\delta_{K+1}$ since for any given positive integer $K\geq
2$ and any $1/\sqrt{K+1}\leq t<1$, there always exist a $K$-sparse $\x$ and a
matrix $\A$ satisfying $\delta_{K+1}=t$ for which OMP may fail to recover the
signal $\x$ in $K$ iterations. Moreover, the constraint on the minimum
magnitude of the nonzero elements of $\x$ is weaker than existing results.
