Sparse recovery is one of the most important methods for single snapshot DOA estimation. Due to fact that the originall0-minimization problem is a NP-hard problem, we design a new alternative fraction function to solve DOA estimation problem. First, we discuss the theoretical guarantee about the new alternative model for solving DOA estimation problem. The equivalence between the alternative model and the original model is proved. Second, we present the optimal property about this new model and a fixed point algorithm with convergence conclusion are given. Finally, some simulation experiments are provided to demonstrate the effectiveness of the new algorithm compared with the classic sparse recovery method.
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