MATLAB Implementation of Direction of Arrival Estimation Using Compressive Sensing

In this paper, we introduce how to implement Direction of Arrival (DOA) estimation using compressive sensing technology in MATLAB. DOA estimation refers to determining the direction of arriving waves in transmitted signals or detected signals. This technology has wide applications in wireless communications, radar systems, sonar systems, and other related fields. Implementing DOA estimation using compressive sensing technology can effectively reduce computational costs while maintaining accurate estimation performance even in noisy environments. The implementation typically involves creating a sparse representation of the signal space using a sensing matrix and solving the optimization problem through algorithms like L1-minimization or greedy approaches such as Orthogonal Matching Pursuit (OMP). In this implementation, we will detail how to use MATLAB to: - Construct the measurement matrix and sparse basis - Formulate the compressive sensing model for DOA estimation - Implement reconstruction algorithms to recover the sparse signal - Calculate the direction angles from the recovered sparse coefficients We will provide practical case studies and code examples using MATLAB's Signal Processing Toolbox and Optimization Toolbox functions. These examples will help readers better understand the application of this technology, including how to handle array signal processing, design appropriate sensing matrices, and evaluate estimation performance under different signal-to-noise ratios. The code implementation will demonstrate key functions such as sparse signal reconstruction, angle spectrum calculation, and performance metrics evaluation.