Sparse Reconstruction Method for DOA Estimation Based on Dynamic Dictionary and Negative Exponent Penalty

This paper proposes a novel sparse representation method for direction of arrival estimation based on dynamic dictionary and negative exponent penalty. The dynamic dictionary can eliminate the off-grid effect and the negative exponent penalty is capable of strengthening the sparse constraint to improve the performance. The basis is regarded as a part of the optimal target and the cross iteration is utilized to jointly update the dictionary and sparse support in this method. Based on the propositions of the penalty function, the penalty function is designed to replace of l(1) norm because of its unbiasedness and stronger sparse constraint. The regularization parameter is simplified as a constant due to pre-white process, which greatly extends the application range of the proposed method. The simulation results show that the proposed method can efficiently reduce the off-grid effect and the over-complete rate of the original dictionary. Compared with the conventional sparse representation methods, it has better performance and lower computation complexity.