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This paper deals with the problem of estimating the directions of arrival (DOA) of multiple source signals from a single observation vector of an array data. In particular, four estimation algorithms based on the theory of compressed sensing (CS), i.e., the classical ℓ 1 minimization (or Least Absolute Shrinkage and Selection Operator, LASSO), the fast smooth ℓ 0 minimization, and the Sparse Iterative Covariance-Based Estimator, SPICE and the Iterative Adaptive Approach for Amplitude and Phasedoi:10.1186/1687-6180-2014-120 fatcat:q3hxxsmeh5crjefzkqun7tpvke