MATLAB Simulation Source Code for ROOT-MUSIC Algorithm

The ROOT-MUSIC algorithm is a high-resolution Direction of Arrival (DOA) estimation method based on subspace decomposition. Compared to conventional MUSIC algorithms, it replaces spectral peak search with polynomial root-finding, significantly reducing computational complexity.

The core principle involves eigendecomposition of the received signal covariance matrix to construct a noise subspace, transforming the traditional spectral function into a polynomial root-solving problem. By solving for the roots of this polynomial, the algorithm directly estimates signal source directions, eliminating the computationally intensive spectral peak scanning process required in traditional MUSIC implementations.

In MATLAB simulation implementations, key steps typically include: first constructing an array signal reception model and computing the covariance matrix; then performing eigenvalue decomposition on the covariance matrix to extract the noise subspace; next constructing the polynomial and finding roots closest to the unit circle; finally calculating signal source angles from the phase information of these roots. Code implementation often utilizes MATLAB's built-in functions like eig() for matrix decomposition and roots() for polynomial solving.

This root-finding approach not only enhances computational efficiency but also improves resolution performance in low Signal-to-Noise Ratio (SNR) scenarios or when dealing with closely spaced signal sources, making it a significant optimization technique in array signal processing applications.