The ongoing automation of driving functions in cars leads to a massive growth in the number of automotive radar sensors, and thus to more radar interference. An approach for actively mitigating interference between automotive radars is the interference-aware cognitive radar (IACR). One major challenge for IACR is, however, sensing of a large spectral band (e.g. 77-81GHz) potentially available for radar operation. In this paper, we present a cost-efficient spectrum sensing method based on linear sweeping over a wide spectral band. The signal resulting from the sweep is lowpass filtered prior to sampling, which allows a significant bandwidth reduction down to few tens of MHz. In digital domain, the captured signal is pulse-compressed with a bank of matched filters. The output image of the time-frequency space provides a basis for identification of interference-free regions and a subsequent adaptation for the next measurement cycle. The performance of the proposed approach is studied in simulation and demonstrated with a prototype. The results indicate the feasibility of such spectrum sensing module for automotive radar both in terms of performance and cost.