ESPRIT Algorithm for Direction of Arrival Estimation

This article discusses the ESPRIT algorithm and its application in Direction of Arrival (DOA) estimation. ESPRIT (Estimation of Signal Parameters via Rotational Invariance Techniques) is an efficient signal processing technique used for estimating signal direction cosines. The algorithm operates by decomposing array signals into two key components for DOA estimation. The first component is the signal subspace, which can be computed through Singular Value Decomposition (SVD) - typically implemented using functions like numpy.linalg.svd() in Python or svd() in MATLAB. The second component consists of matrices that describe signal projections within this subspace. These projection matrices are derived from the eigenvectors of the covariance matrix, calculable using covariance matrix estimation functions followed by eigenvalue decomposition routines such as numpy.linalg.eig() or eig() in MATLAB. ESPRIT essentially represents a subspace-based DOA estimation method that leverages both signal subspace properties and covariance matrix characteristics. The core implementation involves creating overlapping subarrays, computing sample covariance matrices, performing eigenvalue decomposition to identify signal and noise subspaces, and finally solving the rotational invariance equation to extract DOA estimates.