Array Signal Processing: Classical Algorithms and Implementation Approaches

The article highlights that array signal processing employs various classical algorithms such as the MUSIC (Multiple Signal Classification) algorithm and ESPRIT (Estimation of Signal Parameters via Rotational Invariance Techniques) algorithm. These algorithms are particularly valuable for preservation due to their significant roles and widespread applications in the signal processing domain. From an implementation perspective, MUSIC algorithm typically involves constructing a covariance matrix from array sensor data, performing eigenvalue decomposition to separate signal and noise subspaces, and then using the orthogonality between these subspaces to estimate signal directions through peak searching in the spatial spectrum. The algorithm's core MATLAB functions often include eig() for eigenvalue decomposition and peak-finding routines for direction-of-arrival estimation. ESPRIT algorithm leverages the rotational invariance property of sensor arrays, requiring at least two identical subarrays with displacement invariance. Implementation generally involves signal subspace estimation via eigenvalue decomposition, followed by rotational invariance operations to obtain parameter estimates without spectral peak searching. Key implementation steps often utilize matrix manipulation functions like svd() for singular value decomposition and inv() for matrix inversion to solve the rotational invariance equation. Both algorithms represent fundamental direction-of-arrival estimation techniques where MUSIC provides high-resolution spectral estimates while ESPRIT offers computational efficiency through closed-form solutions, making them essential components in modern array signal processing systems.