The microwave Doppler radar sensor enables a non-contact approach for measuring movement in various applications. One of the most challenging issues is radar signal demodulation because it requires accurate DC offset compensation. Existing works either require a complicated setup procedure or are sensitive to environmental changes. In this reported work, a compressed sensing based approach to effectively demodulate a radar signal is discussed. Through ℓ 1 minimisation, the proposed method can reliably demodulate noisy signals with large measurement residuals. To validate the algorithm, three sets of experiments were run to evaluate the demodulation performance. Experimental results show that the proposed method is promising in both simulation and real-case studies.