## 4 Results
### Power Consumption  
We quantified the power consumption at the sensor node using the Avrora simulator described in Section 3.4. We assume that 23 EEG channels were being sampled with a sampling rate of 128 Hz. The maximum payload size in a data packet is 114 bytes, besides 13 bytes of medium access control (MAC) data. The total power consumption was broken down into (1) the operating system and code execution in the microcontroller (MCU); (2) wireless communication on the transmitter and (3) flash I/O. Each approach was simulated for 600 seconds, and the results are shown in Table 3. The effects of the epoch size and CR on the power consumption were also tested. Furthermore, we assessed the computational complexity of the considered feature extraction techniques by determining the number of basic operations (additions, assignment, comparison and multiplication) required to compute the feature of one channel in each epoch. The number of operations performed is listed in Table 4.  
As expected, the transmission of the entire EEG data incurs the highest power consumption at \(32.50\) mW, where the transmitter accounts for 76% of the total power consumption. While this approach does not perform any data processing at the sensor side, a considerable amount of power is consumed by the microcontroller to format the data for transmission. Since the raw EEG data are transmitted at every sampling period as opposed to at the end of every epoch (_i.e._, every 512 sampling periods), the formatting of data packets results in a microcontroller power consumption that is more than twice as high as that of the approaches employing data reduction. For the EEG compression approach, it can be seen that the power consumption of both the microcontroller and the transmitter is significantly reduced at all considered CRs, providing up to 82% savings in total system power consumption relative to the approach that transmits the entire EEG signals. Nonetheless, additional power consumption was incurred by the flash I/O, due to accessing of the random measurement matrix stored in the flash. The CR has marginal effects on the total power consumption. We next look at the approach of transmitting only the features of the EEG signals. Among the considered feature extraction techniques, nonlinear autocorrelation incurs the lowest power consumption. Compared to the approach that transmits entire EEG signals and the approach that transmits compressed EEG, the transmission of the nonlinear autocorrelation feature \begin{table}
\begin{tabular}{l c c c c} \hline \hline
**Data Transmitted** & **MCU** & **Transmitter** & **Flash** & **Total** \\ \hline Entire EEG & 7.72 & 24.78 & 0.00 & 32.50 \\ Compressed EEG (CR = 10 : 1) & 2.84 & 1.20 & 2.13 & 6.17 \\ Compressed EEG (CR = 20 : 1) & 2.93 & 0.81 & 2.13 & 5.86 \\ Energy (\(N=256\)) & 2.47 & 0.097 & 0.00 & 2.57 \\ Energy (\(N=768\)) & 2.46 & 0.032 & 0.00 & 2.49 \\ Line Length (\(N=256\)) & 2.36 & 0.096 & 0.00 & 2.45 \\ Line Length (\(N=768\)) & 2.34 & 0.032 & 0.00 & 2.37 \\ Nonlinear Autocorr (\(N=256\)) & 2.21 & 0.097 & 0.00 & 2.30 \\ Nonlinear Autocorr (\(N=768\)) & 2.19 & 0.032 & 0.00 & 2.23 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Power consumption of different data reduction approaches (in milliwatts). MCU, microcontroller; Nonlinear Autocorr, nonlinear autocorrelation. reduces the power consumptions by a factor of 93% and 64%, respectively. The energy savings mainly come from the wireless transmitter: the feature extraction techniques map segments of the EEG signal of length \(N\) points to a single value, which is equivalent to a CR of \(N:1\), allowing a tremendous reduction in the amount of data to be transmitted. More importantly, because the feature extraction was performed directly on the raw EEG signals, this approach essentially yields the same seizure detection performance as the approach that transmits the entire EEG signals and then performs feature extraction and classification on the server side when perfect wireless channels are assumed.