2.1 Aoyagi et al. Model

One of the fundamental channel models of the IEEE 802.15.6 subgroup was provided by Aoyagi et al. It is based on the simple Friis formula, where an additional term was added in order to describe shadowing [9]. This additional term N is a Gaussian distributed function with a mean value 0 dB and standard deviation σ_N dB, which can be determined based on statistical fitting [4]. Particularly, the path loss observed at a receiving node located at distance d from a transmitter is expressed as

$PL{(d)}_{dB}=\alpha \log (d)+b+N,$ (2)

(2)

where α and b are coefficients of linear fitting.

Based on that model, the authors provided a set of measurements considering several frequency bands suitable for WBAN operation. More details on the measurement setup, derivation, and data analysis are given in [9]. Experiments took place in different environments, i.e., in a hospital room and an anechoic chamber. The anechoic chamber provides ideal transmission conditions since it eliminates any possible reflections from the surroundings.

During the experiment process, several antennas were located on the human body, including the left hand, left upper arm, left ear, head, shoulder, chest, right rib, left waist, thigh, and ankle. The received measurements consisted of a proper set of empirical results that were properly fitted to the linear model of (2) using the least square method. The measurements took possible human body turnarounds into account, i.e., LOS and NLOS situations were considered in the experiment as well.

The propagation distance between a transmitter and receiver was scaled and varied from 100 to 1,000 mm. Different frequency bands were used and the results obtained are depicted in Table 2. Roughly speaking, five submodels were distinguished, namely A, B, C, D, and E, which refer to the five frequency bands where experiments took place, i.e., 400–450 MHz, 608–614 MHz, 950–956 MHz, 2.4–2.5 GHz, and 3.1–10.6 GHz, accordingly. The parameters, A, B, and σ_N for each sub-model differ from each other and are clearly outlined for the two environments (hospital room and anechoic chamber). It can be shown that the path loss effects caused by the presence of the human body are greater in an anechoic chamber, in comparison to the hospital room, due to the reflections from the walls. This can be verified in [9, Figure 3] where analytical path loss results for all models are illustrated using proper diagrams.

2.2 Dolmans and Fort Model

A more complicated model was suggested by Dolmans and Fort [10]. The measurements took place in an office environment for 915 MHz and 2.45 GHz.

The channel parameters were obtained using measurements from receiving nodes placed in front of and on the back of a human body. The transmitter was worn at approximately shoulder height. Several path-loss models were tested to fit the measurement data. The combined exponential-linear saturation model was found to give the best fit with the measurement data. That happened since the path loss follows an exponential decay around the perimeter of the body and flattens out as distance increases, due to energy received from multi-path reflections of the indoor environment [8].

The path loss according to that model is expressed as

$PL{(d)}_{dB}=-10\log (P_0^{-m_{0}d}+P_1)+{\sigma }_P{n}_P,$ (3)

(3)

where P₀ is the average loss close to the antenna, m₀ is the average decay rate in dB/cm for the surface wave moving around the perimeter of the body, P₁ is the mean attenuation of components radiated away from the body and reflected back to the receiver, σ_P is the log-normal variance in dB around the average representing the variations measured at different body and room locations, and n_P is a Gaussian variable of zero mean and unit variance.

The authors also provided a model of the flat small-scale fading observed at the measured data. They examined several distributions such as Rayleigh, lognormal, Nakagami-m, and Rician using maximum-likelihood parameter estimates and found that the Rician distribution reflects the most adequate model. The Rician distribution is characterized by a parameter, K, defined as the ratio of the specular component to the random multi-path component powers [10]. This parameter decreases when the receiver is moved away. The K-factor is expressed in dB as

$K_{dB}=K_0-m_K{P}_{dB}+{\sigma }_K{n}_K,$ (4)

(4)

where K₀ is the fit with measurement data for the K-factor for low path loss, m_k is the slope of the linear correlation between path loss and K-factor, P_dB is the path loss in dB, σ_k is the log-normal variance of the measured data between path loss and K-factor, and n_k is the Gaussian variable with zero mean and unit variance.

Regarding narrowband systems, where frequency selective fading appears, the authors estimated the delay spread from the cumulative density function for antenna separations of 15 and 45 cm. The delay spread is modeled with a normal distribution. Table 3 summarizes the parameter values for the two frequency bands where the model is valid.

2.3 Miniutti et al. Model

This model deals with measurements of on-body narrowband wireless channels at the frequencies of 820 MHz and 2.36 GHz [11]. The experiments took place in an office environment where several antennas were located on the human body. The aim was to estimate the path loss assuming three different human actions, i.e., standing, walking, and running. As the authors declare, the innovation of their study compared to other ones lies in the examination of continuous movement of the human body on the wireless channel. Table 4 lists the body locations and the separations in cm of transmitters and receivers used.

The multi-path transmission around the body and the surrounding environment also causes a fading appearance. A significant amount of fading also occurs due to the movement of the human body. The distribution of the normalized received power was described using a probability density function that obtains the best match for all scenarios. The Gamma distribution was proven the best fit to average fade duration. Moreover, the same distribution fitted to a dB scale was the best fit to fade magnitude [8].

An analytical description of the experimental process and the instrumentation equipment is provided in [11]. The path loss at a given time t is obtained as

$PL{(d)}_{dB}=P_{tX}-P_{rX}+G_{amplifiers}-L_{cable},$ (5)

(5)

where P_tX is the transmitted power, P_rX the RMS received power, G_amplifiers the amplifier gain, and L_cable the cable loss. Table 5 shows the average path loss for each action and antenna placement for the two frequency bands. In general, the path loss is greater at 2.36 GHz than at 820 MHz.

2.4 Astrin Model

Astrin performed measurements of a body channel taken at 13.56 MHz in order to be used for an IEEE standard [12]. The body channel at that frequency has a link loss similar to free space and can be used for body area network applications. However, due to the small available bandwidth, only low data rates of a few kbps can be transmitted. Therefore, the BANs operating at those frequencies can be used to signal an emergency condition or to transmit reliably a “wake up” signal to a sleeping BAN node [12].

The measurements were taken at specific locations on a live human body and are presented in Table 6. The signals received at various distances are shown in Table 7.

2.5 Aoyagi et al., Power Delay Profile Model

A power delay profile (PDP) model for the range 3.1 to 10.6 GHz was proposed by Aoyagi et al. [9]. The power delay profile of a channel represents the average power of the received signal in terms of the delay with respect to the first arrival path in multi-path transmission. Since signals in WBANs are usually transmitted following multiple paths, the channel response seems like a series of pulses. This mainly appears at these specific bands where highly frequency-selective channels are observed [9].

The PDP model is characterized by the following equations:

$\begin{array}{l}h(t)=\sum _{l=0}^{L-1}{\alpha }_l{e}^{j{\varphi }_l}\delta (t-t_l)\hfill \\ 10\log {\left|{\alpha }_l\right|}^2=\{\begin{array}{cc}0& l=0\\ {\gamma }_0+10\log \left(e^{-\frac{t_l}{\Gamma }}\right)+S& l\ne 0\end{array}\hfill \\ p(t_l|t_{l-1})=\lambda e^{-\lambda (t_l-t_{l-1})}\hfill \\ p(L)=\frac{{\overline{L}}^L{e}^{\overline{L}}}{L!}\hfill \end{array},$ (6)

(6)

where φ_l is the phase for the l-th path and follows a uniform distribution over (0,2π), α_l is the path amplitude for the l-th path, t_l is the path arrival time, L is the number of the arrival paths, δ(t) is the Dirac function, Γ is an exponential decay with a Rician factor γ₀, S is a normal distribution with zero mean and standard deviation of σ_s, λ is the path arrival rate, and $\overline{L}$ is the average number of the L. The corresponding parameters are given in Table 8.

Table 8

PDP Model Parameters

αl	γ0	−4.6 dB
	Γ	59.7
	σS	5.02 dB
tl	1/λ	1.85 ns
L	$\overline{L}$	38.1

2.6 Dolmans and Fort Wideband Model

Dolmans and Fort proposed an ultra wideband (UWB) model in the range 3 to 10 GHz that satisfies the requirements for IEEE standards [10]. Wideband models are more complex than narrowband ones since there are more reflections in the channel. In the UWB range the propagation though the body is negligible and signal transmission is achieved through diffraction around the body and reflections from the surrounding environment.

The authors performed experiments in an anechoic chamber. A set of antennas was placed on a human body. The measurements were performed in six planes separated by 7 cm along the vertical axis of the torso. The reader is referred to [10] for more details.

The empirical power decay model was used and found to fit the numerical results obtained in an adequate manner, i.e.,

$PL{(d)}_{dB}=P_0\left[dB\right]+10n\log \frac{d}{d_0}.$ (7)

(7)

Table 9 shows the corresponding parameters. It is clearly seen that a much lower exponent is measured when the propagation is along the front (n≈3) rather than around the torso (n≈6).

2.7 Kang et al. Model

Kang et al. proposed a UWB body surface model at the frequency bands of 3.1 to 5.1 GHz, and 7.25 to 8.5 GHz, respectively [13]. At first the body posture effects were taken into account. The transmitter antenna was located in the left waist and receiver antennas were placed in various positions. Measurements were carried out in an anechoic chamber and office environments. The results are shown in Tables 10 and 11. All values are in dB scale.

Then the effect of body movement was examined, i.e., an arm and a leg were moved in a forward or side direction during measurements. Tables 12 and 13 summarize the experimental results.

2.8 Kim et al. Model

Kim et al. proposed a dynamic statistical channel model for the IEEE 802.15.6 [14]. The measurements were performed in a radio anechoic chamber using a real-time channel sounding system at 4.5 GHz and bandwidth of 120 MHz. Measurements focused on capturing the fading effect that appears due to the movement of the human body. The transmitter was fixed on or around the navel and the measurements were conducted one by one at 10 receiver positions placed at the specific locations shown in Table 14.

The authors tried to fit the measurement results by using some well-known probability density functions such as normal, log-normal, and Weibull distributions, and found the best match of them. In general, it was observed that the normal distribution provides a best fit of the still postures, the log-normal distribution shows a good match in cases of still postures and small movements, whereas the Weibull distribution can represent much better large movement behaviors. Table 15 summarizes the findings.

Tables 16, 17, and 18 present the various parameters for the three distributions. The values of the log-normal distribution in Table 16 are in decibels. The values in parentheses are negative log-likelihood values by which the best fit distribution were obtained (less means better fit).

3.1 CWC Oulu University Model

The Centre of Wireless Communications (CWC) at Oulu University of Finland performed extensive measurements at the Oulu University Hospital, focusing on the UWB band [15]. The aim of the work was to generate realistic WBAN channel models to be used in designing WBAN applications for hospital use. The results obtained were compared with the ones provided by the IEEE group.

The measurements took place at an anechoic chamber, classroom, and different hospital rooms. Three hospital cases were examined, i.e., a surgery room, a conventional ward room, and a corridor. The last two environments took into account the specific propagation characteristics that are valid, whereas the anechoic chamber was used to validate the measurement system performance. The frequency range lies between 3.1 GHz and 10 GHz, and 100 consecutive frequency responses were taken using a proper vector network analyzer [15]. Table 19 presents the parameters used during the experimental process.

Two situations where a patient was either lying down or standing were considered. For more information about the experimental process and the measurements setup scenarios the reader is referred to [16] and the references therein. Roughly speaking, two cases were examined, A1 and A2, referred to as on-on-links and on-off-links. In A1 cases, the antenna positions were changed to cover more links.

The channel model was deduced from the measurement data yielding to the double-cluster model. The fast decaying first cluster corresponds to the effect of a human body and the second cluster occurs from the surrounding reflections [17]. The path amplitude decay is given as

$10\log \left|{\alpha }_l\right|=\{\begin{array}{c}\begin{array}{cc}0,& l=0\end{array}\\ \begin{array}{cc}{\gamma }_{01}+10\log \left(e^{-\frac{{\tau }_l}{{\Gamma }_1}}\right),& 1\le l\le l_1,\end{array}\\ \begin{array}{cc}\sum _{m=1}^M\left({\gamma }_{02m}+10\log \left(e^{-\frac{{\tau }_l}{{\Gamma }_{2m}}}\right)\right)& l_2\le l\le L-1,\end{array}\end{array},$ (8)

(8)

where γ₀₁, γ_02m are the Rician factors and Γ₁, Γ_2m the exponential decaying factors for the two clusters. M is the number of sub-clusters within the second cluster and l₁ and l₂ are the number of multi-path components in the first and second cluster, respectively. The amplitude variations are modeled with a log-normal distribution having zero-mean and standard deviation, σ. The time difference between the consecutive arriving paths follows the exponential distribution, i.e.,

$p(t_l|t_{l-1})=\{\begin{array}{cc}{\lambda }_1{e}^{-{\lambda }_1(t_l-t_{l-1})},& 1\le l\le l_1\\ {\lambda }_2{e}^{-{\lambda }_2(t_l-t_{l-1})},& l_2\le l\le L-1\end{array},$ (9)

(9)

where t is the arrival time following a Poisson distribution and λ is the rate of path arrival in a cluster. Finally, the number of arrival paths L also follows a Poisson distribution as

$p(L)=\frac{{\mu }_L^L{e}^{{\mu }_L}}{L!},$ (10)

(10)

where μ_L is the average of L. Table 20 shows values for these parameters found using the least square method.

3.2 Wang et al. Model

Wang et al. derived a channel model in the UWB band for on-body communications. The model takes into account the statistical variations of several body postures and movements [18]. It was derived based on a realistic human body model, and numerical electromagnetic field analysis techniques were used. Specifically, a dipole transmitter was placed on the left chest and five receivers were located on the right chest, the left and right waists, and the two ears. Nine postures were used for standing, ten for walking and running, and six for sitting. To characterize the UWB model the authors applied a proper modification of the Saleh-Valenzuela model [19]. A detailed analysis can be found in [2,18].

At first, the path loss for the five links was estimated based on a simple path loss formula; the results are shown in Table 21.

Then, the average power delay profile was shown to decay exponentially whereas the log-normal distribution was found to provide the best fit to the power distribution in the multi-paths. The authors found that the inter-path delay that is related to the temporal delay between two successive paths follows the inverse Gaussian distribution, i.e.,

$f(x,\mu ,\lambda )={\left(\frac{\lambda }{2\pi x^3}\right)}^{\frac{1}{2}}{e}^{-\frac{\lambda {(x-\mu )}^2}{2{\mu }^{2}x}}.$ (11)

(11)

The parameters of the model are depicted in Table 22, where γ is the time constant for power decay, σ is the standard deviation of power distribution, τ₀ is a constant representing the mean arrival time of first path, τ_k-τ_k−1 represents the inter-path delay following the inverse Gaussian distribution, and Ω₀ is the mean power gain of the first path.

A discrete time impulse response function applied to the five transmission links with the corresponding parameter values is then implemented based on the modified Saleh-Valenzuela model:

$h(t)=\sum _{k=0}^K{a}_k\delta (t-t_k),$ (12)

(12)

where α_k is the multi-path power gain and t_K is the delay of the kth multi-path component corresponding to the arrival time of the first path. The model implementation is thoroughly discussed in [18].

3.3 Reusens et al. Model

Reusens et al. investigated the propagation channel between two half-wavelength dipoles at 2.45 GHz, placed near a human body [20]. Propagation measurements for different parts of a body were performed on real humans in a multi-path environment. Path loss was also numerically investigated with simulations. The channel parameters were extracted from the measurement and simulation data.

For the measurements along the arm, the transmitter was located on the wrist and the receiver at various positions towards the shoulder. The measurements for the back and the torso were performed by placing the transmitter at different positions at the shoulder height and the moving receiver below the transmitter. For the leg the transmitter was located at the ankle and the receiver was moved toward the knee. Moreover, an average path loss model for the whole human body was obtained through fitting of all measurement data. Eq. (7) was used to estimate the path loss between the transmitting and the receiving antennas as a function of the distance. Table 23 presents the parameter values of the fitted path-loss models.

Simulations with a realistic human body phantom were also performed and were in agreement with the measurements. The cumulative distribution functions of the deviation of measured path loss and models were found to follow the lognormal distribution.

3.4 Queen’s University of Belfast Models

The wireless communications research group at the Queen’s University of Belfast is quite active on channel modeling for on-body communications. Over the years, the group has performed extensive research in order to examine the propagation aspects of wearable communications systems for a range of environments [21]. Much of the research focus for WBAN applications has been centered on the unlicensed industrial, scientific, and medical (ISM) bands at 868 MHz and 2.45 GHz.

In [22], stationary and mobile user scenarios for on-body communications at 868 MHz were investigated. Twelve on-body propagation paths, located on the upper torso and limbs, were considered. Measurements were taken in an anechoic chamber, open office area, and hallway environments. The authors focused on the fading effect appearance. They identified that two-thirds of the paths were Nakagami distributed while the remaining were Rician. The majority of the Nakagami paths occurred when the user was stationary. The performance of three diversity combination schemes for two-branch spatial on-body diversity systems was investigated in [23].

In [24], fading characteristics or a WBAN operating in an outdoor environment at 2.45 GHz were presented. Both stationary and moving users were examined. When the user was stationary, a small amount of fading was observed for stationary users. When the user was moving, small-scale fading significantly increased, characterized by the Nakagami distribution.

Several other studies have also been performed. Interested readers are directed to the group website [25] for more information.

3.5 University of Birmingham and Queen Mary University Models

Experiments on on-body communications were also performed by research teams of the universities of Birmingham and Queen Mary, University of London [3]. One such experiment is discussed in [26] where the propagation path loss of an on-body channel was measured at 2.45 GHz. First, the antennas were attached to the body at a number of positions and orientations, and measurements were taken inside an anechoic chamber. Next, measurements inside of a laboratory were performed that indicated significant differences in path loss. Finally, additional measurements were also taken while walking on the campus of the University of Birmingham. Movements caused variations in the distance between the antennas, which made the channel variability quite severe.

In [27] the path gain and its variations were examined in some realistic scenarios. Short-term and long-term fading statistics were investigated. It was shown that the short-term fading was best described by a Rician distribution with the K-value log-normally distributed and the long-term fading by a gamma distribution.