DOA Estimation Using Fourth-Order Cumulants

Fourth-order cumulants applied in Direction of Arrival (DOA) estimation represent a signal processing method based on higher-order statistics. Traditional approaches typically rely on second-order statistics (such as covariance matrices), whereas fourth-order cumulants can capture non-Gaussian characteristics of signals, thereby offering superior robustness for source localization in non-Gaussian noise environments. In code implementation, this involves constructing a fourth-order cumulant matrix from the array's received signals using tensor operations or specialized cumulant calculation functions.

The core algorithm principle involves computing the fourth-order cumulant matrix from array received signals and extracting features from the signal subspace. Unlike second-order statistics, fourth-order cumulants can suppress Gaussian noise effects while preserving phase information of signals. Through eigenvalue decomposition or similar subspace methods, the direction of arrival can be estimated from the cumulant matrix. A typical implementation would include steps like: 1) Forming the fourth-order cumulant tensor, 2) Performing matrix unfolding operations, 3) Applying subspace decomposition techniques to identify signal directions.

The key advantage of this method lies in its ability to handle coherent signal sources (completely correlated signals), whereas traditional covariance-based methods typically fail in such scenarios. Additionally, fourth-order cumulants provide higher resolution, making them suitable for DOA estimation in dense multipath environments. From a programming perspective, this translates to better performance in challenging signal conditions with proper array calibration and cumulant matrix conditioning.

In practical implementation, this approach typically integrates with algorithms like MUSIC (Multiple Signal Classification) or ESPRIT (Estimation of Signal Parameters via Rotational Invariance Techniques). The implementation workflow generally includes: constructing the fourth-order cumulant matrix, performing signal subspace analysis, and finally determining DOA through spectral peak search. Code implementation would involve functions for cumulant calculation, matrix decomposition, and peak detection algorithms to identify direction angles.