A compressive sampling algorithm recovers approximately a nearly sparse vector x
from a much smaller "sketch" given by the matrix-vector product $\Phi.x$. Settings
in the literature make different assumptions.  Some require robustness to noise
(that is, the signal may be far from sparse), but the matrix $\Phi$ is only
guaranteed to work on a single fixed x with high probability--it may not be
re-used arbitrarily many times. Others require $\Phi$ to work on all $x$
simultaneously, but are much less resilient to noise.
We examine compressive sampling of a RADAR signal.
Through a combination of theory and assumptions, we show how a single matrix $\Phi$
can be used repeatedly on multiple input vectors $x$, and still give the best
possible resilience to noise. Appeared in SSP2012.