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Reconstructing the interference-plus-noise covariance matrix instead of searching for the optimal diagonal loading factor for the sample covariance matrix is a good method for calculating the adaptive beamforming coefficients. However, when the directions-of-arrival (DOAs) and the number of the interferences are unknown and the steering vector has an error, the reconstructed interference-plusnoise covariance matrix might not be accurate, which degrades the performance of adaptive beamforming. Here, we propose a robust Capon beamforming approach, which is suited to the sparse array with the array steering error and the unknown interference DOAs. In particular, by drawing a modified optimization problem and the mean shift model of the interference covariance matrix, we propose the robust beamforming with the importance resampling based compressive covariance sensing, which is shown to outperform the classical beamforming method based on reconstructing the interference-plus-noise covariance matrix. The key to our approach is the new solution of the reconstructing method and the important functions. The excellent performance of the proposed approach for interference suppression is demonstrated via a number of numerical examples.

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