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In this paper, we address the problem of recovering complex-valued signalsfrom a set of complex-valued linear measurements. Approximate message passing(AMP) is one state-of-the-art algorithm to recover real-valued sparse signals.However, the extension of AMP to complex-valued case is nontrivial and nodetailed and rigorous derivation has been explicitly presented. To fill thisgap, we extend AMP to complex Bayesian approximate message passing (CB-AMP)using expectation propagation (EP). This novel perspective leads to a concisederivation of CB-AMP without sophisticated transformations between the complexdomain and the real domain. In addition, we have derived state evolutionequations to predict the reconstruction performance of CB-AMP. Simulationresults are presented to demonstrate the efficiency of CB-AMP and stateevolution.

Concise Derivation of Complex Bayesian Approximate Message Passing via Expectation Propagation