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Abstract

The uniform geometrical theory of diffraction and ray tracing technique is used to simulate ultra wideband signal multipath propagation characteristics. The simulation model covers indoor office and outdoor corridor with thick wall and metal doors. The range of path loss exponent of distance is obtained by regression analysis, and the lognormal distribution about shadowing fading is got by the fitting and test. The distance-dependence path loss in the indoor and indoor to the corridor present lognormal distribution characteristics. Through the comparative research, the signal of the transmission metal door has a decisive influence on the corridor environment.

Keywords

Uniform geometrical theory of diffraction ray tracing ultra wideband path loss shadowing fading

Introduction

In the recent years, plentiful scenarios channel were measured using different measurement methods because of the limitations of ultra wideband (UWB) channel standard model IEEE802.15.3a and IEEE802.15.4a. These scenes included indoor office, indoor residential, indoor parking area, human body, and factory. The research on the propagation loss of UWB signal is mainly focused on the measurement method. S Sangodoyin and S Niranjayan¹ used the multiple input multiple output (MIMO) technique to measure the characteristics of the outdoor near-ground and found out that the path loss showed a slight dependence on frequency. CU Bas and S Ergen² constructed the propagation channel model of intra-vehicular wireless sensor networks. Deterministic modeling methods such as ray tracing method and finite difference time domain (FDTD) method are gradually applied in the channel measurement. S Priebe et al.³ used the frequency domain ray tracing approach to simulate the THz indoor propagation channel and validated the correctness of the results with the measurement data. FJB Barros et al.⁴ built a site-specific beam tracing model to describe indoor radio propagation channel of UWB. These studies show that the path loss of distance-dependent large-scale fading is in accord with the lognormal distribution. However, there are few researches on the large-scale channel characteristics that signal transmit thick wall and the metal door to the corridor environment. This article is based on the ray tracing and uniform geometrical theory of diffraction (UTD) to simulate model in complex environments, analyzes path loss exponents and shadow fading characteristics for indoor and indoor to corridor with thick wall and metal door environments.

Simulation environment

This article selected the office and outdoor corridor for simulation environment as shown in Figure 1. Specific objects include nine office tables, nine computers, two double-metal doors, three single-metal doors, two file cabinets, a laboratory furniture, a material cabinet, a wooden locker, a vertical air conditioning, and a water dispenser. The 0.4-m-thick brick wall is bushed with gypsum powder. The material of floor, corridor, and ceiling, respectively, are wooden, ceramic tile, and aluminum. Some material properties are shown in Table 1.

Figure 1.

Ichnography of office and corridor environment.

Table 1.

Properties of part materials.

Material	$ε_{γ}$	$σ (S / m)$
Brick wall	3.58	0.11
Glass	6.06	0.35
Plaster	2.02	−
Melamine MDF	4.7	−
Metal	−	$\infty$

The simulation model is accomplished by Wireless Insite and AutoCAD. The transmitter (Tx) is located in the center of the office (4, 3.1, and 1.2 m) with radiant power 10 dBm. The waveform is Gaussian pulse at bandwidth of 2 GHz with center frequency of 7.3 GHz. There are seven receiver routes that range from A to G at the height of 0.9 m and the interval of 0.2 m, two receiver sets RxA and RxB to detect the power distribution in the whole space. The rays number of refraction, transmission, and diffraction are set to 4, 5, and 1, because the number of secondary reflection and transmission are no longer increase with the increasing setting of rays. Shooting and bouncing ray (SBR) method is used in the simulation. Figure 2 shows the final simulation model.

Figure 2.

Simulation model.

Path loss in simulation environment

The pass loss depends on frequency and distance between the transmitter and receiver in a UWB channel, and according to the literature,^1,5,6 the formula is as follows

PL (f, d) = PL (d) \times PL (f)

(1)

Here, the distance-dependence path loss is emphatically studied.

Under ideal circumstances, the dependence of the path loss on distance in free space is⁷

PL (d) [dB] = 10 \log_{10} (\frac{P_{T}}{P_{R}}) = 10 \log_{10} (\frac{{(4 π)}^{2} d^{2}}{G_{T} G_{R} λ^{2}})

(2)

where $PL (d) [dB]$ is the path loss at distance d in decibels, $P_{T}$ is the time-averaged radiated power, $P_{R}$ is the received power, $λ$ is the wavelength of the signal, and $G_{T}$ and $G_{R}$ are gains of the transmitting and receiving antennas, respectively. The typical value of 1 m far away from transmitter is regarded as a reference point $d_{0}$ , and the following equation could be got referenced by $P_{R} (d_{0})$ that represents receiving power at the reference point

P_{R} (d) = P_{R} (d_{0}) {(\frac{d_{0}}{d})}^{2}

(3)

The equation of logarithmic is

PL (d) [dB] = PL (d_{0}) + 10 \log_{10} {(\frac{d}{d_{0}})}^{2}

(4)

where $PL (d_{0})$ is the path loss at distance $d_{0}$ in decibels.

However, in the actual complex environment of wireless communication, receiving signals with attenuation features are superposition of multipath signal with transmission, diffraction, and reflection, which are different from the single channel of free space to arrive. According to the theory of propagation model and measurement-based model, when the receiving distance increases, the average power of the received signal is exponentially decreasing. In the multipath environment, equation (4) can be rewritten as⁸

PL (d) = PL (d_{0}) + 10 n \log_{10} (\frac{d}{d_{0}}) + X_{σ}

(5)

where n is the path-loss exponent, and $X_{σ}$ is a zero-mean Gaussian random variable with standard deviation $σ$ representing the random deviations in the model. Literatures^1,5,6 both illustrated the rationality of equation (5) in large-scale fading for measurement-based model. It should be noted that the random variables are expressed in decibels, and received signal is the result of the sum of the number of random variables in logarithmic. From the central limits theorem, the shadow fading $X_{σ}$ is normal statistical properties. Therefore, $PL (d)$ and $X_{σ}$ are lognormal random variables in natural unit with the probability density for normal distribution, but different in mean value. This is consistent with the expression of the literature.^9,10

However, whether the path loss of the office scene and indoor to corridor in software simulation model obeys the lognormal distribution or not still needs further validation.

Path loss of indoor environment

The distribution of space power received from the RxA of interior sets is shown in Figure 3.

Figure 3.

Space power of indoor.

The radiation power fluctuation is stable around the Tx, but there is obvious attenuation in the four corners. Set the six routes, except Route D, to detect the path loss principle. Among those routes, Route A and C extend to the corridor from the transmitter, and Route B, E, and F extend to the corner.

The loss data receiving from Route F are shown in Figure 4 as a scatter diagram. In order to get the value of $PL (d_{0})$ and n, equation (5) is rewritten as

Y_{i} = a + n x_{i} + {X_{σ}}_{i}

(6)

where $a = PL (d_{0})$ , $x = 10 \log_{10} (d / d_{0})$ , $Y = PL (d)$ , and ${X_{σ}}_{i}$ is the ith observed value of the random deviation. The least square estimation algorithm is used to obtain $\hat{a}$ and $\hat{n}$ . A linear regression fit for the scatter plot in Figure 4 shows the anticipated monotonic dependence of path loss on distance, the estimated value $\hat{a}$ is 49.40 dB, and $\hat{n}$ is 2.35. The value of $\hat{a}$ is close to the theoretical value 48.9 dB.

Figure 4.

Linear regression fitting.

Regression significance test

The regression significance test is used to determine a significance regression equation. When the hypothesis $H_{0} : n = 0$ is true, here are

F = \frac{SSR}{SSE / (N - 2)} ~ F (1, N - 2)

(7)

SSR = \sum_{i = 1}^{N} {({\hat{y}}_{i} - \bar{y})}^{2}

(8)

SSE = \sum_{i = 1}^{N} {(y_{i} - {\hat{y}}_{i})}^{2}

(9)

where SSR is regression sum of squares, SSE is residual sum of squares, $\bar{y}$ is mean value of $y_{i}$ , and ${\hat{y}}_{i}$ is regression value. $α$ is given as a significant level. $H_{0}$ is false if the inequality $F \geq F_{α} (1, N - 2)$ is established, and regression equation can be considered significant. Especially, if $F \geq F_{0.01} (1, N - 2)$ , it is highly significant and marked as H; if $F_{0.05} (1, N - 2) \leq F < F_{0.01} (1, N - 2)$ , it is significant and marked M; and if $F < F_{0.05} (1, N - 2)$ , it is not significant and marked L. The parameters of linear regression indoor of six paths and test results of the analysis are shown in Table 2.

Table 2.

Analysis of regression and significance test.

Route	State	$\hat{a}$	$\hat{n}$	F	$F_{0.05} / F_{0.01}$	Test
A	LOS (0–4 m)	42.65	2.34	28.25	4.54/8.68	H
B	LOS (0–4 m)	48.49	1.91	23.69	4.32/8.02	H
C	NLOS (0–3 m)	48.26	2.19	17.85	4.75/9.33	H
E	LOS (0–4 m)	47.21	1.69	26.07	4.38/8.18	H
F	NLOS (0–4 m)	49.40	2.35	44.14	4.38/8.18	H
G	LOS (0–4 m)	47.99	1.37	23.93	4.14/7.47	H

As can be seen from the table, the path loss exponent n is less than 2 in the region that the office furniture cause severe multipath components overlap in line of sight (LOS) scene or quasi-LOS, but greater than 2 in non-line-of-sight (NLOS) paths of obvious barriers or LOS paths of less furniture. In the literature¹¹ that uses measurement method, n is 1.76 in LOS office environment and 3.07 in NLOS environment. In another measurement method,¹²n is 1.3 in LOS office environment and 2.3 in NLOS environment. According to the comparison, the results of simulation method are close to the measuring method in office environment. This suggests that the attenuation rate of signal with reflection and refraction is less than free space in LOS or quasi-LOS, but the signal after transmission in Hard-NLOS or remote environment fade rapidly.

Path loss of indoor to corridor environment

The distribution of space power received from the RxB sets of corridor is shown in Figure 5. The signal that transmitted by the metal door is reflected by the wall near where forms a regional strong power. Route D is set to detect the path loss principle in the central corridor. The strongest received signal is detected at the length of 7.8 m, so record data of 0–7.8 m as D_l, 7.8–15 m data of as D_r. Most of the strength of multipath components is blocked by walls, but the transmission of walls and metal doors superimposed on each other and coupled with different sides of the environment result in different power loss of the left and right. The comparison diagram of regression analysis with the two sets is obtained as Figure 6. The parameter estimation results are respectively ${\hat{a}}_{l} = 72.08 dB$ , ${\hat{n}}_{l} = 3.07$ and ${\hat{a}}_{r} = 71.04 dB$ , ${\hat{n}}_{r} = 3.04$ . Both of the fitting degree is highly significant and estimated results are slightly different. Eventually, the merged data are $\hat{a} = 70.82 dB$ and $\hat{n} = 3.17$ . Note that d is the relative distance of the strongest power point to each receiver in the corridor instead of distance between transmitter and receiver.

Figure 5.

Space power of corridor.

Figure 6.

Comparison of regression analysis.

The analysis of the data for Route A in the corridor shows that the loss is reduced and present a highly significant linear characteristic with the distance increasing between transmitter and receiver, the results is shown in Figure 7, and get the intercept and slope are 153 dB and −11.8, respectively. The same rule is suitable for Route C, and these results well explain the reason of the phenomenon of Figure 5.

Figure 7.

Data of Route A in corridor.

All these indicate that the path loss of indoor to corridor is piecewise characteristic, which can be expressed as

L_{p} (d) = {\begin{matrix} 42.65 + 2.34 \times 10 \log_{10} (\frac{d}{d_{0}}) + {X_{σ}}_{1}, 0 < d < 4 m \\ 153 - 11.8 \times 10 \log_{10} (\frac{d}{d_{0}}), 4.3 m < d < 6 m \end{matrix}

(10)

where d is the distance between transmitter and receiver outside the door, and ${X_{σ}}_{1}$ represents shadow fading. $L_{p} (d)$ is the predicted value of the loss on the metal gate path that is considered as the radiant point and then can predict the power coverage using the linear path loss of the central corridor.

The above discussion is attenuation rule of the UWB signal that transmit metal door to the corridor. Next, the direct relation of distance-dependence path loss between transmitter and receivers is discussed. The distance between the indoor transmitter Tx and the corridor receiver is $d_{r}$ . According to equation (5), the linear regression analysis method is used to get Figure 8. By the analysis results, the loss characteristics on both sides of metal doors present a high-degree linearity. The path loss characteristics of indoor to the corridor, which can be related to the receiver and transmitter distance, are shown in equation (11)

L_{p} (d_{r}) = {\begin{matrix} 170 - 11.57 \times 10 \log_{10} (\frac{d_{r}}{d_{0}}) + {X_{σ}}_{2}, \\ left side of the door \\ - 33 + 11.58 \times 10 \log_{10} (\frac{d_{r}}{d_{0}}) + {X_{σ}}_{3}, \\ right side of the door \end{matrix}

(11)

where ${X_{σ}}_{2}$ and ${X_{σ}}_{3}$ are shadow fading on both sides of the corridor. The result shows that the path loss is highly symmetrical, which indicates that the signal of the transmission thick wall reaches the corridor is less affected, and the conclusion is consistent with the above analysis.

Figure 8.

Regression analysis based on receiver and transmitter distance.

Shadow fading

Shadow fading indicates the differentials between the actual path loss and the value of the linear regression. Rigorous statistical method to determine the distribution of shadow fading of $X_{σ}$ after linear regression analysis of each course is still required. Chi-square goodness-of-fit test is used due to the distribution characteristics and parameters are unknown. A hypothesis $H_{0} : X_{σ} ~ N (μ, σ^{2})$ is got by taking data of Route D as an example, and cumulative distribution functions are as follows

F (x_{σ}; μ, σ) = \frac{1}{\sqrt{2 π} σ} \int_{- \infty}^{x_{σ}} \exp {- \frac{1}{2 σ^{2}} {(x_{σ} - μ)}^{2}} d x_{σ}

(12)

the maximum likelihood estimate of $μ$ and $σ$ are

μ = \frac{1}{N} \sum_{i = 1}^{N} x_{σ i} = 0, σ = \sqrt{\frac{1}{N} \sum_{i = 1}^{N} (x_{σ i} - \bar{x})^{2}} = 3.77

(13)

The Fisher K. Pearson theorem of the following form is used in test

χ^{2} = \sum_{i = 1}^{k} \frac{{(n_{i} - N {\hat{p}}_{i 0})}^{2}}{N {\hat{p}}_{i 0}} \approx χ^{2} (m - r - 1)

(14)

where $n_{i}$ is the actual frequency of falling into the interval, m is the number of partitions, r is number of unknowns, and $N {\hat{p}}_{i 0}$ is expected value of frequency. ${\hat{p}}_{i 0}$ is derived from the following formulas

{\begin{matrix} {\hat{p}}_{10} = F (a_{1}; μ, σ) \\ {\hat{p}}_{i 0} = F (a_{i}; μ, σ) - F (a_{i - 1}; μ, σ), i = 2, 3, \dots, k - 1 \\ {\hat{p}}_{k 0} = 1 - F (a_{k - 1}; μ, σ) \end{matrix}

(15)

where $a_{k}$ can be obtained with the HIST instruction in MATLAB. The results are listed in Table 3. The distribution characteristics of pictorial diagram are shown in Figure 9.

Table 3.

Frequency distribution table.

Interval	( $- \infty$ , −6.72]	(−6.72, −3.97]	(−3.97, −1.23]	(−1.23, 1.51]	(1.51, 4.25]	(4.25, 6.99]	(6.99, $+ \infty$ ]
$n_{i}$	3	4	17	21	12	5	3
$N {\hat{p}}_{i 0}$	2.44	7.06	14.68	18.42	13.95	6.37	2.08

Figure 9.

Distribution characteristics.

$a_{k}$ is used as the interval value, and then $χ^{2} = 3.16$ , $χ_{0.05}^{2} (4) = 9.49$ , the hypothesis is accepted. It is validated that the assumption follows a normal distribution. Shadow fading on each path by the test is subject to normal, and the statistical parameters for the routes are shown below

X_{σ} ~ {\begin{matrix} N (0, 6 . 67^{2}), RouteA \\ N (0, 5 . 69^{2}), RouteB \\ N (0, 4 . 20^{2}), RouteC \\ N (0, 3 . 77^{2}), RouteD \\ N (0, 4 . 35^{2}), RouteE \\ N (0, 4 . 82^{2}), RouteF \\ N (0, 4 . 93^{2}), RouteG \end{matrix}

(16)

Conclusion

The path loss of UWB signal indoor obeys the lognormal distribution with the loss exponents ranging from 1.37 to 2.35, and the standard deviation of the shadow fading changing from 4.35 to 6.67. Comparing with other measured method of indoor office, the deterministic modeling method is effective in researching UWB channel. Two methods are used to analyze pass loss that from indoor to corridor with thick wall and metal door, the results shows that pass loss are highly symmetrical on both sides of the metal door and satisfy piecewise lognormal distribution. The central corridor loss exponent is particularly 3.17 and shadow fading standard deviation is 3.77. The signal of the transmission metal door has a decisive influence on the corridor environment.

Footnotes

Academic Editor: Jaime Lloret

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: The authors are very grateful for the support of the National Natural Science Foundation of China (Grant No. U1504604) and Academician Workstation Research Grant Funds.

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