Abstract: ‍ ‍The radar-centric Dual Function Radar and Communication （DFRC） system with communication as the secondary function， is mainly used in the military field. This system capitalizes on the hardware and spectral resources of the radar to communicate with cooperative targets via transmitting dual-function signal. As a result， the integrated signal design is one of the key scientific issues. Due to the presence of non-uniform， changeable and strong independent clutters mixed with radar detection signals in the electromagnetic countermeasure environment， the echo received by DFRC system contains clutters which increases the difficulty of target detection. In this paper， based on the prior knowledge of sidelobe signal-dependent clutters and targets， we formulate the radar-centric DFRC signal design optimization problem through relying on the maximization of the Signal Interference to Noise Ratio （SINR） to enhance radar detectability. Meanwhile， the mainlobe width and sidelobe constraints to cohere the beampattern main energy on the spatial region of interest are forced， respectively. Besides， variable modulus restriction to comply with the current hardware technique. A Sequential Block Enhancement （SBE） framework that alternately updates each waveform in each emitting antenna is developed to monotonically increase SINR. Each block involves the Dinkelbach’s Iterative Procedure （DIP）， Sequential Convex Approximation （SCA） and Interior Point Method （IPM） to obtain single waveform. The computational complexity and convergence of the algorithm are analyzed. The designed radar-centric DFRC signal can realize both detection and communication functions simultaneously in sidelobe signal-dependent clutters.