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We propose the AMLSS method for DOA estimation of narrow-band signals. In this method, the distribution of covariance matrix estimation error is used for Maximum Likelihood estimation of potential source signals variances. This leads to a nonnegative LASSO sparse model for which a new criterion is proposed to determine the regulation parameter. Simulation results show that the performance of this method in estimation of the number of sources is more accurate than the Picard, MUSIC, and SPICE methods. Also, it outperforms Picard and SPICE methods in accurate DOA estimation.