There are two kinds of FMCW waveform, which are slow-ramp FMCW and fast-ramp one. In some applications like automotive radar sensors, fast-ramp FMCW waveform is usually preferable for the improved target resolving capability in multi-target situation when compared with slow-ramp one. Usually fast-ramp FMCW waveform uses up or down chirps only. But, sometimes, the waveform has to be generated with up and down chirps alternatively due to hardware limitations. In this case, the computational load, memory usage and velocity ambiguity are increased due to the separated signal processing of up and down chirps. This paper proposes the signal processing method for the fast ramp FMCW waveform using both up and down chirps. The simulation and test results show the proposed new waveform and its signal processing method is acceptable for FMCW radar sensors with lower complexity.