This paper presents the application of Compressive Sensing (CS) theory in radar signal processing. CS uses the sparsity property to reduce the number of measurements needed for digital acquisition, which causes reduction in the size, weight, power consumption, and the cost of the CS radar receiver. Complex Approximate Message Passing (CAMP) algorithm is a fast iterative thresholding algorithm which is used to reconstruct the undersampled sparse signal and improves its Signal-to-Noise Ratio (SNR) [12- 16]. In present work, the superiority in performance of applying the CAMP algorithm in radar signal processing compared to the Digital Matched Filter (DMF), and the simple envelope detector is proved through the Receiver Operating characteristic (ROC) curves.