Array signal processing technology has been widely applied in research fields such as radar, sonar, and positioning due to its advantages of extensive spatial coverage, strong anti-interference capability, high signal gain, and superior signal resolution. Traditional array signal processing techniques are based on the Nyquist sampling theorem, which poses challenges in practical applications, such as high computational load and difficulties in achieving real-time performance. Compressive sensing (CS) theory, also known as compressed sampling principle, reconstructs the original signal accurately or approximately with only a small number of samples by leveraging the sparsity and compressibility of signals. This paper combines CS theory with the Orthogonal Matching Pursuit (OMP) algorithm, namely the CS-OMP algorithm, and applies it to Direction of Arrival (DOA) estimation, thereby realizing DOA estimation based on compressive sensing theory. Additionally, the performance of the traditional DOA estimation algorithm, the Multiple Signal Classification (MUSIC) algorithm, is compared under different scenarios, and the impact of parameters such as the number of array elements, snapshot count, and signal-to-noise ratio on the performance of the CS-OMP algorithm is further explored. This provides a novel and effective approach for complex signal processing.