  Approximate message passing (AMP) and its variants, developed based on loopy
belief propagation, are attractive for estimating a vector x from a noisy
version of z = Ax, which arises in many applications. For a large A with i. i.
d. elements, AMP can be characterized by the state evolution and exhibits fast
convergence. However, it has been shown that, AMP mayeasily diverge for a
generic A. In this work, we develop a new variant of AMP based on a unitary
transformation of the original model (hence the variant is called UT-AMP),
where the unitary matrix is available for any matrix A, e.g., the conjugate
transpose of the left singular matrix of A, or a normalized DFT (discrete
Fourier transform) matrix for any circulant A. We prove that, in the case of
Gaussian priors, UT-AMP always converges for any matrix A. It is observed that
UT-AMP is much more robust than the original AMP for difficult A and exhibits
fast convergence.
  A special form of UT-AMP with a circulant A was used in our previous work
[13] for turbo equalization. This work extends it to a generic A, and provides
a theoretical investigation on the convergence.
