Robust principal component analysis (RPCA) provides an effective preprocessing strategy for moving target indication tasks in radar signal processing. By decomposing radar observation data into low-rank background and sparse target components, RPCA enables basic clutter suppression and target enhancement. However, it suffers from low computational efficiency, sensitivity to manually tuned parameters, and a high false alarm rate, especially in complex clutter environments. To address these limitations, this work adopts a deep unfolding network architecture inspired by RPCA, which embeds traditional iterative algorithms into a neural network framework, significantly improving both computational efficiency and detection performance. This work first analyzes the optimization methods of the RPCA algorithm. Then, it embeds the algorithm into a deep neural network and optimizes its iterative parameters using a comprehensive dataset. Finally, the trained network is applied to radar observation matrices to achieve clutter suppression and target detection. Simulation results demonstrates that RPCANet achievs superior performance compared to RPCA, particularly in reducing false alarms and enhancing detection in strong clutter scenarios.