Ultrasound attenuation coefficient estimation (ACE) can be utilized to quantify liver fat content, offering significant diagnostic potential in addressing the growing global public health issue of non-alcoholic fatty liver and other chronic liver diseases. Among ACE methods, the reference frequency method (RFM) proposed recently possesses the advantages of being system-independent and not requiring reference phantom. However, the presence of large oscillations in frequency power ratio decay curves leads to unstable ACE results with RFM, originating from noise as well as constructive and destructive interference in the backscattered signal's power spectrum. To address this issue, we propose an improved RFM version where a single-scatterer power spectrum estimator is incorporated to restore interference free single-scatterer power spectrum, thereby reducing oscillations in the frequency power ratio decay curves and greatly improving the accuracy of ACE.