DOA Estimation Using a Single Snapshot: Implementation with Modified UCA-ESPRIT and Modified UCA-ROOT-MUSIC Algorithms

This paper introduces a novel method for direction cosine estimation utilizing only a single snapshot, employing two enhanced algorithms: Modified UCA-ESPRIT based on joint diagonalization and Modified UCA-ROOT-MUSIC, an augmented version of the UMVDR algorithm rooted in Root-MUSIC principles. To facilitate deeper understanding, the authors provide accompanying code that demonstrates key implementation aspects, including array signal preprocessing, covariance matrix reconstruction for coherent signals, and eigenvalue decomposition techniques. The code illustrates practical considerations such as phase mode excitation for uniform circular arrays, root-solving procedures for polynomial equations in Modified UCA-ROOT-MUSIC, and subspace rotation operations in Modified UCA-ESPRIT. Through hands-on experimentation with this code, readers can examine critical algorithmic components like spatial smoothing for decorrelation, direction finding resolution thresholds, and computational complexity optimization. This resource serves as both an educational tool for mastering algorithm implementation and a practical reference for applying these techniques in real-world scenarios involving coherent signal processing.