# Power Autonomy Estimation of Low-Power Sensor for Long-Term ECG Monitoring
## 5 Validation of the Models and Power Consumption Analysis
### Analysis of Sensor Autonomy  
To translate power consumption to sensor autonomy, we divide the battery capacity by the average current consumption in the selected sensor mode. The analyzed sensor has an integrated 240 mA h lithium-ion battery that stores enough energy for several days of continuous ECG signal streaming. The results of ECG sensor autonomy estimation based on measured average current consumption and estimated current consumption are collected in Table 6. The results show that by quadrupling the ECG sampling rate and thus quadrupling the amount of bytes transferred, the sensor autonomy is reduced by a factor of two. The typical autonomy of modern smartphones, assuming an average user, is around one day, while the sensor on a single charge lasts for around four days with 512 sps and more than eight days with 128 sps. When the sensor is neither in active mode nor in shutdown mode, it stays in idle mode, where advertising takes place with average advertising power consumption \(P_{adv\_avg}=1.308\) mW, which gives us 31.5 days of autonomy while waiting to start ECG measurements. Thus, with regular weekly use, shutting down the sensor seems unnecessary. This further simplifies the usage for non-tech-savvy users. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**TX [dBm]** & **Sampling [sps]** & \
\begin{tabular}{c} **Autonomy (\(I_{measured}\))** \\ **[days]** \\ \end{tabular} &
\begin{tabular}{c} **Autonomy (\(I_{model}\))** \\ **[days]** \\ \end{tabular} & **Error [\%]** \\ \hline \multirow{4}{*}{0} & 128 & 8.65 & 8.69 & +0.46 \\  & 256 & 6.46 & 6.28 & \(-2.79\) \\  & 512 & 4.08 & 3.76 & \(-7.84\) \\ \hline \multirow{4}{*}{\(-6\)} & 128 & 8.72 & 8.79 & +0.80 \\  & 256 & 6.54 & 6.39 & \(-2.29\) \\  & 512 & 4.15 & 3.86 & \(-6.99\) \\ \hline \multirow{4}{*}{\(-12\)} & 128 & 8.76 & 8.84 & +0.91 \\  & 256 & 6.57 & 6.45 & \(-1.82\) \\  & 512 & 4.21 & 3.92 & \(-6.89\) \\ \hline \multirow{4}{*}{\(-18\)} & 128 & 8.79 & 8.87 & +0.91 \\  & 256 & 6.61 & 6.48 & \(-1.97\) \\ \cline{1-1}  & 512 & 4.23 & 3.95 & \(-6.62\) \\ \hline \hline \end{tabular}
\end{table} 
Table 6: ECG sensor autonomy estimation based on measured average current consumption and estimated model-based current consumption. Model error is expressed as percentage of the measured value. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**TX [dBm]** & **Sampling [sps]** & \(P_{model}\) **[mW]** & \(I_{model}\) **[mA]** & \(P_{measured}\) **[mW]** & \(I_{measured}\) **[mA]** & **Error [\%]** \\ \hline \multirow{4}{*}{0} & 128 & 4.752 & 1.151 & 4.774 & 1.156 & \(-0.43\) \\  & 256 & 6.580 & 1.593 & 6.393 & 1.548 & +2.91 \\  & 512 & 10.994 & 2.662 & 10.123 & 2.451 & +8.61 \\ \hline \multirow{4}{*}{\(-6\)} & 128 & 4.701 & 1.138 & 4.737 & 1.147 & \(-0.78\) \\  & 256 & 6.467 & 1.566 & 6.311 & 1.528 & +1.83 \\  & 512 & 10.703 & 2.592 & 9.932 & 2.405 & +7.78 \\ \hline \multirow{4}{*}{\(-12\)} & 128 & 4.671 & 1.131 & 4.712 & 1.141 & \(-0.88\) \\  & 256 & 6.400 & 1.550 & 6.282 & 1.521 & +1.91 \\  & 512 & 10.529 & 2.549 & 9.809 & 2.375 & +7.33 \\ \hline \multirow{4}{*}{\(-18\)} & 128 & 4.658 & 1.128 & 4.700 & 1.138 & \(-0.88\) \\  & 256 & 6.371 & 1.543 & 6.245 & 1.512 & +2.05 \\ \cline{1-1}  & 512 & 10.456 & 2.532 & 9.767 & 2.365 & +7.06 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Comparison of measured and model-based power and current consumption for active mode. Model error is expressed as percentage of the measured value. The most influencing parameter on the sensor autonomy is the ECG sampling rate. Sampling rate directly imposes requirements on the length of connection interval, which has to be, on one hand, short enough to enable transfer of all recorded ECG data, while, on the other hand, long enough not to waste energy with unnecessary empty connection events. By decreasing the length of the connection interval, the density of transmission events increases, which consequently increases the average power consumption.