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 x from the nonlinear measurements of a linear transform output z = Ax. 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 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.