  In deterministic compressive sensing, one constructs sampling matrices that
recover sparse signals from highly incomplete measurements. However, the
so-called square-root bottleneck limits the usefulness of such matrices, as
they are only able to recover exceedingly sparse signals with respect to the
matrix dimension. In view of the flat restricted isometry property (flat RIP)
proposed by Bourgain et al., we provide a partial solution to the bottleneck
problem with the Gabor system of Legendre symbols. When summing over
consecutive vectors, the estimate gives a nontrivial upper bound required for
the bottleneck problem.
