dRTI: Directional Radio Tomographic Imaging
\alignauthor{Bo Wei$^\dag$$^\forall$$^\ddag$
Ambuj Varshney$^\S$
Wen Hu$^\ddag$$^\forall$
Neal Patwari$^\varnothing$$^\bigtriangleup$
Thiemo Voigt$^\forall$$^\S$
Chun Tung Chou$^\dag$
Radio tomographic imaging (RTI) enables device free localisation of people and objects in many challenging environments and situations. Its basic principle is to detect the changes in the statistics of some radio quality measurements in order to infer the presence of people and objects in the radio path. However, the localisation accuracy of RTI suffers from complicated radio propagation behaviours such as multipath fading and shadowing. In order to improve RTI localisation accuracy, we propose to use inexpensive and energy efficient electronically switched directional (ESD) antennas to improve the quality of radio link behaviour observations, and therefore, the localisation accuracy of RTI. We implement a directional RTI (dRTI) system to understand how directional antennas can be used to improve RTI localisation accuracy. We also study the impact of the choice of antenna directions on the localisation accuracy of dRTI and propose methods to effectively choose informative antenna directions to improve localisation accuracy while reducing overhead. We evaluate the performance of dRTI in diverse indoor environments and show that dRTI significantly outperforms the existing RTI localisation methods based on omni-directional antennas. % by up to 39.7\%. %In this paper, we investigate the benefits and overhead of directional antennas in Radio Tomographic Imaging (RTI). RTI observes the radio link behaviours %, i.e. changes in signal strength measurement made by a wireless network, % to infer the existence of (new) obstructive objects in the area of interest, which enables device free localisation in Non Line of Sight (NLOS) environment (``see through the walls'') and is significantly less intrusive compared to traditional methods such as camera surveillance. Therefore, RTI has many potential applications such as health care (assisted living), security, and military. However, the localisation accuracy of RTI suffers from complicated radio propagation behaviours such as (deep) fading and shadowing, in particular in NLOS environments. In order to improve the RTI localisation accuracy, we propose to use inexpensive and energy efficient Electronically Switched Directional (ESD) antennas to improve the quality of radio link behaviour observations, and therefore, the localisation accuracy of RTI. We implement an end-to-end RTI system with ESD antennas (dRTI), and study the impact of link behaviour quality of directional communications enabled by the directional antennas. %%\av{I would instead mention the "impact of link quality behaviour because of the directional transmissions and receptions/ directional communication" instead. Directional antennas enable directional communication which results in different link quality behaviour . %We evaluate the proposed dRTI in both LOS and NLOS environments, and show that dRTI outperforms %%\tv{I would put ``outperforms'' %state-of-the-art RTI systems based on mean-based RTI (mRTI), variance-based RTI (vRTI), and multi channel RTI (cRTI) using omni-directional antennas %\av{ again i would instead mention omnidirectional communication. you should also take note that configuring ESD antenna to omni-directional mode is different from using omni-directional antenna. %by up to 47.4\%. % %\begin{figure[!ht] % \centering % \includegraphics[scale = 0.7]{figure/testonmap.pdf % \caption{ test on map \label{testonmap %\end{figure
background.tex
\vspace{-2mm}
\section{Background} 
\label{sec:background}

The mathematical notations used in this paper are summarised in Table~\ref{tab:notation}.


% \subsection{Mathematical Notations}\label{subsec:notation}




%Before introducing the background and our suggested method,
%We first introTable~/we present the notations for the following sections.\\
%Let us first introduce the necessary mathematics notations used in this paper, all of which
%are collectively listed in Table~\ref{tab:notation}.

%\begin{tabular}{p{45pt} p{170pt}}
\begin{table}[th]
\footnotesize
\centering
\caption{Mathematical Notations}
\begin{tabular}{| l | p{6.5cm} |}
% \begin{tabular}{l | p{6.5cm} |l| l | p{6.5cm}}
\hline 
 Symbol    & Description \\ \hline
%Symbol    & Description   && Symbol    & Description \\
%\cline{1-2} \cline{4-5}
$M$ &Number of links in the network\\
$N$ & Number of voxels in the AoI \\ 
$R_i(t)$ & RSS measurement for link $i$ at time $t$ (omni only) \\ 
$\bar{R}_i$ & Mean RSS measurement for link $i$ during calibration (omni only) \\ 
$y_i(t)$ & link quality statistics for link $i$ at time $t$ \\
$y$ & a ${M}\times{1}$ vector of link quality statistics  \\
$x$ & a ${N}\times{1}$ vector of tomographic image \\
$F_i$ & The set of selected \emph{Pattern Pair}s for link $i$ \\ 
$R_{i,j}(t)$ & RSS measurement for link $i$, \emph{Pattern Pair} $j$ at time $t$ (dRTI only) \\
$\bar{R}_{i,j}$ & Mean RSS measurement for link $i$, \emph{Pattern Pair} $j$ during calibration (dRTI only) \\
%$A$		& a weight matrix, $A_{ij}$ is the weight of the voxel $j$ for link $i$ &&
%$n$           & noise\\
%$P_{rx}(i,t)$ & received power of link $i$ at time $t$&&
%$P_{tx}(i,t)$ & transmit power of link $i$ at time $t$\\
% $PA(i,t)$ & total power loss of link $i$ at time $t$&&
% $L(i,t)$ & path loss  of link $i$ at time $t$ for omni direction antennas\\
%  $\hat{L}(i,t)$ & path loss  of link $i$ at time $t$ for directional antennas&&
%$S(i,t)$& shadowing loss of link $i$ at time $t$\\
%$F(i,t)$& fade level  of link $i$ at time $t$&&
%$n(i,t)$& measurement noise  of link $i$ at time $t$\\
%$\phi$ & zenith&&
%$\theta$ & azimuth\\ 
%$f(\phi,\theta)$ &  a function describing the gain of signal's direction relative to the antennas ($\phi$) and ($\theta$&&
%$x(\phi,\theta)$ & the environment offset function\\
%$n_{receiver}$  & number of chose directions of receiver for \emph{Pattern Pair} combination&&
%$n_{transmitter}$ & number of chose directions of transmitter for \emph{Pattern Pair} combination \\
%$r_{i,j}(t)$ & the \emph{normalised} RSS from $i$-th link \emph{Pattern Pair} of $j$-th receiver direction at time $t$ &&
%$h_{i,j}$		& the \emph{normalised}  mean of RSS measurement from $i$-th link \emph{Pattern Pair} of $j$-th receiver receiver in the calibrating period \\
%% $F_{i}$	&antenna link \emph{Pattern Pair} set for $i$-th receiver. &&
%$t_1$		& the beginning time of the calibrating period. &&
%$t_2$		& the end time of the calibrating period. \\
%$R_{i,j}(t)$  & $y_{i}(t) = \text{observation\_function}({R_{i,j}(t)}), {j}\in{Fp_{i}}$ &&  
%$n_p$ 	&the length of $F_{i}$, ${n_p} = \left | {F_{i}} \right | $ \\
%%$L$	&link set in the RTI wireless network. \\
%$Fp_{i}$	& chosen antenna link \emph{Pattern Pair} set for $i$-th receiver &&
%$n_c$ 	&the length of $Fp_{i}$, ${n_c} = \left | {Fp_{i}} \right | $ \\
\hline
\end{tabular}
\label{tab:notation}
\end{table}

\vspace{-2mm}
\subsection{Radio Tomographic Imaging}
\label{subsec:bgRTI}

%Let $y =  \{{y_1}, {y_2}, ...,y_{i},... , {y_{|L|}} \}$ represent the RSS variance indicator for each link, where $L$ is the set of the link. Let $x = \{ {x_1}, {x_2}, ..., {x_i}, ..., {x_{M}}\}$ denote the image vector, where $M$ is the number of image vectors and $x_i$ is a measurement for the current object presence for voxel $i$.
%\cite{WilsonRTI:2010} proposes a model for RTI, which is utilised in the several RTI applications \cite{WilsonVRTI:2011,KaltiokallioBP12,ZhaoKRTI:2013,Kaltiokalliograndma2012,maas2013toward}. In this paper, this model is also exploited for RTI. 

The aim of RTI is to localise the people and objects (Note: we will also use obstructions to refer to people or objects because this is how RTI ``sees" them.) within an AoI by using sensors placed around the periphery of the AoI. We assume that the AoI is divided into voxels, see Fig.~\ref{fig:example1}. The sensors exchange packets periodically in order to monitor the Received Signal Strength (RSS) of the links over time. In RTI, all links are assumed to be \emph{asymmetric}. 

RTI localises the obstructions in the AoI in two steps. A \emph{tomographic image} is first computed from the RSS measurements, and then a Kalman filter uses the computed image to localise and track the obstructions.  

We use the RTI model introduced in~\cite{WilsonRTI:2010} to compute the tomographic image. This model is also used in many other RTI works~\cite{KaltiokallioBP12,Kaltiokalliograndma2012,maas2013toward,WilsonVRTI:2011, ZhaoKRTI:2013}. Let $R_i(t)$ denote the RSS measurement of the $i$-th link at time $t$. We use $R_i(t)$ to compute some link quality statistics $y_i(t)$ for link $i$. These link statistics $y_i(t)$ will be used to compute the tomographic image later on. We consider the following link quality statistics in this paper. 

%\begin{itemize}
%\item  
\textbf{Mean based RTI (mRTI):}
The \emph{original} mRTI method is proposed in~\cite{WilsonRTI:2010} where RTI is used in an \emph{open} outdoor environment. This is a fairly simple radio environment where radio signal attenuation is due mainly to LOS path loss. The effect of an obstruction in a radio link is to decrease the RSS values of that link. Therefore, one may detect the presence of an obstruction in the link $i$ at time $t$ by testing whether $R_i(t)$ has decreased from a base value. The mRTI method requires a calibration period where obstructions are absent in the AoI. During this period, the sensors exchange packets in order to determine the mean RSS of each link. Let $\bar{R}_i$ be the mean RSS of link $i$ over the calibration period. The original mRTI uses the link statistics $y_i(t) = R_i(t) - \bar{R}_i$ for link $i$. 

We will be concerned with RTI in an indoor environment in this paper. We will see later on that, in the indoor environment, the presence of an obstruction in a radio link can cause the RSS of the link to decrease, increase or stay at the same value. The original mRTI therefore does not work well. In this paper, we use mRTI to mean the \emph{modified} link statistics $y_i(t) = |R_i(t) - \bar{R}_i|$ where absolute value is used because the RSS can increase or decrease. 

%In an indoor environment, the effect of an obstruction on RSS is unpredictable. The obstruction can increase, decrease or even have no effect on the RSS measurements. Therefore, a possible link quality behaviour observation is to see whether the RSS measurements have changed from a base value. We assume a calibration period where the sensors exchange packets to obtain the mean RSS for each link. Let $\bar{R}_i$ be the mean RSS for link $i$. For mRTI, we define $\text{observation\_function}(R_i(t)) = | R_i(t) - \bar{R}_i |.$ The motivation for using absolute value is because RSS can increase or decrease. We remark that~\cite{WilsonRTI:2010} uses a very similar observation function except that absolute value is not used. Note that~\cite{WilsonRTI:2010} considers an open outdoor environment where the effect of an obstruction is to decrease the RSS. We will refer to this method as mRTI. 

\textbf{Variance based RTI (vRTI):}
The vRTI~\cite{WilsonVRTI:2011} method uses the variance of a window of $v$ measurements as the link quality statistics, i.e. $y_i(t) = var(R_i(t), ...,$ $R_i(t - v + 1))$. Since this method does not require a base value, no calibrations are required. % It has also been shown to work well in an indoor environment. 

%\item  \textbf{Weighted-variance based RTI}
%\needtocheck{Not edited yet. Do we use this at all?} 
%The third one is similar to the second one, but instead of the summary of $R_{i,j}(t)$, it summarise the $n$-th power of the elements from $R_{i,j}(t)$, i.e. $y_{i}(t) = \sum_{k\in {Fp_i}}{R}^{n}_{i,k}$. 
%\end{itemize}

%\textcolor{red}{Section~\ref{subsec:observation} should be move to Background}

% \subsection{Link Quality Behaviour Observation Build Method} \label{subsec:observation}
%The goal of our RTI wireless networks is to take advantage of $M$ links for the tracking or localising the person moving in the area. 
%Section~\ref{subsec:antennachoose} already introduces how to pick the patter pairs for each pair of a transmitter and a receiver.
%In this section, we discuss three methods to make link quality behaviour observation.
%i.e. for each link $i$, RSS measurement vector $r_i$ is a ${n_c}\times{1}$ vector, and $\{{{r_{i,j}}}\},{j\in {Fp_i}}$ is the element in the vector $r_i$. The link quality observation for link $i$ at time $t$ is expressed as $y_{i}(t) = \text{observation\_function}({R_{i,j}(t)}), {j}\in{Fp_{i}}$. Three methods to build observation\_function() are introduced as follows.
%$y$ is a ${M}\times{1}$ vector which is the observation of the link. 
%After we use the antenna patter pair chosen method in ~\ref{subsec:antennachoose}, we have $n_c$ pattern pairs for each links. 

%$r_i$ is a ${n_c}\times{1}$ vector $\{{{r_{i,j}}}\},{j\in {Fp_i}}$, $r_{i}(t)$ is used to build $y_{i}(t)$.

%There are three method we can use $r_{i}$ to build $y_{i}$. 


%The first one is mean based RTI method. For this method, RTI needs three periods, the first one is empty-area calibration, the second step is antenna pattern pair choosing, and the last one is to apply RTI method to calculate the image of the monitored objects. 

%In the empty-area calibration period from $t_a$ to $t_b$, the monitored area needs to be empty so that the beacons from all ESD antenna directions are collected by all the direction of  the receivers' ESD antennas.  RSS vector of each pattern pair is averaged over the whole empty-area calibrating period. 
%For each link, there are $n_p$ antenna pattern pairs, for our ESD antenna  $n_p = {6}\times{6}=36$. The average RSS value $h_{i,j}$ for each antenna patter pair in the empty-area calibration period is calculated.
%denoted as $\tilde{R_{ij}}$ calculated by $\frac{1}{{t_b}-{t_a}}\sum_{k=t_a}^{t_b}(R_{ij}(k)), {1}\leq {j} \leq {n_p}$.

%In the second step, the antenna pattern pair chosen method introduced in ~\ref{subsec:antennachoose}  is applied.



% \subsection{Imaging Estimation and Tracking} \label{subsec:imaging}
%As introduced in Section ~\ref{subsec:bgRTI}, the attenuation image is estimated by the link quality behaviour observation using Tikhonov regulation method, and the Kalman filter is used for increasing the tracking performance. 

%Two methods have been proposed  to build the link quality behaviour observation $y$ from RSS measurements. The first method is mRTI \cite{WilsonRTI:2010} which requires a calibration period to estimate the mean RSS for each link. The vector $y$ is obtained from subtracting the new RSS measurements from the mean RSS of the corresponding link. The mRTI method may be not effective in the NLOS ``through-wall'' environment, so the authors of \cite{WilsonVRTI:2011} propose vRTI which uses the variance of RSS for each link to construct $y$. Another advantage of vRTI is that it does not require a calibrating period and is therefore suitable for applications such as hostage rescue. 
%

We collect the $y_i(t)$ for all the $M$ links in the WSN to form the link quality statistics vector $y$. We use $y$ to estimate the tomographic image $x$ which is a $N \times 1$ vector where $N$ is the number of voxels in the AoI. Each element of $x$ corresponds to a voxel. If the $i$-th element of $x$ has a larger value, then the chance of the obstruction \bo{is} in the $i$-th voxel is higher. Fig.~\ref{fig:example3} shows an example tomographic image as an heat map (best view in colour). It can be seen that the true location of the obstruction, which is marked by a cross, is in an ``hot" area. To obtain $x$ from $y$, the RTI model in~\cite{WilsonRTI:2010} assumes that $y$ and $x$ are linearly related: 
\begin{equation}
y = A x + n  \label{eqn:rtimodel}
\end{equation}
where $n$ is a noise vector and $A$ is a $M \times N$ matrix. The $(i,j)$ element of $A$ is given by~\cite{WilsonRTI:2010,WilsonVRTI:2011}: 
% A is the weight matrix given in, $A_{ij}$ denotes the weight of the voxel $j$ for  the link $i$, which is expressed by Equation \ref{eqn:rtiweight}.
\begin{equation}
A_{ij} =  \frac{1}{ \sqrt{d} } \begin{cases}1 & \quad \text{ if } d_{ij}(1) + d_{ij}(2) < d +  \lambda \\0 & \quad \text{ otherwise }  \end{cases}, \label{eqn:rtiweight}
\end{equation}
where $d$ is the distance between the nodes of link $i$, $d_{ij}(1)$ and $d_{ij}(2)$ are the distances from the voxel $j$ to the two nodes of link $i$, and $\lambda$ is a parameter to tune the width of the ellipse. If $A_{ij}$ is non-zero, then it means voxel $j$ is close to the line connecting the nodes of link $i$ and is likely to contribute to the variation that is found in the link quality statistics $y_i(t)$. The non-zero elements of $A_{ij}$ for a given link $i$ form an ellipse, see Fig.~\ref{fig:example1} where the shaded voxels indicates those $A_{ij}$ that are non-zero for the link consisting of the two nodes shown in the figure. 

%\subsection{RTI and VRTI Methods}\label{subsec:bgRTInVRTI}
 
%In terms of building RSS by each link, two methods have been proposed.

%To show the advantage of the ESD antennas for RTI, we use the attenuation-based RTI  \cite{WilsonRTI:2010}and variance-based RTI\cite{WilsonVRTI:2011} to build the RSS observation.
%To show the advantage of the ESD antennas for RTI, we use the attenuation-based RTI and variance-based RTI to build the RSS observation.


%\subsection{Regulation Model}\label{subsec:bgregulation}
Since the number of voxels $N$ is normally greater than the number of links $M$, Eq.~(\ref{eqn:rtimodel}) is under-determined and has to be solved by using Tikhonov regularization. The estimated tomographic image is then input into a Kalman filter for location estimation and tracking. The details can be found in~\cite{WilsonRTI:2010, WilsonVRTI:2011}. 


%A tomographic image $\hat{x}$ can be estimated by using the Tikhonov regularization~\cite{WilsonRTI:2010, WilsonVRTI:2011} and least squares estimators~\cite{PatwariEffect2008,ZhaoNoise2011}. In detail, $\hat{x}$ can be estimated by  
%\begin{equation}
%x =  \Psi  y   \quad \text{ where }  \Psi  = (A^{T} A +  {\sigma_{n}^2} C_{x}^{-1})^{-1} A^{T} , \label{eqn:rtireg}
%\end{equation}
%In Equation~\ref{eqn:rtireg}, $C_{x}$ is the covariance matrix of $x$ whose $(i,j)$ element is ${\sigma_{x}^2} e^{-d_{ij}/ \delta }$ ~\cite{ZhaoRobust2011}.
%%\begin{equation}
%%[C_{x}]_{ij} ={\sigma_{x}^2} e^{-d_{ij}/ \delta } , \label{eqn:cx}
%%\end{equation}
%where ${\sigma_{x}^2}$ is the variance of the monitored object presence, $d_{ij}$ is the distance between the voxel $i$ and voxel $j$, and $\delta$ is a correlation distance parameter. $\Psi$ is a constant calculated once before tomographic image reconstruction.
%

\vspace{-2mm}
\subsection{Electronically Switched Directional Antenna}\label{subsec:esd}
%\textcolor{red}{this subsection is not added yet, the following texts here are for occupying the places to calculate the total number of pages}
%\textcolor{red}{this subsection is alpha version}

\input{Tex/spida.tex}

esd_related.tex
%There has been existing work on the use of the directional antenna in both low-power sensor network and IEEE 802.11 networks.  omniRTI_links_v2
Directional communications have been studied in both WiFi networks and WSNs. 
The challenges imposed by directional communications at the MAC layer have been extensively studied over the past few years \cite{1348118,4359017,832169,Choudhury:2002:UDA:570645.570653,Takai:2002:DVC:513800.513823}. %There are recent empirical studies which have explored directional communications. 
%However, a vast majority of the existing work have explored the use of  the directional antennas in an outdoor environment\cite{Navda:2007:MUS:1247660.1247684, Patra:2007:WDI:1973430.1973437, Raman:2005:DEN:1080829.1080847}.  Mobisteer\cite{Navda:2007:MUS:1247660.1247684} demonstrates improved network connectivity between a mobile vehicle and fixed access point using directional antennas. WildNet \cite{Patra:2007:WDI:1973430.1973437} demonstrates long distance point to point links  in an outdoor environment using high gain directional antenna. However, in all these studies in the outdoor environment, the line-of-sight(LOS) dominates and there is very little multi-path effect reducing the complexity. 
%However, indoors environment is increasingly complex because of the extensive multi-path scattering and fading. 
While the majority of the work is in outdoor environments, recent works showed that directional communications is useful in indoor environments as well.
Blanco et al.  observed that directional antennas can lead to performance improvement over omni in an indoor environment and made an important observation that LOS direction did not always have the strongest signal strength in~\cite{Blanco:2008:ESB:1791949.1791967}.  
Liu et al. suggested that solutions developed for outdoor environments with directional communications might not work well in indoor environments, but demonstrated improved network capacity on the usage of directional communications~\cite{Liu:2009:DII:1592568.1592589, Liu:2010:PEI:1859995.1860020}. Lakshmanan et al.~highlighted
 that the benefits of directional communications are mostly resulted from the link gains instead of spatial medium reuse  in indoor environments \bo{\cite{Lakshmanan2010}}. % \cite{Lakshmanan:2010:MSR:1889324.1889330}.  



In WSNs, Giorgetti et al.~demonstrated that a four-beam patch antenna could increase transmissions ranges and decrease signal variability and interference suppression from WiFi networks in~\cite{giorgetti07directional}. Voigt et al.~investigated indoor link dynamics for
directional communications and observed that the best direction for communications depended on the wireless channels used~\cite{thiemo}.  
Varshney et al. demonstrated that, in an indoor environment, directional transmissions and receptions together could significantly alleviate wireless contentions, which allowed better usage of the available wireless channels in~\cite{AmbujSPIDA}. 

To the best of our knowledge, this paper is the first to study the feasibility and performance of RTI for localisation and tracking with directional communications. 
%However,  with all these studies there is lack of clear empirical results quantifying performance improvements in an indoor environment with NLOS communication because of the directional communication.

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%@inproceedings{Blanco:2008:ESB:1791949.1791967,
% author = {Blanco, Marc and Kokku, Ravi and Ramachandran, Kishore and Rangarajan, Sampath and Sundaresan, Karthik},
% title = {On the Effectiveness of Switched Beam Antennas in Indoor Environments},
% booktitle = {Proceedings of the 9th International Conference on Passive and Active Network Measurement},
% series = {PAM'08},
% year = {2008},
% isbn = {3-540-79231-7, 978-3-540-79231-4},
% location = {Cleveland, OH, USA},
% pages = {122--131},
% numpages = {10},
% url = {http://dl.acm.org/citation.cfm?id=1791949.1791967},
% acmid = {1791967},
% publisher = {Springer-Verlag},
% address = {Berlin, Heidelberg},
%} 


% @INPROCEEDINGS{1348118, 
%author={Choudhury, R.R. and Vaidya, N.F.}, 
%booktitle={Network Protocols, 2004. ICNP 2004. Proceedings of the 12th IEEE International Conference on}, 
%title={Deafness: a MAC problem in ad hoc networks when using directional antennas}, 
%year={2004}, 
%pages={283-292}, 
%keywords={ad hoc networks;carrier sense multiple access;directive antennas;radio receivers;radio transmitters;telecommunication congestion control;ad hoc network;carrier sense multiple access;communication failure;directional antenna;media access control protocol;omnidirectional antenna;Ad hoc networks;Array signal processing;Computer networks;Computer science;Deafness;Design engineering;Directional antennas;Intelligent networks;Media Access Protocol;Transmitters}, 
%doi={10.1109/ICNP.2004.1348118}, 
%ISSN={1092-1648},}
% 
%@ARTICLE{4359017, 
%author={Korakis, T. and Jakllari, G. and Tassiulas, L.}, 
%journal={Mobile Computing, IEEE Transactions on}, 
%title={CDR-MAC: A Protocol for Full Exploitation of Directional Antennas in Ad Hoc Wireless Networks}, 
%year={2008}, 
%volume={7}, 
%number={2}, 
%pages={145-155}, 
%keywords={access protocols;ad hoc networks;directive antennas;CDR-MAC protocol;ad hoc wireless network;circular directional request to send;directional antenna;directional transmission;medium access control protocol;IEEE 802.11;MAC;Wireless communications;directional antennas}, 
%doi={10.1109/TMC.2007.70705}, 
%ISSN={1536-1233},}
%
% @INPROCEEDINGS{832169, 
%author={Young-Bae Ko and Shankarkumar, V. and Vaidya, N.F.}, 
%booktitle={INFOCOM 2000. Nineteenth Annual Joint Conference of the IEEE Computer and Communications Societies. Proceedings. IEEE}, 
%title={Medium access control protocols using directional antennas in ad hoc networks}, 
%year={2000}, 
%volume={1}, 
%pages={13-21 vol.1}, 
%keywords={access protocols;directive antennas;packet radio networks;MAC protocol;directional antennas;medium access control protocols;wireless ad hoc networks;Access protocols;Ad hoc networks;Adaptive arrays;Broadband antennas;Directional antennas;Directive antennas;Intelligent networks;Media Access Protocol;Multiaccess communication;Packet radio networks}, 
%doi={10.1109/INFCOM.2000.832169}, 
%ISSN={0743-166X},}

%
% @inproceedings{Choudhury:2002:UDA:570645.570653,
% author = {Choudhury, Romit Roy and Yang, Xue and Ramanathan, Ram and Vaidya, Nitin H.},
% title = {Using Directional Antennas for Medium Access Control in Ad Hoc Networks},
% booktitle = {Proceedings of the 8th Annual International Conference on Mobile Computing and Networking},
% series = {MobiCom '02},
% year = {2002},
% isbn = {1-58113-486-X},
% location = {Atlanta, Georgia, USA},
% pages = {59--70},
% numpages = {12},
% url = {http://doi.acm.org/10.1145/570645.570653},
% doi = {10.1145/570645.570653},
% acmid = {570653},
% publisher = {ACM},
 %address = {New York, NY, USA},
% keywords = {ad hoc networks, carrier sensing, directional antennas, medium access control},
%} 

%@inproceedings{Takai:2002:DVC:513800.513823,
% author = {Takai, Mineo and Martin, Jay and Bagrodia, Rajive and Ren, Aifeng},
% title = {Directional Virtual Carrier Sensing for Directional Antennas in Mobile Ad Hoc Networks},
% booktitle = {Proceedings of the 3rd ACM International Symposium on Mobile Ad Hoc Networking \&Amp; Computing},
% series = {MobiHoc '02},
% year = {2002},
% isbn = {1-58113-501-7},
 %location = {Lausanne, Switzerland},
% pages = {183--193},
% numpages = {11},
% url = {http://doi.acm.org/10.1145/513800.513823},
% doi = {10.1145/513800.513823},
% acmid = {513823},
% publisher = {ACM},
% address = {New York, NY, USA},
% keywords = {IEEE 802.11, carrier sensing, directional antenna systems, medium access control, mobile ad hoc networks},
%} 

%@inproceedings{Korakis:2003:MPF:778415.778428,
% author = {Korakis, Thanasis and Jakllari, Gentian and Tassiulas, Leandros},
 %title = {A MAC Protocol for Full Exploitation of Directional Antennas in Ad-hoc Wireless Networks},
% booktitle = {Proceedings of the 4th ACM International Symposium on Mobile Ad Hoc Networking \&Amp; Computing},
% series = {MobiHoc '03},
% year = {2003},
% isbn = {1-58113-684-6},
% location = {Annapolis, Maryland, USA},
% pages = {98--107},
% numpages = {10},
% url = {http://doi.acm.org/10.1145/778415.778428},
% doi = {10.1145/778415.778428},
% acmid = {778428},
% publisher = {ACM},
% address = {New York, NY, USA},
% keywords = {IEEE 802.11, directional antenna systems, medium access control, mobile ad hoc networks},
% } 
%
%
%
%
%
%
%
%
%
%
%



experiment.tex
\vspace{-2.5mm}
\section{Evaluation} \label{sec:experiments}

%In this Section, we evaluate the performance of proposed dRTI with extensive experiments.
\vspace{-2.5mm}
\subsection{Goals, Metrics and Methodology}
\label{subsec:goals}
The goals of our evaluation are to study: 1) whether dRTI can lead to better tracking accuracy
in comparison to previous approaches based on omni-directional antennas and multi-channel RTI (cRTI); 
2) the performance of Location, Fade Level and PRR \emph{Pattern Pair} \bo{selection methods}; and 3) the energy overhead of dRTI.

We use two metrics to measure the tracking accuracy.
%(red path in Fig.~\ref{fig:trackingopen, fig:trackingwall, fig:trackingwall3}) for different methods. 
1) \emph{Root Mean Squared error (RMSE):} RMSE ($e_{rms}$) characterises the mean tracking error over the experiment and is defined as:
\begin{equation}
e_{rms} =  \sqrt{ \frac{1}{t_d-t_c} \sum_{t = t_c}^{t_d} { \hat{e} (t)^2}  } , \label{eqn:errrms}
\end{equation}
where, $t_c$ and $t_d$ are the experiment start time and end time respectively, and $\hat{e} (t)$ is the tracking error at time $t$, which is expressed as   
\begin{equation}
{ \hat{e}(t)} =   \parallel {\hat{x}(t)-x_g(t)} \parallel , \label{eqn:errrms1}
\end{equation}
where $\hat{x}(t)$ and $x_g(t)$ are the coordinates of the estimated location and ground truth at time $t$ respectively. 
2) \emph{Cumulative distribution function (CDF):}  CDF of an error level $\ell$ is the probability that the tracking error is less than or equal to $\ell$.
% % FN and FP
\bo{
3) \emph{Radio link attenuation false negative(FN) and false positive(FP):}  
 The definitions of these two qualities have already been discussed in Section~\ref{sec:hypoFNFP}. We will present FN and FP as a percentage. FN (FP) is the ratio of the number of FN (FP) links to the total number of links. 
}
\vspace{-2.5mm}

\subsubsection{Hardware and Software}
\label{subsubsec:hardware}
We deployed a network of seven nodes with ESD antennas and one base station, which collected the RSSI measurements from all the nodes and transferred 
them to a PC for RTI and tracking via a serial cable. We used the nodes, which have the same hardware (TelosB and ESD antenna with six directions) and operating system (Contiki) as those used in Section~\ref{subsubsec:setup}. TelosB nodes with CC2420 transceivers operate in the 2.4 GHz ISM band and the radio channels were picked from a list \{11, 15, 18, 21, 26\} as in~\cite{KaltiokallioBP12}.  For cRTI, we used 4 channels because it showed the best tracking performance~\cite{KaltiokallioBP12}.

The nodes run a simple token passing protocol in a TDMA 
fashion similar to SPIN\footnote{SPIN: TinyOS code for RSS collection. SPIN: TinyOS code for RSS collection
\url{http://span.ece.utah.edu/spin}} to produce and collect radio link RSSI measurements.
At a particular time, only one node transmitted packets, and the rest of the nodes received packets to measure pairwise RSS. 
The transmitter sent one packet per channel for cRTI and six packets per direction for dRTI in each round. The receivers \emph{dynamically} switched
antenna directions to try to collect one packet from each direction.

As introduced in Section~\ref{subsec:bgRTI}, if the value of a voxel in the RTI image has a larger value compared to the rest, it is
likely that an obstruction (a person) is located in this voxel. As in previous work~\cite{WilsonRTI:2010,WilsonVRTI:2011}, we
use the index of the voxel that has the largest value in the image as the estimated location of the person since 
we have one person only in the experiments. We further apply a Kalman filter to produce the
trajectory of the person. 
We use a voxel width of 0.2 metre, and $\lambda$ in Eq.~(\ref{eqn:rtiweight}) as 1.5 metres.
A webcam was deployed in AoI to record ground truth for tracking.
%The parameters used in the RTI are listed in Table~\ref{tab:parameter}.
%\begin{table}[ht]
%\begin{center}
%   \centering
%   \caption{dRTI tracking parameters}
%    \begin{tabular}{ | l | l | l |   }
%\hline
%Parameter & Value & Description  \\ \hline  
%$p$& $0.2$  & Voxel width(m)\\ \hline
%$\lambda$ & $1.5$ & the eclipse width parameter  \\ \hline
%$ \sigma_{x} $ & $0.5$ & Voxel standerd deviation \\ \hline
%$ \delta_{c} $ & $3.0$ & correlation coeffience \\ 
%    \hline
%    \end{tabular}
%\end{center}
%\label{tab:parameter}
%\end{table}

%For each experiment, we tune the parameter to show the good tracking performance. $Q$ indicates the person walking speed, and $R$ is the noise of the measurement. Larger $R$ would let Kalman filter trust the predicted location from Kalman filter over the estimated from Tikhonov regularization. 
%For each experiment and each channel, the channel quality varies, so $R$ is different for cRTI and dRTI. As dRTI and mRTI\&vRTI are conducted in the same channel, they share the same parameter.

%\begin{table}[ht]
%\begin{center}
%   \centering
%   \caption{Kalman filter parameters}
%\begin{tabular}{|l|l|l|l|p{3cm}|}
%\hline
%\multicolumn{3}{|l|}{Parameter}                           & Value & Description                                    \\ \hline
%\multicolumn{3}{|l|}{Q}                                   & 0.02  & Variance of person walking speed               \\ \hline
%\multirow{6}{*}{R} & \multirow{3}{*}{Exp. 1} & dRTI       & 1     & \multirow{6}{*}{Variance of measurement noise} \\ \cline{3-4}
%                   &                         & mRTI\&vRTI & 1     &                                                \\ \cline{3-4}
%                   &                         & cRTI       & 0.5   &                                                \\ \cline{2-4}
%                   & \multirow{3}{*}{Exp. 2} & dRTI       & 0.15  &                                                \\ \cline{3-4}
%                   &                         & mRTI\&vRTI & 0.15  &                                                \\ \cline{3-4}
%                   &                         & cRTI       & 1.5   &                                                \\ \hline
%\end{tabular}
%\end{center}
%\label{tab:kalman}
%\end{table}



\vspace{-2.5mm}
\subsubsection{Experiment Description}
We conducted 4 experiments in our lab. Experiments 1 and 3 were conducted in a large open room for testing in a LOS environment. The black dots in Fig.~\ref{fig:mRTILOS} show how the 7 nodes were placed in these experiments. Experiments 2 and 4 were conducted in a NLOS or ``through-wall'' environment. Seven nodes were placed in 4 adjacent rooms with 4 nodes in one room and 1 node each in the other 3 rooms, see Fig.~\ref{fig:mRTINLOS}. There was normal office equipment such as desk and computers in those 3 rooms with one node each. 
The walls between the rooms are made of either wood or glass.

Experiments 1 and 2 were designed to study the tracking performance of different \emph{Pattern Pair} selection methods in LOS and NLOS environments respectively. For the purpose of comparison, we also include the tracking performance of using all 36 \emph{Pattern Pairs}, which is termed as \emph{dRTI-All}. Experiments 3 and 4 aimed to compare the tracking accuracy of: dRTI (RSS mean and RSS variance), omni RTI (mRTI and vRTI) and cRTI (both mean and variance based). 

%\subsection{Setting}
%%The goal of the experiments is to track a person and to show the advantage of the ESD antenna for indoor open space and through-wall RTI.
%In this section, we perform experiments to show the advantage of ESD antennas for indoor ``open space'' and ``through-wall'' RTI and and the efficiency of the the metric for selecting the ``best'' antenna pattern pairs. This ESD antenna is operated in 2.4GHz ISM band with Tmote Sky node using a CC2420 radio. 
%For dRTI tracking experiments, all the nodes with ESD antennas are operated on a channel picked in a channel set $\{11, 15, 18, 21, 26\}$, which depends on the channel quality. Before the experiment, we measure the channel quality by applying the metric proposed by~\cite{noda2011quantifying} and pick a channel with minimum interference and maximum channel quality.
%A mbxxx node with baud rate 460800 bps is plugged into the laptop as the base station to collect RSS measurement observed from ESD antenna and omni-directional configuration as well for comparison. We use 7 Tmote Sky nodes with ESD antennas to build the wireless network for RTI.  At particular time, only one node performs as a transmitter to send packets in each direction or omni-directional configuration, while the rest of the nodes collects packets in each direction and omni-directional configuration to measure pairwise RSS. For guaranteeing the receivers can collect RSS measurement for each pattern pair, the transmitter needs to send 6 beacons in each direction of the antenna, and the receivers' antenna direction also change by the schedule at the same time. 
%%6 out of 7 beacons are for the ESD antennas' 6 different directions, and 1 beacon is for the omni-directional configuration.
%After one transmitter sends packets in each direction, it sends a packet in omni-directional configuration, and other EDS antennas also perform as the omni-directional to receive the packet to make the RSS measurement for omni-directional configuration combination.
%To record the ground truth, a web camera is deployed in AoI.
%
%\subsection{Goals, Methodology and Metrics}
%
%Our Goal in this experiments is to show the advantage of the EDS antennas for RTI. 
% For this purpose, we evaluate the performance of dRTI
%both in LOS environment (Experiment 1) and NLOS ``through-wall'' environment (Experiment 2). 
%FIgure \ref{fig:largeopen,fig:largeopenwall} shows the deployment of the nodes in these two experiment environments. 
%In Experiment 1 (LOS ``open space'' Experiment) , we deploy our 7 nodes with ESD antennas into AoI, a 4m$\times$7m laboratory. We also use 7 nodes for  Experiment 2( NLOS ``through wall'' experiment), but put three nodes into three offices adjoining the laboratory. The wall between the laboratory and the offices is made of either wood or glass.  
%The monitored person walks in the monitored area. To make the path clear and easy to label the ground truth, the monitored person walks in a square path, see the ground truth path in Figure~\ref{fig:trackingopen} and~\ref{fig:trackingwall}. 
%
%In addition, we compare dRTI with the state-of-the-art RTI method mRTI, vRTI, and cRTI using omni-directional configuration in each experiment.
%However,
%because the environmental change may affect the RSS measurement~\ref{ZhaoRobust2011}, the performance may not be comparable in different time.
%We need gets rid of the influence of the environmental changes and make the the fair comparison for the different RTI methods.
%Therefore dRTI along with mRTI\&vRTI or cRTI are integrated to the system in the  experiments. 
%When EDS antennas send packets iteratively In the experiments, the packets for mRTI, vRTI or cRTI are sent right after those for dRTI. 
%Before the presenting the experiments, we use the experiment RSS measurement dataset to present the efficiency and adequacy of the patter pair selection method for dRTI. 
%
%To indication the performance of dRTI as well as mRTI\&vRTI or cRTI  using omni-directional antenna,
%Root Mean Squared Error(RMSE) $e_{rms}$ is used as the metric 
%for comparing the estimated path(red path in Fig.[add figure]) with the ground truth(blue path in Fig.[add figure]).
%
%$e_{rms}$ is calculated as
%\begin{equation}
%e_{rms} =  \sqrt{ \frac{1}{t_d-t_c} \sum_{t = t_c}^{t_d} { \hat{e} (t)^2}  } , \label{eqn:errrms}
%\end{equation}
%where, $t_c$ is the beginning time of tracking, $t_d$ is the end time of tracking, and $\hat{e} (t)$ is the estimated error at time $t$, which is expressed as   
%\begin{equation}
%{ \hat{e}(t)} =   \parallel {\hat{x}(t)-x_g(t)} \parallel , \label{eqn:errrms}
%\end{equation}
%where $x_g$ it the coordinate of ground truth at time $t$.
%

\vspace{-2.5mm}
\subsection{Comparing Different \emph{Pattern Pair} Selection Methods}
%Before presenting the dRTI tracking performance, the pattern patter pair needs to be chosen. 
%To show the efficiency of pattern pair selection methods, 
%We use the RSS measurement data in Experiment 1 and Experiment 2. 
%Among the three methods, Fade Level method perform best.
For both Experiments 1 (LOS) and 2 (NLOS), we apply the three \emph{Pattern Pair} selection methods to compare their performance. For each experiment, both mean and variance based statistics are used. For the mean based dRTI in the LOS environment, Fig.~\ref{fig:locationmeanlos} shows that the Fade Level and PRR methods perform similar to each other, and converge to the performance of dRTI-All when the number of \emph{Pattern Pairs} is larger than 5. For the variance based dRTI, Fig.~\ref{fig:fadelevelmeanlos} shows that the PRR method performs best and is even better than 
dRTI-All. The last result is not surprising because, from Fig.~\ref{fig:patternpairBoth}, we know that some \emph{Pattern Pairs} are more informative than others, and some \emph{Pattern Pairs} are even less informative than omni. These results also show that using all \emph{Pattern Pairs} is not necessarily better, and judicious selection can help improve performance and reduce overhead.
. 

% The figure also shows that Fade Level and Location converge to dRTI-All when the number of \emph{Pattern Pair}s is 9 or more.
%\tv{you have already said that PRR performs better than dRTI-All}


%For the mean based method(see Fig.~\ref{fig:locationmeanlos}, Fig. ~\ref{fig:fadelevelmeanlos}, Fig.~\ref{fig:prrmeanlos} for Experiment 1, and Fig.~\ref{fig:locationmeannlos}, Fig. ~\ref{fig:fadelevelmeannlos}, Fig.~\ref{fig:prrmeannlos} for Experiment 2), Fade Level method performs best whose $e_{rms}$ decreases when the number of patter pair increases and keep stable after arriving at a threshold. 

\begin{figure}[ht]
    {    \centering
     \subfigure[mean based RTI.]{
        \includegraphics[scale = .23]{figure/patterpair/open-mean-eps-converted-to.pdf}
        \label{fig:locationmeanlos}
    }
   \subfigure[variance based RTI]{
        \includegraphics[scale = .23]{figure/patterpair/open-variance-eps-converted-to.pdf}
        \label{fig:fadelevelmeanlos}
    }
        \caption{The tracking performance of \emph{Pattern Pair} selection methods in the indoor LOS environment (\emph{Experiment 1})}
        \label{fig:chosenpatternpair_los}}
          \vspace{-2.5mm}
\end{figure} 

\begin{figure}[ht]
      {  \centering
     \subfigure[mean based RTI.]{
        \includegraphics[scale = .23]{figure/patterpair/wall-mean-eps-converted-to.pdf}
        \label{fig:locationmeannlos}
    }
   \subfigure[variance based RTI]{
        \includegraphics[scale = .23]{figure/patterpair/wall-variance-eps-converted-to.pdf}
        \label{fig:fadelevelmeannlos}
    }
    \caption{The tracking performance of \emph{Pattern Pair} selection methods in the indoor NLOS ``through-wall'' environment (\emph{Experiment 2})}
    \label{fig:chosenpatternpair_nlos}}
      \vspace{-2.5mm}
\end{figure} 

In the NLOS ``through-wall'' environment, variance based RTI (Fig.~\ref{fig:fadelevelmeannlos}) significantly outperforms mean based (Fig.~\ref{fig:locationmeannlos}) because the radio propagation environment is significantly more complicated than that of the LOS environment. Overall, Fig.~\ref{fig:chosenpatternpair_nlos}
%~\ref{fig:locationmeannlos} and \ref{fig:fadelevelmeannlos} 
shows that the Fade Level method is consistently better than the other methods. This is because the Fade Level method attempts to select the \emph{Pattern Pairs} that are \emph{least in deep fade} to provide the most information as discussed in Section~\ref{subsubsec:fade_level_method}.
% \tv{can we explain why Fade level is best?}
Therefore, for Experiments 3 and 4, we will use the \emph{Fade Level} method for \emph{Pattern Pair} selection and use 9 \emph{Pattern Pairs}. 


%\emph{we chose Fade Level method and the number of \emph{Pattern Pair}s equaled to 9 as the parameter of dRTI} in next section to compared
% to the performance of traditional RTI and cRTI.



Fig.~\ref{fig:chosenpatternpair_los} and \ref{fig:chosenpatternpair_nlos}
%~\ref{fig:locationmeanlos}, \ref{fig:fadelevelmeanlos}, \ref{fig:locationmeannlos} and \ref{fig:fadelevelmeannlos}
 also show that the Location method  performs poorly compared to the other methods. Nevertheless, it can still provide reasonably good tracking performance (approximately $0.5$ metre) for both LOS (Fig.~\ref{fig:locationmeanlos}) and NLOS (Fig.~\ref{fig:fadelevelmeannlos})
environments. Furthermore, the Location method does not require calibration, which makes it very useful in emergency response applications. 


%As for comparing the three methods in mean-based RTI and variance-based RTI, 
%%Expect Fade Level method, 
%Location method and PRR method in RSS based RTI cannot performs as good as there in variance based RTI. 
%On the other hand, the performance of Fade Level method is not different to the optimal performance in variance-based method.
%Talking about the the variance-based methods, Fade Level method still shows the best performance, while the performance of Location method is close to Fade Level method when the number of selected patter pair number arrives at 9 for Experiment 1 and
%1 for Experiment 2.
%For PRR method in both experiments, $e_{rms}$ get the similar level of the other two methods after the number of the pattern pair gets 9.
%
%Since Fade Level method performs best among three method and the performance does not increase after the number of pattern pair get 4, we use fade level method in the following experiments and set 4 as the default number of patter pair. 



%pairselectionbigfigure_crop
%\begin{figure*}[!ht]
%    \centering
%     \subfigure[]{
%        \includegraphics[scale = .1]{figure/LOS/location_mean.eps}
%        \label{fig:locationmeanlos}
%    }
%   \subfigure[]{
%        \includegraphics[scale = .1]{figure/LOS/fadelevel_mean.eps}
%        \label{fig:fadelevelmeanlos}
%    }
%    \subfigure[]{
%    \includegraphics[scale = .1]{figure/LOS/PPR_mean.eps}    
%    \label{fig:prrmeanlos}
%    }
%    \subfigure[]{
%    \includegraphics[scale = .1]{figure/LOS/location_variance.eps}    
%    \label{fig:locationvariancelos}
%    }
%   \subfigure[]{
%        \includegraphics[scale = .1]{figure/LOS/fadelevel_variance.eps}
%        \label{fig:fadelevelvariancelos}
%    }
%   \subfigure[]{
%        \includegraphics[scale = .1]{figure/LOS/PPR_variance.eps}
%        \label{fig:pprvariancelos}
%    }
%
%   \caption{performance of pattern pair selection methods in Experiment 1: LOS ``open space'' environment (a) Location(mean based) (b) Fade Level(mean based) (c) PPR(mean based) (d) Location(variance based)  (e)Fade Level(variance based)(f)PRR(variance based)}\label{fig:chosenpatternpairOpen}
%\end{figure*}
%
%\begin{figure*}[!ht]
%    \centering
%      \subfigure[]{
%        \includegraphics[scale = .1]{figure/NLOS/location-mean.eps}
%        \label{fig:locationmeannlos}
%    }
%   \subfigure[]{
%        \includegraphics[scale = .1]{figure/NLOS/fadelevel-mean.eps}
%        \label{fig:fadelevelmeannlos}
%    }
%    \subfigure[]{
%    \includegraphics[scale = .1]{figure/NLOS/PPR-mean.eps}    
%    \label{fig:prrmeannlos}
%    }
%   \subfigure[]{
%    \includegraphics[scale = .1]{figure/NLOS/location-variance.eps}    
%    \label{fig:locationvariancenlos}
%    }
%    \subfigure[]{
%        \includegraphics[scale = .1]{figure/NLOS/fadelevel-variance.eps}
%        \label{fig:fadelevelvariancenlos}
%    }
%   \subfigure[]{
%        \includegraphics[scale = .1]{figure/NLOS/PPR-variance.eps}
%        \label{fig:pprvariancenlos}
%    }
%
%   \caption{performance of pattern pair selection methods in Experiment 2: NLOS ``through-wall'' environment (a) Location(mean based) (b) Fade Level(mean based) (c) PPR(mean based) (d) Location(variance based)  (e)Fade Level(variance based)(f)PRR(variance based) }\label{fig:chosenpatternpairWall}
%\end{figure*}
% 

\begin{figure*}[th]
{
    \centering
       \subfigure[mRTI]{
        \includegraphics[scale = .6]{figure/LOS_exp3/map/mRTI_LOS.pdf}
        \label{fig:mRTILOS}
    }
    \subfigure[cRTI (RSS mean)]{
    \includegraphics[scale = .6]{figure/LOS_exp3/map/cRTIm_LOS.pdf}    
    \label{fig:cRTImLOS}
    }
     \subfigure[dRTI (RSS mean)]{
        \includegraphics[scale = .6]{figure/LOS_exp3/map/dRTIm_LOS.pdf}
        \label{fig:dRTImLOS}
    }
     \caption{The tracking performance of mean based RTI in the LOS experiment of omni RTI, cRTI, and dRTI. The red lines 
     are the trajectory estimation by different methods, and the dotted blue lines are the ground truth (\emph{Experiment 3}).}
           \label{fig:trackinglos_mean}
           }
       \vspace{-2.5mm}
\end{figure*}


\subsection{Comparing omni RTI, cRTI and dRTI}
\label{subsec:comprti}
%\vspace{-2.5mm}

Note that in this section we use mRTI and vRTI to refer to the mean-based and variance-based  \emph{omni} RTI because \bo{these} are names used in previous work. For dRTI and cRTI, it will be clear from the heading whether it is mean or variance based. 


\subsubsection{\emph{Experiment 3}: LOS  environment} \label{subsubsec:los}


\vspace{-2.5mm}
\begin{table}[ht]
\footnotesize
   \centering
   \caption{$e_{rms}$ of mean based RTI in LOS experiment (\emph{Experiment 3}).}
    \begin{tabular}{ | l | l | l | l | }
\hline
method & mRTI  & cRTI & dRTI \\   \hline
$e_{rms} $(m) & $0.9054$  & $0.7872$ &$0.5221$ \\ 
  \hline
    \end{tabular}
      \label{tab:LOSerror_mean}
  \vspace{-2.5mm}
\end{table}

\textbf{Mean based methods:} Fig.~\ref{fig:trackinglos_mean} shows the tracking performance of mRTI, cRTI and dRTI in the indoor LOS environment. It depicts that the trajectory estimation 
of dRTI is significantly closer to the ground truth compared to both mRTI and cRTI. Table~\ref{tab:LOSerror_mean}
shows the $e_{rms}$ of mRTI, cRTI and dRTI are 0.9054 m, 0.7872 m, and 0.5221 m respectively.
dRTI achieved a tracking performance improvement of approximately 42\% (compared to mRTI) and 
approximately 34\% (compared to cRTI).  The CDFs for different
mean based RTI methods are presented in Fig.~\ref{fig:cdfmLOS}. The results show
that the 90th percentile tracking errors for mRTI, cRTI, and dRTI
were approximately 1.5 m, 1.2 m and 0.7 m respectively. dRTI achieved
performance improvements of approximately 53\% (compared to mRTI) 
and 42\% (compared to cRTI) respectively.




\begin{figure}[ht]
{
\centering
  % \subfigure[CDF for mean based RTI methods]{
        \includegraphics[scale = .35]{figure/LOS_exp3/CDF-mean-eps-converted-to.pdf}
        \caption{The CDFs of mean based RTI methods (\emph{Experiment 3}).}
            \label{fig:cdfmLOS} 
            }
        %}
    \vspace{-2.5mm}
\end{figure}

\textbf{Variance based methods:} Fig.~\ref{fig:trackinglos_variance} shows the tracking performance of vRTI, cRTI and dRTI demonstrating that the trajectory estimation 
of dRTI is significantly closer to the ground truth compared to both vRTI and cRTI.
Table~\ref{tab:LOSerror_variance}
shows, the $e_{rms}$ of vRTI, cRTI and dRTI are 0.7196 m, 0.5565 m, and 0.4340 m respectively.
dRTI achieved a tracking performance improvement of approximately 40\% (compared to vRTI) and 
approximately 22\% (compared to cRTI).  The CDFs for different
variance based RTI methods are presented in Fig.~\ref{fig:cdfvLOS}. The 90th percentile tracking errors for vRTI, cRTI, and dRTI
were approximately 1.1 m, 0.75 m and 0.7 m respectively. dRTI achieved
performance improvements of approximately 36\%  (compared to vRTI) 
and 7\% (compared to cRTI) respectively.



\begin{figure*}[ht]
{
    \centering
       \subfigure[vRTI]{
        \includegraphics[scale = .6]{figure/LOS_exp3/map/vRTI_LOS.pdf}
        \label{fig:vRTILOS}
    }
    \subfigure[cRTI (RSS variance)]{
    \includegraphics[scale = .6]{figure/LOS_exp3/map/cRTIv_LOS.pdf}    
    \label{fig:cRTIvLOS}
    }
    \subfigure[dRTI (RSS variance)]{
        \includegraphics[scale = .6]{figure/LOS_exp3/map/dRTIv_LOS.pdf}
        \label{fig:dRTIvLOS}
  }

    \caption{The tracking performance of variance based RTI in the LOS experiment of RTI, cRTI, and dRTI. The red lines 
     are the trajectory estimation by different methods, and the dotted blue lines are the ground truth (\emph{Experiment 3}).}
     \label{fig:trackinglos_variance}
     }
       \vspace{-2.5mm}
\end{figure*}

\begin{table}[ht]
\footnotesize
   \centering
   \caption{$e_{rms}$ of  variance based RTI in LOS experiment (\emph{Experiment 3}).}
    \begin{tabular}{ | l | l | l | l | }
\hline
method & vRTI  & cRTI & dRTI \\   \hline 
$e_{rms} $\bo{(m)} & $0.7196$ & $0.5565$  & $0.4340$ \\
 \hline
    \end{tabular}
\label{tab:LOSerror_variance}
  \vspace{-2.5mm}
\end{table}


%\begin{figure} [ht]
%    %\subfigure[]{
%     \centering
%    \includegraphics[scale = .30]{figure/LOS_exp3/dRTIxy_los_exp2.pdf} 
%    \caption{The tracking performance in X and Y coordinates for variance based dRTI.}
%    \label{fig:xyLosVaraince}
%    %}
%\end{figure}

\begin{figure}[ht]
   { \centering
    %\subfigure[CDF for variance based RTI methods]{
    \includegraphics[scale = .35]{figure/LOS_exp3/CDF-variance-eps-converted-to.pdf} 
    %}
  \caption{The CDFs of variance based RTI methods (\emph{Experiment 3}).}
      \label{fig:cdfvLOS}
  }
    \vspace{-2.5mm}
  %\label{fig:}
\end{figure}  



%\begin{figure}[!ht]
%    \centering
%    \includegraphics[scale = 0.4]{figure/LOS/RMSE-bar-LOS.eps}
%    \caption{ RMSE in for different methods in Experiment 1 \needtocheck{(not add yet)} }\label{fig:chosenpatternpair}
%\end{figure} 



% this part is about the FN and FP for experiment 3
\begin{figure}[ht]
    {    \centering
     \subfigure[mean based RTI.]{
        \includegraphics[scale = .35]{figure/FNFP/open_fading9_mean-eps-converted-to.pdf}
        \label{fig:FNFPmeanlos}
    }
   \subfigure[variance based RTI]{
        \includegraphics[scale = .35]{figure/FNFP/open_fading9_var-eps-converted-to.pdf}
        \label{fig:FNFPvarlos}
    }
        \caption{The statistics for Radio Link Attenuation FN and FP in the indoor LOS environment (\emph{Experiment 3})}
        \label{fig:FNFP_los}}
          \vspace{-2.5mm}
\end{figure} 
\textbf{Radio Attenuation FN and FP:} 
\bo{
Fig.~\ref{fig:FNFP_los} shows the statistics of radio link attenuation FN and FP. 
%It is a tradeoff between the number of FN and FP. We can clear see the line of dRTI is below those of m/vRTI and cRTI, which indicates the summary of FN and FP of dRTI is smaller than that of omni-directional RTI and cRTI. 
 The figure compares three classes of methods: m/vRTI,cRTI and dRTI. For each method, we vary the threshold used to determine whether a link is FP and FN. We know from the standard theory on statistical hypothesis testing that there is a trade-off between FP and FN. This trade-off is clearly visible in the figure. We know that if a method can achieve lower FP and FN, then it is a better method. It is clear from Fig.~\ref{fig:FNFP_los} that dRTI has the lowest FP and FN compared with the other two methods. 
 These statistics support the hypotheses in Section \ref{sec:hypoFNFP} and explain the reason why dRTI perform better than omni-directional RTI and cRTI. 
}


%===============================%

\vspace{-2.5mm}
\subsubsection{\emph{Experiment 4}:  NLOS ``Through-wall'' environment} 
\label{subsubsec:nlos}

\begin{table}[ht]
\footnotesize
   \centering
   \caption{$e_{rms}$ of mean based RTI in NLOS experiment (\emph{Experiment 4}).}
    \begin{tabular}{ | l | l | l | l | }
\hline
method & mRTI  & cRTI & dRTI \\   \hline 
$e_{rms} $\bo{(m)} & $1.4922 $  & $0.8580 $ & $0.7506 $ \\   
 \hline
    \end{tabular}
\label{tab:NLOSerror_mean}
  \vspace{-2.5mm}
\end{table}


\textbf{Mean based methods:} Compared to the performance in the LOS environment in Section~\ref{subsubsec:los},
the NLOS ``through-wall'' environment is significantly more challenging for RTI, and the
tracking errors are significantly higher for all RTI methods.
However, Fig.~\ref{fig:trackingwall_mean} shows the tracking performance of 
mRTI, cRTI and dRTI in a NLOS ``through-wall'' environment. It demonstrates that the trajectory estimation 
of dRTI is significantly closer to the ground truth compared to both mRTI and cRTI. Table~\ref{tab:NLOSerror_mean}
shows, the $e_{rms}$ of mRTI, cRTI and dRTI are 1.4922 m, 0.8580 m, and 0.7506 m respectively.
dRTI achieves a tracking performance improvement of approximately 50\% (compared to mRTI) and 
approximately 12\% (compared to cRTI).  The CDFs for different
mean based RTI methods were showed in Fig.~\ref{fig:cdf_mean_4}. The 90th percentile tracking errors for mRTI, cRTI, and dRTI
were  approximately 2.4 m, 1.3 m and 1.2 m respectively. dRTI achieved
performance improvements of approximately 50\% (compared to mRTI) 
and 8\% (compared to cRTI) respectively.

%In this experiment, we compare dRTI with mRTI, vRTI and cRTI. Both RSS variance based RTI (Fig. \ref{fig:trackingwall_variance}) and RSS mean based RTI(Fig. \ref{fig:trackingwall_mean}) are  present. 
%From Fig. \ref{fig:trackingwall_variance} and Fig. \ref{fig:trackingwall_mean}, dRTI performance the best(Fig. \ref{fig:dRTIvNLOS} and Fig.~\ref{fig:dRTImNLOS} ) , while the tracking performance of mRTI(see Fig. \ref{fig:mRTINLOS}) or vRTI(see Fig. ~\ref{fig:vRTINLOS}) cannot show the accurate results in the most of the time.  Even so, the tracking performance of cRTI(see Fig.~\ref{fig:cRTIvNLOS} and Fig. ~\ref{fig:dRTImNLOS}) is clearly not as good as dRTI(see Fig.~\ref{fig:dRTIvNLOS} and Fig. ~\ref{fig:dRTImNLOS}). The performance of cRTI is better than vRTI and mRTI, because the multiple channels are used for RTI and fade level channel selection method is applied to choose the ``best'' channels for RTI. 
%To show the intuition of the accuracy for dRTI, we also present the tracking performance in X and Y coordinates(See Fig.~\ref{}).

\begin{figure*}[ht]
{
    \centering
       \subfigure[mRTI]{
        \includegraphics[scale = .60]{figure/NLOS/mRTI_NLOS.pdf}
        \label{fig:mRTINLOS}
    }
    \subfigure[cRTI (RSS mean)]{
    \includegraphics[scale = .60]{figure/NLOS/cRTIm_NLOS.pdf}    
    \label{fig:cRTImNLOS}
    }
     \subfigure[dRTI (RSS mean)]{
        \includegraphics[scale = .60]{figure/NLOS/dRTIm_NLOS.pdf}
        \label{fig:dRTImNLOS}
          \vspace{-2.5mm}
    }
     \caption{The tracking performance of mean based RTI in the NLOS ``through-wall'' experiment of RTI, cRTI, and dRTI. The red lines 
     are the trajectory estimation by different methods, and the dotted blue lines are the ground truth (\emph{Experiment 4}).}
          \label{fig:trackingwall_mean}}
\end{figure*}

\begin{figure}[ht]
   { \centering
   %\subfigure[CDF for mean based RTI methods]{
        \includegraphics[scale = .35]{figure/NLOS/CDF-mean-s4-eps-converted-to.pdf}
        \label{fig:cdfmNLOS}
    %}
    \label{fig:cdfNLOS}
  \caption{The CDFs of mean based RTI methods (\emph{Experiment 4}).}
  \label{fig:cdf_mean_4}
  }
    \vspace{-2.5mm}
\end{figure}  


\begin{table}[ht]
\footnotesize
   \centering
   \caption{$e_{rms}$ of variance based RTI in NLOS experiment (\emph{Experiment 4}).}
     \begin{tabular}{ | l | l | l | l | }
\hline
method & vRTI  & cRTI & dRTI \\   \hline 
$e_{rms} $\bo{(m)} & $1.0432 $ & $0.8574 $ & $0.6734 $ \\ 
\hline
    \end{tabular}
    \label{tab:NLOSerror_variance}
  \vspace{-2.5mm}
\end{table}


\textbf{Variance based methods:} Previous work showed that variance based RTI methods significantly outperformed
mean based RTI methods in NLOS ``through-wall'' environments~\cite{WilsonVRTI:2011}.
Our results in Tables~\ref{tab:NLOSerror_mean} and \ref{tab:NLOSerror_variance} also confirm this finding.
Furthermore, Fig.~\ref{fig:trackingwall_variance} shows that the trajectory estimation 
of dRTI is significantly closer to the ground truth compared to both vRTI and cRTI. Table~\ref{tab:NLOSerror_variance}
also
shows, the $e_{rms}$ of vRTI, cRTI and dRTI are 1.0432 m, 0.8574 m, and 0.6734 m respectively.
dRTI achieves a tracking performance improvement of approximately 35\% (compared to vRTI) and 
approximately 21\% (compared to cRTI).  The CDFs for different
variance based RTI methods are presented in Fig.~\ref{fig:cdf_variance_4}. The 90th percent of tracking errors for vRTI, cRTI, and dRTI
were  approximately 1.7 m, 1.2 m and 1 m respectively. dRTI achieves
performance improvements of approximately 41\% (compared to vRTI) 
and 17\% (compared to cRTI) respectively.



\begin{figure*}[ht]
    {\centering
       \subfigure[vRTI]{
        \includegraphics[scale = .6]{figure/NLOS/vRTI_NLOS.pdf}
        \label{fig:vRTINLOS}
    }
    \subfigure[cRTI(RSS variance)]{
    \includegraphics[scale = .6]{figure/NLOS/cRTIv_NLOS.pdf}    
    \label{fig:cRTIvNLOS}
    }
            \subfigure[dRTI(RSS variance)]{
        \includegraphics[scale = .6]{figure/NLOS/dRTIv_NLOS.pdf}
        \label{fig:dRTIvNLOS}
  }
  %\vspace{-2.5mm}
    \caption{The tracking performance of variance based RTI in NLOS ``through-wall'' experiment of RTI, cRTI, and dRTI. The red lines 
     are the trajectory estimation by different methods, and the dotted blue lines are ground true (\emph{Experiment 4}).}
    \label{fig:trackingwall_variance}}
    \vspace{-2.5mm}
\end{figure*}


%\begin{figure} [ht]
%    %\subfigure[]{
%        \centering
%      \includegraphics[scale = .30]{figure/NLOS/dRTIxy_nlos_s4.pdf} 
%    \label{fig:cdfvNLOS}
%    \caption{The tracking Performance in X and Y coordinates}
%    %}
%\end{figure}

\begin{figure}[ht]
    %\subfigure[CDF for variance based RTI methods]{
{\centering    
    \includegraphics[scale = .35]{figure/NLOS/CDF-variance-s4-eps-converted-to.pdf} 
    \label{fig:cdfvNLOS}
     \caption{The CDFs of variance based RTI methods (\emph{Experiment 4}).}\label{fig:cdf_variance_4}
    %}
    }
    \vspace{-2.5mm}
\end{figure}


% the part shows the statistics of for Experiment 4
\begin{figure}[ht]
      {  \centering
     \subfigure[mean based RTI.]{
        \includegraphics[scale = .35]{figure/FNFP/wall_fading9_mean-eps-converted-to.pdf}
        \label{fig:FNFPmeannlos}
    }
   \subfigure[variance based RTI]{
        \includegraphics[scale = .35]{figure/FNFP/wall_fading9_var-eps-converted-to.pdf}
        \label{fig:FNFPvarnlos}
    }
    \caption{The statistics for Radio Link Attenuation FN and FP  in the indoor NLOS ``through-wall'' environment (\emph{Experiment 4})}
    \label{fig:FNFP_nlos}}
      \vspace{-2.5mm}
\end{figure} 

\textbf{Radio Attenuation FN and FP:} 
\bo{
Fig.~\ref{fig:FNFP_nlos} shows similar results compared to those discussed in Section~\ref{subsubsec:los}. The figure shows that dRTI has the lowest number of FP and FN compare to those of omni-directional RTI and cRTI. 
%These statistics support the hypotheses in Section \ref{sec:hypoFNFP} and explain the reason why dRTI perform better than omni-directional RTI and cRTI. 
}

%the best performance omni directional RTI achieved in LOS and NLOS environment is 0.7196 m and 1.0432 m respectively. 
%The best performance cRTI achieved in LOS and NLOS environment is 0.5565 m and 0.8574 m respectively. 
%the best performance dRTI achieved in LOS and NLOS environment is 0.4340 m and 0.67 m respectively.
%dRTi outperformed 


%Table~\ref{tab:NLOSerror} shows  $e_{rms}$ for each method, which can give the same conclusion. dRTI performs than the-state-of-the-art RTI method cRTI, vRTI and mRTI based on omni-directional antennas.  


%\begin{figure}[!ht]
%    \centering
%    \includegraphics[scale = 0.4]{figure/NLOS/RMSE-bar-NLOS.eps}
%    \caption{ RMSE in for different methods in Experiment 2 }\label{fig:chosenpatternpair}
%\end{figure} 

%To look into the tracking performance, we make the Cumulative distribution function(CDF) for the tracking error in Fig.~\ref{fig:cdfNLOS}.  Fig.~\ref{fig:cdfvNLOS} is the CDF for variance-based RTI methods, which shows about 85\% of tracking error of dRTI is below 1 meter, while this percentage for cRTI and vRTI is no more than 60\%.  
%Fig.~\ref{fig:cdfvNLOS} also confirms the similar fact for mean-based RTI, 80\% of the tracking error for dRTI is below 1 meter, while cRTI and mRTI only have 60\% and 50\% of the tracking error below 1 meter respectively. 
%For the comparison between RSS variance based and RSS mean based method, even though $e_{rms}$ is close, the maximum error for RSS mean based RTI (1.7 meter for dRTI with RSS mean) is higher than that for RSS variance(1.3 meter for dRTI with RSS mean).   


%\vspace{-2.5mm}
%\subsection{Practical Issue in the ``Through-wall'' Experiment}
%The tracking results in Fig.~\ref{fig:praticalissue} is from an ``through-wall'' RTI experiment by dRTI with RSS variance.
%
%In the experiment, we find the location of the nodes have a change to affect the tracking accuracy. As there are only 7 nodes with EDS antenna for localising the monitored person deployed in our experiment, the density is quite low compared to other RTI experiments like experiments in~\ref{ZhaoRobust2011, KaltiokallioBP12, ZhaoKRTI:2013,Kaltiokalliograndma2012,WilsonRTI:2010,WilsonVRTI:2011}. Therefore, it is critical to optimise the deployment of the nodes. As the low density of the nodes, 7 nodes need to be deployed around AoI uniformly.  However, from the observation in Fig.\ref{fig:praticalissue}, the distance between the nodes with an EDS antenna  and AoI affects the localisation performance. Specifically, in the area emphasised by the green circle, the monitored person walks too close to the nodes(see the blue square in Fig.~\ref{fig:praticalissue}), so the estimated path(see the red path in the green circle in Fig.~\ref{fig:praticalissue}) is not accurate in this area. On the other hand, the estimated path in the other area is good. 
%
%In the experiment, we plan to walk away from the nodes in the green circle. Actually, another option is to move the node away from the path, but the node is so close to the wall which is impossible to move it away much further.
%
%\begin{figure}[!ht]
%    \centering
%    \includegraphics[scale = 0.7]{figure/praticalissue_v2.pdf}
%    \caption{ Example of practical issue}\label{fig:praticalissue}
%\end{figure} 
%
%
%
%From this part, we come to the conclusion that the nodes are not able to be deployed too close to AoI, otherwise the system may fail to give the accurate estimation near the node(s).
%


\vspace{-2.5mm}
\subsection{Energy Cost}
We measured the energy consumption of our dRTI system by connecting a node to a 10 ohm resistor in series of the power supply and measured the voltage across the resistor by an oscilloscope. %When the node send the packets, we store and observer the voltage for the energy consumption.
For small beacon packets whose payload length is 5 bytes, consisting of node ID (2 bytes), transmit direction (1 byte), and sequence number (2 bytes), the energy consumption was approximately 55 $\mu$J. For large packets for transferring RSS measurements to the base station with payload length of 62 bytes, the energy consumption was approximately 179 $\mu$J.
 %The frequency of sending the small packets is 36 per 0.8 second, while that of the large packet is 1 per 0.8 seconds. 
 The transmission time for the 5-byte beacon packets and 62-byte large packets were approximately 0.72 ms and 2.85 ms respectively.
The energy consumption was measured when the transmit power is set to the maximum value of 31.



intro.tex
\vspace{-2mm}
\section{Introduction}\label{intro}
\label{sec:intro}
% the whole idea
This paper explores the use of \bo{directional} antennas to improve the accuracy of radio tomographic imaging (RTI).
RTI uses a network of small inexpensive wireless devices, placed in the periphery of an Area of Interest (AoI), to estimate the locations of people and objects within the AoI~\cite{WilsonRTI:2010,WilsonVRTI:2011}. A distinguishing feature of RTI is that it is \emph{device free}~\cite{Youssef:2007} in the sense that the people and objects to be tracked do not have to wear any special purpose devices on them. This makes RTI significantly less intrusive compared with many other localisation methods which require people/objects to carry a radio device or tag. In addition, RTI can function in many challenging environments. RTI can work in both line-of-sight (LOS) and non-LOS (NLOS) environments. RTI can work with no or poor lighting conditions because it uses radio waves rather than visible light. The wireless devices for RTI can be placed outside the walls to enable them to \emph{see through walls} or smoke to locate people or objects within the walls. Therefore, RTI has
a broad range of applications in emergency response, security (e.g. hostage rescue), health care, and assisted living etc.~\cite{bocca2013radio,Kaltiokalliograndma2012}.

%This paper explores the use of directional antennas to improve the accuracy of Radio Tomographic Imaging (RTI).
%RTI uses a network of small inexpensive wireless devices, placed in the periphery of an Area of Interest (AoI), to estimate the locations of people and objects within the AoI~\cite{WilsonRTI:2010,WilsonVRTI:2011}. A distinguishing feature of RTI is that it is \emph{device free} in the sense that the people and objects to be tracked do have not to wear any special purpose devices on them ~\cite{Youssef:2007}. This makes RTI significantly less intrusive compared with many other localisation methods which require people/object to carry a radio device or tag. In addition, RTI can function in many challenging environments. RTI can work in both Line-of-Sight (LOS) and Non-LOS (NLOS) environments. RTI can work with no or poor lighting conditions because it uses radio waves rather than visible light. The wireless devices for RTI can be placed outside the walls to enable them to ``\emph{see through the walls}" or smoke to locate people or objects within the walls. Therefore, RTI has
%a broad range of applications in emergency response, security (e.g. hostage taking), health care, and assisted living etc.~\cite{bocca2013radio,Kaltiokalliograndma2012}.
%
%

\begin{figure}[t]
\center
   %  \includegraphics[scale = 0.25]{figure/example.pdf}

   \subfigure[]{
        \includegraphics[scale = .22]{figure/example2-v3.pdf}
        \label{fig:example2}
    }
   \subfigure[]{
        \includegraphics[scale = .24]{figure/example1-v3.pdf}
        \label{fig:example1}
    }
       \subfigure[]{
        \includegraphics[scale = .21]{figure/example1c-v4-eps-converted-to.pdf}
        \label{fig:example3}
    }

    \caption{(a) A person blocks two radio links, creating a NLOS environment.  (b) The AoI is divided into voxels. An ellipse is used to model the area of attenuation between a pair of nodes.  (c) An example of an RTI image. The blue cross indicates the truth location of the obstruction. (Best view in colour.)}
    \label{fig:example}
    \vspace{-5mm}
\end{figure} 


%(a) Localisation using wireless waves. (b)An example image of radio tomography  (Picture view best in colour). The blue cross in (b) indicates the ground truth obstruction location.

The key idea behind RTI is that people/objects in the AoI present themselves as \emph{obstructions} to radio waves. For example, in Fig.~\ref{fig:example2}, a person stands in the paths of two radio links, and her presence can be detected by observing the \emph{changes} of some statistics of the qualities of the radio links. A more conspicuous change in these radio link quality statistics will result in better location estimate, as well as reduce the number of false positives and negatives. Previous work on RTI relies on omni-directional antennas, which radiate power isotropically in the horizontal plane. Multipath radio channels experience \emph{multipath fading}, in which arriving waves unpredictably experience constructive or destructive interference. Directional antennas reduce the spatial extent of significant multipath, and thus the effects of fading, by focusing the radiated power in some given directions. 
%\av{ I would mention Electronically Switched Directional Antennas. Not all directional antennas can be electronically controlled to set the direction of the maximum antenna gain. eg. simple Yagi Antenna} 
The benefits of RTI with directional antennas (dRTI) are twofold compared to their omni-directional counterparts. First, the presence of obstructions which block the direct paths will have significantly more impact on the link quality behaviour of directional antennas. Second, the 
presence of obstructions which are \emph{outside} the direct paths will have significantly less impact on the link quality of directional antennas. 
Therefore, directional antennas  can provide significantly better link quality observations to improve the RTI localisation accuracy. 

%RTI relies on radio link quality observations to estimate the presences of obstructions to the radio link peers. Therefore, in order
%to produce accurate tomography/tracking results, accurate 
%%\tv{I would put ``accurate'' to avoid having quality twice} 
%link quality behaviour  estimation is crucially important. Previous work relies on omni-directional antennas, which have an isotropic
%propagation model and suffer from complicated radio propagation behaviour such as \emph{deep fading} and \emph{shadowing}, especially in
%NLOS cluttered environments. On the other hand, directional antennas may be able to \emph{dynamically} focus the radiated power in one given direction. 
%%\av{ I would mention Electronically Switched Directional Antennas. Not all directional antennas can be electronically controlled to set the direction of the maximum antenna gain. eg. simple Yagi Antenna} 
%As a  result, the benefits of RTI with directional antennas (dRTI) are twofold compared to their omni-directional counterparts. First, the presences of obstructions 
%which block the direct paths will have significantly more impact on the link quality behaviour of directional antennas. Secondly, the 
%presences of obstructions which are \emph{outside} the direct paths will have significantly less impact on the link quality of directional 
%antennas. 
%In the other words, \emph{the variance of link quality will increase significantly when an object blocks the direct paths of radio links}.
%Therefore, directional antennas  can provide significantly better link quality observations in the presences of
%obstructions and improve the RTI localisation results. 





Directional antennas have been explored to improve the communication \bo{performance} on mobile phones and wireless networks previously~\cite{AmiriSani:2010:DAD:1859995.1860021, Liu:2009:DII:1592568.1592589}. 
%\av{I would cite relevant work here - e.g. SIGCOMM 2009,MOBICOM 2010}. 
However,
traditional directional antennas such as Yagi antennas have a large form factor and consume a large amount of energy to move from one direction to another direction, which makes them unsuitable for resource-impoverished Wireless Sensor Networks (WSNs) with small nodes. On the other hand,
 Electronically-Switched Directional (ESD) antennas \cite{nilsson2009directional} are significantly more energy efficient compared to transitional directional antennas,
 and enable \emph{dynamic} electronic control of direction of maximum gain. 
 % \av{ I would mention here - "these allow electronic control of direction of maximum antenna gain and have been shown feasible for low-power sensor networks}
Recently, Mottola et al.~\cite{LucaSecon2013} leveraged ESD antennas to alleviate wireless contention in WSNs. In this paper, we, for the first
time, explore the use of ESD antennas to improve RTI localisation accuracy. We detail the feasibility studies for an inexpensive and energy 
efficient dRTI WSN system with ESD antennas and answer the fundamental questions whether and to what extent dRTI
systems can improve tracking performance in practice. 

Although dRTI can significantly improve localisation accuracy, its overhead
 due to the use of directional antenna are high. Consider a transmitter and receiver, each equipped with a directional antenna that yields $n$ different directions, the total number of antenna direction pairs is $n^2$. Hence, conducting link quality measurements on all the possible antenna direction pairs results in higher communication overhead
 and energy consumption. Moreover, not all $n^2$ antenna direction pairs are useful for RTI localisation estimation. We therefore investigate three different methods to select antenna direction pairs to reduce overhead
 while maintaining accurate position estimation. The contributions of this paper are as follows:

%\begin{itemize}
1) We conduct comprehensive investigations to demonstrate that directional antennas can produce sharper changes in radio link quality statistics (both mean and variance) compared to their omni-directional counterparts. 

2) We carry out studies to understand how the choice of directional antenna pairs can impact on the radio link quality statistics. Based on these studies, we propose three methods to choose the best directional antenna pairs
%\av{We should not use term antenna links, directional links or maybe best directional to transmit and receive}  
to increase the accuracy of RTI while reducing the overhead of the system.
%\item We design dRTI,  which explores directional communications to improve the localisation and tracking accuracy of RTI, and present an energy efficient directional
%\av{ as I see in the paper, we do not clearly state how we improve the energy efficiency of the RTI system. as wen had earlier mentioned, energy is not an issue. should we use energy efficiency as an argument here ?} 
%SN RTI system with ESD antennas. 
%\tv{if we say energy efficient, I guess we need to say something about the energy consumption (have not checked if we do)} 

3) We design and implement dRTI, the first system that improves indoor tracking accuracy through the use of ESD antennas, and evaluate the performance of the proposed dRTI system in 
realistic LOS and NLOS environments. Our results show that the proposed dRTI system can improve the localisation 
accuracy significantly compared to state-of-the-art RTI system based on the mean of link quality (mRTI)~\cite{WilsonRTI:2010}, the variance of 
link quality (vRTI)~\cite{WilsonVRTI:2011} and multi-channel RTI (cRTI) using omni-directional antennas.
%\end{itemize}

The rest of this paper is organised as follows. Section~\ref{sec:background} presents background on RTI and ESD antennas. Section ~\ref{sec:methods} presents a few different studies: (1) The impact of obstructions on the link quality statistics for both directional and omni-directional antennas; (2) The variation of link quality statistics for different choices of directional antenna pairs. Based on these studies, we propose three different methods to choose effective directional antenna pairs to reduce overhead
 in dRTI. We present comprehensive evaluations of our dRTI system in Section~\ref{sec:experiments}. Related work is presented in Section~\ref{sec:related}. Finally, we conclude the paper 
%and discuss the future research directions 
in Section~\ref{sec:conclusion}.






method.tex
\vspace{-2mm}
\section{Radio Tomographic Imaging with Directional Communications}
\label{sec:methods}
%In this section, we discuss 

\vspace{-2mm}
\subsection{Superiority of Directional Communications}
\label{subsec:superiority}
An important question concerning the use of directional communications in RTI is how directional antennas can produce better RTI results compared to  omni. Since RTI relies on the change of link quality statistics to infer the presence of an obstruction, we can try to answer this question by comparing the impact of obstructions on the link quality in omni-directional and directional communications. The following discussion assumes power is measured in decibels. 

%The link quality behaviour observation is applied by RTI technology to estimate the attenuation image of the presence, so it is important to understand the radio propagation model to explain the advantage of directional antennas for RTI.
%To estimate the attenuation image of the presence, radio tomographic imaging technology takes advantage of the RSS measurement change when the monitored object attenuates the link. 

For omni-direction communications, the received power $P_{rx}(i,t)$ of link $i$ at time $t$ is given by~\cite{WilsonRTI:2010}: 
\begin{equation}
P_{rx}(i,t) = P_{tx}(i,t) - A(i,t) + n(i,t) \label{eqn:rssmodel}
\end{equation}
where 
\begin{equation}
A(i,t) = L(i,t) + S(i,t) - F(i,t)  \label{eqn:rssPL}
\end{equation}
where $P_{tx}(i,t)$ is the transmitter transmission power and $n(i,t)$ is the measurement noise. The term $A(i,t)$ is the total attenuation consisting of three parts: path loss $L(i,t)$, shadowing loss $S(i,t)$ and fading loss $F(i,t)$. The RSS measurement $R_i(t)$ for link $i$ is a quantised version of the received power $P_{rx}(i,t)$. In an open outdoor environment, an obstruction causes large shadowing loss and results in a drop in the link RSS. This can be detected by the original mRTI as discussed in Section~\ref{sec:background}. However, the indoor NLOS environment is \emph{drastically} different. Multi-path fading in an indoor environment can cause both constructive and destructive interference. This means that, when an obstruction blocks a radio link, the RSS of that link can \emph{decrease}, \emph{increase}, or even \emph{remain unchanged}. In this situation, vRTI, which uses the variance of RSS as the link quality statistics, performs better than the original mRTI~\cite{WilsonVRTI:2011}.  



%as the indicator of the motion~
 %In other words, when the link is blocked, the larger RSS variance improves the RTI performance.
%\emph{Intuitively, when a LOS link is blocked, a larger decrease of RSS value for mRTI or a larger RSS variance (vRTI) will 
%improve the performance of RTI.} 

 \begin{figure*}[htb]
    \subfigure[RTI with omni-directional antennas. ]{
      \includegraphics[scale = 0.42]{figure/omniRTI_links_v2-eps-converted-to.pdf}
    \label{fig:rti_omni}
    }
    \subfigure[The produced image from (a) (Picture view best in colour). ]{
     \includegraphics[scale = 0.42]{figure/omniRTI_imaging_v2-eps-converted-to.pdf}
    \label{fig:image_omni}
    }
   \subfigure[RTI with \emph{directional} antennas.]{
       \includegraphics[scale = 0.42]{figure/dirRTI_links_v2-eps-converted-to.pdf}
    \label{fig:rti_dir}
    }
   \subfigure[The produced image from (c) (Picture view best in colour).]{
     \includegraphics[scale = 0.42]{figure/dirRTI_imaging_v2-eps-converted-to.pdf}
    \label{fig:image_dir}
    }
    \caption{Omni-directional RTI vs dRTI. The thicknesses of lines in (a) and (c) are proportional to the vRTI link quality statistics. The crosses show the true location of the obstruction. Fig.~(b) shows that the RTI image with a large localisation error because of a deep fade between Nodes 2 and 5 in (a). However, this fade has little impact on dRTI estimation shown in (d). }
    \label{fig:links_dir_vs_omni}
\end{figure*} 

%\tv{Fig 2, caption third line is someting wrong with the sentence}
 
% \begin{figure*}[htb]
%    \subfigure[RTI with omni-directional antennas. ]{
%     \includegraphics[scale = 0.28]{figure/omniRTI_links_v2.eps}
%    \label{fig:rti_omni}
%    }
%    \subfigure[The produced image from (a) (Picture view best in colour). ]{
%     \includegraphics[scale = 0.28]{figure/omniRTI_imaging_v2.eps}
%    \label{fig:image_omni}
%    }
%   \subfigure[RTI with \emph{directional} antennas.]{
%     \includegraphics[scale = 0.28]{figure/dirRTI_links_v2.eps}
%    \label{fig:rti_dir}
%    }
%   \subfigure[The produced image from (c) (Picture view best in colour).]{
%     \includegraphics[scale = 0.4]{figure/dirRTI_imaging_v2.eps}
%    \label{fig:image_dir}
%    }
%    \caption{Omni-directional RTI vs dRTI. The thicknesses of lines in (a) and (c) are proportional to the vRTI link quality statistics. The crosses show the true location of the obstruction. Fig.~(b) shows that the RTI image with a large localisation error because of deep fade between Nodes 2 and 5 in Fig.~(a). However, this fade had little impact on dRTI estimation shown in (d). }
%    \label{fig:links_dir_vs_omni}
%\end{figure*} 

For directional communications, the received power $P_{rx}(i,t)$ between a pair of transmission and received antennas (here the index $i$ refers an antenna pair) depends on their relative orientation specified by zenith $\phi$ and azimuth $\theta$. \cite{AndersonDirMol2009} proposes the model: 
 \begin{equation}
P_{rx}(i,t)  \propto f(\phi,\theta)  \times x(\phi,\theta)
\label{eqn:rssdir}
\end{equation}
where $f(\phi,\theta)$ is a direction-specific antenna gain function and $x(\phi,\theta)$ is an environment-specific offset function. The directional-specific gain is often touted as the advantage of using directional antennas for communication because the transmitter and receiver can focus their respective sending and receive antenna gains to boost the signal-to-noise ratio of the communication~\cite{ramanathan2001performance, winters1998smart}. This generally holds for outdoor LOS communication. However, the question of whether directional antennas offer any advantages in an indoor environment, where NLOS and multi-path effects dominate, has only been studied recently. These studies are all empirical because it is difficult to model the environment-specific offset function $x(\phi,\theta)$ analytically. 

In the study by Lakshmanan et al.~\cite{Lakshmanan2010}, the authors place a pair of wireless devices, each equipped with a MIMO antenna array, in an indoor environment. One device acts as the transmitter and the other acts as a receiver. The channel gains from the different antennas on the transmitter device to those on the receiver device are measured. The measurements show that these channel gains vary greatly. This means a slight change in antenna location can cause big changes in channel gain. In another study, Sani et al.~\cite{AmiriSani:2010:DAD:1859995.1860021} measure the channel gain in many different orientations by changing the sending and receive directions of the directional antennas. They find that directional antennas outperform omni over a large range of orientations but are significantly worse over a small range of orientations in an indoor environment. 

What do all these results mean for RTI? First, studies on the impact of obstructions on link quality of directional communication in an indoor environment do not exist. Second, radio propagation in an indoor environment is full of surprises and the only way to find out the truth is through real experiments. We therefore conduct our own experiments to determine, whether and to what extent, dRTI can improve the localisation accuracy. These experiments and their results will be described in this section and the next. 

In order to motivate future sections,
%\tv{is this a correct use of future?}, 
Fig.~\ref{fig:links_dir_vs_omni} compares the localisation error between omni-direction RTI and dRTI. These experiments are conducted within 10 ms of each other so their channel conditions can be assumed to be \emph{comparable}. The RTI image for omni in Fig.~\ref{fig:image_omni} shows a larger error compared to that of dRTI in Fig.~\ref{fig:image_dir}. In order to explain this difference, we look at the vRTI link quality statistics, which are indicated by the thickness of the lines connecting the node pairs, in Fig.~\ref{fig:rti_omni} and Fig.~\ref{fig:rti_dir} for omni and directional. 
Fig.~\ref{fig:rti_omni} shows that a deep fade between Nodes 2 and 5 has led omni-vRTI to believe that an obstruction is likely to be present between these two nodes, as shown by the high value of tomographic image for the voxels around the line joining these nodes. However, this deep fade had little impact on dRTI. 
%Furthermore, RTI reply on the \emph{change}, compared
% to RSS mean (mRTI), or the variance (vRTI) of radio link quality behaviour observations instead of the link quality observations themselves.
%, which is the difference between the transmit power and received power.
%In the specific channel of the same environment, the shadowing loss $S(i,t)$, the fade level $F(i,t)$ and the measurement noise $n(i,t)$ are considered as constant for both a directional antenna and an omni-directional antenna. Therefore the path loss $L(i,t)$ is the only variable in Equation ~\ref{eqn:rssPL}. 
Our hypothesis is that \emph{directional communication is sensitive to obstruction over a large range of orientations. This results in both larger changes in RSS and larger RSS variance. Moreover, these changes are less affected by fading.} 
%, and is more robust to noise.} 
We will provide empirical evidence to support this hypothesis next.  
 
 %Furthermore, the empirical RSS measurement from our experiments shows the directional antenna pair is more sensitive to the attenuation and robust to the noise.


%We investigate the theoretical evidence about the advantage of the directional antenna, but 
%After investigation, we have not found a feasible and effective radio propagation model to explain the advantage of the directional antennas in the indoor multi-path environment.
% Even though the difficulty of modelling se.

%The empirical RSS measurement is collect by a pair of transmitter and receiver which are deployed into two rooms. The material of the wall between two rooms is made of glass and wood. 

\vspace{-2mm}
\subsection{The Impact of Directional Communications on RSS Changes and Variance}
\label{subsec:variance}
This section presents empirical evidence that directional antenna links, when obstructed, produce larger changes in RSS and larger RSS variance in most antenna directions.  
%To verify the hypothesis of the advantage of directional antennas for the RTI systems, 

\vspace{-2mm}
\subsubsection{Experimental Setup}
\label{subsubsec:setup}
We employ two TelosB nodes running the Contiki operating system. Each node has an ESD antenna with 6 parasitic elements equally spaced at 60$^{\circ}$ apart. The nodes can \emph{dynamically} change the sending direction to one of the six directions or send omni-directionally by setting a digital output pin. It takes less than 1ms to change the sending direction. The RSS Indicator (RSSI) values are read from the TI CC2420 transceivers and converted to RSS values in dBm according to the transceiver datasheet. 

We conduct experiments in both indoor LOS and NLOS (``through-wall'') environments in our lab. We only report the results of the NLOS experiment here because we observe similar results for the LOS environment. For the NLOS environment, we place the two nodes, approximately 3 meters apart, in two different rooms. The wall between the rooms is made of glass and wood. We label the antenna directions with a number from 1 to 6. The \emph{Direction 1}s of the two nodes face each other, see Fig.~\ref{fig:antennafacing}. A person walks through the link of the two nodes \emph{multiple times} to block it. 

The transmitter sends small packets to the receiver in each of the six directions, as well as omni-direction as fast as possible, and the receiver receives the packets from all six directions and omni-direction. The transmission node ID, direction, and the sequence number are included in the packets. When the receiver receives a packet, it appends the receive direction and RSSI value into the packet as well. Therefore, we can figure out the transmit direction, receive direction and RSS value of each received packet. 
For a radio link from a transmitter to a receiver, there are 36 possible \emph{transmit-receive antenna direction pairs} and we will refer to them as  \emph{Pattern Pairs}. Furthermore, there are two links (uplink and downlink) between two nodes.

\begin{figure}[htb]
   \centering
    \includegraphics[scale = 0.45]{figure/Antenna_face_photo_v2.pdf}
    \caption{The physical ESD antenna directions of two nodes}\label{fig:antennafacing}
\end{figure} 

%\tv{In the figure it should say between the two nodes ``two directions face each other'' (remove to)}

%In this way, directional antennas enable multiple direction pair choices for two nodes. For example, instead of one link between the transmitter and receiver, 
%the direction of maximum antenna gain of ESD antenna can be configured to six different directions. 

\begin{figure*}[!ht]
  \centering
    \subfigure[RSS measurement change]{
        \includegraphics[scale = .20]{figure/largervarRSS-eps-converted-to.pdf}
        \label{fig:largervarRSS}
    }
     \subfigure[mRTI]{
    \includegraphics[scale = 0.25]{figure/largermean2bar-eps-converted-to.pdf}  
    \label{fig:largermeansta}
    }
    \subfigure[vRTI]{
    \includegraphics[scale = 0.25]{figure/largervar-eps-converted-to.pdf}  
    \label{fig:largervarsta}
    }
    \caption{ (a) RSS measurement of a selected \emph{Pattern Pair} and the omni-directional antenna. (b) The average mRTI over 36 \emph{Pattern Pairs} versus mRTI of omni. (c) The average vRTI over 36  \emph{Pattern Pairs} versus vRTI of omni. The error bars indicate one standard deviation.}\label{fig:largervariance}
\end{figure*} 

\vspace{-2mm}
\subsubsection{The Impact to RSS Changes and Variance}
% \av{ I am not able to see connection between uplink,downlink and 36 possible directional configuration between the sender and the receiver}. 
%The two nodes transmitted small packets to each other in each directional direction and omni-direction.  the ESD antenna that we used in this paper has six directions
Fig.~\ref{fig:largervarRSS} shows the RSS measurements of one of the \emph{Pattern Pairs} and omni when a person attenuates the radio signal between time 50 and 55. It is clear that the \emph{Pattern Pair} has a significantly bigger change in RSS measurement than omni. We compute the mRTI and vRTI of the RSS measurements for the 36 \emph{Pattern Pairs} and omni. (Note that mRTI and vRTI in Section \ref{subsec:bgRTI} are defined for a link. We simply consider a \emph{Pattern Pair} as a link in the calculation.) We compare the average mRTI and vRTI over the 36 \emph{Pattern Pairs} against that of omni in Fig.~\ref{fig:largermeansta} and \ref{fig:largervarsta}. These figures show that both the change in RSS and variance of RSS are bigger for directional antennas. In particular, the average RSS variance over all 36 \emph{Pattern Pairs} is almost twice that of omni. This experiment demonstrates that \emph{directional communications are indeed more sensitive to the obstruction, and produce larger changes in RSS and larger changes in RSS variance}.
%\tv{eith are indeed and produce larger or is indeed and produces larger}
Fig.~\ref{fig:largermeansta} and \ref{fig:largervarsta} also show the standard deviation of the mRTI and vRTI over the 36 \emph{Pattern Pairs}. The standard deviation is of almost the same magnitude as the average. We will discuss the variation of mRTI and vRTI among the \emph{Pattern Pairs} later. 




%Because the multi-path effect in the indoor environment, the relationship between the transmit power and the received power is not easy to predicted. 
%\cite{AndersonDirMol2009} suggests a model for the environmental effects on the directional antenna in wireless network, which is applied in our paper to explain the advantage of the directional antennas for RTI.  In ~\cite{AndersonDirMol2009} , a model for the path loss in the radio propagation considering the antenna gain as well as the environmental effect is suggested as Equation \ref{eqn:rssdir}.
%\begin{equation}
%P_{rx}(i,t) = P_{tx}(i,t) \times G_{tx} \times |PL| \times G_{rx} \times x \label{eqn:rssdir}
%\end{equation}
%where $PL$ is the path loss, $G_{tx}$ is the transmitter's antenna gain and $G_{rx}$ is the receiver's antenna gain. For the omni-directional antenna, the antenna gain is the constant The environmental offset $x$ is also considered to calculate the received power. The gain for the directional antennal depends on its zenith ($\phi$) and azimuth ($\theta$), denoted as $G_{tx} = g_{tx}(\phi,\theta)$ and $G_{rx} = g_{rx}(\phi{'},\theta{'})$. So Equation ~\ref{eqn:rssdir} can be also denoted as 
% \begin{equation}
%P_{rx}(i,t) = P_{tx}(i,t) \times g_{tx}(\phi,\theta) \times PL \times g_{rx}(\phi',\theta') \times x \label{eqn:rssdir}
%\end{equation}
%For the omni-directional antenna and directional antenna, we assume the amplitude of the path loss $PL$ is equal in the same environment, as well as the amplitude of the environmental effect offset $$x$. Therefore, the  gain of the directional antenna differs the received power. 
%In Equation \ref{eqn:rssdir}, $PL$ is a complex-valued path loss, relating the path between the transmitter and the receiver. $PL$ can be also expressed as $PL  = |PL|e^{ \varphi }$, and $\varphi$ is related to the location of the transmitter and the receiver. The same method is applied to $x$, i.e. $x = |x|e^{ \varphi' }$. In the real indoor environment, the transmitter discards the power in all the directions, we assume there is one main path for a pair of the transmitter and the receiver in our case. Therefore, Equation \ref{eqn:rssdir} is rewritten as 
%
% \begin{multline}
%P_{rx}(i,t) = max_{l \in paths} P_{tx}(i,t) \times g_{tx}(\phi_l,\theta_l) \\ \times 
% |PL|e^{ \varphi_l } \times g_{rx}(\phi_l',\theta_l') \times |x|e^{ \varphi'_l }   \label{eqn:rssdir}
%\end{multline}

%Here is the discussion about Equation ~\ref{eqn:rssdir}. When the transmitter and the receiver are deployed in the specific environment, we assume the same path is picked for both the situation that the pair of transmitter and receiver are directional and omni. 
%In this situation, the directional antenna pair and the omni antenna pair can share the amplitude of the environmental offset $|x|$ and the path loss $|PL|$. 
%In other words, for the omni-directional antenna and directional antenna, we assume the amplitude of the path loss $PL$ is equal in the same environment, as well as the amplitude of the environmental effect offset $x$. Therefore, the gain of the directional antenna differs the received power. 

%To support this, we take an example of the gain combination of the directional antenna pair. We assume the directional antenna only has three types of gain in the horizontal, largest gain or ``peak lobe'', medium gain or ``side lobe'', and small gain or ``back lobe''. In terms of the omni-directional antenna, the antenna gain is assumed as the same as the medium gain of the directional anttena.
 

%The following  figures ~\ref{fig:gain} show how the directional antenna gain affects the received power.
%Figure ~\ref{fig:gaindirbest} illustrates both the transmitter the receiver are using the direction with maximum gain, while Figure ~\ref{fig:gainomni} shows the gain for the omni-directional antenna. Since $PL$ is assumed as a constant, the received power of the directional antenna is larger than that of the omni-directional antenna, which lower the possibility of deep fading for the directional antenna. 
%When the link between the transmitter and the receiver is blocked by a person, $PL$ drops to $PL'$. 
%We also assume in the same environment, the same $PL'$ is applied to both the omni-directional antenna and the directional antenna. Therefore, the larger product  $g_{tx}(\phi,\theta)$ and $g_{rx}(\phi{'},\theta{'})$ amplifies the amplitude of RSS decrease, this explains the reason why the directional antenna performs larger RSS variance when the link is attenuated. 
%better than the omni-directional antenna in term of RTI.
%In other words, two ``peak lobe'' combination improves the RSS decrease amplitude compared with the omni-directional antenna pair. 

%Figure ~\ref{fig:gaindirok}   shows the receiver gain is represented by the much lower "side lobe", which is not able to perform as good as the example in Figure ~\ref{fig:gaindirbest} . As for the example in Figure ~\ref{fig:gaindirworst}, both the receiver and the transmitter use the 'back lobe'. RSS in this situation is even lower than that of the omni-directional antenna.

%\begin{figure*}[htb]
%    \subfigure[example of gain for omni-directional antenna ]{
%     \includegraphics[scale = .4]{figure/gain-omni.pdf}
%    \label{fig:gainomni}
%    }
%    \subfigure[example of gain for directional antenna ]{
%     \includegraphics[scale = .4]{figure/gain-dir-best.pdf}
%    \label{fig:gaindirbest}
%    }
%   \subfigure[example of gain for directional antenna ]{
%     \includegraphics[scale = .4]{figure/gain-dir-ok.pdf}
%    \label{fig:gaindirok}
%    }
%   \subfigure[example of gain for directional antenna ]{
%     \includegraphics[scale = .4]{figure/gain-dir-worst.pdf}
%    \label{fig:gaindirworst}
%    }
%   \caption{The example of gain for an omni-directional antenna and a directional antenna}\label{fig:gain}
%\end{figure*} 

%\subsection{Advantage of Directional Antennas}





%To verify our above hypothesis on the impact of the accuracy of the RTI systems by directional antennas, we conducted experiments in an indoor environment with two nodes as follows. We separated two nodes into 4 $m$ distance in a large empty room.  As introduced in Section~\ref{sec:background}, our ESD antennas have six directions and direction 2 and 6 are adjoining directions to direction 1 of our ESD antenna, shown in Figure~\ref{fig:antenna}.
%The \emph{direction 1}s of the two nodes face to each other, and a person walks through the LOS of two nodes \emph{twice} to block the links. The transmitter sends small packets to the receiver in each direction and omni-direction as well, and the receiver collects the packets also from both all the direction and omni-direction.
%The two nodes transmitted small packets to each other in each directional direction and omni-direction.
%\begin{figure}[t]
%    \subfigure[ESD antenna directions ]{
%     \includegraphics[scale = .3]{figure/Antenna_photo.pdf}
%    \label{fig:antenna}
%    }
%    \subfigure[the physical ESD antenna directions of two nodes]{
%     \includegraphics[scale = .3]{figure/Antenna_face_photo.pdf}   
%    \label{fig:antennafacing}
%    }
%\end{figure} 

%Circle 4 from Figure~\ref{fig:advantageESDAlargeroom} shows the RSS measurement when both the transmitter and the receiver use direction 1, which shows a more clearly drop when a person blocks the links than the drop in Circle 3 from Figure~\ref{fig:advantageESDAlargeroom} which presents both the receiver and transmitter perform the omni-directional. 
%In the contrast, the RSS measurement  in Circle 4 from Figure~\ref{fig:advantageESDAlargeroom} does not show very clear decrease when the links are blocked, because  the transmitter and receiver both use direction 4, which has ``back lobe''. 
\vspace{-2mm}
\subsubsection{Radio Link Attenuation False Negatives and False Positives} \label{sec:hypoFNFP}
%while variance changes when the link quality either decreases or increases in the presence of an obstruction, 
  
We say that a radio link attenuation \emph{false negative}\bo{\emph{(FN)}} has occurred if the RSS measurements remain stable (i.e., with little change and small variance) in the presence of an obstruction in the LOS path (e.g., within the shaded area in Fig.~\ref{fig:example1}). Similarly, we say that a radio link attenuation \emph{false positive}\bo{\emph{(FP)}} has occurred if the link quality RSS measurements change significantly when no obstructions are present in the LOS path. Both \emph{false negatives} and \emph{false positives} frequently occur in RTI systems, especially in the NLOS cluttered environments. These errors can significantly impact on the accuracy of RTI localisation. 

%As introduced,  
%the unexpected RSS measurement of a link in the NLOS environment may also causes \emph{false negatives} and \emph{false positives}. Specifically speaking,
%As showed in earlier sections, directional communications over a large range of orientation produce larger RSS measurements change and is more robust to fading. One of the direct benefits for RTI systems is that directional communications can reduce
% \emph{false negatives} and \emph{false positives}.
%We also investigate how to exploit directional antennas to reduce both \emph{false negatives} and \emph{false positives} in the RTI systems. 

A benefit of directional antennas is that they can reduce the instances of false positives and negatives. Fig.~\ref{fig:FPFN} shows examples of the RSS measurement from experiments when omni-direction communications produce \emph{false positives} (see Fig.~\ref{fig:FP}) and \emph{false negatives} (see Fig.~\ref{fig:FN}), but not for \emph{some} directional \emph{Pattern Pairs}. 
As a result, direction communications can indeed improve the accuracy of RTI systems. The poor localisation accuracy of Fig.~\ref{fig:image_omni} for omni directional antenna is a result of a \emph{false positive} in the link quality between Nodes 2 and 5, and \emph{false negative} in the link quality near Nodes 6 and 7. We have observed many instances of such behaviour in other experiments. 
\bo{See Section~\ref{subsec:comprti} for the details about the statistics in the experiments.}
 
\begin{figure}[htb]
    \centering
        \subfigure[example of false positive]{
        \includegraphics[scale = .25]{figure/FPv3-eps-converted-to.pdf}
        \label{fig:FP}
    }
    \subfigure[example of false negative]{
    \includegraphics[scale = .25]{figure/FNv3-eps-converted-to.pdf}    
    \label{fig:FN}
    }
    \caption{Examples of false positive and false negative. (a) Omni direction communication produces a \emph{false positive} without the presence of obstructions; (b) Omni direction communication produces a \emph{false negative} in the presence of an obstruction.}\label{fig:FPFN}
\end{figure}

%Directional antennas enable multiple directions for two nodes. For example, instead of two links (uplink and downlink) between two nodes, the ESD antenna that we used in this paper has six directions. Hence there are 36 link choices between two nodes. We call each choice a \emph{Pattern Pair}. 
%Because directional antennas 
%enable a large number of \emph{Pattern Pairs}, they have the ability to reduce the probability of ``false negatives''. Furthermore, 
%%directional antennas focus most of the radio energy in specific directions for a \emph{Patter Pair}
%directional antennas focus the radiated power in a specific direction, which enable them to reduce the probability of ``false negatives''. 
%This improves the accuracy of the RTI system significantly compared to omni-directional antennas as well, in particularly in a cluttered indoor environment such as 
%``through-wall'' tomographic imaging.
%\av{ We mention that ESD antennas generate large number of pattern pairs, and they concentrate radiated power in intended direction of communication. How it improves RTI is unclear from this paragraph}


%due to the wall or the stationary objects existing in the monitored area in the indoor environment, the variance of the link is unpredictable~\cite{WilsonVRTI:2011}. The attenuation of the link may cause RSS drop as expected, or keep stable or even increase.  This propose the challenge to RTI, which needs RSS variance as indicator of the motion. 
% However, in the actual indoor environment, this may not happen because the multi-path effect causes the received signal to be in deep fade. It is even more complex When there is wall in the  LOS.
%We investigate to take advantage of the EDS antenna. The higher RSS variance is observed by using the ESD antenna in RTI when the object blocks the links.  
%Since our EDS antenna has 6 directions, for a pair of transmitter and receiver, each direction of the receiver can collect the packets from 6 direction of the transmitter, so there are 36 direction choices for a pair of transmitter and receiver. We call each choice '"Patter Pair". The EDS antenna give the more gain compared with omni-directional which is useful for RTI, especially the through wall tomographic imaging. 

%Our antenna has six directions, shown in Figure ~\ref{fig:antenna}. Direction 2 and 6 are adjoining directions to direction 1 of our ESD antenna.
%\begin{figure}[t]
%    \subfigure[ESD antenna directions ]{
%     \includegraphics[scale = .3]{figure/Antenna_photo.pdf}
%    \label{fig:antenna}
%    }
%    \subfigure[the physical ESD antenna directions of two nodes]{
%     \includegraphics[scale = .3]{figure/Antenna_face_photo.pdf}   
%    \label{fig:antennafacing}
%    }
%\end{figure} 
%
%
%To verify our above hypothesis on the impact of the accuracy of the RTI systems by directional antennas, we conducted experiments in an indoor environment with two nodes as follows. We separated two nodes into 4 $m$ distance in a large empty room.  The \emph{direction 1}s of the two nodes face to each other, and a person walks through the LOS of two nodes \emph{twice} to block the links. The two nodes transmitted small packets to each other in each directional direction and
% omni-direction.
% at \textcolor{blue}{xx Hz} in turn.
%\textcolor{blue}{we need to define what is direction 1}. 
%The data from this experiment also demonstrate the the directional antenna has the ability to diminish the change of ``false positives'' and ``false negatives''. Figure~\ref{fig:FPFN} shows the example of ``false positive'' and ``false negative''.
%Fig.~\ref{fig:advantageESDAlargeroom} shows that RSS values from the omni-directional antennas did not have significant variances when the link was blocked (``false negative''), while some of the directional antenna \emph{Pattern Pairs} showed a dramatic decrease. For example, when the direction of the receiver was $1$ and the direction of the transmitter was $1$, as
%well as the direction of receiver was $6$ and the direction of the transmitter was $2$.  Fig.~\ref{fig:advantageESDAlargeroom} shows that the omni-directional antenna 
%inks did not change significantly when the person blocked the link, which demonstrates the advantage of directional antennas for RTI systems in 
%reducing the number of ``false negatives''. 
%\textcolor{blue}{we need an example of ``false positive''}.
%\begin{figure}[!ht]
%    \centering
%        \subfigure[example of false positive]{
%        \includegraphics[scale = .4]{figure/RSS_FP.pdf}
%        \caption{Column Reduction v.s. Random Pick}
%        \label{fig:FP}
%    }
%    \subfigure[example of false negtive]{
%    \includegraphics[scale = .4]{figure/RSS_FN.pdf}    
%    %\caption{Cricket: Accuracy versus SNR for varying number of projections}
%    \label{fig:FN}
%    }
%    \caption{Examples of false positive and false negative.}\label{fig:FPFN}
%\end{figure}
%For a pair of transmitter and receiver, there are $6 \times 6 = 36$ direction combinations.
\vspace{-2mm}
\subsection{Directional \emph{Pattern Pair} Selection}
\label{subsec:antennachoose}

The number of \emph{Pattern Pairs} between two nodes can be large. Each of the nodes that we use in this paper has an ESD antenna with 6 parasitic elements. The maximum number of \emph{Pattern Pairs} between 2 nodes is $36 \times 2 = 72$ where the $2$ comes from the uplink and downlink. This means  there are significant transmission overhead to make RSS measurements from all \emph{Pattern Pairs}. This may make the dRTI system difficult to scale to larger sizes.

Furthermore, intuitively, one may think that the \emph{Pattern Pair} with antennas directly pointing to each other (e.g. \emph{Direction 1}s in Fig.~\ref{fig:antennafacing}) should be the ``best'' choice. \emph{Is that true?} Let us look at the mRTI and vRTI for all 36  \emph{Pattern Pairs} in Fig.~\ref{fig:patternpairMean} and Fig.~\ref{fig:patternpairVar} respectively. The answer is that the intuition is \emph{not true}, similar to the earlier finding in wireless mesh networks~\cite{Subramanian:2009:ECS:1530748.1530784}. 
For example, for vRTI in Fig.~\ref{fig:patternpairVar}, the \emph{Pattern Pair} with antennas directly pointing to each other is the first bar from the left which does not have the maximum RSS variance when the link is blocked by an obstruction. However, if both nodes choose Direction 6 (see Fig.~\ref{fig:antennafacing}), this gives the first bar from the right in Fig.~\ref{fig:patternpairVar} which has a higher vRTI. The maximum variance is produced by the \emph{Pattern Pair} between Direction 2 of the receiver and Direction 3 of the transmitter, which is the ninth bar from left in Fig.~\ref{fig:patternpairVar}. 

Similar to the earlier discovery in~\cite{AmiriSani:2010:DAD:1859995.1860021,Lakshmanan2010}, Fig.~\ref{fig:patternpairMean} and \ref{fig:patternpairVar} also show: (1) The link qualities vary significantly between the \emph{Pattern Pairs}; (2) Some \emph{Pattern Pairs} have bigger change/variance than omni but some do not. Therefore, we need to investigate intelligent methods to select the best directional 
\emph{Pattern Pair}(s) to increase the localisation accuracy and to decrease the transmission overhead
 of dRTI systems.
To this end, we introduce three selection methods to choose directional link \emph{Pattern Pair}(s).

%Fig.~\ref{fig:patternpairVar} indicates
%there are significant transmission overhead
 %to make the link quality behaviour observation by 
%the RSS measurement  from all the \emph{pattern pairs}. 




%Back to the experiments with two ESD antennas in two rooms,

%From Figure \ref{fig:advantageESDAlargeroom}, the pattern pair whose direction is 1 for both the transmitter and the receiver is intuitively "best" one, but does not perform the best in terms of RSS mean value when the link is not blocked or the RSS variance when the link is blocked. 
%
%Fig.~\ref{fig:advantageESDAlargeroom} also shows that not all \emph{pattern pairs'} link quality changed when they are blocked by an obstruction.
%This illustrates that there are significant transmission overhead
% to produce the RSS measurement for extra \emph{pattern pairs}. 
%Therefore, we will investigate how to choose the best  \emph{pattern pairs} to improve the accuracy and to reduce the transmission overhead
 %(to make the systems scalable to more nodes) of RTI systems in Section~\ref{subsec:antennachoose} .

\begin{figure}[htb]
    \centering
       \subfigure[mRTI]{
    \includegraphics[scale = 0.2]{figure/largermean36bar-eps-converted-to.pdf}  
    \label{fig:patternpairMean}
    }
    \subfigure[vRTI]{
    \includegraphics[scale = 0.2]{figure/patternpairVar-eps-converted-to.pdf}  
    \label{fig:patternpairVar}
    }
    \caption{The mRTI (a) and vRTI (b) link quality statistics for the 36 \emph{Pattern Pairs}. The horizontal line shows the mRTI (a) and vRTI (b) for omni. 
}
   % \includegraphics[scale = 0.5]{figure/patternpairVar.eps}
    %\caption{ RSS variance of all the pattern pairs}\label{fig:patternpairVar}
    \label{fig:patternpairBoth}
\end{figure} 
%\begin{figure}[!ht]
%    \centering
%    \includegraphics[scale = 0.25]{figure/RSS_2_pattern_pair.eps}
%    \caption{ RSS variance comparison between the directional antenna and omni-directional antenna when the two nodes are in the large open room}\label{fig:patternpair}
%\end{figure} 

%The increasing number of chosen antenna pattern pair the antenna pairs increase the imaging performance, but it costs more energy for all the transmitter to send more beacons for the collection of the receivers. The decrease of the number of the antenna pattern pairs will decrease the transmission energy for the whole RTI network and also the transmission time which allows the wireless RTI network contains more nodes for RTI. 
%Here we show the reason why the partially antenna patter pair chosen can save the energy and total transmission time, we decide only use partially the directions of the antenna, $N_{receiver}$ directions of the receiver and $N_{transmitter}$ directions of the transmitter. There are $k$ nodes \{$N_1$,$N_2$,...,$N_k$\} in the wireless RTI networks. When $N_i$ is the transmitter, without any partially antenna patter pair chosen, $N_i$ needs to send 36 beacons totally, for each direction of $N_i$, it needs to send 6 beacons for the collection of one of the receiver directions. 
%When using partially antenna patter pair chosen, the transmitter only need to send $N_transmitter$  beacons in each directions instead of 6, which can save (6-$N_{transmitter}$)/6 energy and time for sending beacons. The reason the transmitter also needs to send beacons in each direction is that the best direction between each pair of nodes may be different. 
%The more details about the metric to choose the best antenna pattern pair(s) will be discussed in ~\ref{subsec:antennachoose}. 
%
%\subsection{RTI, VRTI using directional antenna}
%Mean-based radio tomographic imaging and variance-based radio tomographic imaging are proposed ~\cite{WilsonRTI:2010}. Instead of using a variety of omni-directional antennas, we investigate to take advantage of part or all of antenna pattern pairs for radio tomographic imaging.
%
%For in the NLOS link, the RSS measurement is unpredictable, which may decrease, increase or keep unchanged when the link is attenuated. Instead of traditional mean-based RTI method, we applied the absolute value of the difference in RSS to image the moving objects.
%
%The radio tomographic imaging includes the three period, the first one is empty-area calibration, the second step is antenna pattern pair choosing, and the last one is to apply RTI method to locate the objects. 
%
%In the empty-area calibration period, the monitored area needs to be empty so that the beacons from all ESD antenna directions are collected by all the direction of ESD antennas the receiver.  RSS vector of each pattern pair is averaged over the whole empty-area calibrating period. The RSS vector are used into two purposes. 
%First, the RSS vector collected in the empty-area calibrating supplies mean-based RTI the baseline for differencing the RSS collected in the monitoring period. Second, the pattern pairs of each pair nodes for RTI can be chosen  according to RSS measurements the empty-area calibration.
%
%
%For choosing the antenna pattern pairs, we either take the advantage of the signal strength during the empty-area calibrating period or the monitoring period, or the physical location and orientation of antennas.  The details will be discussed in \ref{antennachoose}. 
%
%In final part, either attenuation-based RTI or variance-based RTI is used for tracking the subjects by using the chosen pattern pairs of each pair of nodes with EDS antenna.
%
%
%\subsection{Selection Methods for Choosing Best Antenna Pattern Pairs} 


%A plenty of antenna pattern pairs supply the ESD antenna with the opportunities for anti-fading, but also pose challenges to choose the best pattern pair(s) for RTI. For solving this problem, we propose three methods of choosing the best antenna pattern pair(s) for increasing the accuracy of radio tomographic imaging.
%
%For choosing the antenna pattern pairs, we either take the advantage of the signal strength during the empty-area calibrating period or the monitoring period, or the physical location and orientation of antennas.

%The first method is based on the RSSI mean of all the antenna patten pairs of the empty-area calibration measurements, the second one is the based on the RSSI variance of all the antenna patten pairs when the monitored objects are in the monitored area, while the third method choose the best antenna pattern pair according to the location of the nodes and the direction of the antennas. The details are as following.

%Here are the notations:


%\begin{tabular}{p{45pt} p{170pt}}
%\hline
%Symbol    & Description  \\
%\hline \hline
%$r_{i,j}(t)$ & RSS from $j$-th pattern pair of $i$-th receiver at time $t$.      \\
%$h_{i,j}$		&the mean of RSS measurement from $j$-th pattern pair of $i$-th receiver in the calibrating period. \\
% $F_{i}$	&antenna pattern pair set for $i$-th receiver. \\
%$n_p$ 	&the length of $F_{i}$, ${n_p} = \left | {F_{i}} \right | $ \\
%$L$	&link set in the RTI wireless network. \\
%$Fp_{i}$	& chosen antenna pattern pair set for $i$-th receiver. \\
%$n_c$ 	&the length of $Fp_{i}$, ${n_c} = \left | {Fp_{i}} \right | $ \\
%$ta$		& the beginning time of the calibrating period. \\
%$tb$		& the end time of the calibrating period. \\
%$y$		&a ${M}\times{1}$ vector which is the observation of the links, $M = \left | {L} \right | $. \\
%$R_{i,j}(t)$  &$y_{i}(t) = observationfunction({R_{i,j}(t)}), {j}\in{Fp_{i}}$ \\
%$n_{receiver}$  &the number of chose directions of receiver for pattern pair combination\\
%$n_{transmitter}$ &the number of chose directions of transmitter for pattern pair combination\\
%\hline
%\end{tabular}


%\tv{I think it would be very nice to add one sentence that says why this method seems reasonable to give the reader som intuition about the choice}
%\begin{itemize}
\vspace{-2mm}
\subsubsection{Location Method}
%\textbf{Location method} 
This method chooses the best \emph{Pattern Pairs} based on the physical location and orientation of the antennas. Intuitively, the \emph{pattern pair} whose antennas are pointing to each other (resp. pointing in the opposite directions) should have the strongest (weakest) signal strength at the receivers, and also have higher (lower) probability to show significant RSS variances when the link between the transmitter and the receiver nodes is blocked by an obstruction. 
%
%
%At the same time, the \emph{pattern pair}, whose antennas are pointing in the opposite directions, should have the weakest signal strength at the receivers and have lower probability to show significant RSS variances when the link between the transmitter node and the receiver node is blocked by an obstruction.
Though our earlier discussion shows that this intuition does not produce the best \emph{Pattern Pair}. Nevertheless, we find from Fig.~\ref{fig:patternpairMean} and \ref{fig:patternpairVar} that those \emph{Pattern Pairs} that are roughly facing each other do generally give a significantly higher link quality statistics (mRTI or vRTI) than omni directional antennas. Furthermore, this selection method \emph{does not require an initial calibration phrase} as the other methods we will introduce, which is important for some applications such as emergency response~\cite{maas2013toward}.
 
For this method, we record the orientation of antennas during deployment stage. Then, according to the physical orientation of the antennas, we select $n_{transmitter}$ directions for the transmitting node $N_1$ and $n_{receiver}$ directions for the receiving node $N_2$. Let $N_1 N_2$ denote the line connecting nodes $N_1$ and $N_2$. For the transmitter node $N_1$, we compute the angles (magnitude only) between the antennas on node $N_1$ and the line $N_1 N_2$, and select the directions corresponding to the $n_{transmitter}$ smallest angles. Similar method applies to choosing $n_{receiver}$ directions on $N_2$. In practice, we choose $n_{transmitter} = n_{receiver}$ because each node has to be transmitter and receiver. This means the number of \emph{Pattern Pairs} selected is always a square number. Fig.~\ref{fig:patternchoice} shows an example with $n_{transmitter} = n_{receiver} = 2$.  

%first draw an imaginary line between $T$ and $R$ and select the $n_{transmitter}$ antennas which are closest to the line $TR$ 
%
%
%calculate the ranks of the \emph{Pattern Pairs} and select the top $n$ pairs. 
%%\tv{we have figures in other papers (e.g. REALWSN) that show that among the three best directions should be the one pointing physically in the right direction and the two nbeighboring one should be the best}
%%The detail of the antenna pattern pair chosen method is described as follows which is shown in Figure . 
%Specifically, for a transmitter ($N_{1}$ at location $T$) and  a receiver ($N_{2}$ at location $R$), we aim to select $n_{receiver}$ directions for $N_2$ and $n_{transmitter}$ directions for $N_1$. 
%We denote the directions of $N_1$ as\{${TD_{t1}},{TD_{t2}},...,{TD_{tn}}$\} , 
%and select the $n_{transmitter}$ directions which have \emph{minimal relative angel}  $\angle{RTD_{ti}}$ as the directions of the transmitted.
%We apply the same method for the transmitter ($N_2)$.
%We denote directions of the $N_2$ as\{${RD_{r1}},{RD_{r2}},...,{RD_{rm}}$\} , and select the $N_{receiver}$ directions which have minimal  relative angle $\angle{TRD_{rj}}$ as the directions of the receiver. 
%Fig.~\ref{fig:patternchoice} shows the example that 2 directions of receiver and transmitter are chosen by the Location method.

\begin{figure}[ht]
    \centering
    \includegraphics[scale = 0.25]{figure/Antenna_direction_choice.pdf}
    \vspace{-5mm}
    \caption{The figure shows the 2 directions of receiver and transmitter chosen by the Location method.}
    \label{fig:patternchoice}
\end{figure} 
 \vspace{-2mm}

\vspace{-2mm}
\subsubsection{Fade Level Method}
\label{subsubsec:fade_level_method}
%\item \textbf{Fade level method} 
Wilson and Patwari define fade level in a radio link as a continuous function between the two extremes of \emph{deep fade} and \emph{anti-fade} in~\cite{wilson2012fade}. A link in deep fade will experience high variance as a person moves in a \emph{wide} area,
which may produce \emph{false positives} when the person is outside the LOS path of a \emph{Pattern Pair}, e.g., outside the shadowed area in Fig.~\ref{fig:example1}. On the other hand, an anti fade \emph{Pattern Pair} is affected by constructive
multi path interference.  The link quality varies significantly less, but the radio signal attenuates significantly when a
person is present in the LOS of the \emph{Pattern Pair}. Therefore, deep fade \emph{Pattern Pair} is less informative for dRTI,
and we would like to select the \emph{Pattern Pairs} that have minimum deep fade level as in~\cite{KaltiokallioBP12}.

The Fade Level method collects RSS measurements of all the \emph{Pattern Pairs} with an \emph{empty} AoI during the calibration period $t \in [t_1, t_2]$. 
During the calibration, 
%each node transmits beacons from each direction sequentially. Furthermore, 
the transmitter node sends a number of (e.g., 6) packets sequentially in each direction so that receiver nodes can at least receive one packet in each antenna direction. 
%For example, the ESD antenna, which we used, has six directions, and the transmitter nodes send six beacons at each direction. Altogether, the transmitter node needs to send 36 beacons in each round. 
After a fixed number of rounds (e.g.,  50), the Fade Level method chooses the \emph{Pattern Pairs} with small fade levels. 
Specifically, for a \emph{Pattern Pair} between direction $i$ of a transmitter $N_{1}$ and 
direction $j$ of a receiver $N_{2}$,
it computes the \emph{normalised} RSS measurements $h_{i,j}$ during calibration period ($t \in$ $[t_1, t_2]$) as 
\begin{equation}
h_{i,j} =  \sum_{t=t_1}^{t_2}{r_{i,j}(t)} 
\label{equ:fade_level}
\end{equation}
where 
% the \emph{normalised} RSS measurements from $i$-th link \emph{Pattern Pair} of $j$-th receiver direction at time $t$ as
\begin{equation}
r_{i,j}(t) =  P_{rx}(i, j, t) - P_{tx}(i, t) 
\label{equ:normalised_rss}
\end{equation}
where $P_{tx}(i, t)$ is the transmission power of $N_1$ in direction $i$ at time $t$, and $P_{rx}(i, j, t)$ is the RSS measurement 
of receiver $N_2$ at direction $j$ for the packets transmitted from $N_1$ in direction $i$ at time $t$. 

As in~\cite{KaltiokallioBP12}, we 
use $h_{i,j}$ as a measure of the fade level, and if $h_{i,j}$ is smaller, the \emph{Pattern Pair}
is in a deeper fade. Therefore, the 
Fade Level method selects the top $k$ \emph{Pattern Pairs} with maximum 
\emph{normalised} RSS measurements ($h_{i,j}$) from the 36 \emph{Pattern Pairs} between $N_1$ to $N_2$.
 
%  Specifically, the same transmission power for each transmitter keeps unchanged when conducting the experiments, so the measured RSS indicates the fade level. 
%For each ${i}\in{L}$,   RSS mean $h_{i,j}$ is calculate as $h_{i,j} =  \sum_{t=ta}^{tb}{r_{i,j}(t)} $ after the calibrating period(from $ta$ to $tb$), the top $n$ \emph{pattern pairs} with maximum RSS mean $h_{i,j}$ are chosen to be the candidates for RTI.
%\item 

\vspace{-2mm}
\subsubsection{Packet Reception Rate (PRR) Method}
%\textbf{PRR method} 
Intuitively, Packet Reception Rate (PRR) is a also good proxy for link quality because good quality links
tend to have higher PRR. The PRR method also has the same calibrating period where the PRR for all \emph{Pattern Pairs} are measured. The PRR method selects the $k$ \emph{Pattern Pairs} between transmitter node $N_1$ and receiver node $N_2$ that have the highest PRR during the calibration period.  

%We remark that the Fade Level and PRR methods can choose any number of \emph{Pattern Pairs} but the number of \emph{Pattern Pairs} chosen by the Location Method is always a square number. We will investigate the performance of each directional \emph{Pattern Pair} selection method by experiments in Section~\ref{sec:experiments}. 


%
%with the
%highest PRR during the calibration period $[ta, tb]$, from $N_1$ to $N_2$
% as the link quality behaviour observations for dRTI.
%
%
%as Fade Level Method, except that PRR has 
%a direction selection metric different to Eq.~(\ref{equ:fade_level}). Instead,
%from the total 36  directional \emph{Pattern Pair}s from transmitter $N_1$ to receiver $N_2$ , PRR method measures
%th PRR for each \emph{Pattern Pair}
%, and select the top $k$ 


% For each link ${i}\in{L}$, the measured packet reception rate(PRR) in the calibrating period is sorted, and the top $n$ \emph{pattern pairs} with maximum PRR are picked to build the link quality behaviour observation vector.
%\item 


 %\end{itemize}

%The first method is based on the RSS values of all the \emph{pattern pairs} collected in the empty area measurements during calibration stage. During the calibration, each node transmits beacons from each direction sequentially. Furthermore, the transmitter node sends a number of beacons at each direction so that receiver nodes can receive one beacon in each antenna direction. For example, the ESD antenna, which we used, has six directions, and the transmitter nodes send six beacons at each direction.  Altogether, the transmitter node needs to send 36 beacons in each round. After a fixed number of rounds, e.g.,  50,  the top $n$ \emph{pattern pairs} with maximum average RSS mean values are chosen to be the candidates for RTI.

%The second method selects the best  \emph{pattern pairs} based on the  physical location and orientation of antennas. Intuitively, the \emph{pattern pairs} whose direction face to each other should have the strongest signal strength at the receivers, and also have higher probabilities to show significant RSS variances when the link between the transmitter node and the receiver node is blocked by an obstruction.
%\textcolor{blue}{we need figure to show what we mean by nodes facing each other and opposite to each other.}
%The \emph{pattern pairs}, which have opposite directions, 
%should have the weakest signal strength at the receivers and have lower probabilities to show significant RSS variances when the link between the transmitter node and the receiver node is blocked by an obstruction.
%In order to use this method, we need to measure the locations of the nodes and the orientation of antennas during deployment stage. Then, according to the physical orientation of the antennas, we calculate the ranks of the \emph{pattern pairs} and select the top $n$ pairs. 
%\tv{we have figures in other papers (e.g. REALWSN) that show that among the three best directions should be the one pointing physically in the right direction and the two nbeighboring one should be the best}

%The detail of the antenna pattern pair chosen method is described as follows which is shown in Figure . For a pair of nodes \{ $N_{1}, N_{2}$ \}, $n_{receiver}$ directions of the receiver and $n_{transmitter}$ directions of the transmitter are chosen for RTI, First $N_{1}$ is seen as transmitter, the location of the antenna denoted as $R$, when a node is transmitter, the node is seen as a point $T$, the 6 direction of the receivers denoted as\{${RD_{r1}},{RD_{r2}},...,{RD_{r6}},$\} , the $N_{receiver}$ directions which have minimal  $\angle{TRD_{ri}}$ are picked for the directions of the receiver. For the transmitter, the same method is applied, the 6 direction of the transmitter denoted as\{${TD_{t1}},{TD_{t2}},...,{TD_{t6}},$\} , the $n_{transmitter}$ directions which have minimal  $\angle{RTD_{ti}}$ are picked for the directions of the receiver. 


%
%
%\emph{Remark:} Location method has less directional \emph{Pattern Pair} selection options compared to the other two methods because it chooses the same number of transmit directions  and receive directions, e.g., ${n_{receiver}} = {n_{transmitter}}$. For example, the options for the Location methods for the ESD antennas we used are $\{1, 4, 9, ..., 36\}$ \emph{Pattern Pair}(s) from 
%a transmitter $N_1$ to a receiver $N_2$. While the options for the other methods are from 1 to 36.
%, the chosen pattern pair set whose size is ${{n_c}\times{1}}$ is denoted as $P_i$.
%There are pros and cons for the different methods. While the first method does not require to record the orientation of the antenna during deployment, but it needs calibration. 
%\tv{I do not understand if you want to select a method already here?}

% \textcolor{red}{Section~\ref{subsec:observation} should be move to Background. Most of this will go. Need to sort out the pattern pairs calculation. CTC}

\vspace{-2mm}
\subsection{Link Quality Statistics for dRTI} \label{subsec:observation}


%The goal of our RTI wireless networks is to take advantage of $M$ links for the tracking or localising the person moving in the area. 
%Section~\ref{subsec:antennachoose} already introduces how to pick the patter pairs for each pair of a transmitter and a receiver.
%In this section, we discuss three methods to make link quality behaviour observation.
%i.e. for each link $i$, RSS measurement vector $r_i$ is a ${n_c}\times{1}$ vector, and $\{{{r_{i,j}}}\},{j\in {Fp_i}}$ is the element in the vector $r_i$. The link quality observation for link $i$ at time $t$ is expressed as $y_{i}(t) = \text{observation\_function}({R_{i,j}(t)}), {j}\in{Fp_{i}}$. Three methods to build observation\_function() are introduced as follows.
%$y$ is a ${M}\times{1}$ vector which is the observation of the link. 
%After we use the antenna patter pair chosen method in ~\ref{subsec:antennachoose}, we have $n_c$ pattern pairs for each links. 

%$r_i$ is a ${n_c}\times{1}$ vector $\{{{r_{i,j}}}\},{j\in {Fp_i}}$, $r_{i}(t)$ is used to build $y_{i}(t)$.

%There are three method we can use $r_{i}$ to build $y_{i}$. 



%The first one is mean based RTI method. For this method, RTI needs three periods, the first one is empty-area calibration, the second step is antenna pattern pair choosing, and the last one is to apply RTI method to calculate the image of the monitored objects. 

%In the empty-area calibration period from $t_a$ to $t_b$, the monitored area needs to be empty so that the beacons from all ESD antenna directions are collected by all the direction of  the receivers' ESD antennas.  RSS vector of each pattern pair is averaged over the whole empty-area calibrating period. 
%For each link, there are $n_p$ antenna pattern pairs, for our ESD antenna  $n_p = {6}\times{6}=36$. The average RSS value $h_{i,j}$ for each antenna patter pair in the empty-area calibration period is calculated.
%denoted as $\tilde{R_{ij}}$ calculated by $\frac{1}{{t_b}-{t_a}}\sum_{k=t_a}^{t_b}(R_{ij}(k)), {1}\leq {j} \leq {n_p}$.

%In the second step, the antenna pattern pair chosen method introduced in ~\ref{subsec:antennachoose}  is applied.

In Section \ref{subsec:bgRTI} we present the mean and variance based link quality statistics for omni RTI. We adopt similar statistics for dRTI but they have to be modified to take into account the \emph{Pattern Pairs}. Let $F_i$ denote the set of selected \emph{Pattern Pairs} for link $i$. Let $R_{i,j}(t)$ denote the RSS measurement at time $t$ for the $j$-th \emph{Pattern Pair} of link $i$. The link quality statistics for dRTI are:

\begin{itemize}
\item  \textbf{RSS mean}
Let $\bar{R}_{i,j}$ be the mean RSS over the calibration period for the $j$-th \emph{Pattern Pair} in link $i$. The \emph{RSS mean} statistics $y_i(t)$ for link $i$ for dRTI is $y_i(t) = \sum_{j \in F_i} | R_{i,j}(t) - \bar{R}_{i,j}|$.  


%As introduced, for in the link in indoor environment, the RSS measurement is unpredictable, which may decrease, increase or keep unchanged when the link is attenuated. If the RSS measurement at time $t$ decreases as expected or increases, we can also take advantage of this change as an indicator for RTI. Different from traditional mean-base RTI method, we use the absolute value of the RSS change instead of the difference of the RSS measurement, i.e. in time $t$ in the monitoring period, for the pattern pair $j$ of the link $i$,  $R_{i,j}(t) = \left |  {r}_{i,j}(t)-{h}_{i,j} \right |$,  and $y_{i}(t) = \sum_{k\in {Fp_{i}}}R_{i,k}$.

\item  \textbf{RSS variance}
The \emph{RSS variance} statistics for dRTI is computed over a window of $v$ measurements. The link quality statistics $y_i(t)$ for link $i$ for dRTI is $y_i(t) = \sum_{j \in F_i} var(R_{i,j}(t), ...., R_{i,j}(t - v + 1))$



%The second one is using the RSS variance measurement, and this method does not have to conduct empty-area calibration period, which depends on the antenna pair chosen metric. After the antenna pair chosen metric gives  the antenna pair selection set $Fp_{i}$ for link $i$, we use the current RSS measurement at time $t$ ${r}_{i,j}(t)$ and the past $n_{rv}$ RSS measurement ${r}_{i,j}(t-1),{r}_{i,j}(t-2),...,{r}_{i,j}(t-n_{rv})$ , $R_{i,j}(t)=VAR\{{{r}_{i,j}(t),{r}_{i,j}(t-1),{r}_{i,j}(t-2),...,{r}_{i,j}(t-n_{rv})}\}$, $y_{i}(t)$ is also calculated by the summary of the elements from $R_{i}(t)$, i.e. $y_{i}(t) = \sum_{k\in {Fp_i}}R_{i,k}$.


%\item  \textbf{Weighted-variance based RTI}
%The third one is similar to the second one, but instead of the summary of $R_{i,j}(t)$, it summarise the $n$-th power of the elements from $R_{i,j}(t)$, i.e. $y_{i}(t) = \sum_{k\in {Fp_i}}{R}^{n}_{i,k}$. 
\end{itemize}
%

%In the next section, we will compare the performance of various RTI methods. We will use omni-directional RTI with mRTI and vRTI as the benchmarks. For dRTI, there are two link quality statistics and three \emph{Pattern Pairs} selection methods. 

%\subsection{Imaging Estimation and Tracking} \label{subsec:imaging}
%As introduced in Section ~\ref{subsec:bgRTI}, the attenuation image is estimated by the link quality behaviour observation using Tikhonov regulation method, and the Kalman filter is used for increasing the tracking performance. 

%the RTI problem can be modelled as $y = A x +n$. $y$ is the observation which is introduced in Section~\ref{subsec:observation}, $Q$ is the weighting matrix show in the (background section), and $n$ is the noise vector.
%The image vector $\hat{x}$ is estimated by the Tikhonov regulation method, i.e. $\hat{x} =  \Psi  y$. 
%Assume there exists only one person in the monitored area, the location of the objects is determined by finding the voxel with largest value in  $\hat{x}(t)$. $ k = \underset{i}\argmax{\hat{x}(t)_{i}}$

%For increasing the performance of the tracing, the estimated location $k$ is input to the Kalman filter.


%=============still here Bo==============


%using the variance of RSS measurement, this method does not have to conduct empty-area calibration period, which depends on the antenna pair chosen metric. After the the antenna pair chosen metric gives  the antenna pair chosen set $P_i$ for each link, we use the current RSS measurement $\hat{R}_{ij}(t)$ and the past $n_{rv}$ RSS measurement $\hat{R}_{ij}(t-1),\hat{R}_{ij}(t-2),...,\hat{R}_{ij}(t-n_{rv})$ , $R_{ij}(t)=VAR\{{\hat{R}_{ij}(t),\hat{R}_{ij}(t-1),\hat{R}_{ij}(t-2),...,\hat{R}_{ij}(t-n_{rv})}\}$, $R_{i}(t)$ is also calculated by the summary of $R_{ij}(t)$, i.e. $R_{i}(t) = \sum_{k\in {P_i}}R_{ik}$

% Instead of traditional mean-based RTI method, we applied the absolute value of the difference in RSS to image the moving objects.

%The RSS vector are used into two purposes. First, the RSS vector collected in the empty-area calibrating supplies mean-based RTI the baseline for differencing the RSS collected in the monitoring period. Second, the pattern pairs of each pair nodes for RTI can be chosen  according to RSS measurements the empty-area calibration.


%Mean-based radio tomographic imaging and variance-based radio tomographic imaging are proposed ~\cite{WilsonRTI:2010}. Instead of using a variety of omni-directional antennas, we investigate to take advantage of chosen antenna pattern pairs for RTI.


%For in the NLOS link, the RSS measurement is unpredictable, which may decrease, increase or keep unchanged when the link is attenuated. Instead of traditional mean-based RTI method, we applied the absolute value of the difference in RSS to image the moving objects.

%The radio tomographic imaging includes the three period, the first one is empty-area calibration, the second step is antenna pattern pair choosing, and the last one is to apply RTI method to locate the objects. 

%In the empty-area calibration period, the monitored area needs to be empty so that the beacons from all ESD antenna directions are collected by all the direction of ESD antennas the receiver.  RSS vector of each pattern pair is averaged over the whole empty-area calibrating period. The RSS vector are used into two purposes. 
%First, the RSS vector collected in the empty-area calibrating supplies mean-based RTI the baseline for differencing the RSS collected in the monitoring period. Second, the pattern pairs of each pair nodes for RTI can be chosen  according to RSS measurements the empty-area calibration.


%For choosing the antenna pattern pairs, we either take the advantage of the signal strength during the empty-area calibrating period or the monitoring period, or the physical location and orientation of antennas.  The details will be discussed in \ref{antennachoose}. 

%In final part, either attenuation-based RTI or variance-based RTI is used for tracking the subjects by using the chosen pattern pairs of each pair of nodes with ESD antenna.



related.tex
\vspace{-2mm}
\section{Related work}\label{sec:related}
%In this section, we cover research in RTI and directional communications most relevant to dRTI.
\vspace{-2mm}
\subsection{RF-Based Device Free Localisation}

Ultra-wideband (UWB) impulse radar devices have been studied for through-wall imaging. They transmit wideband impulses, and estimate the distance to a scatterer by measuring the time delay of the echo. %
% Some companies including Cambridge Consultants~\cite{Cambridge:Online}, Time Domain~\cite{TimeDomain:Online}, Camero Tech~\cite{CameroTech:Online} have commercialised UWB tomographic imaging devices.
UWB impulse radar typically performs well at short range. However, the accuracy decreases at long range because of limited transmit power and $d^4$ scattering losses \cite{WilsonRTI:2010}. 

Recently, many RSS-based device-free localization methods have been proposed.  Youssef et al.\ used the variance or change in RSS to detect a person crossing a link~\cite{Youssef:2007}.  Patwari and Agrawal proposed to use tomography to estimate an image of the AoI based on the signal attenuation of many radio links (mRTI)~\cite{PatwariEffect2008}, which they called RTI. However, their following work in~\cite{WilsonVRTI:2011} showed that mRTI was ineffective in the ``through-wall'' setting  because the radio signal statistics behaved unexpectedly. Their experiment showed the RSS 
measurements may decrease, keep stable or even increase when a link was blocked by an obstruction. Therefore, instead of using mRTI, they proposed to use the variance-based RTI (vRTI) in~\cite{WilsonVRTI:2011}. Later, Kaltiokallio et al.\ proposed to use multiple independent channels to increase the performance of 
RTI (cRTI) in~\cite{KaltiokallioBP12}. In cRTI, performance improves with the number of channels measured. Channel diversity requires more bandwidth compared to single-channel RTI, and is limited by the number of ``clean'' or interference-free radio channels.  \emph{With ubiquitous use of wireless technologies such as WiFi, it becomes more and more difficult to dedicate bandwidth, particularly in ISM bands, for RTI systems.} To this end, the proposed dRTI requires only one channel, the same as the traditional single-channel RTI.

RSS fingerprint-based methods for device free indoor localisation and tracking have been investigated in~\cite{Xu:2012,Xu:2013}.  Fingerprint-based methods do not require the sensor coordinates to be known, and they adaptively learn the multipath characteristics of an environment.  This paper shows that use of directional antennas in a wireless network increases the effect that a person has on the RSS.  Further, having a diversity of directional patterns effectively increase the dimension of the RSS fingerprint.  Both effects could be applied to improve the accuracy of RSS fingerprint-based methods as well, although the focus in this paper has been on RTI. 

Fingerprint-based methods require training periods in which a person is required to walk in each voxel in the AoI while the systems collect RSS fingerprints, as well as an empty-room training period. In contrast, mRTI requires only the empty-room training period, and vRTI requires no training period.  vRTI is advantageous since training is not possible in emergency response applications, however, vRTI is cannot detect static objects in the AoI.   Edelstein and Rabbat proposed a method to identify the background (no person obstructing) RSS from a radio link that has periods of obstruction and no obstruction \cite{10.1109/TMC.2012.206}. This work is complementary to the approaches in~\cite{10.1109/TMC.2012.206,ZhaoKRTI:2013} and could add directionality to improve their performance.  

Adib and Katabi recently proposed WiVi to count the number of people ``through-wall'' and recognise simple gestures based on WiFi signals in~\cite{Adib:2013:STW:2486001.2486039}.  WiVi can count the number of people and estimate their relative velocity.  Pu et al.\ developed WiSee, which demonstrated high classification accuracy among a set of nine gestures, using Doppler shift measurements and machine learning \cite{pu2013whole}.  In contrast, this paper focuses on tracking the absolute positions of people indoors.

\vspace{-2mm}
\subsection{Directional Communications}
\input{Tex/esd_related}

related_spida.tex
\subsection{Direction Antenna}
Electronically Switched Directional antennas allow software based control of the direction of the maximum antenna gain. These have been shown feasible for the resource constrained environment of the low power sensor network. The feasibility has been demonstrated by Nilsson~\cite{nilsson09directional}, Prieditis et al. and Giorgetti et al.~\cite{giorgetti07directional} with their prototype antennas. Giorgetti et al.  discuss a four beam patch antenna. The antenna consists of four planar patch antennas arranged in a box like structure that can be controlled electronically. They integrate the antenna with TelosB nodes~\cite{polastre05telos}, and demonstrated increased transmission range, decreased signal variability and interference suppression from IEEE 802.11 networks. The ESD antennas discussed by Nilsson  and Prieditis et al. are based on the concept of Electrically Switched Parasitic Element (ESPE). These antennas consists a of central monopole antenna surrounded by a number of parasitic elements. The reactance between the elements can be electronically controlled. Prieditis et al.  designed an ESPE based antenna and integrated it with TelosB nodes. They observed improved communication range at the same energy cost. Nilsson designed the Sics Parasitic Interference Directional Antenna (SPIDA). SPIDA is an implementation of the ESPE design. SPIDA's six parasitic elements can be individually grounded or isolated. When all parasitic elements are isolated the antenna is configured in omni-directional mode. When all elements are grounded except one, the direction of the maximum antenna gain is towards the direction of the isolated element. \"Ostr\"om added software-based control to SPIDA and demonstrated that the SPIDA prototype concentrates the radiated power in the given directions~\cite{Ostrom:2010:EES:1947841.1947856}. 

spida.tex
ESD antennas are able to electronically control the direction of the
maximum antenna gain, which is feasible for the resource constrained 
WSNs as demonstrated earlier~\cite{giorgetti07directional, nilsson2009directional}.
%by Giorgetti et al.[?] , Nilsson et al. [?] and Prieditis et al [?].
%can't find the Prieditis citation
%Giorgetti et al. design a four beam patch antenna and
%integrated it with TelosB mote in~\cite{giorgetti07directional}.
Nilsson~\cite{nilsson2009directional} has designed an ESD antenna based on the concept of Electrically-Steerable
Parasitic Array Radiator (ESPAR). 
ESPAR antennas consist of a
central monopole surrounded by a number of parasitic elements.
%, which
%elements are 
%are loaded with reactance, which can be electronically
%controlled, and allows the control of the direction of the maximum
%antenna gain dynamically. 
In the simplest form, the parasitic elements can be 
either grounded or isolated allowing them to 
act as reflectors when grounded and as directors
when isolated. 
%Since this is controllable by software, 
%this allows the control of the direction of the maximum
%antenna gain dynamically. 


In this paper, we use ESPAR antennas, each of which has six parasitic elements designed by 
Nilsson~\cite{nilsson2009directional}. The parasitic elements can be
individually grounded or isolated via software APIs.
When all the parasitic elements
are grounded except one, the direction of the maximum antenna gain is
towards the direction of the isolated element.
We use this configuration for the dRTI experiments. 
When all the parasitic
elements are isolated, we have an omni-directional configuration of the
antenna. We use this configuration for omni RTI and cRTI experiments. 
The antenna gain varies as an offset circle from
approximately 7 dB to -4 dB in the horizontal plane. 
%This antenna is

%%%==== Ammbuj Edited 2 
%ESD antennas are able to electronically control the direction of the maximum antenna gain. These are feasible for the resource contained environment of low-power sensor networks. This has been demonstrated
%by Giorgetti et al.[?] , Nilsson et al. [?] and Prieditis et al [?]. Giorgetti et al. discusses discuss a four beam patch antenna and integrates it with TelosB mote. Nilsson et al. and Prieditis et al discusses ESD antenna based 
%on the concept of Electrically-Steerable Parasitic Array Radiator (ESPAR). ESPAR antennas consists of a central monopole surrounded by a number of parasitic elements. These elements are loaded with reactance, 
%which can be electronically controlled. This allows the control of the direction of the maximum antenna gain. In the simplest form, the parasitic elements can be either grounded or isolated. When the parasitic 
%element is grounded, it acts as deflector and when it is isolated, it acts as directors.
%
%We use ESPAR antenna design with six parasitic elements for the experiments done in this paper. The parasitic elements can be individually grounded or isolated. When all the parasitic elements are grounded except one, 
%the direction of the maximum antenna gain is towards the direction of the isolated element. When all the parasitic elements are isolated, we have omni- directional configuration of the antenna. The antenna gain varies as 
%an offset circle from approximately 7 dB to -4 dB in the horizontal plane. This antenna is similar in design to one suggested by Nilsson [?]. The radiation characteristics of the antenna is comparable to other state-of-the-art
%antennas [?, ?, ?] for WSN.


%%==========Ambuj Edited==============%%
%ESD antennas allow software based control of the direction of the maximum antenna gain. We use a specific type of ESD antennas based on the concept of Electronically Switched Parasitic Element (ESPE). These antennas consist of central monopole surrounded by number of parasitic elements. The reactance between the elements can be electronically controlled. This enables control of the direction of the maximum antenna gain.  ESPE antennas have been shown feasible for the resource constrained environment of low-power sensor network by Nilsson [?] and Prieditis et al. .

%Nilsson designed the Sics Parasitic Interference Directional Antenna (SPIDA). SPIDA's six parasitic elements can be individually grounded or isolated.  When the parasitic element is grounded, it acts as deflector and when it is isolated, it acts as directors. When all the parasitic elements are isolated the antenna is configured in omni-directional mode. When all the elements are grounded except one, the direction of the maximum antenna gain is towards the direction of the isolated element. The grounding/isolation of parasitic elements can be controlled in software this enables software based control of the direction of the maximum antenna gain. The antenna gain is designed to vary as an offset circle from approximately 7 dB to -4 dB in the horizontal plane. The SPIDA antenna is easy to construct, and the radiation characteristics is comparable to other state of the art antennas in WSN. Thus, we construct and use ESD antennas based on the SPIDA for the experiments conducted in this paper.



%%==========Bo Edited==============%%
%ESD antennas are able to electronically control the direction with the maximum antenna gain, which is enabled by Electronically Switched Parasitic Element (ESPE)~\cite{nilsson2009directional}.
%ESPE antennas have been shown feasible for the resource constrained environment of low-power sensor network
%These antennas consist of central monopole surrounded by parasitic elements, and the reactance between the elements can be electronically controlled to enable the the specific direction with maximum antenna gain. 
%
%
%In this paper, we construct and use ESD antennas based on the design of SICS Parasitic Interference Directional Antenna (SPIDA)~\cite{nilsson2009directional}.
%SPIDA's six parasitic elements can be individually grounded or isolated.  When the parasitic element is grounded, it acts as deflector and when it is isolated, it acts as directors. When all the parasitic elements are isolated, the ESD antenna is configured in omni-directional. 
%When all the elements are grounded except one, the direction of the maximum antenna gain is towards the specific direction of the isolated element. 
%The grounding/isolation of parasitic elements can be controlled in software electronically, which also saves energy to change the direction. 
%The antenna gain is designed to vary as an offset circle from approximately 7 dB to -4 dB in the horizontal plane. 
%
%SPIDA is also easy to construct, and the radiation characteristics is still comparable to other state-of-the-art antennas[\textcolor{red}{please add the reference}] for WSN. Thus, we construct and use ESD antennas based on SPIDA for the experiments conducted in this paper.





main.tex
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\begin{document}

\title{dRTI: Directional Radio Tomographic Imaging}
%
% You need the command \numberofauthors to handle the 'placement
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\author{
\alignauthor{Bo Wei$^\dag$$^\forall$$^\ddag$, Ambuj Varshney$^\S$, Wen Hu$^\ddag$$^\forall$,\\ Neal Patwari$^\varnothing$$^\bigtriangleup$, Thiemo Voigt$^\forall$$^\S$, Chun Tung Chou$^\dag$} \\
\affaddr{$^\dag$ University of New South Wales, Sydney, NSW, Australia} \\
\affaddr{$^\forall$ SICS, Stockholm, Sweden}\\
\affaddr{$^\ddag$ CSIRO Computational Informatics, Brisbane, Queensland, Australia}\\
\affaddr{$^\S$ Uppsala University, Uppsala, Sweden}\\
\affaddr{$^\varnothing$ University of Utah, Salt Lake City, Utah, USA}\\
\affaddr{$^\bigtriangleup$ Xandem Technology, Salt Lake City, Utah, USA}\\
 \email{\{bwei,ctchou\}@cse.unsw.edu.edu$^\dag$, ambuj.varshney@it.uu.se$^\S$, wen.hu@csiro.au$^\ddag$, } 
% \email{ambuj.varshney@it.uu.se$^\S$}
%\email{wen.hu@csiro.au$^\ddag$}
\email{npatwari@ece.utah.edu$^\varnothing$, thiemo@sics.se$^\forall$}
 %\email{thiemo@sics.se$^\forall$}
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Authors
}
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% Just remember to make sure that the TOTAL number of authors
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% number that will appear in the \additionalauthors section.

\maketitle
\begin{abstract}
Radio tomographic imaging (RTI) enables \emph{device free} localisation of people and objects in many challenging environments and situations. Its basic principle is to detect the changes in the statistics of some radio quality measurements in order to infer the presence of people and objects in the radio path. However, the localisation accuracy of RTI suffers from complicated radio propagation behaviours such as multipath fading and shadowing. In order to improve RTI localisation accuracy, we propose to use inexpensive and energy efficient electronically switched directional (ESD) antennas to improve the quality of radio link behaviour observations, and therefore, the localisation accuracy of RTI. We implement a directional RTI (dRTI) system to understand how directional antennas can be used to improve RTI localisation accuracy. We also study the impact of the choice of antenna directions on the localisation accuracy of dRTI and propose methods to effectively choose informative antenna directions to improve localisation accuracy while reducing overhead. We evaluate the performance of dRTI in diverse indoor environments and show that dRTI significantly outperforms the existing RTI localisation methods based on omni-directional antennas.
% by up to 39.7\%.



%In this paper, we investigate the benefits and overhead of directional antennas  in Radio Tomographic Imaging (RTI). RTI observes the radio link behaviours
%, i.e. changes in signal strength measurement made by a wireless network, 
% to infer the existence of (new) obstructive objects in the area of interest, which enables \emph{device free} localisation in Non Line of Sight (NLOS) environment (``\emph{see through the walls}'') and is significantly less intrusive compared to traditional methods such as camera surveillance. Therefore, RTI has many potential applications such as health care (assisted living), security, and military. However, the localisation accuracy of RTI suffers from complicated radio propagation behaviours such as (deep) fading and shadowing, in particular in NLOS environments. In order to improve the RTI localisation accuracy, we propose to use inexpensive and energy efficient Electronically Switched Directional (ESD)  antennas to improve the quality of radio link behaviour observations, and therefore, the localisation accuracy of RTI. We implement an end-to-end RTI system with ESD antennas (dRTI), and study the impact of link behaviour quality of directional communications enabled by the directional antennas. 
%%\av{I would instead mention the "impact of link quality behaviour  because of the directional transmissions and receptions/ directional communication" instead. Directional antennas  enable directional communication which results in different link quality behaviour} .  
%We evaluate the proposed dRTI in both LOS and NLOS environments, and show that dRTI outperforms 
%%\tv{I would put ``outperforms''}
%state-of-the-art RTI systems based on mean-based RTI (mRTI), variance-based RTI (vRTI), and multi channel RTI (cRTI) using omni-directional antennas %\av{ again i would instead mention omnidirectional communication. you should also take note that configuring ESD antenna to omni-directional mode is different from using omni-directional antenna.} 
%by up to 47.4\%. 
%
%\begin{figure}[!ht]
%    \centering
%    \includegraphics[scale = 0.7]{figure/testonmap.pdf}
%    \caption{ test on map  }\label{testonmap}
%\end{figure} 
\end{abstract}

%\category{H.4}{Information systems Applications}{Miscellaneous}
%
%\terms{Design, Experimentation, Performance}
%
%\keywords{Device-free, Radio Tomography, Electronically-switched directional  antennas, Localisation, Tracking}
%
\input{Tex/intro}
\input{Tex/background}
\input{Tex/method}
\input{Tex/experiment}
\input{Tex/related}

\vspace{-2mm}
\section{Conclusions}\label{sec:conclusion}
In this paper, we investigate how directional antennas can be used to improve localisation accuracy of RTI. We implement dRTI and show that obstructions have a greater impact on the link quality of directional links. This in turn significantly improves the localisation accuracy of dRTI. Since the number of antenna direction pairs between two dRTI nodes can be large (e.g., 36 in our dRTI system), we further propose methods to effectively select informative antenna direction pairs to reduce communication and energy overhead. We evaluate the proposed dRTI system in different indoor environments. Our extensive experiments show that dRTI significantly outperforms omni-directional RTI and multi-channel RTI
in both line-of-sight (LOS) and non-LOS ``through-wall'' environments. 

%by up to  compared to the omni-directional RTI and by up to \needtocheck{23\%} compared to recently proposed multi channel RTI. 



%pattern pair selection methods, which aim to selec the ``best'' direction pattern pairs to increase the tracking performance and reduce communication overhead. 
%We evaluated proposed dRTI system with experiment, which showed that dRTI increased the performance by up to 47\% compared to the omni-directional RTI.
%and by  up to 23\% compared to recently proposed multi channel RTI. 
%
%
%In this paper, we explore the advantages of directional communications for RTI to track people. 
%%We explain theoretically why the directional antenna can show the better accuracy for RTI, and conduct experiment to show its ability for decrease the possibility of ``false negative'' and ``false positive''. 
%We conduct experiments to show how directional communications, compared to omni directional counterparts,
%can significantly increase the variances with the presence of a person between two nodes, which in turn improve the performance of RTI based on variance in NLOS environment.  Since the number of direction pairs between two nodes can be large (e.g., 36 in the proposed dRTI system), we further propose the pattern pair selection methods, which aim to selec the ``best'' direction pattern pairs to increase the tracking performance and reduce communication overhead. 
%We evaluated proposed dRTI system with experiment, which showed that dRTI increased the performance by up to 47\% compared to the omni-directional RTI.
%and by  up to 23\% compared to recently proposed multi channel RTI. 
%%These results show radio tomographic imaging can benefit significantly from the application of EDS antennas. We also discuss how to optimize the deployment of the wireless nodes to increase the localizaing accuracy.
%

%ACKNOWLEDGMENTS are optional
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%Acknowledgement goes here.

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%Appendix A

%Appendix goes here.

% That's all folks!
\end{document}

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