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This study addresses the problem of discrete signal reconstruction from theperspective of sparse Bayesian learning (SBL). Generally, it is intractable toperform the Bayesian inference with the ideal discretization prior under theSBL framework. To overcome this challenge, we introduce a novel discretizationenforcing prior to exploit the knowledge of the discrete nature of thesignal-of-interest. By integrating the discretization enforcing prior into theSBL framework and applying the variational Bayesian inference (VBI)methodology, we devise an alternating optimization algorithm to jointlycharacterize the finite-alphabet feature and reconstruct the unknown signal.When the measurement matrix is i.i.d. Gaussian per component, we further embedthe generalized approximate message passing (GAMP) into the VBI-based method,so as to directly adopt the ideal prior and significantly reduce thecomputational burden. Simulation results demonstrate substantial performanceimprovement of the two proposed methods over existing schemes. Moreover, theGAMP-based variant outperforms the VBI-based method with i.i.d. Gaussianmeasurement matrices but it fails to work for non i.i.d. Gaussian matrices.

Sparse Bayesian Learning Approach for Discrete Signal Reconstruction