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Digitally modulated radar systems, such as phase-modulated continuous wave (PMCW), often struggle with high bandwidth demands for fine-range resolutions, posing challenges for cost-effective automotive applications. To address this issue, we propose a stepped-frequency PMCW (SF-PMCW) radar waveform in which the instantaneous bandwidth of a single pulse is extensively reduced while the range resolution is beyond the theoretical limit imposed by the instantaneous bandwidth. The proposed waveform spans a synthetic bandwidth across multiple pulses, achieving range estimates comparable to those typically achieved with higher instantaneous bandwidths. Simultaneously, the requirements for analog-to-digital converters (ADCs) are relaxed. Simulations have been performed to demonstrate the performance. The results indicate that the proposed SF-PMCW waveform with an instantaneous bandwidth of 100MHz can achieve range estimates as good as a PMCW waveform with an instantaneous bandwidth of 1GHz.