MATLAB Implementation of ESPRIT Algorithm for High-Resolution Signal Parameter Estimation

ESPRIT (Estimation of Signal Parameters via Rotational Invariance Techniques) algorithm is a high-resolution signal parameter estimation method widely used in radar, communication, and acoustic applications. Based on subspace decomposition principles, it accurately estimates signal parameters such as frequency and direction of arrival. ### Algorithm Core Concept ESPRIT algorithm utilizes the rotational invariance property of signal subspaces by decomposing received signals into signal and noise subspaces. By analyzing signal subspace characteristics, it extracts parameter information without requiring peak search operations, resulting in higher computational efficiency compared to other methods. ### Implementation Approach Data Acquisition and Modeling: Assume received signals consist of multiple complex exponential signals with additive noise interference. In MATLAB implementation, this typically involves creating a signal model using exp() functions and adding complex Gaussian noise. Covariance Matrix Computation: Construct the covariance matrix from received signals and perform eigenvalue decomposition to distinguish signal and noise subspaces. Key MATLAB functions include cov() for covariance calculation and eig() or svd() for matrix decomposition. Subspace Partitioning: Select eigenvectors corresponding to the largest eigenvalues to form the signal subspace. Implementation involves sorting eigenvalues in descending order and selecting the dominant eigenvectors using MATLAB's sort() and matrix indexing operations. Rotational Invariance Analysis: Exploit the rotational invariance property of signal subspaces to construct matrix equations, solved via least squares or eigenvalue decomposition methods. Code implementation typically uses the backslash operator () for least squares solutions or eig() for eigenvalue problems. Parameter Estimation: Extract signal parameters such as frequency or Direction of Arrival (DOA) from the solution results. This involves mathematical operations like angle calculation using atan2() function and frequency conversion. ### Application Scenarios Radar Systems: High-precision estimation of target angles and frequencies Wireless Communications: Direction of Arrival (DOA) estimation for multipath signals Acoustic Signal Processing: Analysis of sound source localization or vibration frequencies ESPRIT algorithm implementation in MATLAB primarily relies on matrix operations and eigenvalue decomposition, demonstrating superior performance compared to traditional FFT methods, particularly maintaining high estimation accuracy under low signal-to-noise ratio conditions.