Abstract: Slice interference has the characteristics of both suppression and deception interference, posing a huge challenge to radar target detection. In response to this issue, a method is proposed for designing and processing linear frequency modulation (LFM) signals based on cyclic prefix (CP). Firstly, a signal model is established for anti-interference detection waveform and slice interference, and a pulse compression algorithm is used based on CP to achieve target range estimation. Then, under constant modulus conditions, an optimization problem model is established with the goal of maximizing the signal to interference plus noise ratio (SINR) of pulse compression output. Due to the NP-hard nature of the optimization problem, an envelope constrained conjugate gradient algorithm is proposed to obtain an approximate solution. Finally, the effectiveness of the proposed method is demonstrated through simulation results.