Methods for Solving Signal Direction of Arrival (DOA) Estimation

Estimating signal Direction of Arrival (DOA) constitutes a fundamental problem in array signal processing, with extensive applications in radar systems, wireless communications, and acoustic signal processing. An effective approach involves transforming DOA estimation into a Multiple Measurement Vector (MMV) problem and solving it using joint sparsity constraints.

The core methodology implements the following computational framework: First, spatial discretization divides the DOA search range into multiple angular grids, converting the estimation problem into a sparse signal recovery task. Since array-received signals typically exhibit sparsity (originating from only a few directions), sparse optimization techniques become applicable. Implementation-wise, this involves creating an overcomplete dictionary matrix where each column corresponds to a steering vector for a specific grid angle.

The method subsequently formulates the problem as an MMV model, where measurement data from different time snapshots are represented as linear combinations of sparse signals under varying measurement vectors. Compared to Single Measurement Vector (SMV) models, MMV leverages the common sparsity pattern across multiple snapshots to enhance estimation accuracy. Algorithmically, this can be implemented using block sparse recovery algorithms that process multiple measurement vectors simultaneously.

Finally, by imposing joint sparsity constraints (such as mixed L2,1-norm regularization), the solution's sparsity is enhanced while ensuring consistent sparse patterns across different snapshots. This approach effectively suppresses noise interference and improves DOA estimation robustness and resolution, making it suitable for challenging scenarios like low signal-to-noise ratios or coherent signals. Code implementation typically involves solving convex optimization problems using algorithms like Group LASSO or Sparse Bayesian Learning with appropriate regularization parameters.