Chapter 4

Body Area Channel Modeling

4.1 Introduction

Body area communications differs from traditional radio communications due to human body proximity effects. Human body tissue is a complicated frequency-dependent dielectric material with relatively high permittivity and certain conductivity. Radio signals propagating in the body area are significantly affected by human body tissue (Zasowski et al., 2006). Propagation mechanisms in the body area are also frequency-dependent as introduced in Chapter 2. The resulting received signal is subject to the transmission channel, the distance between the transmitter and the receiver, transmitter and receiver antenna positions, tissue dielectric properties along the transmission channel, body curvature and so on. Channel modeling is the initial step to explore and investigate the body area communications. An adequate propagation channel model is essential for the design of a body area communication system. The ultimate performance limits of body area communication systems, as well as the performance of practical systems, are determined by the channel they operate in.

Body area channels can be classified into wearable channels and implant channels according to the locations of the transmitter and receiver devices on or in or off the body. Wearable channels have all of the devices on body, while implant channels have some devices in body which communicate with on- or off-body devices. Figure 4.1 illustrates several typical body area channels (IEEE P2009), in which channel A is an in-body channel, B is an in- to on-body channel, C is an on-body channel and D is an on- to off-body channel. On-body channel C is the wearable channel and can be characterized as a line-of-sight (LOS) or non-line-of-sight (NLOS) channel depending on the way the electromagnetic waves propagate between the two devices. The scenario with one device on the front of the body and the other device on the back of the body is characterized as a NLOS propagation, in which the electromagnetic waves may experience loss due to diffraction around the body. Channels A and B are typical implanted channels. Wireless capsule endoscope technology will make use of channel B where the ingestible capsule can take pictures during its course through the digestive tract after being swallowed and transmit the real-time biological data from inside the body to on-body medical devices. Alternatively, the medical receiver may be located off the body at a certain short distance and therefore a channel consisting of B and D can be generated. An implanted pacemaker in the chest, communicating with an on-/off-body device, also brings about an implant channel resembling B or B plus D.

The wave propagation characteristics in the human body area are very complicated. There are absorption phenomena in the human body due to the lossy dielectric properties of body tissues as well as scattering due to the heterogeneous nature of body tissues. The transmitted signal is therefore largely attenuated. Moreover, diffractions and creeping waves exist along the body surface, where shadow fading arises due to the diffraction in the shadowed regions of the body. In addition, since the human body might take various postures, or one or more body parts may move during the communication period, multiple paths are created between the transmitter and receiver so that a transmitted signal can traverse. Consequently a received signal may end up being the superimposition of several attenuated, delayed, time-varying and eventually distorted replicas of a transmitted signal. For different body area channels, the dominant channel characteristics may vary. An on-body channel may suffer from multipath fading and shadowing due to body postures and movements more than an in-body channel, while an in-body channel undergoes severe signal decay during transmission inside the body more than an on-body channel. For different frequency candidates, like UWB, MICS and HBC, the channel characteristics will also differ due to the frequency-dependent dielectric properties of body tissues. Channel modeling needs to incorporate the wave propagation characteristics in the body area in the context of different channel types as well as different frequency bands.

In this chapter, we will generalize the channel model into a path loss model or a multipath channel model. The path loss model mainly describes the channel loss, including propagation loss, absorption loss as well as diffraction loss, while the multipath channel model focuses on the time-domain characteristics of the body area channel, particularly the multipath propagation characteristic. We will first address the path loss models for UWB, MICS and HBC bands in both on-body and in-body transmission channels. Then we will investigate the multipath channel model especially for on-body UWB. The methodology of characterizations and parameterizations of the UWB multipath channel will be described in detail.

4.2 Path Loss Model

4.2.1 Free-Space Path Loss

Path loss is the reduction/attenuation in power (density) of an electromagnetic wave as it propagates in a specific environment. In general, the path loss is due to many effects, such as free-space loss, refraction, diffraction, reflection, aperture-medium coupling loss, and absorption. In free space, path loss is influenced by terrain contours, environment, propagation medium, the distance between the transmitter and the receiver, and the height and location of antennas. Path loss involves propagation losses caused by the natural expansion of the radio wave front in free space, absorption losses/penetration losses when the signal passes through lossy media, diffraction losses when part of the radio wave propagation is obstructed by an obstacle, and losses caused by other phenomena.

In wireless communications, path loss is usually expressed in decibels and can be represented by the path loss exponent in the following simple formula

(4.1)

where PL_dB is the path loss in decibels, n is the path loss exponent, d is the distance between the transmitter and the receiver, usually measured in meters, and C is a constant which accounts for system losses. This equation is referred to as the log-distance path loss model. The value of the path loss exponent is normally in the range of 2–6. The loss exponent of 2 is for propagation in free space. Larger exponent values are for lossy environments. In buildings, stadiums and other indoor environments, the path loss exponent can reach values in the range of 4–6.

The Friis transmission equation is usually used for the path loss in free space. It gives the power received by one antenna under idealized conditions when another antenna at a certain distance away is transmitting a known amount of power. The basic form of the Friis transmission equation is as follows:

(4.2)

which shows the ratio of power available at the output of the receiving antenna to power input to the transmitting antenna , where and are the gains of the transmitting and receiving antennas, respectively, is the wavelength, and is the distance. Assuming two isotropic antennas, the free-space path loss in decibels can be expressed by a simplified formula:

(4.3)

where the wavelength and distance have the same units. This simplified form applies only under ideal conditions: (1) no feed line or miscellaneous losses; (2) no obstructions or no multipath propagation; (3) no atmospheric absorption; (4) correctly aligned and polarized transmitter and receiver antennas; and (5) single frequency is assumed. It can be seen that the path loss exponent in free space is 2 according to Equation 4.3. In addition, it must be kept in mind that this equation is only accurate in the far field where spherical spreading can be assumed; it does not hold close to the transmitter, that is, in the near field region.

4.2.2 On-Body UWB Path Loss

In order to investigate the on-body UWB path loss characteristics, we need to assign the transmitter and receiver on the human body. In a practical scenario, many low power transmitters in the sensor mode send data from various spots on the body to one receiver in the master mode. A wireless network with multiple transmitters and one receiver on the body is therefore constructed. However, in the derivation of the path loss model using a numerical approach, multiple transmitter antennas on the body interact with each other and consequently result in an inexact electric field value in terms of on-body path loss evaluation. On the other hand, a set-up of one transmitter at a fixed position and multiple receivers at various different positions results in a low computation efficiency since a statistical analysis over the whole body is needed. Therefore, in order to enhance the computation efficiency, one transmitter antenna and multiple receiving points are constructed on an anatomical human body model. Although it is not consistent with the realistic usage scenario, this does not affect the analysis or the conclusions.

Figure 4.2 shows the numerical simulation set-up for the on-body path loss on a human body with a Hertzian dipole fixed on the left chest as the transmitter and multiple receiving points distributed along the whole body surface. The transmission distance is calculated around the perimeter of the body since it has been shown that waves diffract around the body in the UWB band (Fort et al., 2006; Zasowski et al., 2006). The receiving points are separated by 10 cm in the longitudinal direction, while the separation between receiving points in the horizontal is 2 cm. Using the FDTD method, a total of 869 receiving points are calculated which consists of 250 points on the front, 345 points on the side and 274 points on the back of the body. Both the transmitter and the receiving points have a spacing distance of 2 mm above the body surface.

Since the UWB frequency band ranges from 3.1 to 10.6 GHz, the practically usable skin depth of the biological tissue in this frequency band is only several millimeters. This suggests that the surface tissue layers should dominate the propagation characteristics of the body. In fact, based on the computational comparison between the received voltages for a homogeneous body model comprising only skin and a heterogeneous body model comprising 51 different tissue types, it is found that the differences in the received voltages under these two situations never exceed 5%. Therefore we can assume a homogeneous human body of skin and employ the one-relaxation Debye equation to simulate its dielectric properties (Gabriel, 1996).

The choice of the transmitted pulse is crucial since it affects the energy spectral density (ESD) of the transmitted signal. The widely used UWB signal is based on a Gaussian pulse which can be generated the most easily by a pulse generator (Benedetto and Giancola, 2004). A Gaussian pulse can be represented by the following expression

(4.4)

where A is the amplitude, is the variance and is a shape factor.

Gaussian derivatives have a zero DC offset which facilitates the pulses to be radiated in an efficient way. Actually, Gaussian derivatives have been widely adopted to shape the UWB signal since a Gaussian pulse can have infinite differentiations. The nth-derivative Gaussian pulse is given by

(4.5)

and the corresponding Fourier transform is

(4.6)

One of the most efficient and popular pulse derivatives is the second derivative of a Gaussian function (Win and Scholtz, 2000), described by

(4.7)

Other pulse shapes have also been proposed such as the Laplacian (Conroy, LoCicero, and Ucci, 1999), compositions of Gaussian pulses and derivatives (Hämäläinen et al., 2001), and Hermite pulses (Ghavami et al., 2002).

The pulse shape factor and differentiation order are the two most significant parameters affecting the pulse waveform and ESD. Pulse duration is directly proportional to the shape factor . Increasing enlarges the pulse duration and conversely will decrease the pulse bandwidth. Therefore, adjusting the pulse duration can create an appropriate bandwidth for various UWB applications. Differentiation of the Gaussian pulse waveform can change the pulse shape without changing the pulse duration. However, differentiation influences both peak frequency and bandwidth of the pulse; increasing differentiation order can result in higher peak frequencies of the transmitted pulse. Differentiation is therefore an effective means of putting transmitted energy to higher frequency bands.

The ESD of a signal describes how the energy of a signal is distributed with frequency. If is a finite-energy signal, the ESD of the signal can be defined as the square of the magnitude of the continuous Fourier transform of the signal where the energy is taken as the integral of the square of the signal. The can be expressed as follows

(4.8)

where is the angular frequency and is the continuous Fourier transform of , and is its complex conjugate.

We now use the typical second-derivative Gaussian pulse as shown in Figure 4.3(a) as the transmitted UWB pulse. As described above, pulse width is directly related to the shape factor α. A pulse width of 280 ps is used in order to have most of the energy between 3.1 GHz and 10.6 GHz. Figure 4.3(b) shows the corresponding ESD characteristics where the –10 dB bandwidth covers the whole UWB band with a central frequency around 6.5 GHz. With different pulse width, the 10 dB bandwidth and the central frequency will change accordingly.

The path loss can be obtained from the following equation

(4.9)

where and are the amounts of transmitted and received energy, which can be calculated from the transmitted and the received pulse voltage waveforms. As shown in Figure 4.2, the transmitting Hertzian dipole can locate along three orthogonal directions x, y and z. According to the radiation characteristics of the Hertzian dipole, the orientation of the transmitting dipole and received field components perpendicular to the human body are advantageous for wave diffraction around the body. In addition, the antenna gains are also needed as a function between the transmitter and receiver for removing the antenna effect, although the antenna effect is usually difficult to remove completely because the body area propagation is in a near-field region. Figure 4.4 shows the calculated path loss with both y-directed transmitting and receiving components versus distance on the human body model. It is clear that the path loss increases with distance as expected, and that there is a large variance around the mean path loss. Keep in mind, in Figure 4.4, the horizontal axis is not the straight-line distance but the one traveled by the wave around the perimeter of the body between the transmitter and the receiving points, because the major components reaching the receivers are due to diffraction around the body.

There are two potential path loss models for possible fitting to the calculated results. One is according to the empirical power decay law as

(4.10)

where is the path loss at distance and is the path loss exponent. The other is according to an exponential fitting as

(4.11)

where is the excitation coefficient and is the attenuation coefficient.

The fitting results for the calculated path loss data based on the two equations in the least-square-error sense are also shown in Figure 4.4 by the solid line and the dashed line, respectively. As can be seen, comparing with Equation 4.11, Equation 4.10 gives a better fitting, which suggests that the power decay law is more appropriate for the UWB path loss modeling on the human body. This finding is identical to the results in Fort et al. (2006).

In fact, the path loss model in Equation 4.10 is essentially similar to the log-distance path loss model in Equation 4.1. Table 4.1 shows the estimated and for all three directed transmitting dipoles and receiving components. is obtained at m. It is found that the path loss at the first 0.1 m is around 43–83 dB, and the exponent n is around 2–5. Furthermore, for the transmitter, the y-directed dipole yields a smaller reference path loss . On the other hand, at the receiving points, the z-directed field components always have the smallest path loss exponent n. Taking the two parameters into consideration, the y-directed transmitting dipole and z-directed receiving component may be the best option from all of the results.

Table 4.1 Estimated and in the log-distance path loss model for various directed transmitter antenna and receiving components.

As noticed from Figure 4.4 there is a large fluctuation in the simulated path loss values around the fitted mean path loss. Actually, the fluctuation of the simulated path loss is mainly due to the shadowing effect of the body. The shadowing is induced by the diffraction in the shadowed regions of the body. The multipath-induced fading from body postures is not taken into account here since a static human body model is assumed. Shadowing can directly result in the variations of the received signal at the receiver front-end. The amplitude variation caused by shadowing is often defined as the difference between the calculated path loss values and the mean path loss. It can be modeled using a log-normal distribution with a standard deviation according to the log-distance path loss model in Equation 4.10 which represents the mean path loss. Combination of both the statistical variance of path loss and the fitted mean path loss can result in a complete path loss model.

A comprehensive path loss model can be therefore rewritten as follows

(4.12)

where is the difference of the calculated path loss values in decibels and the mean path loss in decibels derived from Equation 4.10 at the same distance. Such a model is called as a static shadow fading channel afterwards. represents the shadow fading in decibels with normal distribution since the logarithm of a log-normal distribution is normally distributed. It has a mean value 0 dB and standard deviation . reflects how concentrated the path loss is around its mean value as well as the degree of the shadow fading strength. The parameter of the shadow fading can be determined based on statistical fitting. Figure 4.5 shows the fitted cumulative distribution function (CDF) of normal distribution for the shadow fading with y-directed transmitter and the total receiving component. The standard deviation is fitted as , which illustrates the large variance of the path loss values due to the strong shadowing effect around the human body.

4.2.3 In-Body UWB Path Loss

As shown in Chapter 2, the interaction of electromagnetic waves and the human body differs with different frequencies. For different communication scenarios in the body area, frequency selection should be designed to facilitate the wave propagation for specific communication purposes. The recent research results for the on-body UWB propagation (Fort et al., 2006; Zhao et al., 2006; Taparugssanagorn et al., 2008; Wang et al., 2009) and the in-body UWB propagation (Khaleghi and Balasingham, 2009; Wang, Masami, and Wang, 2011) has concluded that requirements on frequencies are different due to different operating environments. For UWB, wearable body area networks may cover the full band from 3.1 to 10.6 GHz, while implant body area networks have to be limited in the low band, for example from 3.4 to 4.8 GHz. This is because the skin depth or the penetration depth of human tissue becomes very small with increasing frequency.

We introduce here two in-body UWB channels in the context of two implant communication services. One is wireless capsule endoscope for non-invasive gastrointestinal tract imaging, in which the exterior receiver is assumed to be on the torso surface. This scenario builds an in-body to on-body channel around the abdomen district. The other service is the radio communication from an implanted cardiac pacemaker or other electronic implants inside the chest area with an off-body medical device. This communication scenario forms an in-body to off-body channel in the chest area.

4.2.3.1 In-Body to On-Body UWB Path Loss

Differing from the on-body UWB path loss, the in-body channel investigation should employ a heterogeneous human body model so as to accurately explore the wave propagation in the in-body channel.

Wireless capsule endoscope was first introduced in 2001 (Qureshi, 2004). The ingestible capsule can take pictures during its course through the digestive tract after being swallowed. It can therefore transmit real-time biological data from inside the body to exterior medical instruments, which aids the non-invasive diagnosis. A UWB capsule endoscope has also been proposed to ensure real-time video monitoring of the internal parts of a patient's body. Some research work has been done about radio signal propagation inside the human body within the FCC allocated UWB frequency band (Chavez-Santiago et al., 2009; Shi and Wang, 2010). Highly frequency-dependent signal attenuation has been concluded within the UWB band, which creates a big challenge for UWB capsule system design.

Figure 4.6 shows an anatomically based human body model with an on-body elliptic disk dipole antenna to receive the capsule endoscope data. The elliptic disk dipole antenna is optimized to operate on the body surface. The dimensions of major axis radius a and minor axis radius b are adjusted to be a = 7 mm and b = 5 mm, which yields a voltage standing wave ratio (VSWR) smaller than 2.0 from 3.4 to 4.8 GHz. The VSWR is defined as , where is the antenna reflection coefficient which can be calculated from the antenna input impedance. A value of VSWR smaller than 2.0 is usually acceptable in practical applications.

The receiving antenna is taken to be at five locations on the front of the body on the abdomen, as shown in Figure 4.6. On the other hand, the transmitting antenna of the capsule endoscope is taken to be a 4-mm-long dipole. It moves mainly along the small intestine at 33 locations, and at each location it has three different directivities (x, y, and z) respectively. As a result, for each on-body receiver location, there are 99 sets of data for extracting the path loss and shadow fading characteristics.

In the characterization of the in-body to on-body channel for the capsule endoscope application, a sine-modulated Gaussian pulse with a center frequency of 4.1 GHz and a pulse width of 2.1 ns is used as the transmitted UWB signal in order to have most of the energy in the UWB low band. The signals are received by the on-body receivers. Then the path loss is obtained from

(4.13)

where is the transmitted signal voltage, is the received signal voltage calculated by FDTD simulation, denotes the Fourier transform, = 3.4 GHz and = 4.8 GHz.

According to the propagation mechanism as discussed in Chapter 3, the signal exponentially attenuates inside a lossy dielectric medium. However, the finite thickness of the human body makes the log-distance path loss model in Equation 4.12 applicable to approximate the exponential attenuation behavior over a short distance such as the body cross-section thickness. In the log-distance path loss model, the mean path loss can be fitted based on the reference path loss at a distance = 0.05 m. Figure 4.7 shows the FDTD-calculated path losses (symbols) and the fitted mean path losses (curve). The results for the receiver located in front of the abdomen (Rx1) are demonstrated. Figure 4.8 gives the CDF of shadow fading for Rx1. It is found that the shadow fading follows the normal distribution. The mean value is of course zero, and the standard deviation is = 8.2 dB. The derived fitting parameters for all five receiver locations in terms of the least-square-errors are shown in Table 4.2. The fitting parameters are similar at different receiver locations. Moreover, due to the rapid attenuation inside the human body at UWB frequencies, the path loss exponent n looks large. The standard variance of the shadow fading is in the range of 7.1–8.5 dB.

Table 4.2 Fitted parameters for path loss expression.

4.2.3.2 In-Body to Off-Body UWB Path Loss

Figure 4.9 shows an anatomical human body model with an elliptic disk dipole antenna implanted in the chest for cardiac pacemaker application. The body model is the upper part of the anatomically based whole body human model. The elliptic disk dipole antenna is implanted at a depth of about 1.5 cm, just between the fat and muscle layer, from the left-chest surface. To cover the UWB low band from 3.4 to 4.8 GHz, the antenna is designed to have a major axis radius a = 12 mm and a minor axis radius b = 10 mm, which yields an acceptable VSWR over the frequency band of 3.4–4.8 GHz both inside and outside the human body. Although the antenna is not small enough for practical implant applications, its flat VSWR characteristic with frequency is suitable to derive a general-purpose channel model. Using two of the above-described elliptic disk dipole antennas, one as the transmitting antenna inside the body and the other as the receiving antenna outside the body, the in-body to off-body channel can be characterized based on the FDTD numerical calculation. The UWB signal to be transmitted is also a sine-modulated Gaussian pulse with a center frequency of 4.1 GHz and a pulse width of 2.1 as in the previous in-body to on-body UWB path loss case.

As for the location configurations of the implanted transmitter and external receiver, as shown in Figure 4.9, the transmitting antenna is embedded inside the left chest. It covers a total of 20 locations ranging from 1.1 to 2.3 cm from the chest surface along the transverse plane and 2 cm in the coronal plane. This is to take into account the randomness of the implanted location in actual usage. Meanwhile, location variation can be used to imitate the implanted position change due to human respiration. The receiver is assumed to be an external coordinator to collect the medical data transmitted from the implanted antenna. It is located in a 10 cm square area in the front of the left chest at a distance of up to 40 cm from the chest surface. For each square area, nine receiver locations are considered to cover the randomness in receiver location setting. As a result, 180 combinations of the transmitter and receiver are simulated in total.

Figure 4.10 shows the average path loss versus the distance from the implant transmitter location. It is found that the path loss at the body surface, that is, at a distance d = 1.5 cm from the transmitter, is about 54 dB. At the off-body receiver location at a distance up to 40 cm from the body surface, the path loss seems to decay in an exponential manner. Also in Figure 4.10, an approximate curve

(4.14)

is given to fit the calculated average path loss in the least-square-error sense, where d₀ is the implant depth with a typical value of 1.5 cm. Equation 4.14 exhibits fair agreement with the FDTD calculated result when A = 251188.6 or 54 dB and α = 8.8 m⁻¹. The exponential decay of power versus distance in the body vicinity is identical to the basic wave feature at the boundary of air and a dielectric medium. Table 4.3 lists the fitted parameters.

Table 4.3 Fitted parameters for path loss expression.

d0 (m)	AdB	α (m−1)
0.015	54	8.8

4.2.4 In-Body MICS Band Path Loss

MICS as a standard medical implant communication band between 402 MHz and 405 MHz provides a low bit rate communication service compared with the UWB low band. Since it utilizes narrow band signals, the path loss characteristics in the MICS band are derived based on the ratio of the received average power and transmitted average power, rather than the ratio of energy as in the UWB case. The wireless capsule endoscope scenario is employed again here to address the in-body to on-body MICS band path loss characteristics.

Similar to the in-body to on-body UWB capsule endoscope case, the transmitting antenna is set to be a 4-mm dipole located at 30 different locations inside the human digestive system, including four locations in the esophagus, four locations in the stomach, nine locations in the small intestine and 13 locations in the large intestine, respectively. The receiving antenna is a 20-mm dipole which locates around the body torso. Figure 4.11 shows the configuration of the seven receiver locations: Rx1, Rx2, and Rx3 at the belly region, Rx4 and Rx5 at the torso side, and Rx6 and Rx7 at the back. The receiving dipoles are along the body height direction at a spacing distance of 4 mm from the body surface.

The derivation of the path loss is based on the following equation

(4.15)

where and are the transmitted and received average power, respectively.

As for the UWB path loss, the MICS path loss can also be fitted to the log-distance path loss model in Equation 4.12. Figure 4.12 shows the FDTD-calculated path loss results as well as the fitted log-distance path loss model for the receiver location Rx1. Based on the log-distance path loss model, is 49.7 dB at a reference distance = 0.05 m and the path loss exponent n is 5.5. Figure 4.13 shows the CDF of the shadow fading for the receiver at location Rx1. The normal distribution is found to provide the superior fitting. The mean value is zero and the standard deviation is = 8.1 dB. Table 4.4 lists the fitted parameters of the log-distance path loss model for all seven receiver locations around the body.

Table 4.4 Fitted parameters for path loss expression.

A more detailed path loss model for capsule endoscope in the MICS band is developed to also take into account the angle θ between the transmitting and receiving antennas (Aoyagi et al., 2010). The model is based on a combination of FDTD simulation and phantom experiment. The derived path loss formula is as follows

(4.16)

where a is the gradient coefficient (dB/cm), b is the intercept coefficient (dB),

(4.17)

with x_c as a coefficient of difference between the main and crossed electric field direction, and S_dB is the stochastic fluctuation or shadowing due to the organ structure. Table 4.5 gives the corresponding parameters in Equation 4.16, in which σ is the standard deviation for the normal distributed S_dB.

Table 4.5 Fitted parameters for path loss expression.

4.2.5 HBC Band Path Loss and Equivalent Circuit Expression

HBC uses the human body as a positive communication route to transmit data. It is superior to wireless transmission from the point of view of information security and electromagnetic compatibility. This is because (1) the signal is transmitted along the surface of the human body, and (2) radiation to outside the human body is extremely small. To meet these requirements, the tens of megahertz or less frequency band is favorable in HBC. In this frequency band the human body acts as a conducting medium so that we can model the electromagnetic coupling between the human body and the transceiver with capacitors. This structure forms a current loop which consists of the transmitter, body, receiver, and capacitive return path through the external ground. An equivalent circuit expression is useful to understand the transmission characteristics and is helpful in system design. In this section, we first introduce an alternative explanation for the HBC propagation based on surface wave theory. Then we give both a path loss formula and an equivalent circuit expression in the HBC band.

4.2.5.1 Basic Characteristics

HBC is considered mainly to take advantage of electrostatic coupling propagation. However, a surface wave approximation may also be effective to explore its basic characteristic (Wang, Nishikawa, and Shibata, 2009). Let us consider an infinitely long lossy dielectric cylinder in the cylinder coordinate system in Figure 4.14. The electric field will have only and components and the magnetic field will have only an component. In this case, after applying the usual sinusoidal time variation, the Maxwell equations become

(4.18)

.

For a surface wave, the field should decay exponentially with increasing distance along the surface. It is therefore reasonable to assume the electric field where (with the attenuation constant and the phase constant) is the propagation constant along the cylinder surface in the x direction. Then we have (Barlow and Brown, 1962)

(4.19)

where is the propagation constant normal to the cylinder surface, that is, in the r direction, and

(4.20)

(4.21)

Equation 4.19 can be transformed into the standard form of Bessel's equation

(4.22)

by putting . The appropriate solution to Equation 4.22 outside the cylinder surface is

(4.23)

so that

(4.24)

(4.25)

(4.26)

where B is a coefficient, and and are Hankel functions of the first kind. On the other hand, inside the cylinder surface, instead of Equation 4.23 we have

(4.27)

Thus

(4.28)

(4.29)

(4.30)

where B′ is a coefficient, and and are Bessel functions of the first kind.

According to the boundary condition that the tangent components of the fields are continuous at the cylinder surface (r = R), we must have so that

(4.31)

and so that

(4.32)

. From Equations 4.31 and 4.32 we have

(4.33)

In Equation 4.33, , the propagation constant normal to the surface, is the only unknown quantity. Solving the nonlinear equation we can obtain , and substituting it into Equation 4.21 we can obtain , the propagation constant along the cylinder surface. Although Equation 4.33 is a nonlinear equation including special functions, it is possible to use Newton's method to find an approximation solution.

To compare the transmission characteristic on a human body with the assumed surface wave, we consider a circular cylinder as shown in Figure 4.15. The cylinder is a homogeneous medium of 3 cm in radius and 1 m in length. Its dielectric properties are adopted to have two-thirds the values of muscle to simulate a human arm. We make the signal excitation with two pairs of metal electrodes that are shown as the shaded regions at the left end of the cylinder. Each pair of metal electrodes has one signal electrode and two ground electrodes as also shown in Figure 4.15. The signal electrode and the left ground electrode are shorted, and the transmit signal is excited between the signal electrode and the right ground electrode by a voltage source. Such an electrode structure is based on two considerations. First, the major component of the electric field is induced normal to the cylinder surface in order to propagate along the cylinder as an approximated surface wave. Secondly, shorting the signal electrode and the left ground electrode reduces the stray capacitance between them and consequently makes impedance matching with the transmitter easy. An almost symmetric electromagnetic field is made at the top and bottom of the cylinder, and comparison with the theoretical solution of the surface wave becomes possible although a strictly symmetric wave is not induced.

The electromagnetic field analysis in the vicinity of the cylinder surface is possible by using the FDTD method. Then we can extract the electric fields along the cylinder surface and normal to the cylinder surface. Due to the limited length of the cylinder, reflection occurs at the cylinder end. The comparison with the theoretical solution to the surface wave is made in the region which is far enough from the cylinder end so as to reduce the influence of the reflection as much as possible.

Figure 4.16 shows the FDTD-calculated relative electric field distributions in a vertical cross-section. A tendency of the surface wave is seen because the component transmits especially along the cylinder, and it attenuates slowly in the x direction and quickly in the r direction compared with the case of only air. Also, the component is small. Since the and components and the component are more predominant than other components, the transmission on the cylinder surface can be approximately considered as a surface wave.

Although the field distribution in the vicinity of the electrodes is quite complex and is influenced by the electrode structure, it is still possible to extract the propagation characteristics from the field distribution when the observation point is somewhat far from the electrodes. From the FDTD-calculated field distributions, the principal field component indeed decays exponentially with the distance from the transmitter electrodes. We therefore assume at the cylinder surface in the x direction, and in the middle of the cylinder in the r direction. We use this relationship to fit the data in Figure 4.17 based on the least square approximation. The data in Figure 4.17 are first divided into two areas in both the x direction and r direction, and the fitting is then done to the data in the latter area with the curve fitting tool in MATLAB®. In either of the two directions, two straight lines with different inclination rates are used to approximate the exponential field attenuation characteristic.

Next, we pay attenuation to along the cylinder surface in the x direction because it attenuates quickly in the r direction normal to the cylinder surface. We change the exciting frequency from 10 to 150 MHz, and derive the attenuation constant in the x direction along the cylinder surface as described above. On the other hand, we also obtain the theoretical for an ideal infinitely long cylinder using the surface wave theory. Figure 4.18 shows the FDTD-derived and theoretical values from 10 to 150 MHz. The FDTD result shows the same tendency as the theoretical result of the surface wave, and they are in fair agreement. This finding suggests that the signal transmission on the surface of a finitely long cylinder, which has a dielectric constant of the living body, is approximately expressible by the theoretical solution to the surface wave.

Moreover, increase as the frequency rises between 10 MHz and 150 MHz. This is because that the permittivity of the living body decreases with the frequency, which makes the surface wave difficult to hold. A higher dielectric constant means less loss for the surface wave transmission. From Figure 4.18, it is clear that lower frequency is more appropriate for propagation along the human body.

4.2.5.2 Path Loss

Based on a numerical and experimental approach, we derive a path loss formula for a typical HBC application. Figure 4.19 shows the human body model. It is homogeneous and is an average adult male size. The posture simulates a situation of communication by touching a receiver electrode. The transmitter electrode is arranged at 50 locations in total on the human body surface such as the shoulder, waist, belly, chest, and arm. On the other hand, the receiver is set up on the tip of a finger of the left hand. Then, using the FDTD method, we can obtain the received voltage at the receiver electrode, and the path loss from the ratio of the received voltage to the transmitted voltage. It should be noted that there are two kinds of distances between the transmitter and the receiver. One is the straight line distance, and the other is the surface distance along the human body. According to the propagation mechanism, the surface distance should be used for the path loss formulation.

Now we formulate the path loss for the HBC channel. Since the propagation is in a near-field region very close to the excitation source, a log-distance path loss model is no longer applicable. Here we propose the following expression. That is

(4.34)

where and (=) are the losses per unit distance in units of dB/m on the human body, d is the distance between the transmitter and the receiver, and is the path loss at the boundary (d = 0.1 m) of the two regions. Figure 4.20 shows the fitting result of the above expression and the calculated results. The parameters are given in Table 4.6.

Table 4.6 Fitted parameters for path loss expression.

α0 (dB/m)	α1 (dB/m)	PL0,dB
371.2	30.4	35.4

4.2.5.3 Equivalent Circuit Expression

An equivalent circuit expression is also useful to explore the path loss in the HBC band. The simplest equivalent circuit is based on the assumption of the human body as a perfect conductor. This assumption makes the human body a single node. The single node is connected to the transceiver and external ground through lumped equivalent capacitors. Such a capacitive approach is shown in Figure 4.21. However, at tens of MHz or more, the body impedance cannot be ignored in reality. So we have to consider both the resistance component and capacitance component of the body itself, in addition to the capacitive components to the external ground in the equivalent circuit expression. These components will cause signal loss between the transmitter and receiver. Figure 4.22 shows a unit block with a RC parallel network and a shunt capacitor (Cho et al., 2007). The unit block represents one part of the human body and the corresponding electrical coupling. The entire human body can be considered as a cascade of many unit blocks.

When considering a HBC scenario as in Figure 4.19, we can segment the human body into many unit blocks of 10 cm along the body length, and then determine the parameters of the equivalent circuit for each unit block, that is, the impedance of the parallel RC network and the coupling capacitance to the external ground.

The derivation of the impedance of parallel RC network is based on the dielectric properties of the human body. The dielectric properties of the human body are highly dependent on the frequency and tissue types. Due to the significant penetration depth in the HBC band, the human body can be approximated by a homogeneous medium with dielectric properties similar to two-thirds the value of muscle. The conductivity σ is within 0.4–0.5 S/m and the relative permittivity ε_r varies from 44 to 106 in the frequency band of 10–100 MHz. Therefore, the resistance R can be obtained from

(4.35)

and the capacitance C can be obtained from

(4.36)

where L and S are the length and cross-sectional area of a unit block, respectively.

On the other hand, the coupling capacitance to the external ground can be obtained by approximating the unit block as a conductive sphere in free space. For each segment of the body, we have a volume V. If we use a sphere to approximate this volume, the equivalent sphere's radius is

(4.37)

. Then the coupling capacitance can be calculated from

(4.38)

where d is the distance of the center of the sphere to the ground.

It should be noted that the capacitance determined in the above way assumes that the human body is located in an open space. If any large conductive object is nearby, the capacitance will increase due to the existence of an additional coupling path. Moreover, the coupling capacitances between the transceiver grounds and the unit block are highly affected by the body configurations. In most cases, their values are smaller than 1 pF, with a smaller influence on the channel characteristic. An approach for accurately extracting the coupling capacitance is to use a numerical electromagnetic analysis tool to calculate quasi-static field components. Such an approach is especially effective for considering a complicated body shape and structure, but it suffers from a large computation burden.

By cascading these RC unit blocks, we can obtain a complete circuit model of the human body. Table 4.7 gives some typical values for the parameters in the parallel RC unit block, which are calculated using Equations 4.35–4.38. To consider the channel responses at various locations on the body, we can place the transceiver models at corresponding nodes of the equivalent circuit. In the equivalent circuit, the major return path is formed by the electrical coupling between the transceiver grounds and the external ground. A large ground plane or a special electrode for the return path is therefore advantageous to enhance the signal-to-noise ratio (SNR) of the received signal.

Table 4.7 Calculated parameters of equivalent circuit per 10 cm.

Figure 4.23 shows an example of an equivalent circuit with the transmitter and receiver at the torso. The head, torso and leg are modeled using three, five and nine unit blocks, respectively. Figure 4.24 shows simulation results for the path loss as a function of transmission distance by using the equivalent circuit. The simulation is conducted in the circuit simulator SPICE. The path loss is the ratio in decibels of the received voltage at the receiver electrode and the transmitted voltage at the transmitter electrode. Also shown in Figure 4.24 are the measured results. The transmitter electrode is excited by a crystal oscillator, and is fixed at the chest. The receiver is shifted along the body surface to detect the received voltage. The obtained path losses for five people are averaged and indicated by diamond symbols in the figure. It can be seen that the simulated path loss has fair agreement with the measured results. It is also on the same order as the FDTD-calculated version in Figure 4.20. It is worth noting that the path loss does not exhibit significant frequency dependence between 10 MHz and 100 MHz. The distance dependence is also weak compared with other frequency bands. This feature suggests that HBC is a good choice for efficient on-body transmission.

Although this approach only gives a rough estimation for the path loss, it is much simpler and easier to use compared with electromagnetic field numerical simulation or measurement.

4.3 Multipath Channel Model

In wireless communications, the multipath propagation phenomenon is when the transmitted signal travels along many different paths to reach the receiver. The presence of multiple paths between transmitter and receiver introduces complexity in the channel modeling. The complexity depends on the distribution of the multipath intensity, relative propagation time of the waves and bandwidth of the transmitted signal. Therefore, the time-varying properties of the channel must be taken into account in the channel model.

Multipath channel models have already been widely investigated in indoor and outdoor wireless communications. Several models are available for both narrowband and wideband transmissions (Rice, 1959; Saleh and Valenzuela, 1987; Hashemi, 1993); the Saleh–Valenzuela channel model, sometimes abbreviated to the S–V model, has provided a comprehensive and standardized formalization on statistical modeling for indoor multipath propagation. For the body area multipath channel model, some effort has also been made in recent years based on experimental and numerical approaches (Fort et al., 2006; Tang et al., 2006; Zhao et al., 2006; Wang et al., 2009). A generalization of the derived channel model, however, has to take into account the statistical characteristics of body postures and movements.

In this section, we will present a body area UWB multipath channel model based on the classical Saleh–Valenzuela model. The Saleh–Valenzuela model is based on indoor multipath propagation measurements using radar-like pulses, which essentially covers a wideband propagation characteristic. And more importantly, it appears to be extendable to a body area UWB multipath channel model via appropriate modifications. We will first introduce the classical Saleh–Valenzuela model and then investigate in detail the body area UWB multipath channel model with a few modifications to the Saleh–Valenzuela model.

4.3.1 Saleh–Valenzuela Impulse Response Model

It is known that the impulse response model is a convenient model to characterize the multipath channel and any deterministic impulse response can be represented by a discrete tapped delay line model as long as the system is band-limited. The Saleh–Valenzuela model is expressed by a discrete impulse response model as follows

(4.39)

where is the multipath power gain, is the associated phase shift, is the propagation delay, k is the path index and is the Dirac delta function. The parameters , and are treated as virtually time-invariant random variables since the motion rate of the indoor subjects is very slow compared with the potential signaling rates. In this indoor channel model, the multipaths are modeled based on the observation that multipath contributions generated by the same pulse usually arrive in clusters. The clusters are formed by the building structure, while the individual paths are formed by objects in the vicinities of the transmitter and the receiver. The arrival time of the clusters is modeled as a Poisson process. Meanwhile, the multipaths within each cluster also arrive according to a Poisson process with a different rate. The multipath gain is a statistically independent Rayleigh distributed random variable. The is an independent uniform variable over [0,2π).

4.3.2 On-Body UWB Channel Model

Different from the path loss characteristics which can be extracted based on the whole body average, the characteristics of the on-body multipath channels can be expected to differ considerably for different propagation links due to the variability of the link geometry. Moreover, differences in body parts as well as in body curvatures in the vicinities of the transmitter and receiver result in distinct multipath characteristics. Therefore, we need to differentiate different transmission links and assign the transmitter and receiver points on the human model in the context of multipath channel characterization. As described in the path loss modeling, in order to improve the computation efficiency in the FDTD method, one transmitting antenna and multiple receiving points are constructed on the body model.

As shown in Figure 4.25, a Hertzian dipole transmitter is fixed on the left chest and five receiving points are assigned on the right chest, the left and right waists, and both ears, respectively. This assignment results in five transmission links: chest-to-right-chest link, chest-to-left-ear link, chest-to-right-ear link, chest-to-left-waist link and chest-to-right-waist link, respectively. The five transmission links can be considered as typical transmission links for medical and healthcare applications.

Since the on-body multipaths are mainly caused by the body movement, the effects of various body postures are investigated by simulating 35 different postures, as seen in Figure 4.26. The details of the postures are as follows:

Simulating various postures is indispensible in order to obtain a statistical characterization of the transmission channels, since the posture of the user is generally not fixed in medical and healthcare applications.

Since the impulse response of the Saleh–Valenzuela model can be used after appropriate modifications (Molisch et al., 2006) for UWB applications, here we apply and modify the Saleh–Valenzuela model in order to characterize the on-body UWB multipath channel and to obtain the parameters required for the implementation. The modified Saleh–Valenzuela model in the time domain deserves practical implementation in system design and simulation.

4.3.2.1 Power Delay Profile

The power delay profile (PDP), , is a statistical expression of the transmission channel characteristics. It can be derived from the impulse response , that is,

(4.40)

and

(4.41)

where and are the transmitted and the received pulse voltages respectively, is the frequency-domain transfer function, and and denote Fourier transform and inverse Fourier transform, respectively. The PDP characterizes the arrival time of the different multipath contributions versus the received mean power.

In the derivation of the impulse response , frequency-domain windowing has to be applied in the spectral analysis. Frequency-domain windowing can reduce the time side lobes in the impulse response using weighting in the frequency domain. Different windowing functions have different effects on the time-domain derivation. This is mainly because different windows in the frequency domain will result in different time side lobes/spreads as well as different time resolution. Therefore, time side lobe and time resolution are the two most important factors in the windowing function selection. The rectangular window has excellent resolution characteristics, but its first side lobe is only 13.3 dB down. The Hanning window, also called the raised cosine window, can have a first side lobe 32 dB down while its main lobe has been widened compared with the rectangular window with twice the main lobe width of the rectangular window. The wide main lobe represents a degraded time-domain resolution due to a corresponding time spread. The Hamming window is a kind of optimized raised cosine window with simpler coefficients, which is optimized to minimize the maximum side lobe, giving it a peak side lobe level approximately 42 dB down. The Blackman window will result in a much higher peak side lobe compared with the Hanning and Hamming windows while the main lobe width is four times that of the rectangular window. Moderate windows should be selected in between the resolution extreme and side lobe extreme, such as Hanning and Hamming windows. The Hamming window has the same main lobe width as the Hanning window with a much lower time side lobe and hence could be a very good window candidate in the time-domain impulse response derivation.

The Hamming window is therefore employed in and with a frequency bandwidth of 14 GHz in view of the dominating frequency components of the employed second-derivative Gaussian pulses. The time resolution of the inverse Fourier transform for can be approximated as the reciprocal of the bandwidth (1/14 GHz = 0.07 ns) multiplied by the additional window function bandwidth. Since the coefficient of the Hamming window is 2, this results in a 0.14.ns time resolution for the impulse response and the PDP.

Based on the data from all 35 postures, the average power delay profiles (APDPs) for five typical transmission links are shown in Figure 4.27. It can be noted that one cluster is sufficient for describing the PDP in all five representative transmission links. Each peak in the cluster may be attributed to a multipath, which results from the diffraction from the body surface or the reflection from a body part. We should note that no clusters corresponding to the surrounding environment are included and the channel model extraction is limited solely to the human body. From Figure 4.27, as expected, the APDP decays exponentially with the arrival time, that is, it can be approximately expressed as

(4.42)

where and are the mean power gain and the arrival time of the first path, respectively. With the exponential fittings to the data in Figure 4.27, it is found that the decay time constants are 0.21, 0.26, 0.38, 0.30 and 0.5 ns, respectively for chest-to-right-chest link, chest-to-left-ear link, chest-to-right-ear link, chest-to-left-waist link and chest-to-right-waist link, respectively.

4.3.2.2 Power Gain Distribution

The log-normal distribution is reported in Fort et al. (2006) and Zhao et al. (2006) as an excellent fit to the power for all receiver locations. Here, we assume that all of the obvious peaks in the PDP correspond to the multipaths. The multipaths are characterized by identifying the corresponding peaks, and then obtaining the arrival time and the power of the individual paths. The peaks that have power gains up to 30 dB lower than the maximum peak value are taken into account in order to extract the channel parameters, while the other peaks are small enough to be ignored. The power distribution in the first and the second paths are also studied. Some possible candidates, such as the log-normal distribution, Rayleigh distribution, Rice distribution and Weibull distribution, are considered for the power model.

In order to pick the optimal distribution, the classical second-order Akaike information criterion (AIC_c) (Akaike, 1973) is used to rank the fitting results from best to worst. The AIC is a measure of the relative goodness of fit of a statistical model. It is grounded in the concept of information entropy, in effect offering a relative measure of the information lost when a given model is used to describe reality.

The second-order is defined as follows (Burnham and Anderson, 2002)

(4.43)

where is the value of the maximized log-likelihood over the unknown parameters , given the data and the model, is the number of parameters estimated in that model, and is the sample size. This equation is straightforward to compute since the log-likelihood is readily available from the maximum likelihood estimation. Intuitively, the first term indicates that better models have a lower because the log-likelihood reflects the overall fit of the model to the data. The second part of the equation penalizes additional parameters so that the selected model best fits the data with the least number of parameters. In this way, the model with the lowest approximates the “true” distribution with the minimum loss of information.

In practice, the value of the by itself has no meaning. However, the relative values of among the models can be used to rank the models from best to worst and to provide strength of evidence that one model is better than another. To facilitate this, the two following related metrics are normally reported

(4.44)

(4.45)

where is the value for the model index, and is the number of models. Clearly, the best model among the set of models has a ΔAIC of 0. As a rule-of-thumb, suggests substantial evidence for the model, values between 3 and 7 indicate that the model has considerably less support, while values >10 indicate that the model is very unlikely. The Akaike weights () provide a more precise measure of the strength of evidence and can be interpreted as the probability that the model is the best among the whole set of candidates. In addition, the ratio of two AIC weights indicates how much more likely one model is better compared with the other. Clearly, these metrics are more informative than a simple hypothesis test that can only pass or fail a model based on an arbitrary significance level without providing any strength of evidence or ranking. These advantages will become more apparent as we apply the metrics to our data in the following subsections.

As seen from Figure 4.28, the log-normal distribution provides a superior fit to the power distribution in the multipaths. Furthermore, Table 4.8 gives a comparison of the power distribution fitting models for the chest-to-right-waist link and the AIC parameters show further that the log-normal distribution gives the best fitting result. For the chest-to-right-waist link, the average standard deviation of the power variation is 7.87 dB, which will be used in the channel modeling. For other representative links, the conclusion that the log-normal distribution provides a superior fit to the powers still holds, although obviously the standard deviations are different. The physical meaning of the power variation following a log-normal distribution is easily understood, since the wave can be considered to propagate along the body area with magnitudes affected by statistically varying reflection and diffraction coefficients in the form of multiplication.

Table 4.8 Comparison of fitting models of power distribution for the chest-to-right-waist link.

Model
Lognormal	0	0.88
Rayleigh	173.75	0.0
Rice	14	0.0
Weibull	4	0.12

4.3.2.3 Arrival Time of the First Path

For various transmission links, the arrival time of the first multipath varies, and is determined mainly by the direct transmission distance. For all five transmission links, Gamma distribution is fitted to the arrival time data of the first path, in accordance with the AIC. The Gamma fittings of the arrival time of the first path for the five links are shown in Figure 4.29. For example, for the chest-to-right-waist link, the mean value and the standard deviation of the Gamma distribution are found to be 2.0 and 0.03 ns, respectively. The extremely small standard deviation suggests that fixing the arrival time of the first path at the mean value is reasonable.

4.3.2.4 Inter-Path Delay Distribution

An impulse response can be represented by a tapped delay line model. In the on-body UWB transmission, adjacent taps may be influenced by a single physical multipath component, which suggests a correlation. In this case, it is possible to realize an impulse response based on a uniformly spaced tapped delay line model (Molisch et al., 2006). In the present case, however, the dominant multipath components correspond to parts of the body such as the arms, legs and so on due to their varying positions. Most of the multipaths are distinguishable due to the high time resolution of 0.14 ns. Moreover, the simulation results indicate that the correlation coefficient between the first and the second distinguishable multipaths is as weak as 0.2, which allows us to characterize the inter-path delay without resorting to uniformly spaced taps.

The inter-path delay, which corresponds to the temporal delay between two successive paths, represents the characteristics of the arrival time for all multipaths in the on-body transmission channel. In view of the above observations, we can derive the statistical model for the inter-path delay. At first, we identify the delay time of each path from the corresponding peak in the PDP, and then the difference between the arrival times of two successive multipaths can be calculated in order to obtain the inter-path delay. The inter-path delay data obtained in this way are fitted to some candidate statistical distributions, such as the exponential distribution, Weibull distribution, log-normal distribution and inverse Gaussian distribution.

The inverse Gaussian distribution is a two-parameter family of continuous probability distributions. Its probability density function (PDF) is given by

(4.46)

where μ is the mean and λ is the shape parameter. The variance is equal to μ³/λ. As λ tends to infinity, the inverse Gaussian distribution becomes more like a normal distribution. Figure 4.30 shows the results of the inverse Gaussian fitting to the inter-path delay data for all five links. The inverse Gaussian distribution provides a superior fit. Furthermore, Table 4.9 gives a comparison of the two metrics of the second-order for the results of the fitting to the chest-to-right-waist FDTD-calculated data. The second-order indicates further that the inverse Gaussian distribution is the best fitting model. For the chest-to-right-waist link, the mean value of the inter-path delay is 0.33 ns and the standard deviation is 0.2 ns. For other representative links, the inverse Gaussian distribution also provides a superior fit in comparison with other distributions, although the mean values and the standard deviations are, of course, different.

Table 4.9 Comparison of fitting models of inter-path delay distribution.

Model
Inverse Gaussian	0	1
Lognormal	604	0.0
Weibull	792	0.0
Exponential	852	0.0
Gamma	718	0.0

4.3.2.5 Summary of the Derived Model Parameters

Based on the above characterizations and parameterizations, we have determined all statistical models and parameters required for the construction of the channel model. These parameters are summarized in Table 4.10.

Table 4.10 Model parameters for five representative transmission links (Wang et al., 2009). Reproduced with permission from Wang Q., Tayamachi T., Kimura I. and Wang J., “An on-body channel model for UWB body area communications for various postures,” IEEE Transactions on Antennas and Propagation, 57, 4, 991–998, 2009. © 2009 IEEE.

In Table 4.10, according to the Saleh–Valenzuela model, the mean power gain of the first path is related to (the reciprocal of the average path loss in a communication link) as , where is the mean time interval between two multipaths.

4.3.2.6 Measurement Validation

In order to verify the computational results and the statistically constructed model result, measurement is carried out in a full anechoic chamber. The chest-to-right-waist transmission link is taken as the measurement object. Two small-size and low-profile UWB antennas are mounted on the body surface. The transmitting antenna is fixed on the left side of the chest, and the receiving antenna is fixed on the right side of the waist. The measurement is conducted for 8 people, and with 10 body postures for each person, including standing, walking and sitting.

The measurement method is as follows:

By using the approach described in the previous subsections, a characterization and parameterization of the measurement results for the chest-to-right-waist transmission link is conducted. Table 4.11 presents a comparison of the parameters obtained from the FDTD modeling and the measurements. It is clear that good agreement has been achieved, even though it appears that the values of the inverse Gaussian distribution of the inter-path delay are somewhat different. In fact, refers to the shape of the PDF of the inverse Gaussian distribution, and in spite of the twofold difference between the values, there is only a small difference between the shapes of the respective PDFs. In short, the model parameters are in good agreement with the parameters obtained from the measurement, which validates this modeling method.

Table 4.11 Comparison of parameter values in the FDTD model and measurements (Wang et al., 2009). Reproduced with permission from Wang Q., Tayamachi T., Kimura I. and Wang J., “An on-body channel model for UWB body area communications for various postures,” IEEE Transactions on Antennas and Propagation, 57, 4, 991–998, 2009. © 2009 IEEE.

Parameter	Model	Measurements
(ns)	0.47	0.41
(dB)	7.87	8.87
(ns)	2.01	—
(ns)	= 0.33	= 0.30
	= 0.85	= 2.14

4.3.2.7 Channel Model Implementation

Based on the modified Saleh–Valenzuela model and the channel characterization, a discrete time impulse response function applied to these five transmission links is written as

(4.47)

where is the multipath power gain, and is the delay of the kth multipath component relative to the arrival time of the first path.

First, the time delays of the multipaths are induced as follows: the first path is generated at a fixed arrival time, and then a temporal delay between two successive paths is generated according to the inverse Gaussian distribution and added to the arrival time of the previous path.

Next, the gain coefficient for each path is defined as follows

(4.48)

where takes a value of +1 or −1 with equal probability, and

(4.49)

since belongs to a log-normal distribution. From Equation 4.42, we have

(4.50)

and , the mean in Equation 4.49, is written as

(4.51)

All parameters required for the modeling of this simplified impulse response function have already been described in the previous section, and are summarized in Table 4.10.

The propagation models for all five transmission links can be implemented in MATLAB®, and Figure 4.31 shows an implemented impulse response sample for the chest-to-right-waist link with for the sake of simplicity. A MATLAB® code can be found at www.wiley.com/go/wang/bodyarea.

We can compare the FDTD-calculated channel and the modeled channel using the root mean square (RMS) delay spread and the mean excess delay , which measure the effective duration of the channel impulse response. They are two kinds of representations of the impulse response profile and are frequently used to verify channel models. The two metrics are defined as follows (Hashemi, 1993):

(4.52)

(4.53)

where P_R is the multipath mean power. The above expressions show that is defined as the square root of the second central moment of the PDP and is defined as the first moment of the PDP. is a good measure of multipath spread and it gives an indication of the potential inter-symbol interference.

Figures 4.32 and 4.33 show the CDFs of the RMS delay spread and the mean excess delay for two transmission links. As can be seen from the figures, the model matches closely the FDTD-calculated results, and therefore adequately characterizes the transmission links.

4.3.3 In-Body UWB Channel Model

4.3.3.1 In-Body to On-Body Impulse Response

The same methodology as in on-body UWB channel modeling can also be used for in-body to on-body UWB channel modeling. Based on the simulation set-up for capsule endoscope shown in Figure 4.6, we can get 99 impulse responses at each receiving location for the in-body to on-body channel in total. During the process of inverse Fourier transform to get h(t), the Hamming window with a coefficient of 2 is usually applied in the frequency domain in order to limit the transmitted pulse signal to effective frequency components. Since the UWB low band has a bandwidth of 1.4 GHz, the corresponding time resolution of the impulse response h(t) or the PDP p(t) will be 1.43 ns. In other words, multipath components within such a time width cannot be resolved even if more than one multipath arrives and thus have to be simply added up when deriving the impulse responses.

Due to this limited time resolution, we have to divide the time axis into many bins where each bin has a width of 1.43 ns. So in each impulse response or PDP, the first multipath is identified from the first peak of bins, and the second and third multipath components are identified from the successive bins, respectively. Figure 4.34 shows a typical FDTD-derived PDP for the in-body to on-body multipath channel. In this case, the receiving antenna is located in front of the human abdomen as Rx1, while the transmitting antenna is at one of the 33 locations. The first multipath component can be considered as a direct path between the transmitter and receiver. As a consequence, the successive multipath components can be assumed to correspond to the paths diffracted by or scattering from various tissues or organs of the human body. Moreover, the arrival time of the first multipath component can also be estimated by calculating the division of in-body to on-body local distance and the propagation speed in the human body (about a quarter of light speed in free space). The result of about 1.45 ns provides a good agreement with the first multipath component observed in Figure 4.34.

In addition, also from other results of the derived impulse responses and PDPs for different transmitting and receiving pairs, the direct path always turned out to be the strongest path in comparison with the successive two multipath components. Since the power of the third multipath component is more than 25 dB lower than the first one, which is weak enough to be neglected, we take the first two multipath components with a fixed bin width into account as the dominating multipath components. Therefore, we get an approximated discrete time impulse response channel model with only two multipath components, the first multipath component corresponds to the direct path, and the second one corresponds to a dominating diffracted or scattered path.

Figure 4.35 shows an example of an approximated two-path impulse response model at the receiver location Rx1. The amplitude of this two-path impulse response model is calculated from the root of the integrated power within one bin in the corresponding PDP, and the time interval between the two paths is assumed to be the same as one bin width. It can be concluded that a two-path impulse response model is sufficient to produce an appropriate approximation to the received UWB low band signals. It can also be concluded that the in-body to on-body channel characteristics mainly depend on the large attenuation with less influence by the multipath.

Based on such a well approximated two-path model, the multipath power gain distributions are investigated to provide the parameters in statistical terms. Here the multipath powers for the two paths are fitted to some candidate statistical distributions. As shown in Figure 4.36, the normal distribution provides a superior fit to both of the two-path magnitudes in decibels based on the second-order AIC. That is to say, the log-normal distribution fits the multipath powers well. The average standard deviations of the power variation are 16.8 dB. At the same time, a difference of less than 15 dB between the two multipath components exists when the CDF is 0.5.

The arrival time of the first multipath component from the in-body to on-body transmission is significantly determined by direct path transmission, but varies at different transmitter locations as well as with different polarizations. From the FDTD-simulated results, 99 different arrival times of direct path are obtained at each receiver location. It is found that the inverse Gaussian distribution fits well the derived arrival times of direct path also based on the second-order AIC. The mean μ and the standard deviation σ of the inverse Gaussian distribution is 1.3 and 0.54 ns, respectively. Moreover, since the inter-path delay is assumed as a fixed bin width, the second path has the same statistical distribution but a longer mean arrival time of 2.73 ns. Based on the above characterization, the parameters for the two-path impulse response model are summarized in Table 4.12 for the UWB in-body to on-body wireless link.

Table 4.12 Main parameters for in-body to on-body UWB impulse response channel model.

Description	Characteristics	Parameter
1st path
Power	Log-normal	μ1 =− 89.2 dB
		σ1 = 16.8 dB
Arrival time	Inverse Gaussian	μ1 = 1.3 ns
		σ1 = 7.5 ns
2nd path
Power	Log-normal	μ2 =− 102.3 dB
		σ2 = 16.8 dB
Arrival time	1st path + 1.43 ns

4.3.3.2 In-Body to Off-Body Impulse Response

With the same approach, for the simulation set-up in Figure 4.9, we can get 180 impulse responses and PDPs for the in-body to off-body channel. Again, due to the limited time resolution, we have to divide the time axis into many bins where each bin has a width of 1.43 ns in each PDP. Figure 4.37 shows a typical FDTD-derived PDP. The first multipath component can be considered as a direct path between the transmitter and receiver, and the others can be assumed to correspond to the paths diffracted by or scattering from various tissues or organs of the human body. The PDP characterizes the mean power of different multipaths. It is found to decay exponentially with the arrival time. With the exponential fitting to the result in Figure 4.37, it is found that the mean power gain is =− 60.4 dB, the arrival time of the first path is = 0.9 ns and the multipath decay time constant is = 0.23 ns.

In the PDPs, the multipath power is characterized by the bins. The bins that have power which is not 25 dB lower than the maximum value are taken into account in order to extract the channel parameters, while the other components are small enough to be ignored. Then the power gain distribution for each path is investigated, and some possible candidates are considered for the power gain model. Similarly, the second-order AIC is used to rank the fitting results from best to worst. As a result, the log-normal distribution provides a superior fit to the power gain distribution again. Figure 4.38 shows the fitting result for the first and the second paths. Since the amplitudes are expressed in decibels, the normal distribution is applied. The standard deviations of the amplitude variation are = 2.32 dB and = 2.04 dB for the first and second paths, respectively. The small variation is just because of the slight position variation of the transmitter inside the chest.

The arrival time of the first path, determined mainly by the direct transmission distance, varies with the location of the implant transmitter. The inverse Gaussian distribution is fitted to the arrival time of the first path with the mean value = 0.91 ns and shape parameter = 67.2 ns, also in accordance with the AIC. The fitting result is shown in Figure 4.39.

Based on the above characterization and parameterization, the two-path impulse response model and corresponding parameters, which are required for implementing the channel model, are summarized in Table 4.13.

Table 4.13 Main parameters for in-body to off-body UWB channel model.

By using the established channel model, the discrete time impulse response function can be obtained. First, the time delays of the two paths are generated. For the first path, the arrival time is generated according to the inverse Gaussian distribution with the mean = 0.91 ns and the shape parameter = 67.2 ns. Afterwards the arrival time of the second path is generated to be the arrival time of the first path plus 1.43 ns. Next, the gain coefficient for each path is defined according to the log-normal distribution. As an alternative method in the in-body to on-body case, the mean is determined from the exponential power decay formula in Equation 4.42, and the standard deviations are taken from Table 4.13.

To examine the validity of the generated impulse response, the mean delay and the RMS delay spread are calculated and compared with the FDTD-calculated result. Figure 4.40 shows the CDFs of the mean delay and delay spread. As can be seen, the model matches closely the FDTD-calculated result, and therefore adequately characterizes the in-body transmission.

References

Akaike, H. (1973) Information theory as an extension of the maximum likelihood principle. Proceedings of the 2nd International Information Theory Symposium, pp. 267–281.

Aoyagi, T., Takizawa, K., Kobayashi, T. et al. (2010) Development of an implantable WBAN path-loss model for capsule endoscopy. IEICE Transactions on Communications, E93-B (4), 846–849.

Barlow, H.M. and Brown, J. (1962) Radio Surface Waves, Oxford University Press, Oxford, pp. 6–28.

Benedetto, D.M.-G. and Giancola, G. (2004) Understanding Ultra Wide Band Radio Fundamentals, Prentice Hall, New Jersey.

Burnham, K.P. and Anderson, D.R. (2002) Model Selection and Multimodel Inference: A Practical Information-Theoretic Approach, 2nd edn, Springer-Verlag, New York.

Chavez-Santiago, R., Khaleghi, A., Balasingham, I., and Ramstad, T.A. (2009) Architecture of an ultra wideband wireless body area network for medical applications. Proceedings of the 2nd International Symposium on Applied Sciences in Biomedical and Communication Technologies, Bratislava, Slovakia.

Cho, N., Yoo, J., Song, S.-J. et al. (2007) The human body characteristics as a signal transmission medium for intrabody communication. IEEE Transactions on Microwave Theory and Techniques, 55 (5), 1080–1086.

Conroy, J.T., LoCicero, J.L., and Ucci, D.R. (1999) Communication techniques using monopulse waveforms. Proceedings of IEEE Military Communications Conference, vol. 2, pp. 1181–1185.

Fort, A., Desset, C., De Doncker, P. et al. (2006) An ultra-wideband body area propagation channel model - From statistics to implementation. IEEE Transactions on Microwave Theory and Techniques, 54 (4), 1820–1826.

Gabriel, C. (1996) Compilation of the dielectric properties of body tissues at RF and microwave frequencies. Brooks Air Force Technical Report AL/OE-TR-1996-0037.

Ghavami, M., Michael, L.B., Haruyama, S., and Kohno, R. (2002) A novel UWB pulse shape modulation system. Wireless Personal Communications, 23 (1), 105–120.

Hashemi, H. (1993) The indoor radio propagation channel. Proceedings of the IEEE, 81 (7), 943–968.

Hämäläinen, M., Hovinen, V., Iinatti, J., and Latva-aho, M. (2001) In-band interference power caused by different kinds of UWB signals at UMTS/WCDMA frequency bands. Proceedings of the IEEE Radio and Wireless Conference, pp. 97–100.

IEEE P802.15 Working Group for Wireless Personal Area Networks (2009) Channel model for body area network (BAN), IEEE P802.15-08-0780-09-0006.

Khaleghi, A. and Balasingham, I. (2009) Improving in-body ultra wideband communication using near-field coupling of the implanted antenna. Microwave and Optical Technology Letters, 51 (3), 585–589.

Molisch, A.F., Cassiolo, D., Chong, C.-C. et al. (2006) A comprehensive standardized model for ultra wideband propagation channels. IEEE Transactions on Antennas and Propagation, 54 (11), 3151–3166.

Qureshi, W.A. (2004) Current and future applications of the capsule camera. Nature Reviews Drug Discover, 3, 447–450.

Rice, L.P. (1959) Radio transmission into buildings at 35 and 150 MHz. Bell System Technical Journal, 38 (1), 197–210.

Saleh, A.A.M. and Valenzuela, R.A. (1987) A statistical model for indoor multipath propagation. IEEE Journal on Selected Areas in Communications, 5 (2), 128–137.

Shi, J. and Wang, J. (2010) Channel characterization and diversity feasibility for in-body to on-body communication using low-band UWB signals. Proceedings of the 3rd International Symposium on Applied Science in Biomedical and Communication Techniques, Rome, Italy.

Tang, P.K., Chew, Y.H., Ong, L.C. et al. (2006) Small-scale transmission statistics of UWB signals for body area communications. Proceedings of the 64th IEEE Vehicular Technology Conference, pp. 1–5.

Taparugssanagorn, A., Rabbachin, A., Hamalainen, M. et al. (2008) A review of channel modeling for wireless body area network in wireless medical communications. Proceedings of the 11th International Symposium on Wireless Personal Multimedia Communications.

Wang, J., Nishikawa, Y., and Shibata, T. (2009) Analysis of on-body transmission mechanism and characteristic based on an electromagnetic field approach. IEEE Transactions on Microwave Theory and Techniques, 57 (10), 2464–2470.

Wang, J., Masami, K., and Wang, Q. (2011) Transmission performance of an in-body to off-body UWB communication link. IEICE Transactions on Communications, E94-B (1), 150–157.

Wang, Q., Tayamachi, T., Kimura, I., and Wang, J. (2009) An on-body channel model for UWB body area communications for various postures. IEEE Transactions on Antennas and Propagation, 57 (4), 991–998.

Win, M.Z. and Scholtz, R.A. (2000) Ultra-wide bandwidth time-hopping spread-spectrum impulse radio for wireless multiple-access communications. IEEE Transactions on Communications, 48 (4), 679–691.

Zasowski, T., Meyer, G., Althaus, F., and Wittneben, A. (2006) UWB signal propagation at the human head. IEEE Transactions on Microwave Theory and Techniques, 54 (4), 1836–1845.

Zhao, Y., Hao, Y., Alomainy, A., and Parini, C. (2006) UWB on-body channel modeling using Ray theory and subband FDTD method. IEEE Transactions on Microwave Theory and Techniques, 54 (4), 1827–1835.