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In particular, four estimation algorithms based on the theory of compressed sensing (CS), i.e., the classical<jats:italic>\u2113<\/jats:italic><jats:sub>1<\/jats:sub>minimization (or Least Absolute Shrinkage and Selection Operator, LASSO), the fast smooth<jats:italic>\u2113<\/jats:italic><jats:sub>0<\/jats:sub>minimization, and the Sparse Iterative Covariance-Based Estimator, SPICE and the Iterative Adaptive Approach for Amplitude and Phase Estimation, IAA-APES algorithms, are analyzed, and their statistical properties are investigated and compared with the classical Fourier beamformer (FB) in different simulated scenarios. We show that unlike the classical FB, a CS-based beamformer (CSB) has some desirable properties typical of the adaptive algorithms (e.g., Capon and MUSIC) even in the single snapshot case. Particular attention is devoted to the super-resolution property. Theoretical arguments and simulation analysis provide evidence that a CS-based beamformer can achieve resolution beyond the classical Rayleigh limit. Finally, the theoretical findings are validated by processing a real sonar dataset.<\/jats:p>","DOI":"10.1186\/1687-6180-2014-120","type":"journal-article","created":{"date-parts":[[2014,7,30]],"date-time":"2014-07-30T20:10:56Z","timestamp":1406751056000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":115,"title":["Single-snapshot DOA estimation by using Compressed Sensing"],"prefix":"10.1186","volume":"2014","author":[{"given":"Stefano","family":"Fortunati","sequence":"first","affiliation":[]},{"given":"Raffaele","family":"Grasso","sequence":"additional","affiliation":[]},{"given":"Fulvio","family":"Gini","sequence":"additional","affiliation":[]},{"given":"Maria S","family":"Greco","sequence":"additional","affiliation":[]},{"given":"Kevin","family":"LePage","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2014,7,30]]},"reference":[{"key":"681_CR1","doi-asserted-by":"crossref","DOI":"10.1002\/0471221104","volume-title":"Optimum Array Processing Detection, Estimation and Modulation Theory, Part IV","author":"H Van Trees","year":"2002","unstructured":"Van Trees H: Optimum Array Processing Detection, Estimation and Modulation Theory, Part IV. 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