Compressed sensing (CS) is a sampling paradigm
that allows to simultaneously measure and compress signals that
are sparse or compressible in some domain. The choice of a
sensing matrix that carries out the measurement has a defining
impact on the system performance and it is often advocated to
draw its elements randomly. It has been noted that in the presence
of input (signal) noise, the application of the sensing matrix causes
SNR degradation due to the noise folding effect. In fact, it might
also result in the variations of the output SNR in compressive
measurements over the support of the input signal, potentially
resulting in unexpected non-uniform system performance. In this
work, we study the impact of a distribution from which the
elements of a sensing matrix are drawn on the spread of the
output SNR. We derive analytic expressions for several common
types of sensing matrices and show that the SNR spread grows
with the decrease of the number of measurements. This makes
its negative effect especially pronounced for high compression
rates that are often of interest in CS.