Theory and Applications of Array Signal Processing

In the following sections, I will introduce the theory and applications of array signal processing, covering the following implementations:

1. MUSIC Algorithm MATLAB Program

The MUSIC (Multiple Signal Classification) algorithm is a high-resolution spectral estimation method widely used in signal processing and acoustics. This MATLAB implementation demonstrates the core algorithm workflow: constructing the covariance matrix, performing eigenvalue decomposition, identifying signal and noise subspaces, and computing the spatial spectrum through peak searching. The code includes practical considerations like sensor array configuration and signal-to-noise ratio handling.

2. ESPRIT Algorithm MATLAB Program

ESPRIT (Estimation of Signal Parameters via Rotational Invariance Techniques) is a frequency estimation method that exploits the rotational invariance property of signal subspaces. This program implements the TLS-ESPRIT variant, showing how to extract signal parameters from the phase information between array subarrays without requiring spectral peak searching.

3. Root-MUSIC Algorithm MATLAB Program

Root-MUSIC is a high-resolution spectral estimation technique that replaces the spectral search with polynomial rooting. The MATLAB code demonstrates how to form the noise subspace matrix, construct the Root-MUSIC polynomial, and find its roots to directly obtain DOA estimates with improved accuracy and reduced computational complexity compared to conventional MUSIC.

4. Unitary-ESPRIT Algorithm for 2D Angle Estimation in Planar Arrays MATLAB Program

Unitary-ESPRIT extends the ESPRIT algorithm to planar arrays for two-dimensional angle estimation (azimuth and elevation). This implementation showcases real-valued computation through unitary transformations, providing improved numerical stability and reduced computational load while handling the inherent structure of centrosymmetric arrays.

5. Spatial Smoothing MUSIC Algorithm MATLAB Program

Spatial Smoothing MUSIC addresses the limitation of conventional MUSIC in handling coherent signals. The program implements forward/backward spatial smoothing techniques to decorrelate coherent sources, demonstrating subarray partitioning, covariance matrix averaging, and subsequent MUSIC processing for scenarios with multipath propagation.

6. Joint Angle and Delay Estimation (JADE) Algorithm MATLAB Program

JADE is a comprehensive parameter estimation technique that simultaneously estimates signal directions and time delays. The MATLAB code implements the spatio-temporal processing framework, showing how to construct extended covariance matrices and extract both spatial and temporal parameters for complete signal characterization.

7. Propagator Operator DOA Estimation Algorithm MATLAB Program

The Propagator Operator method provides a linear DOA estimation approach that avoids computationally expensive eigenvalue decomposition. This implementation demonstrates how to partition the array manifold matrix, compute the propagator operator, and extract direction estimates through linear operations, offering a good trade-off between performance and computational efficiency.

8. 2D DOA Estimation for L-shaped Arrays using Augmented Matrix Pencil Method MATLAB Program

This program implements an enhanced matrix pencil approach for two-dimensional DOA estimation using L-shaped sensor arrays. The code demonstrates how to construct augmented data matrices from the orthogonal array arms, apply the matrix pencil method for parameter estimation, and pair the automatically paired azimuth and elevation estimates through cross-correlation techniques.