  The phase transition is a performance measure of the sparsity-undersampling
tradeoff in compressed sensing (CS). This letter reports our first observation
and evaluation of an empirical phase transition of the $\ell_1$ minimization
approach to the complex valued CS (CVCS), which is positioned well above the
known phase transition of the real valued CS in the phase plane. This result
can be considered as an extension of the existing phase transition theory of
the block-sparse CS (BSCS) based on the universality argument, since the CVCS
problem does not meet the condition required by the phase transition theory of
BSCS but its observed phase transition coincides with that of BSCS. Our result
is obtained by applying the recently developed ONE-L1 algorithms to the
empirical evaluation of the phase transition of CVCS.
