Off-Grid DOA Estimation Using Alternating Block Coordinate Descent in Compressed Sensing

Abstract

This paper presents a novel off-grid direction of arrival (DOA) estimation method to achieve the superior performance in compressed sensing (CS), in which DOA estimation problem is cast as a sparse reconstruction. By minimizing the mixed k-l norm, the proposed method can reconstruct the sparse source and estimate grid error caused by mismatch. An iterative process that minimizes the mixed k-l norm alternately over two sparse vectors is employed so that the nonconvex problem is solved by alternating convex optimization. In order to yield the better reconstruction properties, the block sparse source is exploited for off-grid DOA estimation. A block selection criterion is engaged to reduce the computational complexity. In addition, the proposed method is proved to have the global convergence. Simulation results show that the proposed method has the superior performance in comparisons to existing methods.

Measurement Matrix Optimization and Mismatch Problem Compensation for DLSLA 3-D SAR Cross-Track Reconstruction

“…Particularly, if the sparsity prior of the sparse signal is taken into consideration, the solution in Equation (6) is equivalent to a MAP estimation in the Bayesian framework [16]. If $\stackrel{false^}{\mathrm{bold-italicx}}\subset \underset{˜}{\mathrm{bold-italicx}}$ holds, i.e., true scatterers are exactly located at the pre-discretized grids, the above-mentioned grid-based CS can give exact reconstruction, otherwise, off-grid effect will arise [10,11,12,13]. For a practical 3-D SAR imaging scene, the true scatterers are scarcely located on the pre-discretized grids, then the off-grid effect will degrade the reconstruction performance.…”

“…Thus, an optimized configuration of the APCs can improve the performance of sparse recovery. In the case of off-grid, i.e., actual scatterers deviate from the imaging grids, the mismatch problem of measurement matrix will arise [ 10 , 11 , 12 , 13 ]. Since a practical scene is always a continuous field with scatterers scarcely on the exact grids, the mismatch problem of measurement matrix is unavoidable and needed to be considered.…”

The Real-Valued Sparse Direction of Arrival (DOA) Estimation Based on the Khatri-Rao Product

“…Most of these traditional DOA estimation algorithms require the source number as a priori information and a large number of snapshots to guarantee the estimation precision. In recent years, the DOA estimation that utilizes the idea of sparse representation has become many scholars’ research hotspot [ 1 , 2 ]. The target signals can be regarded to be sparse in a spatial domain, and their DOAs can be estimated according to the array received data and a redundant dictionary.…”

A Sum-of-Squares and Semidefinite Programming Approach for Maximum Likelihood DOA Estimation

“…Recently, DOA estimation methods based on compressed sensing have been proposed in [12,13,14,15,16,17,18,19,20]. The compressed sensing-based methods enjoy a lot of virtues.…”

“…For example, they are robust to coherent signals, can estimate DOAs with only one snapshot, and detect the number of unknown signals automatically. In general, compressed sensing methods can be divided into three categories: on-grid model-based methods [12,17], grid-based off-grid methods [13,16,18], and gridless methods [14,15,19,20]. On-grid model-based methods choose a fixed discrete grid in the continuous domain of directions as the set of DOA estimates, and assume that the true DOAs are exactly on the grid.…”