  In this paper, we address the problem of recovering complex-valued signals
from 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 no
detailed and rigorous derivation has been explicitly presented. To fill this
gap, we extend AMP to complex Bayesian approximate message passing (CB-AMP)
using expectation propagation (EP). This novel perspective leads to a concise
derivation of CB-AMP without sophisticated transformations between the complex
domain and the real domain. In addition, we have derived state evolution
equations to predict the reconstruction performance of CB-AMP. Simulation
results are presented to demonstrate the efficiency of CB-AMP and state
evolution.
