Joint Estimation of Signal Azimuth and Frequency Using Delay-Based Methods with Uniform Linear Arrays

In this paper, we present a novel method based on uniform linear arrays (ULAs) that employs delay-based techniques for joint estimation of signal azimuth and frequency. The implementation leverages the Multiple Signal Classification (MUSIC) algorithm, which is widely adopted in signal processing applications due to its high resolution capabilities. We provide detailed explanations of the underlying principles and implementation procedures, including key algorithmic steps such as covariance matrix computation, eigenvalue decomposition for signal/noise subspace separation, and peak detection in the MUSIC pseudospectrum. The implementation typically involves constructing delayed signal vectors across array elements, followed by spatial spectral estimation through polynomial root-finding or spectrum peak searching techniques. Additionally, we analyze the method's practical advantages and limitations in real-world scenarios, such as its sensitivity to signal-to-noise ratios and computational complexity considerations. We also propose potential enhancements including robust covariance estimation techniques and subspace tracking algorithms for dynamic environments. This research contributes to deeper understanding of fundamental signal processing principles and provides valuable references for future investigations in array signal processing.