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

Phase retrieval with random Gaussian sensing vectors by alternating projections