## 4 Discussion  
In Table 1, the proposed method, lacking the respiratory components, yielded the smallest RMSE in all scenarios. Differently from the other six methods, it uses all high-order heartbeat harmonics that are not affected by respiration; so, its performance is better and more stable.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Dataset 1 [11], 10 Ghz** & **Dataset 1 [11], 24 Ghz** & **Dataset 2 [26], 24 Ghz** \\ \hline Proposed & 3.88 1 & 4.47 & 6.30 \\ [PERSON] [10] & 13.47 & 16.48 & 8.18 \\ [PERSON] [11] & 13.22 & 15.29 & 9.46 \\ [PERSON] [18] & 8.35 & 8.94 & 12.70 \\ [PERSON] [20] & 10.64 & 13.00 & 8.40 \\ [PERSON] [27] & 9.97 & 7.85 & 9.12 \\ [PERSON] [28] & 6.27 & 8.74 & 8.78 \\ \hline \hline \end{tabular} 1  
\end{table}
Table 1: Estimation RMSE for the two measured datasets. Methods used in previous studies were implemented for comparison, and the proposed method yielded the minimum error.  
Figure 2: Simulated mean square error and asymptotic variance of period estimation with different signal lengths. The simulation results in three cases are all very close to the derived asymptotic variance at high SNR.  
The previously described arctangent demodulation [10] yielded larger RMSEs, especially for dataset 1 where the background clutter and non-orthogonal channels degraded the demodulation performance. Although it performed better for dataset 2, its performance was still not as good as that of the proposed method.  
The performances of the two spectral analyses reported in [11; 18] were also inferior and unstable. The method based on second-order harmonic, described in [18], performed better for dataset 1, while the method based on fundamental frequency, employed in [11], performed better for dataset 2. This is because the dataset 1 has a higher SNR and allows the extraction of second-order harmonic, while the strong noise in dataset 2 masks the harmonics and renders the respiratory interference less important. Compared with maximum likelihood, these methods based on a single spectral line are not suitable for heart rate estimation, because the heartbeat information scattered in many harmonics is not fully utilized. Instead of digital filtering, [27; 28] extracted the heartbeat signal using the wavelet transform and an empirical model decomposition, respectively. A narrow band signal with the most significant heartbeat signal was selected for heart rate estimation, which is similar to band-pass filtering. These methods not only eliminated the low-frequency respiratory component, but also attenuated the high-frequency noise; so, their results may be slightly better than those obtained in [11] but not essentially different.  
On the other hand, also the method described in [20] that carried out a maximum likelihood estimation directly on raw radar signals had an inferior performance, especially for dataset 1. The maximum likelihood estimation derived from the signal model (2) did not consider any interferences and was subjected to them. The unfiltered respiratory harmonics mixed with the heartbeat, resulting in an error that was particularly significant for dataset 1. Different from [20], the proposed method ignores the fundamental frequency of heartbeat to ensure the purity of the signal used for maximum likelihood estimation, thus obtaining better results.