Compressive Sensing DOA Reconstruction Algorithm: Orthogonal Matching Pursuit (OMP)

Compressed Sensing (CS) has revolutionized Direction of Arrival (DOA) estimation by employing sparse signal reconstruction techniques, significantly reducing the sampling rate and computational resource requirements compared to traditional methods. Among various CS algorithms, Orthogonal Matching Pursuit (OMP) stands out as a core tool for compressive sensing DOA reconstruction due to its simplicity and efficiency.

In DOA problems where signals typically exhibit sparsity (meaning only a few directions contain actual signal sources), the OMP algorithm iteratively selects the most matching atoms (corresponding to potential DOA angles) to progressively approximate the original sparse signal. The core algorithmic steps include: residual initialization, atom matching, support set update, and least-squares solution. During each iteration, the algorithm selects the atom most correlated with the current residual from an overcomplete dictionary (such as a steering vector matrix corresponding to uniform angle grids), and optimizes the reconstruction result through an orthogonalization process, ultimately outputting the non-zero positions of the sparse vector (i.e., signal source directions).

Key considerations for MATLAB implementation include: Constructing the overcomplete dictionary must align with the DOA angle discretization strategy; Stopping conditions can be set as predefined sparsity levels or residual thresholds; Optimizing inner product calculations through matrix operations to enhance efficiency. The algorithm typically uses matrix multiplication instead of loop-based computations for correlation measurements.

Compared to traditional MUSIC or Capon algorithms, OMP-based compressive sensing DOA estimation performs better in low signal-to-noise ratio scenarios with limited snapshots, though it requires careful consideration of grid mismatch issues. In practical engineering applications, grid mismatch problems are often addressed by incorporating off-grid correction techniques or dynamic dictionary adjustments to further improve accuracy.