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In this paper, we propose a generalized expectation consistent signalrecovery algorithm to estimate the signal $\mathbf{x}$ from the nonlinearmeasurements of a linear transform output $\mathbf{z}=\mathbf{A}\mathbf{x}$.This estimation problem has been encountered in many applications, such ascommunications with front-end impairments, compressed sensing, and phaseretrieval. The proposed algorithm extends the prior art called generalizedturbo signal recovery from a partial discrete Fourier transform matrix$\mathbf{A}$ to a class of general matrices. Numerical results show theexcellent agreement of the proposed algorithm with the theoreticalBayesian-optimal estimator derived using the replica method.

Generalized Expectation Consistent Signal Recovery for Nonlinear Measurements