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\DOI{10.5802/crphys.208}
\datereceived{2024-05-22}
%%\datererevised{2024-08-12}
\daterevised{2024-08-12}
\dateaccepted{2024-09-13}
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\dateposted{2024-11-07}
\begin{document}

\begin{noXML}

%\makeatletter
%\def\TITREspecial{\relax}
%\def\cdr@specialtitle@english{Energy in the heart of EM waves: modelling, measurements and management}
%\def\cdr@specialtitle@french{L'\'energie au c{\oe}ur des ondes \'electromagn\'etiques : mod\'elisation, mesures et gestion}
%\makeatother

\CDRsetmeta{articletype}{review}

\title{Implantable T\textsubscript{x}--R\textsubscript{x} wireless
systems. An overview of their efficiency analysis through scattering
matrix formalism}

\alttitle{Syst\`{e}mes implantables sans contact. Analyse de
l'efficacit\'{e} du transfert par le formalisme de la matrice de
diffusion}

\author{\firstname{Stavros} \lastname{Koulouridis}\CDRorcid{0000-0002-6102-7798}}
\address{University of Patras, 26504, Rio-Patra, Greece}
\email{stavros.koulouridis@upatras.gr}

\begin{abstract} 
Looking at wireless implantable systems as a pair of or more
T\textsubscript{x}--R\textsubscript{x} components, we discuss how their
efficiency can be calculated in order to achieve an optimum result that
can be evaluated over measurements and literature. To that end,
scattering parameters' notation is introduced instead of
{considerations of the gain, the propagation losses and the
radiation patterns}. Looking at the system as a black box,
remarks on optimum link calculation in relation to frequency, antenna
size, phantom use, matching circuit integration and efficiency
intensifiers are being carried out. International standards for allowed
power and safety levels are added to the discussion. Different
scenarios including telemetry, wireless harvesting and sensor
transmission information are included as examples.
\end{abstract} 

\begin{altabstract} 
En consid\'{e}rant un syst\`{e}me implantable sans contact comme une
paire de composants T\textsubscript{x}--R\textsubscript{x}
(\'{e}metteur-r\'{e}cepteur), l'article montre que l'efficacit\'{e} de
transfert peut \^{e}tre calcul\'{e}e en vue d'obtenir un r\'{e}sultat
optimal pouvant \^{e}tre \'{e}valu\'{e} au moyen de mesures ou de
r\'{e}sultats issus de la litt\'{e}rature. \`{A} cette fin, le
formalisme des param\`{e}tres S (matrice de diffusion) est introduit
\`{a} la place des quantit\'{e}s g\'{e}n\'{e}ralement utilis\'{e}es
(gain, pertes, diagramme de rayonnement). En consid\'{e}rant le
syst\`{e}me comme une bo\^{i}te noire, des remarques sur le calcul de
la liaison optimale sont formul\'{e}es selon la fr\'{e}quence, la
taille de l'antenne, l'utilisation d'un fant\^{o}me, l'int\'{e}gration
de circuits d'adaptation et d'amplificateurs d'efficacit\'{e}. Les
normes internationales relatives \`{a} la puissance autoris\'{e}e et
aux niveaux de s\'{e}curit\'{e} \`{a} respecter sont inclues dans la
discussion. Diff\'{e}rents sc\'{e}narios incluant la
t\'{e}l\'{e}m\'{e}trie, la r\'{e}cup\'{e}ration d'\'{e}nergie sans fil
et la transmission d'informations par des capteurs sont
pr\'{e}sent\'{e}s \`{a} titre d'exemples.
\end{altabstract} 

\keywords{\kwd{Scattering parameters}\kwd{Friis equation}\kwd{Link
budget}\kwd{SAR}\kwd{Wireless harvesting systems}}

\altkeywords{\kwd{Param\`{e}tres S}\kwd{Equation de Friis}\kwd{Bilan de
liaison}\kwd{DAS (d\'{e}bit d'absorption
sp\'{e}cifique)}\kwd{R\'{e}cup\'{e}ration d'\'{e}nergie sans fil}}

\def\thanksname{Note}
\thanks{This article follows the URSI-France workshop held on 21 and 22
March 2023 at Paris-Saclay.}

\maketitle

\end{noXML}

{%\advance\baselineskip by -.1pt
\section{Introduction}\label{secI}

Significant research has been focused on studying, realizing, and
implementing wireless body area networks. Applications include among
others implantable devices for vital data recording, cameras that
wirelessly transmit low-bit images, or wireless energy harvesting
systems for unobtrusive and sustainable implantable sensors. For
example, continuous non-invasive glucose measurements can help diabetes
patients~\cite{1}. Under a usual scenario, an
implantable device will obtain measurements, it will transmit them to
an external relay through an antenna, and the relay will transmit the
information to a party of ``interest'', like a patient, hospital or\break a
doctor. 

Electromagnetic propagation inside the lossy inhomogeneous body which
is composed of various organs of different electric properties causes
increased absorption in the body. In addition, the complex environment
introduces multiple reflections that can derange expected antenna
performance. In addition, the inhomogeneous body structure has an
effect on antenna behavior since it creates impedance mismatches. In
effect the antenna radiation properties are affected by the body and
the optimum performance of an implantable antenna design is not a
straightforward process. 


Research has considered several frequency bands for implantable
sensors' design. Higher frequencies permit the use of larger electrical
designs (while being physically small). However, when the depth
increases, the higher frequencies lead to increased losses, even higher
than the theoretically predicted ones~\cite{2}. In some cases, the
large distances between an external relay and the implantable antenna
makes obligatory the use of smaller frequencies. Of course, the
frequency selection is also related to the specific scenario examined.
Dual (or triple) frequency implantable systems can be also proposed,
sending a wake signal at higher frequency and relaying medical
information at lower frequency~\cite{3}, or using a higher frequency
where nominally higher power is permitted for wireless energy
transfer~\cite{4,5}. Interestingly, when ideal scenarios are
considered, an optimum frequency for the implantable antenna can be
determined~\cite{6}. However, when some of the parameters are altered,
optimum design frequency can actually change.


Wireless Power Transfer systems introduce additional complexity in the
implantable sensor design. First, their use can allow, in some cases,
for battery-less designs or, in general, avoiding use of wires. Still,
a rectenna is to be used, meaning that the receiving antenna needs to
be connected to a rectifying circuit and sometimes voltage boosters or
other electronic components~\cite{5}. In such cases,
the antenna is coupled with the circuit and its design is seen as a
single component, i.e., the ``rectenna'', which introduces additional
design parameters but also adds degrees of freedom in the final
device.


{In other cases, extra} components are introduced in addition to the
implantable antenna{. For example, external ``facilitators''} that are
applied to the body and can increase {implantable antenna reception or
the link with an external antenna are proposed. Or, more than one
implantable antenna may be considered that needs to communicate or
relay information to other components, etc.} 


{Obtaining the optimum design is hence a complex process that can be
affected by different factors. In order to simplify the study and also
offer a measure of achievement, the use of scattering matrix can be
introduced. In that case, we study a system that has two ports and
includes the implanted and the external antenna, the multiple implanted
antennas or all the components that} constitute {the design. In the end
the system has two ports, one input and one output, that can be used to
evaluate the system efficiency and determine its performance. The
simulations can be directly compared with measurements and w}ith
several designs in the litt{e}rature.


{In this paper, after a short introduction into scattering parameters
use for the system under consideration, we determine how the system
efficiency can be calculated for two cases. When simply two antennas
(Section~\ref{secII.A}) are used and when additional circuits connected
to the antennas are considered in the case of harvesting systems for
example (Section~\ref{secII.A.1}). Link budget considerations follow
for telemetry systems. International restrictions for wireless systems
used in implantable designs are then presented, accompanied by power
limitations as reported in international standards. Some examples are
discussed in Section~\ref{secIII}. First, we briefly discuss about
ideal frequency for optimum efficiency when two implantable antennas
are communicating with each other. Then, we examine how antenna size
and radiation pattern can affect efficiency by analyzing four
implantable microstrip antennas operating at MedRadio Band (400~MHz
region). This region is selected, since it seems to be ideal for deeply
implantable systems. When maximum allowed power for antennas is also
considered, discussion for optimum frequency is then carried out, in
order to close a link between an external antenna and an implantable
antenna as is required for telemetry systems. Next, a couple of
rectennas is considered in order to present an example of the necessity
to include circuits in the scattering matrix consideration.
Section~\ref{secIII} ends with a short comment on how added surfaces,
on the skin, can increase the system efficiency. Some very simple
solutions are presented in comparison with much more sophisticated ones
based on metasurfaces for example. Finally, some conclusions are drawn
in Section~\ref{secIV}.}


\section{System overview}\label{secII}
While the implantable antenna design demands considerable efforts, in
order to evaluate the proposed setup performance, the problem needs to
be examined as a system composed of two, three or multiple components.
In a system design point of view, the implantable and the external
antennas or multiple implantable antennas will be part of a two-port
system represented by the well-known scattering $S$-parameters~\cite{7}
{as shown in} Figure~\ref{fig1}. In that system, the communication
between two antennas can be one scattering matrix with individual
scattering parameters, and the intercommunication between antenna pairs
can be represented by a total scattering matrix which has been produced
by a chain of separate scattering matrices. Selection of the system
under examination relates to the problem under investigation. In any
case, we can choose port~1 to be T$_{\mathrm{x}}$ {antenna's feeding
point and port~2 to be R}$_{\mathrm{x}}$ {antenna's
(R}$_{\mathrm{x}}$) reception point. In a multi antenna system, one
antenna would be the T$_{\mathrm{x}}$ {antenna and one other would be
the R}$_{\mathrm{x}}$ {antenna, while the others could be intermediate
parts of the system. The scattering~2 ${\times}$~2~$S$-matrix which is
generated represents the path link between the two antennas
independently of what lies between them. Their input impedance is also
included as part of the scattering matrix. Notably, in such a setting
the two antennas system is the same for examining the
reception/transmission of data or a wireless harvesting setup.
Furthermore, the in-between distance (near, intermediate or far-field
conditions) does not affect the system overview. Hence, the coupling
between the antennas is also included in the matrix. While the $S$-matrix
should be symmetric for a passive and/or linear element system, let us
assume that, in general, we can have an asymmetric system, where
non-linear components can be integrated into the system, and
therefore:}
{\begin{equation}\label{eq1}
S=\left[\begin{matrix}
S_{11} & S_{12}\\
S_{21} & S_{22}
\end{matrix}\right] 
\end{equation}}\unskip
where $S_{12}\neq S_{21}$ and of course $S_{11}\neq S_{22}$ since the
two antennas can be different. $S$-parameter matrix can be obtained from
an electromagnetic solver and/or measurements for the fabricated
system. Notably, comparison between measurements and simulations can be
straightforward, adding another advantage on using $S$-parameters. The
final 2~${\times}$~2 scattering matrix, representing either each
itemized link or the total link, will be connected to a load (either
the R$_{\mathrm{x}}$ {antenna termination or another circuit) and will
be fed by a voltage source with its internal impedance. This is shown
in} Figure~\ref{fig2}}.

\begin{figure}
\includegraphics{fig01}
\caption{\label{fig1}Communication link between implantable antennas or
implantable antennas and external antenna replaced by one or more
scattering matrices. Each scattering matric can represent an antenna
pair. The interconnection between the antenna pairs can be replaced by
a chain of scattering matrices, or at the end by a total scattering
matrix.}
\end{figure}

\begin{figure}
\includegraphics{fig02}
\caption{\label{fig2}$S$-parameter circuit of an antenna pair with
voltage source and termination load.}
\end{figure}

\subsection{Evaluation of system efficiency}\label{secII.A}

In order to calculate the power received from the external or the
implantable antenna, the well-known Friis formula can be utilized. This
predicts the power received from an antenna in relation to the power
radiated from a transmitting antenna, their gain, path loss, antennae's
matching and polarization. It is given by the following equation.
{\begin{equation}
\label{eq2}
P_{\mathrm{r}}=\frac{\lambda ^{2}}{(4\rmpi r)^{2}}\cdot
G_{\mathrm{r}}\cdot G_{\mathrm{t}}\cdot (1-| S_{11}| ^{2})\cdot
(1-| S_{22}| ^{2})\cdot \mathrm{PLF}\cdot P_{\mathrm{t}}
\end{equation}}\unskip
where $P_{\mathrm{r}}$ {and} $P_{\mathrm{t}}$ {are the power received
and transmitted respectively,} $G_{\mathrm{r}}$ {and} $G_{\mathrm{t}}$
{are the antennas' received and transmitted realized gain
respectively,} ${\lambda}$ {is the wavelength of the intermediate
medium,} {\textit{r}} {is the in-between
distance and} {{PLF}} {is the polarization factor (equal to 1
when the antennas are for example aligned and linearly polarized). It
should be noted that the first product term and especially the
wavelength/distance term (i.e.,} ${\lambda ^{2}}/{(4\rmpi
r)^{2}}${) expresses the free space (inside air or in a
homogeneous infinite material) path loss, representing a spherical
plane wave. Hence, far-field conditions and unobtrusive, free of
hurdles, propagation should be observed. When an implantable antenna is
for example receiving signal from an external transmitter the
electromagnetic wave propagates into air and the body while multiple
reflections are occurring as the signal passes through the complex body
environment. To take into account non-ideal propagation (but without
being able to avoid the far-field restriction) the above equation can
be transformed into}
{\begin{equation}
\label{eq3}
P_{\mathrm{r}}=\frac{\lambda ^{2}}{(4\rmpi )^{2}}\left(\frac{1}{r}\right)^{\gamma }\cdot
G_{\mathrm{r}}\cdot G_{\mathrm{t}}\cdot (1-| S_{11}| ^{2})\cdot (1-| S_{22}| ^{2})\cdot \mathrm{PLF}\cdot P_{\mathrm{t}}. 
\end{equation}}\unskip

{Index} {${\gamma}$} {can have theoretically any value from 1 to
infinity. For implantable antenna systems values are definitely higher
than 2. Index} {${\gamma}$}{, in implantable antenna problems is
obtained via simulation or measurements since no theoretical model
exists.} The process involves the curve fitting of measurements
obtained at variable distances~\cite{8}. The outcome
is unique to the system under investigation. Defining the path loss
exponent can be of course useful but, in reality, it cannot offer a
better overview of how well the pair implantable antenna/external
antenna operates. 


{Equation~(\ref{eq2}) permits us to focus on the parameters that affect the
reception of an antenna. These are the transmitting antenna gain, the
receiving antenna gain, the matching of each antenna, the path losses
that occur between the transmitting and receiving antenna and of course
their polarization mismatch. While using Equation~(\ref{eq2}), would make
the case ideal, in reality it is easily understood from the above
discussion that in the case of implantable antenna and external
transmitter, the predicted received power is simply the highest
achievable~\cite{9}, and there can be many factors that can affect this
link. Since we are interested in estimating how well the system
implantable antenna/external antenna behaves, we should actually use
the scattering parameters of $S$-matrix. From the scattering parameter
theory}~\cite{7}, it is very easily understood that: \looseness=-1
{\begin{equation}
\label{eq4}
| S_{21}| ^{2}=\frac{P_{\mathrm{r}}}{P_{\mathrm{t}}}.
\end{equation}}\unskip

In that case from Equation~(\ref{eq2}) 
{\begin{equation}
\label{eq5}
| S_{21}| ^{2}=\frac{\lambda ^{2}}{(4\rmpi r)^{2}}\cdot G_{\mathrm{r}}\cdot G_{\mathrm{t}}\cdot (1-| S_{11}| ^{2})\cdot 
(1-| S_{22}| ^{2})\cdot \mathrm{PLF}.
\end{equation}}\unskip

{It is easily understood that efficiency} {\textit{n}} {of the system
is expressed by the ratio of received power} $P_{\mathrm{r}}$ {over the
transmitted power} $P_{\mathrm{t}}${. Then:}
{\begin{equation}
\label{eq6}
n=| S_{21}|^{2}
\end{equation}}\unskip
where $| S_{21}| ^{2}$ {can be calculated by Equation~(\ref{eq5}). However, it
might be more useful, sometimes, to calculate a slightly altered
efficiency where the mismatch has been removed from the \mbox{calculations.}
This would be useful in the case we would like to study how the
intermediate path can affect the system. Indeed, if we transform
Equation~(\ref{eq5}) into:}
{\begin{equation}
\label{eq7}
\frac{| S_{21}| ^{2}}{(1-| S_{11}| ^{2})\cdot (1-| S_{22}| ^{2})}
=\frac{\lambda ^{2}}{(4\rmpi r)^{2}}\cdot 
G_{\mathrm{r}}\cdot G_{\mathrm{t}}\cdot \mathrm{PLF}
\end{equation}}\unskip
{the right part refers to the system path loss, antenna gain and
polarization factor and therefore it can actually reveal how the
antenna gain (which can be affected by the surrounding complex
environment) and the losses in between can affect the system
``efficiency''} $n'${. In that case we can write}
{\begin{equation}
\label{eq8}
n'=\frac{| S_{21}| ^{2}}{(1-| S_{11}| ^{2})\cdot (1-| S_{22}| ^{2})}.
\end{equation}}\unskip


{Notably, in order to have equivalency with the circuit of}
Figure~\ref{fig2} we should note that received power $P_{\mathrm{r}}=P_{\mathrm{L}}$ when
$Z_{\mathrm{L}}=Z_{0}$ while transmitted power $P_{\mathrm{t}}$ is equal to the power
provided by a source at the T$_{\mathrm{x}}$ antenna input, that is
$P_{\mathrm{t}}=P_{\mathrm{in}}$.

\subsubsection{Evaluation of system efficiency at load. Use of matching
circuits}\label{secII.A.1}


{The system efficiency calculations at the antenna point do not
consider the power offered to the system, or the power that would be
delivered to a load attached at the R$_{\mathrm{x}}$ system
component. In addition, it does not take into account the use of
antenna input impedance in order, for example, to match the antenna to
a harvesting circuit or other kind of circuits implemented in the
design. With reference to} Figure~\ref{fig2}, the
efficiency can be calculated from~\cite{3,10,11}: 
{\begin{equation}
\label{eq9}
n=\frac{P_{\mathrm{L}}}{P_{\mathrm{in}}}=\frac{P_{\mathrm{L}}}{(1-| \rmGamma _{\mathrm{in}}| ^{2})P_{\mathrm{inc}}}=
\frac{| S_{21}| ^{2}(1-| \rmGamma _{\mathrm{L}}| ^{2})}{(1-| \rmGamma _{\mathrm{in}}| ^{2})(1-| S_{22}\rmGamma _{\mathrm{L}}| ^{2})}
\end{equation}}\unskip
where $P_{\mathrm{L}}$ is the power delivered to the load of the receiving
antenna and $P_{\mathrm{in}}$ is the power offered to antenna.
${\rmGamma}_{\mathrm{in}}$ {is the reflection coefficient at port~1 and
is equal~\cite{7} {to}
{\begin{equation}
\label{eq10}
\rmGamma _{\mathrm{in}}=S_{11}+\frac{S_{12}S_{21}\rmGamma _{\mathrm{L}}}{1-S_{22}\rmGamma _{\mathrm{L}}}
\end{equation}}\unskip
{and} ${\rmGamma}_{\mathrm{L}}$ is the reflection coefficient at the load
calculated by}
{\begin{equation}
\label{eq11}
\rmGamma _{\mathrm{L}}=\frac{Z_{\mathrm{L}}-Z_{0}}{Z_{\mathrm{L}}+Z_{0}}.
\end{equation}}\unskip

The $S$-matrix can include, for example, the T$_{\mathrm{x}}$ antenna
with a matching circuit and the R$_{\mathrm{x}}$ antenna which is
connected to a harvesting circuit that will feed the load $Z_{\mathrm{L}}$. It
is noted that the $S$-matrix can be obtained for characteristic
impedance $Z_{0}=50~\rmOmega$. Still, the antenna input impedance can
differ from the ideal $Z_{0}$. The ultimate criterion for such a
design is always the maximization of the system efficiency. In
addition, by relaxing the antenna input impedance requirements, we can
seek much more efficient harvesting circuits.

\subsection{Link budget for wireless communications}\label{secII.B}


For some scenarios thar require telemetry or generally consider the
transmission of information, the link budget needs to be considered.
Link budget should consider the antenna losses, path losses, required
bit rate, antenna gain, etc. Power input is controlled by
electromagnetic compatibility safety standards for maximum power
absorption from the tissues and electromagnetic interference avoidance
and it variates with frequency and antenna size. In order to secure a
communication link, one needs to achieve a positive carrier-to-noise
density ratio $C/N_{0}$ {budget. $C/N_{0}$ describes the strength of
the power wave related to the noise. In} Table~\ref{tabI}, an example
link budget is shown, including parameters to examine and indicative
specifications of a satisfactory communication link~\cite{12,13}.


\begin{table}
\caption{\label{tabI}Link budget parameters{\vspace*{2pt}}}
\begin{tabular}{cccc}
\thead
{Component} & {Description} & {Notation} & {Formula/data} \\
\endthead
\morerows{2}{Transmitter T$_{\mathrm{x}}$} & T$_{\mathrm{x}}$ Power {(}dBW{)} & $P_{\mathrm{Tx}}$ &  \\ 
 & Cable/feeding losses {(}dB{)} & $L_{\mathrm{Tx}}$ &  \\ 
 & T$_{\mathrm{x}}$ Antenna gain {(}dBi{)} & $G_{\mathrm{Tx}}$ & \vspace*{4pt} \\ 
\morerows{1}{Propagation} & Frequency & $f$ &  \\ 
 & Space path loss {(}dB{)} & $P_{\mathrm{Loss}}$ & $10\log_{10}\left(\frac{(4\rmpi )^{2}}{\lambda ^{2}}r^{\gamma }\right)$\vspace*{4pt} \\ 
\morerows{6}{Receiver R$_{\mathrm{x}}$} & R$_{\mathrm{x}}$ Power {(}dBW{)} & $P_{\mathrm{Rx}}$ &  \\ 
 & Cable/feeding losses {(}dB{)} & $L_{\mathrm{Rx}}$ &  \\ 
 & R$_{\mathrm{x}}$ Antenna gain {(}dBi{)} & $G_{\mathrm{Rx}}$ &  \\ 
 & Ambient temperature {(}K{)} & $T_{0}$ & 293 \\ 
 & Boltzman constant & k & $1.38 \times 10^{-23}$  \\ 
 & Noise figure {(}dB{)} & NF & 2.5 \\
 & Noise power density {(}dB/Hz{)} & $N_{0}$ & ${-}$201.7\vspace*{4pt} \\ 
\morerows{4}{Signal quality} & Bit Rate {(}b/s{)} & $B_{\mathrm{r}}$ & $10^{6}$ \\ 
 & Bit error rate & BER & $1\times 10^{-5}$ \\ 
 & $E_{b}/N_{0}$ (ideal PSK) {(}dB{)}  & $E_{b}/N_{0}$ & 9.6 \\ 
 & Coding gain {(}dB{)} & $G_{\mathrm{c}}$ & 0 \\ 
 & Fixing deterioration {(}dB{)} & $G_{\mathrm{d}}$ & 2.5 
\botline
\end{tabular}
{\vspace*{8pt}}
\end{table}

{Cable/feeding losses in} Table~\ref{tabI} {include mismatch losses as
a positive number. In the same manner, space path losses have been
reversed since they should be retracted from final link budget.
Equations to calculate the required link budget follow:}
{\begin{eqnarray}
&\displaystyle N_{0}=10\log_{10}({k})+\log_{10}(T_{i})\   {{(}\mathrm{dB}/\mathrm{Hz}{)}}   \label{eq12}\Seqnsplit
&\displaystyle T_{i}=T_{0}(NF-1)\  {{(}\mathrm{K}{)}} \label{eq13}\Seqnsplit
&\displaystyle \text{Achievable link}~C/N_{0}=P_{\mathrm{Tx}}-L_{\mathrm{Tx}}+G_{\mathrm{Tx}}-P_{\mathrm{Loss}}+P_{\mathrm{Rx}}-L_{\mathrm{Rx}}+
G_{\mathrm{Rx}}-N_{0}\   {{(}\mathrm{dB}/\mathrm{Hz}{)}} \label{eq14}\Seqnsplit
&\displaystyle \text{Required
link}~C/N_{0}=\frac{E_{b}}{N_{0}}+10\log_{10}(B_{\mathrm{r}})-G_{\mathrm{c}}+G_{\mathrm{d}} \  {{(}\mathrm{dB}/\mathrm{Hz}{)}}. \label{eq15}
\end{eqnarray}}\unskip

{For a successful link we should have a positive margin {(}dB{)} where
this is given by Equation~(\ref{eq16})}
{\begin{equation}\label{eq16}
\text{Margin}=\text{Achievable link}~ C/N_{0}-\text{Required link}~ C/N_{0}\ {{(}\mathrm{dB}{)}}.
\end{equation}}\unskip

When the $S$ scattering matrix is used, the link budget can be also
calculated. In that case, $S_{21}$ parameter will include all losses
and gain occurred as can be easily seen by
Equations~(\ref{eq2})--(\ref{eq4}). In that case, $S_{21}$ {in dB will be
given by} 
{\begin{equation}\label{eq17}
S_{21}=G_{\mathrm{Tx}}-L_{\mathrm{Tx}}-P_{\mathrm{Loss}}-L_{\mathrm{Rx}}+G_{\mathrm{Rx}} \  {{(}\mathrm{dB}{)}}. 
\end{equation}}\unskip


And the Achievable and Required Link Budgets, considering
Equation~(\ref{eq4}), will be finally:
{\begin{eqnarray}
&\displaystyle \text{Achievable link}~ C/N_{0}=P_{\mathrm{Tx}}+S_{21}+201.7\   {{(}\mathrm{dB}/\mathrm{Hz}{)}}   \label{eq18}\Seqnsplit
&\displaystyle \text{Required link}~ C/N_{0}=72.1 \  {{(}\mathrm{dB}/\mathrm{Hz}{)}}.\label{eq19}
\end{eqnarray}}\unskip

\subsection{Frequency, safety and radiated power}\label{secII.C}

Implantable devices and systems are mainly developed in sub-GHz or a
few GHz region. While mm waves have been employed for wearable devices,
this is not preferred for the embedded into tissue systems because of
high absorption losses. The device development is regulated by several
organizations around the world. Low MHz and kHz region has been used
for inductive wireless charging and animal tags. However, wireless
device development for communication is not practical and it is not
considered in such low frequencies. 

The main restriction for wireless implantable communication systems,
apart from the operating frequency, is the maximum emitted power. It
should be noted that this restriction is not necessarily related to the
safety of the user but mostly to avoiding electromagnetic interference
issues. Two quantities are usually used. ERP or Effective Radiated
Power which represents the power fed to a matched antenna, and
Equivalent Isotropically Radiated Power or EIRP which represents the
maximum power radiated from an antenna, that is the power fed to
matched antenna (in Watts) times the antenna gain over isotropic
radiator. In an overview of the frequencies (Table~\ref{tabII}), it is
{seen that specific frequencies have very low power limit. In that case
the main goal is to perform close distance communication. In other
cases, high emitted power is allowed, especially when telemetry is
sought.}

\begin{table}
\caption{Typical medical frequencies for implantable devices\label{tabII}
\vspace*{2pt}}
\begin{tabular}{cccc}
\thead
NameTag & {Frequency (MHz)} & {ERP (dBm)} & {Reference} \\
\endthead
\morerows{5}{MedRadio} & 401--406  & ${-}$16  & \cite{16,17,18}  \\
             & 413--419  & ${-}$16{$^{\mathrm{a}}$} &  \cite{16} \\
             & 426--432  & ${-}$16{$^{\mathrm{a}}$} &   \cite{16} \\
             & 438--444  & ${-}$16{$^{\mathrm{a}}$} &   \cite{16} \\
             & 451--457  & ${-}$16{$^{\mathrm{a}}$} &   \cite{16} \\
             & 2360--2400& ${-}$16{$^{\mathrm{a}}$} &   \cite{16} \vspace*{8pt}\\
\morerows{2}{\parbox{4.5cm}{\raggedright\hangindent 1pc Wireless medical telemetry service (WMTS)}}  & 608--614 & 31.8 & \cite{19} \\
 & 1395--1400 & 31.8 & \cite{19} \\
 & 1427--1432 & 31.8 & \cite{19}\vspace*{8pt} \\
\morerows{4}{\parbox{4.5cm}{\raggedright\hangindent 1pc Industrial, scientific and medical services band/ISM}} & 433.05--434.79 & 10                          & \cite{20} \\
                                                     & 863--870        & 14                          & \cite{20} \\
                                                     & 902--928        & 30 (36 EIRP)                & \cite{21} \\
                                                     & 2400--2484      & 30 (36 EIRP){$^{\mathrm{b}}$} & \cite{21} \\
                                                     & 5725--5875      & 30 (36 EIRP){$^{\mathrm{b}}$} & \cite{21}
\botline
\end{tabular}
\xxtabnote{{$^{\mathrm{a}}$} It is assumed that it is incorporated from the main restriction for 401--406 MHz region.}
\xxtabnote{{$^{\mathrm{b}}$} In general, EIRP can be larger for specific cases \cite{21}.\vspace*{2pt}}
\end{table}

{For the frequencies shown in Table~\ref{tabII}, electromagnetic safety
for avoiding effects from electromagnetic waves to humans is
represented by Specific Absorption Rate, or SAR {(}W/kg{)}. SAR is
calculated inside biological tissues and is given by:} 
{\begin{equation}\label{eq20}
\mathrm{SAR}=\frac{\sigma E ^{2}}{2\rho } \  {{(}\mathrm{W}/\mathrm{kg}{)}} 
\end{equation}}\unskip
{where} ${\sigma}$ {and} ${\rho}$ {are tissue conductivity (S/m)
and density (kg/m$^{3}$) respectively while} {\textit{E}} {represents
electric field magnitude. Standards for safety levels, with respect to
human exposure to radiofrequency electromagnetic fields are provided
in} Table~\ref{tabIII}~\cite{14,15}. General public safety is usually
considered.

\begin{table}
\caption{\label{tabIII} SAR safety levels (100~kHz--6~GHz)}
\begin{tabular}{ccc}
\thead
{Exposure conditions} & {General public  SAR {(}W/kg{)}$^{\mathrm{a}}$} & 
\parbox[t]{4.5cm}{\centering Persons in restricted environment SAR (W/kg)$^{\mathrm{a}}$}\vspace*{2pt} \\
\endthead
Whole body & 0.08 & {0.4} \\ 
(Local) head and torso {$^{\mathrm{b}}$} & 2 & {10} \\
(Local) limbs and pinae{$^{\mathrm{b}}$} & 4 & {20} 
\botline
\end{tabular}
\tabnote{{$^{\mathrm{a}}$}~Averaged over 30~min for whole body exposure and
6~min for local exposure.}  
\tabnote{$^{\mathrm{b}}$ Averaged over
any 10~g of tissue formed in cubical volume.}
\end{table}

\section{Investigation of \textit{S}$_{21}$ link}\label{secIII}

\subsection{System efficiency under homogeneous environments}\label{secIII.A}


There is certainly an optimum efficiency that can be achieved by an
antenna. There are several discussions around its definition. In order
to achieve it, ideal environment can be considered. For example,
in~\cite{6} {a capsule antenna embedded in the middle of a three layer
spherical phantom is examined. The three layers represent from center
to surface, muscle, fat and skin tissues. It is verified that an
optimum efficiency exists for such a small antenna (detained in a
specific sphere of small radius) while maximum optimum efficiency
decreases with sphere radius increase. Naturally, such an ideal
environment can be hardly met. Still, the contribution of the work is
significant since it shows that for deep implantation the optimum
frequency becomes lower. It should not be forgotten however that the
antenna electrical size is competing against physical size and
therefore for lower frequencies (Medradio band of 400~MHz for
example), the antenna electrical size needs to be very small leading to
inefficient antennas but with less propagation losses because of the
higher wavelength. On the other hand, the higher frequencies (of
2.4~GHz ISM band for example) allow for electrically larger and of
higher efficiency antennas with the cost of higher body losses because
of the smaller wavelength. This fact leads us to the observation that
while general conclusions can be made for optimum frequency and antenna
size, the T}$_{\mathrm{x}}${{--}R}$_{\mathrm{x}}$ {pair should be
always seen as a system where the system efficiency is obtained\break per
case.} 

In~\cite{22} two identical directive wire dipole antennas are
designed and used to investigate the link between them when they are
both implanted inside a muscle tissue phantom (see Figure~\ref{fig3}).
Examined frequency region varies from 0.8~GHz to 2.8~GHz. Detailed
comparison for a loss-less or lossy environment is carried out
accompanied by measurements when the two antennas are embedded inside
minced pork meat. As shown the achieved measured link (measured $|
S_{21}| ^{2}$) is around ${-}$35 and ${-}$40~dB for 6~cm and 8~cm distance
respectively and for the 1~GHz to 1.2~GHz frequency window where the
antenna is also matched. Interestingly, as discussed in~\cite{22}, a
similar problem for a loop antenna and for a realistic phantom when the
antenna is placed in several positions, reveals the in-body $| S_{21}|
^{2}$ to be around ${-}$50~dB for the same frequency region~\cite{23},
while in~\cite{24} {and a 2.4~GHz bow-tie antenna link for a spherical
three-layer phantom gives a ${-}$70~dB result. As can be seen by the
above results, the simulation scenario examined can reveal different
results and, in that sense, each problem is unique. While general
conclusions can be drawn, results can differentiate when parameters of
the problem do change. Frequency can obviously differentiate the
results.} What is sometimes forgotten, however, is that antenna
behavior and radiation mechanism can also affect the results. Antenna
size can be a crucial\break parameter.

\begin{figure}
\includegraphics{fig03}
\caption{\label{fig3} From~\cite{22}. Link simulation and measurements
for two identical antennas inside tissue environment. (a)~Problem under
investigation; (b)~directive antennas used in the simulation environment 
(dielectric muscle tissue box shown with pink color);
(c)~experimental measurement for minced pork meat.}
\end{figure}

\subsection{System efficiency for complex environments}\label{secIII.B}


{A computational experiment is carried out for four implantable
microstrip antennas taken from~\cite{3,25,26,27} {whose details are shown
in} Table~\ref{tabIV}. Several other antennas could be considered.
Microstrip antennas are usually chosen since they carry a ground plane
and they can support the electronic circuitry on their back. The
antennas of}~\cite{3,25,26,27} {operate in the MedRadio band}~\cite{16},
at 402--405~MHz but they have different size and overall volume. In
Figure~\ref{fig5}d, the $S_{21}$ link is investigated for a $100\times
100\times 100~\mathrm{mm}^{3}$ skin box between two identical versions
of the antennas facing each-other at variable distances. As seen, the
maximum $S_{21}$ link variates from ${-}$25~dB for the larger antenna to
${-}$50~dB for the smaller antenna for a 20~mm in-between distance. The
lowest link variates from ${-}$40~dB to ${-}$85~dB for 80~mm in-between
distance.

\begin{table}
\caption{Implantable antennas tested for link estimation in scenarios
of Figure~\ref{fig4}\label{tabIV}}
\fontsize{9.7}{12}\selectfont\tabcolsep=3pt
\begin{tabular}{ccccc}
\thead
{Antenna} & Design/characteristics & 
\parbox[t]{2.5cm}{\centering Frequency of operation (MHz)} & 
\parbox[t]{2.3cm}{SAR$_{1\mathrm{g}}$ (W/kg)} & 
\parbox[t]{1.5cm}{\centering Volume (mm$^{3}$)} \\
\endthead
``A'' from~\cite{25} & Spiral, one layer & 402--405 & 100 & 3457 \\
``B'' from~\cite{3} & Serpentine, one layer & 402--405, 2.4--2.48 & 360 (402~MHz) & \0608 \\
``C'' from~\cite{26} & Stacked PIFA, double layer & 402--405 & 300 & \0336 \\
``D'' from~\cite{27} & Stacked, serpentine, double layer & 402--405 & 660 & \0\033
\botline
\end{tabular}
{\vspace*{6pt}}
\end{table}

\begin{figure}
\includegraphics{fig04}
\caption{\label{fig4}Implantable microstrip antenna (see 
Table~\ref{tabIV}) in a tissue skin box $100\times 100\times
100~\mathrm{mm}^{3}$ and an external dipole or patch antenna at
broadside or at the side of the implantable antenna. Tests (see
Figure~\ref{fig5}) were run for 402~MHz for the antennas
from~\cite{3,25,26,27} and included either the link calculation between
the external and the implantable antennas (a, b, c) or between the
implantable antennas (d).}
\end{figure}

\begin{figure}
\includegraphics{fig05}
\caption{\label{fig5} $| S_{21}| ^{2}$ {(}dB{)} for either an external
dipole and/or a microstrip patch or two identical implantable antennas
at $f=402$~MHz. Implantable antennas ``A'', ``B'', ``C'', ``D'' are
described in Table~\ref{tabIV}. Cases examined: (a)
External dipole (Figure~\ref{fig4}a) or microstrip
patch (Figure~\ref{fig4}b) on the side when the
external antenna distance $d$ variates and the implantable antenna is
kept at depth $=$ 5~mm; (b) External microstrip patch on the side
(Figure~\ref{fig4}b) or facing the implantable
antenna (Figure~\ref{fig4}c) when the external
distance $d$ variates and the implantable antenna is kept at depth $=$
5~mm; (c) External microstrip patch
(Figure~\ref{fig4}c) with implantable antenna when
the external distance from the box surface is kept constant at 500~mm
and the implantable antenna depth variates; (d) Identical antennas (A,
B, C, D) immersed in the skin box, are facing each-other and their
distance variates. Symmetry over box center is kept.}
\vspace*{3pt}
\end{figure}

{While this distance falls in the near to medium field region, certain
conclusions can be drawn. In comparison to}~\cite{22}
{and for distance of 6~cm, maximum $S_{21}$ {value is at an almost equal
value of ${-}$35~dB. Notably, this happens for different frequencies with a
ratio of~3:1. Of course, the antenna in}~\cite{22} is
intentionally designed to realize an implantable-to-implantable link
and is relatively electrically large. Electrical size can indeed affect
efficiency. As shown in Figure~\ref{fig5}d, 
the smallest antenna achieves multiple
dB lower link as compared to its larger counterparts. In addition, the
four tested antennas do not follow the same linear variation with
distance in the calculated $S_{21}$. The antenna radiation mechanism and the
boundary of the skin box can obviously affect the maximum achievable
link. In addition, there might be an optimum frequency in relation to
the antenna size and tissue properties for minimizing the internal
losses~\cite{6}.

In a homogeneous environment the frequency region of 900~MHz to 1.5~GHz
could be the optimum one~\cite{6,7}. Still, as has been noted,
the implantable antenna design can affect the results while the
non-homogeneous environment has not been extensively studied.


{It should be noted that the calculated SAR$_{1\mathrm{g}}$ {in}
Table~\ref{tabIV} {is for input power of 1~W (30~dbm) and is naturally
high. It has been provided for comparison between the different
antennas. Still, as has been discussed in Section~\ref{secII.C} maximum
allowable power for implantable antennas varies. For example, at
400~MHz band (Medradio) maximum allowable power is ${-}$16~dbm (25~$\upmu$W).
In that case the results in} Table~\ref{tabIV} should be divided by
40,000 (${=}$1~W/25~$\upmu$W).

{When the discussion moves to the link between an implantable antenna
and an external antenna, different remarks could be drawn. Firstly, the
implantable antenna far-field radiation properties need to be taken
into account. Secondly, the external antenna type can also affect the
outcome. Concerning the numerical experiment shown in}
Figure~\ref{fig4}, a ${\lambda}/2$ dipole or a}
${\lambda}/4$ rectangular patch are used as external antennas when
the previously discussed microstrip implanted antennas from}
\cite{3,25,26,27} {(see}
Table~\ref{tabIV}) are immersed inside a $100 \times 100 \times
100~\mathrm{mm}^{3}$ skin box. Experiments include the placement of the
external antenna on the side of the implanted antennas
(Figures~\ref{fig4}a,b) or at broadside facing each
other (Figure~\ref{fig4}c) and calculation of
$S_{21}$ link when the distance of the external antenna to the skin box
surface varies (Figure~\ref{fig5}a for external
antennas on side and Figure~\ref{fig5}b for
comparison between patch on the side and at broadside) or when the
external rectangular patch antenna is kept at fixed distance at
broadside and the implantable antenna depth varies
(Figure~\ref{fig5}c). 


External antennas were placed on the side because multiple
miniaturized microstrip antennas operate at dipole mode. In that case,
the optimum reception occurs when the external antenna is on the side.
For the numerical example investigated, even if we have not followed an
optimum placement between the implantable and the external antenna on
side, the link is higher. Indeed, for the frequency under investigation
(402~MHz), when $S_{21}$ {from the external patch antenna on the side is
compared against $S_{21}$ {from the patch antenna at broadside the link
for the patch antenna on the side is 5 to 10~dB higher (see}
Figure~\ref{fig5}b). The smallest difference occurs
for the smallest implantable antenna. This result holds for distances
from 100~mm to 500~mm. $S_{21}$ {varies almost linearly with the
external antenna distance to the skin box surface.} 

{For the same experiment, when we use the dipole and the patch antennas
on the side, the $S_{21}$ {link is higher for the patch antenna (see}
Figure~\ref{fig5}a). This is normally expected
since the patch antenna has higher gain. Interestingly, the highest
$S_{21}$ difference is more profound for the smallest implantable
antenna. Radiation pattern shape of the internal antenna may be the
cause. In addition, the boundary effects of the skin box on the
smallest antenna could create specific peculiarities. In any case this
is another indication of the uniqueness of each case under
investigation. Finally, when the external patch antenna is kept at
fixed distance (at broadside for example---see
Figure~\ref{fig5}c), implantable antennas depth
does not seem to affect the $S_{21}$ {link. This is obviously the
outcome of the relative low frequency (i.e., 402~MHz) where the
wavelength is relatively large. Since the external distance is kept
constant, the internal ``sub-wavelength'' in-between variable distance
does not influence the results. In that case, the implantable antenna
volume (see} 
Table~\ref{tabIV}) is a more crucial
factor. Depending on the antenna design, skin box edge boundary also
has an effect on the calculated results. In any case, it seems that,
for larger distances of the external antenna or deeply implanted
antennas, the lower frequency can offer a better link level.


{Indeed, when the link between an implantable dipole and an external
dipole antenna is examined and for several sub-GHz frequencies the same
conclusion can be reached. Consider the problem shown in}
Figure~\ref{fig6}. A simple tissue box is considered 100~mm in width,
100~mm in height, 50~mm in depth, filled with an equivalent tissue with
relative dielectric permittivity equal to 2/3 of muscle. It should be
noted that in several problems when homogeneous cubical phantoms are
considered for representing the body, similar dielectric tissue is
considered (for example see} \cite{3}). Two half-wavelength dipoles one
implanted and the other in free space are considered and efficiency
$n'$ (see Equation~(\ref{eq8})) denoted by Ga is calculated for a distance
of up to 2~m. In Table~\ref{tabV}, the frequencies tested are
shown, in relation with dielectric properties used and the allowable
power per frequency (see Table~\ref{tabII}). First, as seen, the
dielectric properties variate very little as is actually expected.
Secondly, the permissible power increases with frequency. From
Figure~\ref{fig6}b we can see that obviously $n'$ {deteriorate much
slower in the 400~MHz group of frequencies as compared to 868~MHz or
915~MHz. This is expected. When permissible power is taken into account
and the achievable link is calculated from Equation~(\ref{eq18})} 
{(here we consider that dipoles are well matched and therefore the denominator
of} $n$ {(Equation~(\ref{eq8}))
does not affect the final result, that is}
$n$ {and} $n'$ (Equation~(\ref{eq6})) are practically the same), it is
obvious that for every frequency a link can close (communication is
successful) since every link is greater than the Required link of
Equation~(\ref{eq19}). However, do not forget that we have considered
maximum power emitted from the antenna. In that sense this link would
be achieved if the T$_{\mathrm{x}}$ antenna was the external to the
body. If we wanted to calculate what is the achievable link for an
implantable antenna transmitting to an external to the body antenna,
then SAR should have been calculated as has been also discussed above.
In other words, while 915~MHz frequency can allow for sending
information to an implantable antenna, the implantable antenna would be
able to close a link at 400~MHz area where the fed power to the
implantable antenna would not create excessive SAR. Furthermore if
larger distances are to be considered, there is a point where the lower
frequency can offer a better link, even for an external
T$_{\mathrm{x}}$ {antenna.} 

\begin{figure}
{\vspace*{2pt}}
\includegraphics{fig06}
\caption{\label{fig6}Simplified numerical test for  $n'$ efficiency
(see Equation~(\ref{eq8})) in {(}dB{)} (noted with Ga) between an implanted half
wavelength dipole inside a 2/3 muscle tissue type box and a free space
half wavelength dipole at various distance and frequencies. Tissue box
has 100~mm width, 100~mm height and 50~mm depth. The implanted dipole
is placed at the box center (25~mm distance from surface).}
{\vspace*{2pt}}
\end{figure}

\begin{table}
\caption{Frequencies tested, dielectric permittivity, allowed effective
power and achievable link at 200~cm for the problem of
Figure~\ref{fig6}\label{tabV}}
\fontsize{9.5}{12}\selectfont\tabcolsep=2.4pt
\begin{tabular}{cccccc}
\thead
 & \multicolumn{2}{c}{\parbox[t]{3.4cm}{\centering Electrical properties of tissue-simulating model}} 
 &  \parbox[t]{2.3cm}{\centering ERP $=$ Effective radiated power} & 
 \parbox[t]{2.5cm}{\centering Achievable link at 200~cm}  & 
 {Frequency band}\vspace*{2pt} \\ \cline{2-3}\cline{4-4}\cline{5-5}\cline{6-6}
\parbox[t]{1cm}{\centering{$f$ (MHz)}} & ${\varepsilon}_{{r}}$ & 
{${\sigma}$ {{(}Si/m{)}}} & 
ERP$_{{\max}}$ (dBm) & 
\parbox[t]{3cm}{\centering${C}/{N}_{0}$ (Equation~(\ref{eq18})) (dB/Hz)}\vspace*{2pt} 
& {Availability} \\
\endthead
402 & 38.07 & 
0.53 & ${-}$16 & 119.7 & \parbox[t]{3.5cm}{\raggedright MEDS radio (worldwide)} \\
433 & 37.91 & 0.54 & 
\mn10 & 124.7 & \parbox[t]{3.5cm}{\raggedright\hangindent 1pc ISM (Europe, Short range devices)}\vspace*{2pt} \\ 
868 & 36.74 & 
0.62 & \mn14 & 119.7 & \parbox[t]{3.5cm}{\raggedright\hangindent 1pc ISM (Europe, Short range devices)}\vspace*{2pt} \\ 
915 & 36.66 & 
0.63 & \mn30 & 133.7 & \parbox[t]{3.5cm}{\raggedright\hangindent 1pc ISM (USA and other parts of the world)}\vspace*{2pt}
\botline
\end{tabular}
{\vspace*{6pt}}
\end{table}


\subsection{Antennas coupled with matching circuits: rectennas}\label{secIII.C}


{For wireless harvesting systems, the antenna is coupled with a
rectifier which is usually based on a combination of diodes and LC
circuits. Other active elements might be also utilized. In that case
the active circuit can be a part of scattering matrix. The circuit will
have an output impedance equal to 50~$\rmOmega$. However the antenna is not
required to be designed at 50~$\rmOmega$ anymore. Hence, the receiver is a
rectenna which is part of the scattering S matrix. In that case the
system can be studied following the discussion in
Section~\ref{secII.A.1}.


{In~\cite{4}, an implantable rectenna is obtained by combining an
antenna (seen in Figure~\ref{fig8}a) and a
harvesting circuit at $f=915$~MHz. Defining the system efficiency as
the ultimate criterion for the final rectenna system, after selecting
the appropriate rectifier circuit the antenna implemented and the
rectifier are combined, the circuit is optimized, and the rectenna is
obtained. Antenna and the rectifier are studied as one system, and the
antenna input impedance is not required to be matched at 50~$\rmOmega$. A
satisfactory efficiency is obtained while satisfying realistic
conditions verifiable by measurements. It should be noted that at some
proposed solutions in the literature, the obtained circuits are tested
under high power which maximizes the efficiency. This is actually
unrealistic due to the several design restriction of implantable
systems.} 


I{n}~\cite{5}, an implantable rectenna system is obtained also at
$f=915$~MHz. The antenna part of the system (see}
Figure~\ref{fig7}) is extremely minimized. It is
found that, taking into account the tissue environment, the antenna
optimum performance is achieved at feeding port impedance $Z=110~\rmOmega$.
Therefore, the rectenna is built with this parameter in mind. System
efficiency is again very good while a very small implantable rectenna
is obtained. Results are verified against measurements.}


\begin{figure}
\includegraphics{fig07}
\caption{\label{fig7} $| S_{21}| ^{2}$ {(}dB{)} between a minimized
circular slot antenna implanted in a cylindrical arm phantom and an
external patch antenna. Implantation depth varies from $D = 10$~mm to
$D=16$~mm. The external patch antenna distance from phantom surface is
set at 200~mm. Implantable antenna volume is 120~mm$^{3}$. A cylindrical
reflector can be also used for electromagnetic focusing as seen in (a).
Results in (c) are without use of reflector while (d) ($S_{21}$ link) and
(e) (realized implantable rectenna gain) present the effect of
reflector use. From~\cite{5}.}
\end{figure}


\begin{figure}
\includegraphics{fig08}
\caption{\label{fig8}$| S_{21}| ^{2}$ {(}dB{)} between an implantable slot
antenna at $f=915$~MHz and a rectangular ${\lambda}/4$ patch antenna.
Implantable antenna is embedded in a cylindrical arm phantom at 10~mm
depth. It has a volume of 285~mm$^{3}$. A matching gel type
(${\varepsilon}_{\mathrm{r}}=20$, $\tan{\delta}=3\times 10^{-3}$) denoted by ML
is also used and it increases effectively the link. Results are
extracted from~\cite{4}.}
\end{figure}

\subsection{System efficiency enhanced by external helpers}\label{secIII.D}


{In implantable R$_{\mathrm{x}}$--T$_{\mathrm{x}}$ {systems and in
order to enhance the $S_{21}$ link between the external and the internal
antennas several external enhancements have been proposed. The most
sophisticated, utilize the so-called metasurfaces which are usually
applied on the skin covering an area relatively larger than the
implantable antenna. Several examples can be found in literature. For
example, in~\cite{28}, a metasurface patch is
proposed. Results show an enhancement of $S_{21}$ link (implantable antenna
reception) around 6~dB. The metasurface patch seems to operate as a
focus lens.
Probably implantable antenna position can greatly affect
the results and hence the system could be sensitive to misplacements.
Similarly, in~\cite{29}, an on-body metasurface is
investigated. Up to 10~dB enhancements is reported. Still the size of
the proposed metasurface could have large physical size. Its
application on the skin could be sensitive to surface modification due
to the body shape, etc.}


{Yet, enhancement can be achieved by implementing much simpler
solutions which can have a similar effect. In~\cite{4},
for an
implantable rectenna coupled with an external antenna, a simple
lubricating gel (appropriate for skin contact) with relative dielectric
permittivity of} ${\varepsilon}_{\mathrm{r}}=20$ and loss tangent equal to
$\tan{\delta}=3\times 10^{-3}$ {is being used (system is shown in}
Figure~\ref{fig8}).
The gel can cover a small area, somewhat larger that
the antenna aperture which is equal to $14\times 15$~mm and can
effectively increase the achieved link by 6--7~dB as seen in}
Figure~\ref{fig8}b. It is noted that the simulated results are verified
by measurements~\cite{4}. As can be understood the gel application is
not sensitive to misplacement or deformation because of the body shape
and can offer a very simple but also effective solution for $S_{21}$ link
increase. 


I{n}~\cite{5}, an alternative path is being proposed.
The proposed implantable rectenna can be implanted in an arm (see
{Figure~\ref{fig7}) while a curved metallic
reflector is introduced in order to increase the link with an external
antenna. The reflector is placed on the opposite side of the arm in
relation with the external antenna. The reflector has a length of
16~cm, is placed at a 5~mm distance from the skin (to consider
clothing) and covers the arm. As seen in}
Figure~\ref{fig7}d, the reflector increases the $S_{21}$
link by 7 to 8~dB. Simulated effect of reflector use, shown in
Figure~\ref{fig7}, has been also verified by
measurements. While the reflector has a relatively large size, its
application on the arm is very practical and can offer a robust
solution for practical applications, insensitive as well to
misplacement or arm shape. 

\section{Conclusions}\label{secIV}

The design of an implantable antenna system that includes
T$_{\mathrm{x}}$ and R$_{\mathrm{x}}$ components is governed by several
parameters. While the operational frequency ranges from 400~MHz to
usually 2.4~GHz or sometimes 5~GHz, depending on the application
considered (e.g., communication between or more implantable components,
wireless transmission of medical data from an implantable sensor to an
external hub, wireless control of an implantable system, wireless
energy transfer) different factors can affect the final design. Since
the outmost measure for an effective design is system efficiency, the
external and implantable antennas can be considered as a system
characterized by a scattering matrix. Calculation of $S_{21}$ parameter is
relatively simple and provides direct comparison with measurements.
When a matching circuit is also considered either for antenna feeding
or for using arbitrary load, this can be also considered as part of the
system. Effectively, $S_{21}$ can be used to cover several scenarios to
obtain the optimum results. To that end, this paper, after determining
$S_{21}$ calculation for covering the above considerations, summarizes how
the link budget can be obtained, what are the safety limits for
implantable systems at frequencies of interest, and which are the
allowable power for external or implantable antennas.

These factors are used to study a number of various scenarios,
including $S_{21}$ link calculation between either implantable antennas
and/or implantable and external to the body antennas. Among others,
this paper also show that while an optimum frequency, for example, can
be determined for achieving an optimum link between two implantable
antennas under ideal environments, different observations can be drawn
when the antenna type, its design and the human phantom are considered.
In addition, antenna size or how the antenna radiates can also define
the link used. Telemetry cases where the external antenna can operate
at its maximum power without violating safety limits are also
considered. Interestingly, it is shown that while 915~MHz frequency
allow for example much higher power use for an external antenna, when
the distance of the external antenna from the body exceeds a limit then
the use of a lower frequency with 20~dB less or lower power emission
can actually secure a successful link. Finally, it is shown that while
meticulously designed metasurfaces applied on the body have been
proposed in order to enhance the link budget, much simpler and more
robust solutions can be utilized. 

In conclusion, the design of an implantable antenna is not exhausted by
defining a minimum size or maximum gain. Many times, the
T$_{\mathrm{x}}$ and R$_{\mathrm{x}}$ components need to be considered
as a system and be investigated using scattering matrixes. This permits
to investigate the effect of different parameters and concurrently
offer a direct connection between simulations and measurements.
Considering the design as a system can allow for generating, at the
end, interesting results that will lead to an optimum, robust and well
thought outcome.

\section*{Declaration of interests}

The authors do not work for, advise, own shares in, or receive funds
from any organization that could benefit from this article, and have
declared no affiliations other than their research organizations.

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