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The Wireless Personal Area Network (WPAN) is one of the fledging paradigms that the next generation of wireless systems is sprouting towards. Among them, a more specific category is the Wireless Body Area Network (WBAN) used for health monitoring. On the other hand, Ultra-Wideband (UWB) comes with a number of desirable features at the physical layer for wireless communications. One big challenge in adoption of UWB in WBAN is the fact that signals get attenuated exponentially. Due to the intrinsic structural complexity in human body, electromagnetic waves show a profound variation during propagation through it. The reflection and transmission coefficients of human body are highly dependent upon the dielectric constants as well as upon the frequency. The difference in structural materials such as fat, muscles and blood essentially makes electromagnetic wave attenuation to be different along the way. Thus, a complete characterization of body channel is a challenging task. The connection between attenuation and frequency of the signal makes the investigation of UWB in WBAN an interesting proposition. In this paper, we study analytically the impact of body channels on electromagnetic signal propagation with reference to UWB. In the process, scattering, reflectivity and transmitivity have been addressed with analysis of approximate layer-wise modeling, and with numerical depictions. Pulses with Gaussian profile have been employed in our analysis. It shows that, under reasonable practical approximations, the human body channel can be modeled in layers so as to have the effects of total reflections or total transmissions in certain frequency bands. This could help decide such design issues as antenna characteristics of implant devices for WBAN employing UWB.

Wireless Body Area Networks (WBANs) have attracted interest in recent years because of a number of promising applications—specifically, in the field of health monitoring. Like everyday attire, in a WBAN, several small nodes are placed directly in, on or around the human body. Since WBAN nodes acquire their power from rechargeable batteries or by energy harvesting, it is essential that they be extremely energy-efficient [

From the _{i}_{i}

The intrinsic impedance of biological material

The Pointing Vector, that is, the power flowing per unit area of cross section (W/m^{2}), gives the power density associated with an EM wave:

For a uniform plane wave, time-average power flow is given by:

The permittivity and frequency may also determine how far the EM wave penetrates into the body. The term depth of penetration (_{p}

Sensor nodes find a human body, when they are placed, to be layered media. Fat, muscles

In this section we consider the case in which two homogeneous half-spaces are separated by an interface at

The goal of this section is to analyze the scattering problem in terms of right- and left-going modes (

We introduce the local velocities

For _{j}_{j}_{j}_{j}_{j}_{j}

We assume that a right-going wave with the time profile

(I) We can consider an initial value problem with initial conditions given at some time _{0} < 0 by:

As shown in the _{0}_{0}_{0}), which lies in the left half-space.

(II) We can consider a point source located at some point _{0} < 0 and generating a forcing term of the from:

As seen in the

In terms of the right- and left-going waves, these two formulations give the same descriptions. We have _{0} (_{0}) _{1}(t, z) = 0 for

Note that the delays introduced in the initial conditions

The pairs (_{0}, _{0}) and (_{1}, _{1}) are coupled by the jump conditions at ^{(+)})^{2} – (^{(−)})^{2} = 1. The matrix

Taking into account the boundary conditions

These coefficients satisfy the energy-conservation relation:

Using (

In this section, we consider the case of a homogeneous slab with thickness L embedded between two homogeneous half-spaces (

We introduce the local velocities
_{2}:

The propagation _{j}_{j}_{j}_{j}

We want to indentify the functions _{0} and _{2}, which give the shapes of the reflected and transmitted waves.

The unknown functions b_{0} and a_{2} can be obtained from the continuity conditions for the velocity and pressure at the two interfaces. At _{j}_{j}_{1}. A convenient and general way to handle these delays is by going to the frequency domain, so that the time shifts are replaced by phase factors. The Fourier transforms of the modes are defined by:

They satisfy the interface conditions:

Introducing the frequency-dependent matrix:

The syplectic matrix _{1}(_{0}(ω) propagates the right- and left-going modes from the left side of the interface 0 to the right side of the interface 1. We find explicitly:

By solving _{2} (_{0} (^{2} − |^{2} = 1. Here
^{2} + | 𝒯̂(^{2} = 1 for all

Let us consider a layer embedded between two homogeneous half-spaces that have the same material properties, _{2} = _{0} and _{2} = _{0}. We then have _{1} = −_{0} and _{1} = _{0}, which implies that the global reflectivity of the layer can be written as:

The reflectivity is periodic with respect to the angular frequency ω with the period _{c}_{1}/

This shows that for any value of the reflection coefficient _{0} of a single interface, there exist frequencies that are fully transmitted or fully reflected by the layer. If we consider the case of strong scattering
_{c}

The total transmission phenomenon is also encountered in situations in which the two half-spaces are different. Indeed, consideration of human body part as an ideal, fully-transmitting layer is certainly beyond perfection. In a microscopic or constituent-wise sense, a human body-part, striated muscle for example, iscomposed of water (70.09%), ether-soluble extract (6.60%), crude protein (21.94%),

_{0} ≠ _{2}, then it is possible to choose the thickness L and the impedance _{1} of the layer so that a given frequency ω will be fully transmitted from one half-space to the other one, which would not be the case in absence of such a layer. From the analysis of the reflectivity function:

One can show that a necessary and sufficient condition for | ̂(^{2} to be zero is that
_{0} ≠ _{2} this in turn enforces one to choose the impedance of the layer to be
_{0} = _{1}) and the thickness _{1}) is half an integer (so that cos(2 _{1}) = −1). Usually the thickness is chosen to be equal to a quarter of the wavelength, meaning _{1}) = ½.

When EM RF waves propagate in freespace, the power received decreases at a rate of (1/^{n}

These nodes exchange data among themselves and also with the base-station. In general, the system model consists of numerous biosensor nodes placed inside the various parts of the human body surrounded by tissues. In particular, for the development of this model, we consider only one transmitting and one receiving antenna separated by a distance

The region of space immediately surrounding the antenna is known as the near field region. The extent of the near field in the case of short dipoles is given by _{0} = _{NF}_{FF}

Consider an elemental oscillating electric dipole in a lossy medium of conductivity σ (S/m), permittivity _{z}

Spherical components of A (_{R}A_{R} + a_{θ}A_{θ} + a_{φ}A_{φ}_{R} = A_{z}cosθ_{θ} =_{z}singθ_{φ}

Solving the above magnetic and electric field equations for lossy medium and expressing in terms of complex impedance

The SAR in the near field is given by [_{corr}^{2}

The power absorbed in the near field of the lossy tissue can be obtained by computing the average SAR over the entire tissue mass in the near field, which is obtained by integrating Δ_{0}):

Neglecting
_{rms}

The power absorbed in the infinitely small volume (^{2}

The total power absorbed in the far field of the lossy tissue between the source and destination antennas can be obtained by computing the average SAR over the entire tissue mass in the far field from distance _{0} to _{0} is the point where the far field starts). This is obtained by integrating Δ

The effective radiated power (ERP) is obtained by subtracting the loss in the near field (_{NF}_{FF}_{T}_{T}_{Loss}_{t}_{Loss}_{NF}_{FF}_{e}

P_{R} in the Near Field: There is no general formula for the estimation of field strength in the near field zone [_{e}^{2}, where _{T}_{NF}_{e}_{e}

P_{R} in the Far Field: On the other hand when the receiving antenna is in the far field region of the transmitting antenna, the power density is dependent on the distance

The power received by the receiving antenna in the far field is _{R}_{e}A_{e}_{e}_{t}_{r}^{−jβ} is involved during the propagation of the wave. Thus, PMBA can be used for calculating the propagation loss using the two

The permittivity of biological tissues depends on the type of tissues (e.g. skin, fat, or muscle), water content, temperature, and frequency. However, the permittivity and frequency may also determine how far the EM wave penetrates into the body. The term depth of penetration (D_{p}) usually quantifies this. It is observed from _{0}, _{0}, _{1}, _{1}, ^{2} versus frequency has been depicted by _{c}_{1}/_{0} = −_{1} = 0.1 (a) and almost 1.0 for a layer with _{0} = −_{1} = 0.9 (b). In ^{2} versus frequency curves have been drawn. Transmitivity has been found to vary periodically with a certain frequency. The period of this frequency band depends upon the choice of the layer thickness _{0} = −_{1} = 0.1, transmitivity is about 1.0 (a) and for a layer with _{0} = −_{1} = 0.9, transmitivity is about 0.9 (b). Here the period is _{c}_{1}/2_{0} = _{1}) and the thickness _{1}) is half an integer (so that cos(2 _{1}) = −1), we can form a fully transmitting layer. Usually the thickness is chosen to be equal to a quarter of the wavelength, meaning _{1}) = ½. Therefore, from the results shown above, we can infer that a layer can either fully reflect or fully transmit any incoming wave at a certain frequency or frequency band. We can use these results to UWB by proper choice of impedance and the thickness L. Power loss in near filed and far field due to absorption has also been analyzed. A propagation loss model (PMBA) for homogeneous tissue bodies has been presented, which compares PMBA with the freespace propagation model (

Employing UWB in WBAN involves a lot of promise, just as there are a number of relevant challenges. We studied the technical feasibility in this regard with a concentration in electromagnetic propagation of the signal across human body. Unlike conventional wireless channels, human body comes with a great deal of structural complexity requiring significantly different design considerations. The reflection and transmission coefficients of human body are heavily dependent upon the dielectric constants as well as upon the frequency. In this work, we investigated a layer-wise model for electromagnetic propagation across the components of the body in regard to such key aspects as scattering, reflectivity, and transmitivity. Naturally, the segmentation in precise layers are not what we come across in a body. But, the approximate model employing homogenization could help assess the aggregate behavior of the wireless communication involving implant devices, thus guiding the potential design issues for antenna characteristics, for instance. We also presented numerical depictions of some of the pertinent signal characteristics. From here on, one could expect to further improve the model in terms of suitable layering and other parameters of approximations.

This research was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea Government (MEST) (No.2010-0018116).

Let us assume that a biological medium is infinite in extent, source-free, isotropic, and homogeneous. The medium is isotropic if

Using following identities:

In view of the fact that equations governing ^{jωt}

Using the relationships in ^{8} m/s) and γ is the propagation constant. This is in general, a complex quantity and may be written in the form:

Using

In this appendix, we use a number of essential transformations of the wave equation that are specific to layered media. We consider the particular case in which the parameters of the medium vary in a piecewise-constant manner; in other words, we consider a stack of layers made of homogeneous media. We study the propagation of a normally incident plane wave, which enables us to reduce the problem to the one-dimensional acoustic wave equations [

In one-dimensional medium the equations for the velocity

A diagonalization of the 2 × 2 matrix gives:

In this representation the material parameters

We consider the special case with a homogeneous medium in which the coefficients

Then if we define:

The equations for A and B decouple:

To fully specify the problem we have to prescribe initial conditions, for instance the velocity and pressure profiles at time

We then translate these initial conditions for

The initial conditions determine the mode decomposition and can be chosen to generate a pure right-going wave (if _{0} ≡ _{0}) or a pure left-going wave (if _{0} ≡ −_{0}).

A more physical way to generate a wave is to assume that the wave vanishes as

By assuming a point source ^{1/2}

As a result, the velocity and pressure fields are:

This means that the source term generates two waves with equal energy that propagates to the right and to the left.

For a channel like the human body where muscle, fat, blood cannot be considered as slabs or layers, we consider the idealized situation in which the parameters vary only with depth, and moreover, we make the important assumption that the variations are on a relatively fine scale. We assume that the scale of variation is small compared to the distance traveled by the pulse, as well as compared to the wavelength of the pulse. One may then expect that the waves are not strongly affected by the impedance in any particular layer. When a pulse propagates through such fine layers, the interaction with each layer is small, and propagation is not much affected. The pulse therefore travels as if the medium were homogeneous with the layers replaced by “averaged” ones. In general, we refer to this homogeneous medium as the homogenized medium. It is also referred to as an effective, average, or equivalent medium. We start by writing the medium parameters in the form

We introduce propagator _{ω}

The matrix _{ω}_{0}_{0} _{1}_{0}_{0}^{iωs} ds

To determine the effective medium that emerges in the limit of fine layering _{n} that are bounded and bounded away from zero. The local speed of propagation is given by:

The convergence is in the almost sure sense, for almost all realizations of the medium, or with probability one with respect to the randomness. In this setting, homogenization in the frequency domain means that we should choose _{ω}

Thus, the harmonic mean of local propagation speeds is the homogenized or effective propagation speed. This effective propagation speed is frequency independent in this example, and therefore it is also the effective propagation speed in the time domain. We can get the transmitted and reflected waves in the Fourier domain:

Power absorption in muscle as a function of depth at different frequencies.

Variation of Penetration depth with frequency.

Scattering of a pulse by an interface.

Scattering of a pulse by an interface separating two homogeneous half-spaces (_{0}, _{0}, _{1}, _{1}, _{0} = _{0} = 1, and _{1} = _{1} = 2. The spatial profiles of the velocity field (a) and of the pressure field (b) are plotted at times

Scattering of a pulse by a single layer.

Reflectivity |̂(^{2} versus frequency for a single layer with _{0} = −_{1} = 0.1 (a) and _{0} = −_{1} = 0.9 (b). The period is _{c}_{1}/

A propagation system consisting of 3 layers; air, human body channel, and a transceiver.

Transmitivity |𝒯̂(^{2} versus frequency for a single layer with _{0} = −_{1} = 0.1 (a) and _{0} = −_{1} = 0.9 (b). The period is _{c}_{1}/2

A Hertzian Dipole.

Field regions around a Hertzian Dipole.

PMBA (tissue medium) and Freespace Pathloss at 2.4 GHz.