MATLAB Implementation of Direction of Arrival Estimation Using Compressed Sensing

Compressed sensing is a revolutionary signal processing technique that breaks through the limitations of traditional Nyquist sampling theorem, enabling efficient sampling and reconstruction under signal sparsity conditions. In Direction of Arrival (DOA) estimation - a classic array signal processing problem - compressed sensing demonstrates unique advantages. The core concept of this program is to formulate the DOA estimation problem as a sparse signal reconstruction problem. First, the signals received by the antenna array are represented as sparse vectors in the angular space, where non-zero elements correspond to the arrival directions of target signals. By constructing a sensing matrix related to the array geometry, the continuous angular domain in physical space is discretized into a sparse representation space. In the implementation, the program likely employs reconstruction algorithms such as Orthogonal Matching Pursuit (OMP) or Basis Pursuit Denoising (BPDN), which can effectively recover the original sparse signal from limited observation data. Compared to traditional MUSIC or ESPIRT algorithms, the compressed sensing approach offers three significant characteristics: first, excellent capability in handling coherent signals; second, requirement of fewer sampling points; third, ability to achieve super-resolution estimation. It's important to note that the performance of this method heavily depends on the coherence of the sensing matrix and the sparsity level of the signal. In practical applications, optimization of the array manifold matrix design and appropriate selection of discretized angular grid density are typically required. MATLAB's powerful matrix computation capabilities and rich optimization toolbox make the implementation of these algorithms efficient and concise. This method has broad application prospects in fields such as radar, wireless communications, and acoustic detection, particularly in scenarios with limited sensor numbers or restricted sampling rates, where it can significantly enhance system performance.