Propagation Loss Measurement of Wireless Body Area Network at 2.4 GHz and 3.35 GHz Bands

Abstract

The main purpose of this work is to measure and analyze the propagation loss of the Wireless Body Area Network (WBAN) in frequency and time domain at two frequency bands, namely 2.4 GHz band with 80 MHz bandwidth and 3.35 GHz band with 500 MHz bandwidth. Four different scenarios (front to front, front to back, front to off-body node and back to off-body node) using many antenna´s locations on the body are used to investigate the channel response (path loss) of WBAN. It is found that the front to front channels and the front to off-body node channels have a low fading. The front to back channels and the back to off-body node channels have a high fading that can be approximated by the Distorted Rayleigh fading. Thus the WBAN range for the front to off-body node scenario is more than the range of the back to off-body node scenario.

Appendix: Distorted Rayleigh Distribution

In probability theory, the Rayleigh distribution is a continuous probability distribution for positive-value random variable x representing the voltage of the received signal. It could also represented in dB giving a rise to positive and negative dB values. The probability density function f(x) is given as:

$$\begin{aligned} f(x) & = \frac{x}{{\sigma^{2} }}e^{{ - x^{2} /2\sigma^{2} }} ,\quad x > 0 \\ & = 0,\quad x \le 0 \\ \end{aligned}$$

(3)

Distorted Rayleigh distribution is a weighted sum of Rayleigh distribution and one or more truncated Gaussian (Normal) Distributions. Distortion can happen in the leading edge, trailing edge or near to the peak of the Rayleigh distribution.

Suppose that X = N (μ, σ²) has a normal distribution and lies within the interval − ∞ ≤ a < b ≤ ∞. Then X conditional on a < X < b has a truncated normal distribution.

Its probability density function f (x), for a ≤ x ≤ b is given by:

$$f\left( x \right) = \frac{{\Phi \left( {\frac{x - \mu }{\sigma }} \right)}}{{\sigma \left( {\Phi \left( {\frac{b - \mu }{\sigma }} \right) -\Phi \left( {\frac{a - \mu }{\sigma }} \right)} \right)}}$$

(4)

where

$$\Phi \left( x \right) = \frac{1}{2}\left( {1 + erf\left( {{\raise0.7ex\hbox{$x$} \!\mathord{\left/ {\vphantom {x {\sqrt 2 }}}\right.\kern-0pt} \!\lower0.7ex\hbox{${\sqrt 2 }$}}} \right)} \right)$$

(5)

In our case a = 0, b = ∞ and $\Phi \left( {\frac{b - \mu }{\sigma }} \right)$ = 0.

The probability density function f(x) _DR of the distorted Rayleigh distribution is given as:

$$f\left( x \right)_{D R} = \mathop \sum \limits_{n = 1}^{N} W_{G,n} f\left( x \right)_{G,n} + W_{R} f\left( x \right)_{R}$$

(6)

where W_G,n is the weight of the Gaussian component n, W_R is the weight of the Rayleigh component

Figure 31 shows the PDF of the Rayleigh distribution where the relative power from the mean value is given in dB for σ = 1.0 and 1.5

Fig. 31

PDF of the Rayleigh distribution given in dB

Figure 32 shows the PDF of the First Type of distorted Rayleigh distribution (sum of 50% of Rayleigh distribution and 50% of a Gaussian one with μ = 3.6 and sigma of 0.8). A peak at 0.1 dB can be noticed and another peak with lower PDF at 11.1 dB can be seen

Fig. 32

PDF of distorted Rayleigh distribution (sum of 50% of Rayleigh distribution and 50% of a Gaussian one with μ = 3.6 and sigma of 0.8). This figure represents the distorted Rayleigh distribution type 1

Figure 33 depicts the PDF of the Second Type of the distorted Rayleigh distribution (sum of 95% of Rayleigh distribution and 5% of a Gaussian one with μ = 0.45 and sigma of 0.1). Two peaks can be seen. The first one is at 0 dB (due to the Rayleigh component) and the second one is at − 6.3 dB (due to the Gaussian component affected by the Rayleigh component)

Fig. 33

PDF of distorted Rayleigh distribution (sum of 95% of Rayleigh distribution and 5% of a Gaussian one with μ = 0.45 and sigma of 0.1). This figure represents the distorted Rayleigh distribution type 2

Figure 34 depicts the PDF of the third type of the distorted Rayleigh distribution (sum of 99% of Rayleigh distribution and 1% of a Gaussian one with μ = 0.05 and sigma of 0.015). Two peaks can be seen. The first one is at 0 dB and the second one is at − 25.9 dB. The first peak is due to the Rayleigh component. The second peak is due to the Gaussian component affected by the Rayleigh component)

Fig. 34

PDF of the Third type of distorted Rayleigh distribution (sum of 99% of Rayleigh distribution and 1% of a Gaussian one with μ = 0.05 and sigma of 0.015)

Figures 32, 33 and 34 show that the distorted Rayleigh distribution has many shapes depending on the weight of and parameters of its components. This means that it can represents the Hypo-Rayleigh, Rayleigh (with zero weight Gaussian distributions) and Hyper-Rayleigh distributions.

Figure 35 displays the PDF of distorted Rayleigh distribution (sum of 87.9% of Rayleigh distribution, 10% of a Gaussian distribution with μ = 5 and sigma of 1, 2% of a Gaussian distribution with μ = 0.6 and sigma of 0.1, and 0.1% of a Gaussian distribution with μ = 0.008 and sigma of 0.003). PDF has peaks at 14 dB, 0 dB, − 3.9 dB and − 41.9 dB. Here, PDF is distorted in three parts of the Rayleigh distribution

Fig. 35

PDF of distorted Rayleigh distribution (sum of 87.9% of Rayleigh distribution, 10% of a Gaussian distribution with μ = 5 and sigma of 1, 2% of a Gaussian distribution with μ = 0.6 and sigma of 0.1 and 0.1% of a Gaussian distribution with μ = 0.008 and sigma of 0.003). This figure represents the mixed distorted Rayleigh distribution with distortion at the three parts of the Rayleigh distribution

Figure 36 shows the PDF of distorted Rayleigh distribution with high Gaussian component. It can be noticed that the probability bellow − 30 dB is very low

Fig. 36

PDF of the distorted Rayleigh distribution with high weight Gaussian component (95% Gaussian component with μ = 2 and σ = 0.6). Note the very low probability bellow − 30 dB