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Phase-modulated continuous wave (PMCW) is a digital modulation waveform being investigated for modern automotive radar systems as a potential alternative to commonly used frequency-modulated continuous wave (FMCW) waveforms. In prior research, we introduced stepped-frequency PMCW (SF-PMCW), a variant of PMCW, which generates a synthetic bandwidth across multiple pulses, allowing lower sampling rates and more cost-effective analog-to-digital converters (ADCs). However, utilizing stepped-frequency waveforms introduces a quadratic phase shift, which causes dispersion in the range-Doppler map, thereby reducing the likelihood of target detection. This work proposes an approach aiming to compensate for the quadratic phase shift. This method decreases the effects of energy dispersion, thereby significantly enhancing target detection performance.