A High-Resolution DOA Estimation Method With a Family of Nonconvex Penalties - 2018


The low-rank matrix reconstruction (LRMR) approach is widely employed in direction-of-arrival (DOA) estimation. As the rank norm penalty in an LRMR is NP-laborious to compute, the nuclear norm (or the trace norm for a positive semidefinite matrix) has been usually employed as a convex relaxation of the rank norm. But, solving a nuclear norm convex drawback might cause a suboptimal resolution of the first rank norm downside. During this Project, we propose to apply a family of nonconvex penalties on the singular values of the covariance matrix as the sparsity metrics to approximate the rank norm. In explicit, we formulate a nonconvex minimization problem and solve it by using a regionally convergent iterative reweighted strategy in order to reinforce the sparsity and backbone. The problem in each iteration is convex and hence will be solved by using the optimization toolbox. Convergence analysis shows that the new technique is in a position to obtain a suboptimal answer. The affiliation between the proposed method and the sparse signal reconstruction is explored showing that our method will be regarded as a sparsity-based technique with the amount of sampling grids approaching infinity. 2 possible implementation algorithms that are based on solving a duality downside and deducing a closed-kind resolution of the simplified drawback also are provided for the convex downside at each iteration to expedite the convergence. Intensive simulation studies are conducted to point out the superiority of the proposed ways.

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