  We shall show that if the restricted isometry constant (RIC)
$\delta_{s+1}(A)$ of the measurement matrix $A$ satisfies $$ \delta_{s+1}(A) <
\frac{1}{\sqrt{s + 1}}, $$ then the greedy algorithm Orthogonal Matching
Pursuit(OMP) will succeed. That is, OMP can recover every $s$-sparse signal $x$
in $s$ iterations from $b = Ax$. Moreover, we shall show the upper bound of RIC
is sharp in the following sense. For any given $s \in \N$, we shall construct a
matrix $A$ with the RIC $$ \delta_{s+1}(A) = \frac{1}{\sqrt{s + 1}} $$ such
that OMP may not recover some $s$-sparse signal $x$ in $s$ iterations.
