  We consider a phase retrieval problem, where we want to reconstruct a
$n$-dimensional vector from its phaseless scalar products with $m$ sensing
vectors, independently sampled from complex normal distributions. We show that,
with a suitable initalization procedure, the classical algorithm of alternating
projections succeeds with high probability when $m\geq Cn$, for some $C>0$. We
conjecture that this result is still true when no special initialization
procedure is used, and present numerical experiments that support this
conjecture.
