Pulse Compression (PC) radars are used to resolve the problem of designing long range radar systems with excellent range resolution. PC provides radar system with additional processing gain that enhances its detection capability. Among the different types of pulse compression waveforms, Linear Frequency Modulated (LFM) signals are the most tolerant to high Doppler shifts. This is why LFM-PC radars are widely utilized with high speed targets. However, the literature lacks a complete mathematical or simulation model to evaluate the its detection performance. This paper introduces a typical simulation model for search radar that is verified mathematically. The proposed model includes matched filter (MF), moving target detector (MTD), two different constant false alarm rate (CFAR) algorithms and LFM signal sidelobes on radar detection are to be considered. Two simulation models are introduced. Firstly, the Matlab simulation is introduced to verify the mathematical model and the theory. Secondly, the SystemVue simulation is applied to be used in the future work with the hardware in the loop facility.