MATLAB Implementation of Compressed Sensing for DoA Estimation

Compressed sensing is a technique that utilizes signal sparsity for efficient sampling, demonstrating superior performance in Direction of Arrival (DoA) estimation. The maximum likelihood-based compressed sensing DoA estimation methods primarily include the following two implementation approaches: Sparse Reconstruction and ML Joint Estimation Method This method first recovers the sparse representation of received signals through compressed sensing algorithms, then applies maximum likelihood estimation to the reconstructed sparse signal. In MATLAB implementation, an overcomplete dictionary matrix is constructed to represent array responses from different directions. The implementation involves solving for sparse coefficients through L1-norm optimization using functions like l1_ls or spgl1, followed by searching for DoA parameters that maximize the likelihood function within the ML framework. Key implementation aspects include proper dictionary design using array manifold vectors and regularization parameter tuning for stable sparse recovery. Compressed Domain Direct ML Estimation Method This approach performs maximum likelihood estimation directly in the compressed measurement domain without explicitly reconstructing the original signal. MATLAB implementation requires deriving the likelihood function expression for compressed measurement data, then using grid search or optimization algorithms (such as fmincon or patternsearch) to find direction parameters that maximize the likelihood function. This method has smaller computational requirements but demands accurate statistical characteristics of the measurement matrix. Implementation considerations include proper measurement matrix design and efficient optimization routine configuration. Both methods have distinct characteristics: the joint estimation method offers better noise resistance but higher computational complexity, while the direct estimation method is more efficient but requires stricter measurement matrix conditions. Practical MATLAB implementation requires careful attention to array manifold matrix construction, regularization parameter selection, and optimization algorithm convergence control. Essential MATLAB functions for implementation include sparse recovery tools, optimization solvers, and array processing utilities from various toolboxes.