Generalized Expectation Consistent Signal Recovery for Nonlinear Measurements

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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.