We propose a novel sparse representation-based direction-of-arrival (DOA) estimation method. In contrast to those that approximate l0-norm minimization by l1-norm minimization, our method designs a reweighted l1 norm to substitute the l0 norm. The capability of the reweighted l1 norm to bridge the gap between the l0- and l1-norm minimization is then justified. In addition, an array covariance vector without redundancy is utilized to extend the aperture. It is proved that the degree of freedom is increased as such. The simulation results show that the proposed method performs much better than l1-type methods when the signal-to-noise ratio (SNR) is low and when the number of snapshots is small.

Recently, Gan and Luo have proposed a direction-of-arrival estimation method for uncorrelated and coherent signals in the presence of multipath propagation [3]. In their method, uncorrelated and coherent signals are distinguished by rotational invariance techniques and the property of the moduli of eigenvalues. However, due to the limitation of finite number of sensors, the pseudo-inverse matrix derived in this method is an approximate one. When the number of sensors is small, the approximation error is large, which adversely affects the property of the moduli of eigenvalues. Consequently, the method in [3] performs poorly in identifying uncorrelated signals under such circumstance. Moreover, in cases of small number of snapshots and low signal to noise ratio, the performance of their method is poor as well. Therefore, in this letter we first study the approximation in [3] and then propose an improved method that performs better in distinguishing between uncorrelated signals and coherent signals and in the aforementioned two cases. The simulation results demonstrate the effectiveness and efficiency of the proposed method.