MATLAB Simulation of Multiple Signal Direction of Arrival (DOA) Estimation Algorithms

Multiple signal Direction of Arrival (DOA) estimation is a key technology in array signal processing, widely applied in radar, sonar, and wireless communication systems. This article explains the implementation principles of several classical DOA estimation algorithms in MATLAB.

The MUSIC algorithm achieves super-resolution estimation by constructing orthogonality between signal subspace and noise subspace. The algorithm implementation involves computing the covariance matrix of received signals, performing eigenvalue decomposition, constructing spatial spectrum functions using noise eigenvectors, and finally determining DOA through spectral peak search. In MATLAB coding, key functions include cov() for covariance calculation and eig() for eigenvalue decomposition.

The Phase Matching (PM) algorithm operates based on phase consistency between array manifold and received data. This method offers higher computational efficiency but relatively lower resolution, making it suitable for real-time applications. The implementation calculates phase matching degrees across different directions to identify optimal matching directions, typically using phase correlation calculations in MATLAB.

The Fourth-order Cumulant method leverages higher-order statistical properties to effectively suppress Gaussian noise interference. By constructing fourth-order cumulant matrices, this approach extends the virtual aperture of arrays, thereby enhancing resolution capability and estimation accuracy. MATLAB implementation requires specialized cumulant calculation functions to handle higher-order statistics.

In MATLAB simulation experiments, proper configuration of array parameters is essential, including element spacing, signal incidence angles, and signal-to-noise ratio (SNR). Comparing spectral estimation results across different algorithms allows visual observation of variations in resolution, estimation accuracy, and noise resistance performance. Simulation code should include parameter initialization sections and comparative plotting functions like plot() or spectrum().

Practical applications require balancing algorithm complexity with hardware implementation constraints. The MUSIC algorithm demands significant computational resources but delivers high precision, while the Phase Matching algorithm is more suitable for embedded platform implementation. The Fourth-order Cumulant method performs excellently in non-Gaussian noise environments but has the highest computational complexity. Code optimization techniques and computational efficiency analysis should be considered during MATLAB implementation.