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\section{System Level Measurements}
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\label{sec:benchmark}
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In this section, we shall study how \name works under \emph{static} conditions--i.e., when the \name wearable platform is stationary, and not mounted on any real user. Through a series of such studies, we shall gain an understanding of how the WiFi RF harvesting interacts with the power drain of the wearable system (which includes the power of the microprocessor, the accelerometer sensor and the RF transmitter). 
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\subsection{Experiment Setup \& Calibration}

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All our experiments were conducted in a meeting room using the antenna setup shown
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in Figure~\ref{fig:antennaarray}.  The WARP system was installed in an office room (roughly 8ftX8ft), with the transmitting and receiving antenna arrays placed at the 2 corners of the table (and 1 meter apart).  For these studies, which involve static devices, we do not perform the periodic AoA estimation process, and assume that the wearable's orientation, relative to the WARP transmitter, is known a-priori.  The transmitter and receiver gain was set to 35 out of 63 (max theoretical power of 20dBm at 63 gain) to reduce interference; thus, \emph{in all experiments, our total transmitted power was well within the EIRP  upper bound}. Unless otherwise stated explicitly, for these studies, the wearable device has the accelerometer sensor sampling at 10 Hz, with its RF frontend transmitting the collected sensor data packets in a burst, once every 1.5 minutes. 
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% We estimate the AoA of these ping packets and then use triangulation to
% estimate the direction to the transmitter antennas and then adjust the beam
% direction accordingly.  The distance between the transmitter and receiver
% array is 1m, the table width is XXXm, and length is XXXm.  To avoid poor AoA
% estimation errors caused by extreme angles (0\degree or 180\degree), we
% tilted the receiver by about 35\degree to increase the overlapped coverage
% between the transmitter and receiver.  The gain of the transmitter and
% receiver was set to 35 out of 63 (max theoretical power of 20dBm at 63 gain)
% to reduce inteference.
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%When we measure harvested power at fixed positions on the table, the energ
%is much more than the power consumption of the wearable, so we want to test
%evaluate how the wearing of the device affect the harvested energy.
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%show microscopic energy characteristics of our system. 
%Because we also explore the feasibility of our system when applied to a
%wearable device, we use the same setup of the WiFi AP as described in the
%next section \ref{sec:experiment}.  However, in this benchmarks, the device
%is placed at some fixed positions without a user wearing it.


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\subsection{Baseline Harvested Energy}
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\begin{figure}[!htb]
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	\centering
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	\includegraphics[height=1.8in,scale=0.25]{nouser.pdf}
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	\vspace{-0.1in}
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	\caption{Differential power (Avg.) of our (static) device}
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	\vspace{-0.1in}
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	\label{fig:residual1}
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\end{figure}
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Our first experiment studied the amount of harvested energy \name could produce, to establish if the overall system was net \emph{energy-positive}--i.e., whether the wearable device could be operated infinitely long purely via RF energy harvesting. We placed our wearable device at three different locations, L1, L2 and L3, that were 1.91, 1.32 and 1.17 meter, respectively, from the transmitter with an angle of 45\degree, 28\degree and 0\degree with respect to the transmitter's antenna array. We measured the voltage of the wearable's supercapacitor before and after
activating \name for 15 minutes.  If the supercapacitor's voltage at the end of the experiment duration is higher than its initial starting voltage, the total harvested energy is greater that consumed by the wearable's components, and \emph{vice versa}. Given the difference in voltage, the total energy stored in the supercapacitor can be computed using the following equation:
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\begin{equation}
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U = \frac{1}{2}CV^2; \; \; \; \; P = \frac{\Delta U}{T};
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\end{equation}
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where $C$ is the capacitance of the super capacitor in Farad (we use a 0.47F
capacitor), $V$ is the voltage in Volt, $U$ is the stored energy in Joule, $P$ is
the power in Watt, and $T$ is the observation duration (15 mins).
In other words, $P$ represents the average power differential (averaged over the 15 minute duration) between the harvested and expended power. 
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\begin{figure}[!htb]
	\centering
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	\includegraphics[height=1.8in,scale=0.3]{capacitorbuffer.pdf}
	\vspace{-0.1in}
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	\caption{Time series of supercapacitor voltage}
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	\vspace{-0.1in}
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	\label{fig:residualtime}
\end{figure}
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Figure~\ref{fig:residual1} shows the results of this experiment.  We see that, in all 3 positions, the average power differential was positive, indicating that, on average, the harvested power is more than sufficient to operate the wearable device. More specifically, in position L2, the power differential is higher than 350 $\mu$W, indicating that WiFi harvesting is \emph{likely to be able to support the operation of multiple additional sensors as well} (as the marginal sensing cost is likely to low, once the basic system component costs of the processor and RF frontend are amortized). In addition, Figure~\ref{fig:residualtime} shows the time series fluctuation in the supercapacitor's voltage level (for position L2). Even in this favorable position, we can see that there are periodic drops in the voltage, with these dips corresponding to the transient periods when the RF frontend transfers the sensor data packets. In particular, by carefully measuring the energy drain with \& without transmissions by the wearable, we find that the RF frontend consumes $\sim30$mW when active.  This graph has two important implications: (a) it underscores the necessity of a supercapacitor to tide over transient periods of deficient power, and (b) by demonstrating that it is impractical to capture the sensing stream continuously, it justifies our ``triggered sensing" paradigm.
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\subsection{Effect of Duty Cycle}
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\begin{figure}[!tbh]
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	\centering
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	\includegraphics[height=1.8in,scale=0.2]{dutycycle.pdf}
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	\vspace{-0.1in}
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	\caption{Differential power (Avg.) vs. AP Trx. Duty cycle.}
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	\vspace{-0.1in}
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	\label{fig:dutycycle}
\end{figure}
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We next study how the residual average power varies with a change in the WARP transmitter's duty cycle (varied between 20-100\%). At present, the WARP transmitter does not implement any CSMA/CA mechanism. Accordingly, a duty cycle of 100\% would imply that the AP was constantly transmitting `power packets', without leaving any opportunity for data packet transmission. Experimenting with smaller duty cycles allows us to mimic the case of a realistic WiFi AP, where such power packet transmissions occur only intermittently, only when the channel is free from other data packet transmissions. 
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Figure~\ref{fig:dutycycle} plots the residual energy (computed, as before, from the voltage change in the wearable's supercapacitor) as function of the duty cycle. As expected, the average differential power is approximately linear with the duty cycle.  More interestingly, even with a duty cycle of 20\%, the differential power is positive ($\sim 50 \mu$W), indicating that the harvested energy is more than sufficient to operate the entire sensing device. From our prior studies~\cite{tran2017}, we know that the average WiFi AP utilization in our campus deployment is below 20\%. These results thus strongly suggest that, in a well-engineered WiFi deployment, it may be possible to support the coexistence of useful WiFi RF energy harvesting with regular WiFi communication.
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\subsection{Effect of Number of Antennas}
\begin{figure}
	\centering
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	\includegraphics[height=1.8in,scale=0.22]{number_antenna.pdf}
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	\vspace{-0.1in}
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	\caption{Harvested Power vs. No. of Antennas.}
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	\vspace{-0.1in}
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	\label{fig:numberantenna}
\end{figure}
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We next varied the number of transmitting antennas in the WARP transmitter and studied the impact on the residual power.  In this experiment, we explicitly plot the \emph{harvested RF power} *using a 10K$\omega$ resistive load) at the supercapacitor--i.e., we disable the wearable system components (microprocessor, sensor and RF frontend). Figure~\ref{fig:numberantenna} plots the resulting values, computed over the 15 minute experimental window.  Matching our intuition, a larger number of antennas allows the transmission beamwidth to be smaller, thereby effectively increasing the density of the delivered RF power. However, in practice, an overly thin beam may be counterproductive if the AoA estimation is not sufficiently accurate: the RF beam may be misdirected and too narrow, resulting in a sharp drop in the power harvested by the wearable. pointed at a direction deviated from the device's true location and thus the device may not be charged at all. 
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\subsection{Beam Adaptation for More than One Devices}
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\label{sec:multiuser}
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In the final set of studies, we studied the behavior of \name in the presence of multiple (2) client devices. In this case, the AP has to make some interesting choices between charging both devices simultaneously or in round-robin fashion. We placed the two devices on the table with two different spacing values: 30cm and 1.7m. We then run the beamforming algorithm with two operational modes: 
\begin{itemize}
\item \emph{Time-multiplexed:} In this mode, the AP attempts to primarily charge only 1 client device at any instant. Given this objective, the AP uses an 8 antenna array (narrow beam) directed towards the current primary client device, before periodically switching the beam to the other client.  We experimented with 3 switching periods: 10 secs, 30 secs and 90 secs. 
\item \emph{Concurrent:} In this mode, the AP seeks to charge both devices simultaneously. In this case, the AP splits into two virtual 4-antenna APs, directed one beam each continuously towards a single client. Note that in this case, the beamwidth is larger, as each virtual AP only uses 4 antennas.
\end{itemize}

Figures~\ref{fig:multiplexclose},~\ref{fig:multiplexfar} and~\ref{fig:edev2beam} plot the average differential power (over the 15 min test period) for the cases of Time-multiplexed (30cm gap), Time-multiplexed (1.7m gap) and Concurrent, respectively. We see that in time-multiplexing mode, the differential power surplus is much greater when the two devices are close to one another: in this case, each narrow beam is able to cover both clients, thereby providing continual charging. (The differences between the two client devices is due to difference in the hand-tuned inductances of the two harvesters.) On the other hand, for the Concurrent case, the power differential surplus is much higher when the devices are spaced apart. In fact, it is likely that, when the clients are closely spaced, the wider 4-array beams overlap and cause destructive interference at each client, thereby creating an overall deficit in the differential power levels. These experiments suggest that time multiplexed mode is preferable if the devices are close to each other, whereas the concurrent mode is superior when the clients are widely separated. (See Section~\ref{sec:discussion} on how this may influence possible future research directions.)

\begin{figure*}[!tbh]
\centering
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\begin{minipage}{.33\textwidth}
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  \centering
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  \includegraphics[height=1.8in, width=2.1in]{multiplexclose.pdf}
  \vspace{-0.1in}	
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  \caption{Time-multiplexed (30cm)}
  \label{fig:multiplexclose}
\end{minipage}%
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\begin{minipage}{.33\textwidth}
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  \centering
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  \includegraphics[height=1.8in, width=2.1in]{multiplexseparated.pdf}
  \vspace{-0.1in}	
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  \caption{Time-multiplexed (1.7m)}
  \label{fig:multiplexfar}
\end{minipage}%
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\begin{minipage}{.33\textwidth}
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  \centering
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  \includegraphics[height=1.8in,width=2.1 in]{2device2beams.pdf} 
  \vspace{-0.1in}	
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  \caption{Concurrent Charging}
  \label{fig:edev2beam}
\end{minipage}
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\vspace{-0.1in}
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\end{figure*}
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%\am{Someone pls. format the captions for Figures 12-14}
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% We continue to evaluate our system to support multiple device concurrently. We placed 2 devices on the table with two different spacing of 30cm and 1.7m respectively. We then run the beamforming algorithm with two operational mode: time multiplexing and concurrent beams.

% In time multiplexing mode, the AP schedule the beam switching at 3 different periods of 10 seconds, 30 seconds and 90 seconds. Although the efficiency of 2 devices are different because of the hand-tuning of the harvester. We can see clearly that the total residual power of the 2 devices is much higher when the 2 device are placed next to each other with 30cm separation. This can be applied to power several items in an wearhouse or mall within the beamwidth.  

% On contrast, in concurrent beams mode, the separated spacing shows significantly better total residual power. Although in the separated spacing mode, one device is moved to the corner closer to the AP, the other device is moved further away from the AP. In general, this experiment suggest that if the devices are close to each other, the system should use time multiplexing, and if they are widely separated, the concurrent beams seems working better.

%% rest commented out by Archan, as it's not super relevant and we don't have time
% \subsection{Transfer Energy at Maximum Tx Power}
% \begin{figure}
	% \centering
	% \includegraphics[scale=0.25]{maxpower.pdf}
	% \caption{Maximum power transfer.}
	% \label{fig:maxpower}
% \end{figure}

% Currently we set Tx gain at 35/63.  This will show the energy at a gain of
% 63

% \subsection{Efficiency of the System}

% \begin{figure}
	% \centering
	% \includegraphics[scale=0.25]{placeholder.pdf}
	% \caption{Efficiency of the system.}
	% \label{fig:efficiency}
% \end{figure}

% Change Tx output power and measure energy (using cable)