Title: Generalized Expectation Consistent Signal Recovery for Nonlinear Measurements,
Abstract: In this paper, we propose a generalized expectation consistent signal
recovery algorithm to estimate the signal $\mathbf{x}$ from the nonlinear
measurements of a linear transform output $\mathbf{z}=\mathbf{A}\mathbf{x}$.
This estimation problem has been encountered in many applications, such as
communications with front-end impairments, compressed sensing, and phase
retrieval. The proposed algorithm extends the prior art called generalized
turbo signal recovery from a partial discrete Fourier transform matrix
$\mathbf{A}$ to a class of general matrices. Numerical results show the
excellent agreement of the proposed algorithm with the theoretical
Bayesian-optimal estimator derived using the replica method.