Implementation of Root-MUSIC Algorithm for Non-Circular Signals

Implementation of Root-MUSIC Algorithm for Non-Circular Signals

In array signal processing, Direction of Arrival (DOA) estimation is a critical problem. Non-circular signals (such as BPSK modulated signals) possess unique statistical properties that can enhance DOA estimation performance. While the traditional MUSIC algorithm performs DOA estimation through spectral peak search, the root-MUSIC algorithm avoids the computational complexity of spectral search by solving polynomial roots.

The root-MUSIC algorithm for non-circular signals first expands the covariance matrix using the signal's non-circular properties, thereby increasing the effective aperture of the array. Subsequently, eigenvalue decomposition divides the received data space into signal subspace and noise subspace. Unlike conventional MUSIC, root-MUSIC transforms the relationship between the array manifold matrix and noise subspace into a polynomial root-finding problem, directly solving polynomial roots to estimate signal directions, which significantly reduces computational load.

Key advantages of this algorithm include: - Enhanced signal subspace resolvability through non-circular property utilization - Computational efficiency improvement by avoiding high-resolution spectral searches via root-finding method - Applicability to both coherent and non-coherent non-circular signal DOA estimation

The root-MUSIC algorithm finds wide applications in radar, communication, and sonar systems, demonstrating superior performance particularly in low signal-to-noise ratio (SNR) or multipath environments.