Electromagnetic Compatibility Evaluation for Vehicular Communication Systems Based on Urban High-Resolution Satellite Remote Sensing Images

Abstract

With the expansion of urban areas and the increase in the number of vehicles, the complexity and harshness of the electromagnetic environment for vehicular communication in cities have significantly intensified. Traditional methods for evaluating the electromagnetic compatibility (EMC) of vehicular communication systems face substantial limitations. With the advancement of high-resolution satellite remote sensing image technology, the acquisition of high-precision urban models has become more accessible, significantly enhancing applications in the field of communication systems. Therefore, a novel EMC evaluation method for vehicular wireless communication systems based on urban high-resolution satellite remote sensing images is proposed in this paper. By analyzing the characteristics of such systems and integrating the requirements of practical urban communication scenarios and vehicular tasks, EMC evaluation indicators were selected, and a hierarchical evaluation indicators system was constructed, comprising target, criterion, and sub-criterion layers. The proposed method leverages the strengths of TOPSIS, AHP, and FCE methods, utilizing quantitative TOPSIS and qualitative AHP to determine the weights of the criterion and sub-criterion layers, respectively. The FCE method was employed to evaluate the EMC of the vehicular wireless communication system. The rationality and feasibility of the method were validated through practical communication experiments conducted with a vehicle in an urban environment.

1. Introduction

The growing urban expansion and rising vehicle numbers have markedly intensified the complexity and harshness of the electromagnetic environment for vehicular communications. These developments present significant challenges to vehicular electromagnetic compatibility (EMC) that cannot be overlooked [1,2,3,4,5,6,7,8]. Electromagnetic interference (EMI) can lead to various complications [9,10,11,12,13], including degraded communication quality, interruptions in normal communication processes, and potential safety risks. Given the importance of vehicular driving safety and communication reliability, it is essential to conduct EMC evaluations in urban environments [14,15,16,17]. Previous studies [14,15,16,17] addressed EMC evaluation standards and simulation approaches, but gaps remain in EMC evaluation for vehicular communication systems.

Due to advancements in vehicular electronic technology, conventional evaluation methods have become outdated and inadequate for assessing EMC in vehicular communication systems [14,15,18,19,20]. Recent studies [15,18,19,20] explored niche EMC aspects such as wireless charging and improved weighting methods; however, these studies fail to address critical issues including the subjectivity in determining evaluation indicator weights and the lack of a combined quantitative–qualitative approach in evaluation results.

Traditional methods face four key limitations: (1) Reliance on lab-based settings limits real-world applicability; (2) subjective selection of EMC indicators often fails to align with communication requirements; (3) subjective determination of indicator weights reduces accuracy; and (4) the lack of integration between qualitative/quantitative methods undermines completeness.

In recent years, the rapid development of remote sensing technology has made the acquisition of remote sensing data more accessible, particularly high-resolution remote sensing images. High-resolution remote sensing data enables city modeling for signal propagation analysis [21,22,23,24,25,26,27], with methods like SBL-based REM [22,24,27] offering ray-tracing capabilities. These high-resolution images enable detailed city modeling essential for realistic simulation of propagation effects critical to EMC, such as signal attenuation and diffraction losses from urban structures.

The application of high-resolution satellite remote sensing images to EMC evaluation of urban vehicular communication systems has significant advantages, including improved accuracy, enhanced realism, and a systematic approach, ultimately contributing to the optimization of vehicular communication systems.

To overcome these limitations, a novel EMC evaluation method based on remote sensing images for urban vehicular communication systems is introduced in this paper. The main contributions of this article are as follows:

(1)

High-resolution satellite remote sensing image technology is employed to acquire urban geographic information data. A communication link model for the urban environment is established based on an accurate city model, incorporating influencing factors such as building occlusion and diffraction loss.

(2)

Addressing the communication requirements of vehicles in urban environments, key EMC performance indicators for the communication system are selected from three dimensions: communication quality, anti-interference capability, and transmission reliability. A hierarchical structure model for EMC evaluation of vehicular wireless communication systems is developed, comprising the target layer, criterion layer, and sub-criterion layer.

(3)

The weights for the criterion layer and sub-criterion layer are determined using the quantitative technique for order preference by similarity to ideal solution (TOPSIS) method and the qualitative analytical hierarchy process (AHP) method, respectively. A comprehensive evaluation of the EMC of vehicular wireless communication systems is conducted through fuzzy comprehensive evaluation (FCE).

(4)

The communication model developed using high-precision satellite remote sensing images was employed to compare the average relative errors of BER (Bit Error Rate) and SNR (Signal-to-Noise Ratio) between simulated and measured results, thereby analyzing the system’s communication performance. Based on the evaluation results, the EMC performance of vehicular wireless communication systems in urban environments are analyzed. Leveraging high-resolution satellite image data, this analysis provides critical references for optimizing vehicular communication system design.

The remainder of this paper is structured as follows. Section 2 briefly introduces related evaluation methods. Section 3 presents an EMC evaluation method for vehicular wireless communication systems based on urban high-resolution satellite remote sensing images, encompassing establishment of indicators, data preprocessing, and the key techniques and process of evaluation. To validate the proposed method, Section 4 utilizes an example of a vehicular communication system, and the performance of the proposed method is discussed. Finally, Section 5 concludes the paper by summarizing the key findings and implications.

2. Related Evaluation Methods

2.1. AHP Method

The AHP method is a systematic method that combines qualitative and quantitative analyses, particularly effective for complex systems with multiple evaluation indicators. Its core idea is to decompose a complex objective into hierarchical levels, simplifying the evaluation process by analyzing each level individually. This approach mirrors human decision making, reducing complexity and difficulty. The AHP method is widely used due to its intuitiveness, ease of understanding, and adaptability to diverse analytical requirements [28,29,30,31].

2.2. TOPSIS Method

The TOPSIS method is a widely used multi-criteria decision-making (MCDM) method [32,33,34,35]. It evaluates alternatives based on their relative closeness to the ideal solution (best possible performance across all criteria) and the negative-ideal solution (worst possible performance). The procedural workflow of this evaluation method is illustrated in Figure 1.

The basic steps of its evaluation are as follows.

Step 1: Construct the initial evaluation matrix $C$.

The assumed evaluation scenario comprises $m$ schemes, each with $n$ evaluation indicators. Equation (1) provides the initial evaluation matrix $C$.

$$C={\left[c_{ij}\right]}_{m\times n}=\left[\begin{array}{cccc}{c}_{11}& c_{12}& \dots & c_{1n}\\ ⋮& ⋮& \ddots & ⋮\\ c_{m1}& c_{m2}& \dots & c_{mn}\end{array}\right]$$

(1)

where $c_{ij}$ is the $j$th indicator of the $i$th plan.

Step 2: Construct the dimensionless initial evaluation matrix $Z={\left[z_{ij}\right]}_{m\times n}$.

Step 3: Construct the normalized matrix $R$.

$$R=\left[\begin{array}{ccc}{r}_{i1}& \dots & r_{in}\\ ⋮& \ddots & ⋮\\ r_{m1}& \dots & r_{mn}\end{array}\right]$$

(2)

where the expression of $r_{ij}$ is shown in Equation (3).

$$r_{ij}={\displaystyle \frac{z_{ij}}{\sqrt{{\displaystyle \sum _{i=1}^n{z}_{ij}^2}}}}$$

(3)

Step 4: Construct the weighted identity matrix $X$.

By multiplying the normalized matrix $R$ obtained in Step 3 with the calculated weight vector $w=\left(w_1,w_2,\dots ,w_m\right)$ of each evaluation index, the weighted evaluation matrix $X$ is expressed as follows:

$$x_{ij}=r_{ij}•w_m$$

(4)

Step 5: Calculate the Euclidean distance.

For the evaluation problem with $m$ feasible solutions $x_i$, the expression is

$$x_i=\left(x_{i1},x_{i2},\dots ,x_{in}\right)$$

(5)

where $i=1,2,\dots ,m$.

Equation (6) is the positive ideal solution ($x_i^{+}$).

$$x_i^{+}={\max }_j\left(x_{ij}\right)$$

(6)

where $i=1,2,\dots ,m;j=1,2,\dots ,n$.

The Euclidean distance between any feasible solution $x_i$ and $x_i^{+}$ is $S_i^{+}$, as defined in Equation (7).

$$S_i^{+}=\sqrt{{\displaystyle \sum _{j=1}^n{\left(x_{ij}-x_j^{+}\right)}^2}}$$

(7)

where $i=1,2,\dots ,m$.

Equation (8) is the negative ideal solution ($x_i^{-}$).

$$x_i^{-}={\min }_j\left(x_{ij}\right)$$

(8)

where $i=1,2,\dots ,m;j=1,2,\dots ,n$.

The Euclidean distance between any feasible solution $x_i$ and $x_i^{-}$ is $S_i^{-}$, as defined in Equation (9).

$$S_i^{-}=\sqrt{{\displaystyle \sum _{j=1}^n{\left(x_{ij}-x_j^{-}\right)}^2}}$$

(9)

where $i=1,2,\dots ,m$.

Step 6: Calculate the relative closeness $C_i$.

$$C_i={\displaystyle \frac{S_i^{-}}{S_i^{-}+S_i^{+}}}$$

(10)

In multi-criteria decision analysis, a solution classified as the positive ideal solution achieves a closeness coefficient ($C_i$) of 1. The closer an alternative’s $C_i$ value is to 1, the more it aligns with the ideal benchmark. Conversely, a solution labeled as the negative ideal solution yields a $C_i$ of 0. The closer an alternative’s $C_i$ value is to 0, the more it deviates from the ideal benchmark. According to the above steps, it is possible to sort and finally find a satisfactory solution.

2.3. FCE Method

FCE is a practical application method of fuzzy mathematics. It primarily employs the principle of fuzzy transformation and the maximum membership degree principle to conduct integrated assessments by considering all relevant factors [36,37,38,39,40]. Its mathematical model usually contains four core elements, which are evaluation indicator set ($U$), evaluation level ($V$), fuzzy relation matrix ($\mathbf{R}$), and evaluation set ($B$). The evaluation flow chart of this evaluation method is shown in Figure 2.

The specific evaluation steps are as follows.

Step 1: Determine the set of evaluation indicators.

The evaluation indicator set $U$ is determined by the evaluation objectives, as shown in Equation (11).

$$U=\left\{u_1,u_2,\dots ,u_N\right\}$$

(11)

where $u_i$ is the $i$th evaluation indicator of the impact evaluation objectives.

Step 2: Determine the evaluation level.

The evaluation level $V$ is given by the evaluation objectives, as shown in Equation (12).

$$V=\left\{v_1,v_2,\dots ,v_p\right\}$$

(12)

where $v_i$ is the $j$th evaluation level, and it is usually described in words.

Step 3: Construct the fuzzy relation matrix.

The fuzzy relation matrix $R$ is constructed as shown in Equation (13).

$$R={[r_{ij}]}_{N\times p}$$

(13)

where $r_{ij}$ is the membership degree of the $i$th index relative to the $j$th level, and it is the possible degree of $v_i$ evaluation of the $u_i$.

Step 4: Determine the weight of each evaluation index.

Each evaluation indicator is assigned $a_i$ to represent its importance, yielding the weight vector $A$ for the evaluation.

$$a_i\ge 0, {\displaystyle \sum a_i}=1$$

(14)

Step 5: Select the synthesis operator and calculate the evaluation result.

The final evaluation set $B$ can be calculated through the matrix $R$ and the weight vector $A$, as shown in Equation (15).

$$\begin{array}{l}B=A•R\\ =\left[a_1,a_2,\dots ,a_N\right]•\left[\begin{array}{cccc}{r}_{11}& r_{12}& \dots & r_{1p}\\ r_{21}& r_{22}& \dots & r_{2p}\\ ⋮& ⋮& \ddots & ⋮\\ r_{N1}& r_{N2}& \dots & r_{Np}\end{array}\right]\\ =\left[b_1,b_2,\dots ,b_p\right]\end{array}$$

(15)

where $R$ is the degree of membership of each evaluation index relative to the evaluation; $A$ is the degree of the relevant evaluation index; and $•$ represents the synthesis operators.

There are three types of synthesis operators, as shown below.

$$S_j=\min \left(1,{\displaystyle \sum _{i=1}^N{a}_i}{r}_{ij}\right),j=1,2,\dots ,p$$

(16)

$$S_j=\underset{i=1}{\overset{N}{\vee }}\left(a_i\wedge r_{ij}\right)=\underset{i}{\max }\left\{\min \left(a_i,r_{ij}\right)\right\},j=1,2,\dots ,p$$

(17)

$$S_j=\underset{i=1}{\overset{N}{\vee }}\left(a_i•r_{ij}\right)=\underset{i}{\max }\left\{a_i•r_{ij}\right\},j=1,2,\dots ,p$$

(18)

3. The Proposed Evaluation Method

This section employs a combined TOPSIS–AHP and FCE approach to evaluate the EMC of vehicular wireless communication systems. The weights for the evaluation indicators are determined using the TOPSIS and AHP methods. Subsequently, the FCE method utilizes these weights to perform the comprehensive evaluation.

3.1. Establish Indicators System

The specific structure of a two-level fuzzy comprehensive evaluation index system for the EMC of a vehicular wireless communication system is shown in Figure 3, with a brief description of each parameter provided below.

The $U$ is the evaluation target. The $U_i$ is the relevant evaluation indicator to $U$. The $u_{ij}$ is the relevant evaluation indicator to $U_i$.

The $U_i$ and $u_{ij}$ must completely reflect the $U$ and $U_i$

$$U=\left\{U_1,U_2,\dots ,U_N\right\},i=1,2,\dots ,N$$

(19)

$$U_i=u_{i1}\cup \dots \cup u_{ij}\cup \dots \cup u_{in} ,i=1,2,\dots ,N$$

(20)

The $U_i$ and $u_{ij}$ cannot be an empty set.

$$U_i\ne \varnothing ,i=1,2,\dots ,N$$

(21)

$$u_{ij}\ne \varnothing ,i=1,2,\dots ,N; j=1,2,\dots ,n$$

(22)

The $U_i$ and $u_{ij}$ cannot be repeated.

$$U_i\cap U_j=\varnothing ,i\ne j,i\in N,j\in N$$

(23)

$$u_{ip}\cap u_{iq}=\varnothing ,p\ne q,p\in j,q\in j$$

(24)

The $A_i$ is a weight vector set of $U_i$ shown in Equation (25). The $A$ is a weight vector set of $U$ shown in Equation (26).

$$A_i=\left[a_{i1},a_{i2},\dots ,a_{in}\right],i=1,2,\dots ,N$$

(25)

$$A=\left[A_1,A_2,\dots ,A_N\right]$$

(26)

3.2. Key Techniques

The evaluation method proposed in this paper consists of two important technical parts: (1) weights determination and (2) evaluation. The process of the evaluation method is shown in Figure 4.

In the weight determination phase, the quantitative TOPSIS method and qualitative AHP method are used to determine the weights of each evaluation indicator in the sub-criterion layer and criterion layer, respectively. The weighting ideas and specific steps are introduced in detail in Section 3.4.

In the evaluation phase, the fuzzy comprehensive evaluation method is used to carry out the two-level evaluation. The evaluation ideas and concrete steps are introduced in detail in Section 3.5.

3.3. Preprocessing Evaluation Data

Since differences in dimensions and value ranges among performance indicators may affect evaluation results, preprocessing the data is essential. A common method is standardization, which transforms diverse data types into a uniform [0–1] scale.

3.3.1. Quantitative Indicators

Quantitative indicators are numerically measurable evaluation criteria.

For “very small” indicators (denoted as $w_{ij}$), lower values indicate better performance. Given $n$ evaluation schemes, $w_{ij}\prime$ can be normalized using Equation (27).

$$w_{ij}\prime ={\displaystyle \frac{\underset{i}{\max }\left\{w_{ij}\right\}-w_{ij}}{\underset{i}{\max }\left\{w_{ij}\right\}-\underset{i}{\min }\left\{w_{ij}\right\}}}$$

(27)

where $i$ is the number of evaluation schemes, $i=[1,2,\dots ,n]$; $j$ is the number of evaluation indicators in the scheme; $\underset{i}{\max }\left\{w_{ij}\right\}$ and $\underset{i}{\min }\left\{w_{ij}\right\}$ are the maximum and minimum values in $w_{ij}$, respectively.

For “very large” indicators (denoted as $w_{ij}$), higher values indicate better performance. Given $n$ evaluation schemes, $w_{ij}\prime$ can be normalized using Equation (28).

$$w_{ij}\prime ={\displaystyle \frac{w_{ij}-\underset{i}{\min }\left\{w_{ij}\right\}}{\underset{i}{\max }\left\{w_{ij}\right\}-\underset{i}{\min }\left\{w_{ij}\right\}}}$$

(28)

where $i$ is the number of evaluation schemes, $i=[1,2,\dots ,n]$; $j$ is the number of evaluation indicators in the scheme; $\underset{i}{\max }\left\{w_{ij}\right\}$ and $\underset{i}{\min }\left\{w_{ij}\right\}$ are the maximum and minimum values in $w_{ij}$, respectively.

For interval indicator $w_{ij}$, performance improves as values approach ideal value $a_j$. Given $n$ evaluation schemes, the normalized value $w_{ij}\prime$ is computed via Equation (29).

$$w_{ij}\prime ={\displaystyle \frac{\max \left\{\left|w_{ij}-a_j\right|\right\}-\left|w_{ij}-a_j\right|}{\max \left\{\left|w_{ij}-a_j\right|\right\}-\min \left\{\left|w_{ij}-a_j\right|\right\}}}$$

(29)

where $i$ is the number of evaluation schemes, $i=[1,2,\dots ,n]$; $j$ is the number of evaluation indicators in the scheme; $\max \left\{\left|w_{ij}-a_j\right|\right\}$ and $\min \left\{\left|w_{ij}-a_j\right|\right\}$ are the maximum and minimum values in the absolute values of the difference between $w_{ij}$ and $a_j$, respectively.

3.3.2. Qualitative Indicators

Qualitative indicators are evaluation criteria that cannot be expressed numerically and are typically described in written form.

Table 1. (a) Numerical qualitative evaluation indicators. (b) Numerical qualitative evaluation indicators.

(a)
Evaluation indicators				Yes (existence or good)				No (inexistence or bad)
Significance				1				0
(b)
$n$	0.1	0.2	0.3	0.4		0.5	0.6		0.7	0.8	0.9
Five levels	Worst	–	Bad	–		General	–		Good	–	Best
Seven levels	Worst	Worse	Bad	–		General	–		Good	Better	Best
Nine levels	Worst	Worse	Bad	Worse than general		General	Better than general		Good	Better	Best

lists two types of such indicators.

3.4. Weights Determination

Based on the evaluation indicator system in Section 3.1 and comparative analysis of weighting methods, this study adopted a combined TOPSIS (quantitative) and AHP (qualitative) approach for indicator weighting.

3.4.1. Weight Determination of the Sub-Criterion Layer (TOPSIS)

Step 1: Standardize the original data.

For $m$ evaluation schemes with $n$ indicators each, the original data matrix $A$ is given in Equation (30).

$$A=\left[\begin{array}{cccc}{x}_{11}& x_{12}& \dots & x_{1n}\\ x_{21}& x_{22}& \dots & x_{2n}\\ ⋮& ⋮& \ddots & ⋮\\ x_{m1}& x_{m2}& \dots & x_{mn}\end{array}\right]$$

(30)

where $x_{ij}$ is the original data.

After standardizing matrix $A$ (Section 3.3), the resulting standardized matrix $A\prime$ is given in Equation (31).

$$A\prime =\left[\begin{array}{cccc}{x}_{11}^{\prime }& x_{12}^{\prime }& \dots & x_{1n}^{\prime }\\ x_{21}^{\prime }& x_{22}^{\prime }& \dots & x_{2n}^{\prime }\\ ⋮& ⋮& \ddots & ⋮\\ x_{m1}^{\prime }& x_{m2}^{\prime }& \dots & x_{mn}^{\prime }\end{array}\right]$$

(31)

where $x_{ij}\prime$ is the standardized data.

Step 2: Dimensionless processing of standardized data.

After applying Equation (30) to remove dimensions from standardized matrix $A\prime$, the resulting dimensionless matrix $A″$ is given in Equation (33).

$$x_{ij}″={\displaystyle \frac{x_{ij}\prime }{\sqrt{{\displaystyle \sum _{i=1}^m{x}_{ij}^{\prime 2}}}}}$$

(32)

$$A″=\left[\begin{array}{cccc}{x}_{11}″& x_{12}″& \dots & x_{1n}″\\ x_{21}″& x_{22}″& \dots & x_{2n}″\\ ⋮& ⋮& \ddots & ⋮\\ x_{m1}″& x_{m2}″& \dots & x_{mn}″\end{array}\right]$$

(33)

where $x_{ij}″$ is the dimensionless data.

Step 3: Calculate the weighting coefficient matrix.

Evaluation index weights are calculated using Equations (28)–(30). These weights form diagonal matrix $W$ (Equation (37)), which is then used with Equation (27) to compute weighting coefficient matrix $Y$ (Equation (38)).

$$\overline{x_j}={\displaystyle \frac{1}{m}}{\displaystyle \sum _{i=1}^m{x}_{ij}″}$$

(34)

$$S_j=\sqrt{{\displaystyle \frac{1}{m-1}}{\displaystyle \sum _{i=1}^m{\left(x_{ij}″-\overline{x_j}\right)}^2}}$$

(35)

$$w_j={\displaystyle \frac{S_j}{\left|\overline{x_j}\right|}},j=1,2,\dots ,n$$

(36)

$$W=\left[\begin{array}{cccc}{w}_1& 0& \dots & 0\\ 0& w_2& \dots & 0\\ ⋮& ⋮& \ddots & ⋮\\ 0& 0& \dots & w_n\end{array}\right]$$

(37)

$$\begin{array}{l}Y=A″•W\\ =\left[\begin{array}{cccc}{x}_{11}″& x_{12}″& \dots & x_{1n}″\\ x_{21}″& x_{22}″& \dots & x_{2n}″\\ ⋮& ⋮& \ddots & ⋮\\ x_{m1}″& x_{m2}″& \dots & x_{mn}″\end{array}\right]•\left[\begin{array}{cccc}{w}_1& 0& \dots & 0\\ 0& w_2& \dots & 0\\ ⋮& ⋮& \ddots & ⋮\\ 0& 0& \dots & w_n\end{array}\right]\end{array}$$

(38)

where $i=1,2,\dots ,m$; $j=1,2,\dots ,n$.

Step 4: Calculate the positive and negative ideal solutions.

$$y^{+}=\left[y_1^{+},y_2^{+},\dots ,y_n^{+}\right]$$

(39)

$$y^{-}=\left[y_1^{-},y_2^{-},\dots ,y_n^{-}\right]$$

(40)

where $y_j^{+}=\underset{1\le i\le m}{\max }\left\{y_{ij}\right\},y_j^{-}=\underset{1\le i\le m}{\min }\left\{y_{ij}\right\},j=1,2,\dots n$.

Step 5: Determine the weights of evaluation indicators.

First, normalize both positive and negative ideal solutions. Then, determine the weights for each evaluation indicator (sub-criterion layer). Equations (41) and (42) provide the weighted solutions, while Equations (43) and (44) give the corresponding weight vectors.

$$z_j^{+}={\displaystyle \frac{y_j^{+}}{{\displaystyle \sum _{j=1}^n{y}_j^{+}}}}, j=1,2,\dots ,n$$

(41)

$$z_j^{-}={\displaystyle \frac{y_j^{-}}{{\displaystyle \sum _{j=1}^n{y}_j^{-}}}}, j=1,2,\dots ,n$$

(42)

$$Z^{+}=\left[z_1^{+},z_2^{+},\dots ,z_n^{+}\right]$$

(43)

$$Z^{-}=\left[z_1^{-},z_2^{-},\dots ,z_n^{-}\right]$$

(44)

3.4.2. Weight Determination of the Criterion Layer (AHP)

Step 1: The AHP method is used to determine the weight value of each indicator in the criterion layer.

Step 2: Perform the calculation procedure of single hierarchical sorting to obtain the weight vector and corresponding eigenvalues.

$${\lambda }_{\max }={\displaystyle \frac{1}{n}}{\displaystyle \sum _{i=1}^N\frac{{(Cw)}_i}{w_i}}$$

(45)

Step 3: Perform a consistency check.

$$\mathrm{CR}={\displaystyle \frac{\mathrm{CI}}{\mathrm{RI}}}$$

(46)

$$\mathrm{CI}={\displaystyle \frac{{\lambda }_{\max }-n}{n-1}}$$

(47)

where

Table 2. Average random consistency index (RI).

$n$	1	2	3	4	5	6	7	8	9
RI	0	0	0.58	0.9	1.12	1.24	1.32	1.41	1.45

lists the RIs.

Step 4: The weight vector of each evaluation index in the criterion layer is obtained.

$$W=\left[w_1,w_2,\dots ,w_N\right]$$

(48)

where $N$ is the number of indicators in the criterion layer.

3.5. Fuzzy Comprehensive Evaluation

When applying fuzzy comprehensive evaluation methods, the multi-level fuzzy model is the common choice. The basic idea of this method is to divide the evaluation indicators into multiple levels according to certain logic and relations.

3.5.1. First-Level FCE

Step 1: Calculate the first-level FCE single-factor evaluation matrix $R_i$.

$$R_i={\left[r_{ijk}\right]}_{n\times p}$$

(49)

where $r_{ijk}$ is the fuzzy membership degree of $u_{ij}$ to the $k$th element in the comment set; $i=1,2,\dots ,N$; $j=1,2,\dots ,n$; $k=1,2,\dots ,p$.

Step 2: Calculate the first-level FCE weight vector $A_i$.

The weight vector $A_i$ of evaluation indicator (sub-criterion layer) is calculated using the quantitative TOPSIS method (based on Section 3.4.1).

$$A_i=\left[a_{i1},a_{i2},\dots ,a_{in}\right]$$

(50)

where $a_{ij}$ is the weight coefficient of each evaluation index $u_{ij}$.

Step 3: Calculate the first-level FCE set $B_i$.

The first-level FCE set $B_i$ (Equation (51)) is calculated using weight vector $A_i$ (Step 2) of evaluation index $U_i$ and single-factor evaluation matrix $R_i$ (Step 1).

$$\begin{array}{l}{B}_i=A_i•R_i\\ =\left[a_{i1},a_{i2},\dots ,a_{in}\right]•{\left[r_{ijk}\right]}_{n\times p}\\ =\left[b_{i1},b_{i2},\dots ,b_{ip}\right]\end{array}$$

(51)

3.5.2. Two-Level FCE

Step 1: Calculate the two-level FCE single-factor evaluation matrix $R$.

$$R=\left[\begin{array}{c}{B}_1\\ B_2\\ ⋮\\ B_N\end{array}\right]=\left[\begin{array}{c}{A}_1•R_1\\ A_2•R_2\\ ⋮\\ A_N•R_N\end{array}\right]$$

(52)

Step 2: Calculate the two-level FCE weight vector $A$.

The weight vector $A$ of evaluation indicator (criterion layer) is calculated using the qualitative AHP method (based on Section 3.4.2).

$$A=\left[A_1,A_2,\dots ,A_N\right]$$

(53)

Step 3: Calculate the two-level FCE set $B$.

The two-level FCE set $B$ (Equation (54)) can be calculated using weight vector $A$ of evaluation index $U$ (Step 5) and the two-level FCE single-factor matrix $R$ (Step 4).

$$\begin{array}{l}B=A•R\\ =A•\left[\begin{array}{c}{A}_1•R_1\\ A_2•R_2\\ ⋮\\ A_N•R_N\end{array}\right]\end{array}$$

(54)

4. Experimental Validation and Analysis

4.1. Experimental Validation

4.1.1. Experimental Setup

The experimental subject of this study is a specialized vehicle (Figure 5). Three such vehicles, labeled Vec1, Vec2, and Vec3, were used in the experiments. Vec1 and Vec2 served as transmitting ends in the communication experiments, while Vec3 acted as the receiving end. Figure 6 shows the EMC performance evaluation indicator hierarchy system of the vehicular wireless communication system. Among these indicators, $u_{11}$, $u_{12}$, $u_{13}$, and $u_{14}$ are determined based on transmitter performance; $u_{21}$, $u_{22}$, and $u_{23}$ are determined by receiver performance; $u_{24}$ is established through practical engineering experience; $u_{31}$ and $u_{32}$ are defined by antenna characteristics; $u_{41}$ and $u_{42}$ are specified according to relevant EMC standards.

The experimental scene is in a specific urban area of Beijing. Figure 7 shows the satellite remote sensing image of the urban area, with an effective resolution of 5 m after fusion processing.

This section investigates vehicular voice communication within the frequency band spanning 30 MHz to 1 GHz, encompassing the complete Very-High-Frequency (VHF) range and partial Ultra-High-Frequency (UHF) spectrum. Within this frequency regime, electromagnetic waves primarily propagate via line-of-sight (LOS) transmission along the terrestrial surface. Figure 8 illustrates three radio propagation paths (communication links), where signal quality is predominantly governed by

(1)

Propagation distance: Direct correlation with path loss;

(2)

Obstruction characteristics: Including building density, dimensional parameters, and spatial distribution along the propagation path.

Table 3. The quantitative measurements of key urban architectural parameters.

Communication Path	1	2	3
Length (km)	21	45	36
Normalized difference built-up index (NDBI) (Within the 50 m buffer zones on both sides of the communication path)	0.43	0.86	0.65
Morphological description	Patchy sparse distribution	Grid-like high-density Pattern	Clustered high-density aggregation
Building density (Within the 50 m buffer zones on both sides of the communication path)	34%	63%	41%

provides quantitative measurements of key urban architectural parameters along these three paths, including but not limited to structural density and average profile dimensions.

Vec1 conducted two randomized communication trials at Position A (designated V1-PA-1 and V1-PA-2) and one trial at Position C (V1-PC). Vec2 performed one randomized trial each at Position B (V2-PB) and Position C (V2-PC). These experimental configurations are sequentially numbered as evaluation schemes 1 through 5. These five trials form four comparative experimental groups:

(1)

Same-position, same-vehicle control group: V1-PA-1 and V1-PA-2.

(2)

Different-position, same-vehicle control group: V2-PB and V2-PC.

(3)

Same-position, different-vehicle control group: V1-PC and V2-PC.

(4)

Different-position, different-vehicle control group: V1-PC and V2-PB; V1-PA-1 and V2-PC (and other possible combinations).

4.1.2. TOPSIS Method Determines the Weights of the Criterion Layer

Considering the specialized nature of vehicular experiments, this study focused exclusively on the test data from the vehicle transmitters, with detailed results presented in

Table 4. Evaluation indicator data of vehicular transmitter in each scheme.

Experimental Sets	V1-PA-1	V1-PA-2	V1-PC	V2-PC	V2-PB
scheme	1	2	3	4	5
The maximum transmitting power $u_{11}$	102	103	105	99	106
The fundamental transmission bandwidth $u_{12}$	670	750	720	580	780
The harmonic rejection ratio $u_{13}$	54	51	49	43	56
The intermodulation rejection ratio $u_{14}$	47	53	58	49	57

.

The weighting coefficient matrix $Y$ (Equation (55)) is derived from Equations (30)–(38).

$$Y=\left[\begin{array}{llll}0.013\hfill & 0.075\hfill & 0.043\hfill & 0.036\hfill \\ 0.013\hfill & 0.066\hfill & 0.041\hfill & 0.041\hfill \\ 0.012\hfill & 0.070\hfill & 0.039\hfill & 0.044\hfill \\ 0.013\hfill & 0.085\hfill & 0.034\hfill & 0.037\hfill \\ 0.012\hfill & 0.054\hfill & 0.044\hfill & 0.043\hfill \end{array}\right]$$

(55)

The positive ideal solution $y^{+}$ (Equation (56)) and negative ideal solution $y^{-}$ (Equation (57)) are determined via Equations (41) and (42).

$$y^{+}=[0.013,0.085,0.044,0.044]$$

(56)

$$y^{-}=[0.012,0.054,0.034,0.036]$$

(57)

The $Z^{+}$ (Equation (58)) and $Z^{-}$ (Equation (59)) are the weights of $y^{+}$ and $y^{-}$, respectively, which are obtained from Equations (43)–(46).

$$Z^{+}=(0.07,0.45,0.24,0.24)$$

(58)

$$Z^{-}=(0.1,0.4,0.25,0.25)$$

(59)

Thus, the sub-criterion layer weight vector set $A_1$ for transmitter performance ($U_1$) is given in Equation (53). Repeating this process yields the corresponding weight vector sets $A_2$, $A_3$, and $A_4$ for receiver ($U_2$), antenna ($U_3$), and communication ($U_4$) performances in Equations (61)–(63), respectively.

$$A_1=(0.1,0.4,0.25,0.25)$$

(60)

$$A_2=(0.2,0.2,0.3,0.3)$$

(61)

$$A_3=(0.6,0.4)$$

(62)

$$A_4=(0.5,0.5)$$

(63)

4.1.3. AHP Determines the Weights of the Criterion Layer

The qualitative AHP method is used to determine the weight of the criterion layer (transmitter performance ($U_1$), receiver performance ($U_2$), antenna performance ($U_3$), and communication performance ($U_4$)). It reflects the performance of the target layer (target $U$).

Table 5. Criterion level index.

The EMC Performance of Vehicle Wireless Communication System	${\mathit{U}}_2$	${\mathit{U}}_1$	${\mathit{U}}_3$	${\mathit{U}}_4$
$U_2$	1	2	3	2
$U_1$	1/2	1	1/3	1
$U_3$	1/3	3	1	2
$U_4$	1/2	1	1/2	1

shows the criterion level index.

The weight vector $W$ in Equation (65) is derived by normalizing matrix $C$ using Equations (64), and (66) is the result for the consistency check of the index weight vector $W$.

$$C=\left[\begin{array}{cccc}1& 2& 3& 2\\ 1/2& 1& 1/3& 1\\ 1/3& 3& 1& 2\\ 1/2& 1& 1/2& 1\end{array}\right]$$

(64)

$$W={[0.417,0.148,0.278,0.157]}^{\mathrm{T}}$$

(65)

$$\mathrm{C}\mathrm{R}=0.085$$

(66)

Equation (66) shows that $\mathrm{CR}<1$, confirming $W$ as the criterion layer weight vector $A$.

$$A=[0.417,0.148,0.278,0.157]$$

(67)

4.1.4. Comprehensive Evaluation

Table 6. Comprehensive evaluation grades definition.

Grades	Best	Better	Good	Normal	Bad
Score	≥0.9	$[0.7,0.9)$	$[0.5,0.7)$	$[0.3,0.5)$	<0.3

lists the evaluation grades and their corresponding scores.

Statistical analysis of the experimental data confirmed that evaluation indicators ($u_{11}$, $u_{12}$, $u_{13}$, …, $u_{42}$) follow normal distributions. Therefore, the membership matrix of each evaluation indicator relative to each evaluation level is calculated by Gaussian Membership Function Equation (68).

$$r_{ij}=e^{-{\displaystyle \frac{{(u_{ij}-c)}^2}{2{\sigma }^2}}}$$

(68)

where $r_{ij}$ is the membership degree of indicator $u_{ij}$ to the $k$th comment level; $c$ is the mean value; and $\sigma$ is the standard deviation.

The single-factor evaluation matrices $R_1$, $R_2$, $R_3$, and $R_4$ correspond to the first-level FCEs of $U_1$, $U_2$, $U_3$, and $U_4$ are calculated by Equation (42), respectively.

$$R_1=\left[\begin{array}{ccccc}0.004& 0.644& 0.37& 0& 0\\ 0.24& 0.75& 0.98& 0.52& 0.27\\ 0& 0.169& 0.89& 0.018& 0\\ 0& 0.64& 0.37& 0& 0\end{array}\right]$$

(69)

$$R_2=\left[\begin{array}{ccccc}0& 0.018& 0.78& 0& 0\\ 0& 0.06& 1& 0.06& 0\\ 0.79& 0.37& 0.018& 0& 0\\ 0.004& 0.644& 0.37& 0& 0\end{array}\right]$$

(70)

$$R_3=\left[\begin{array}{ccccc}0.779& 1& 0.779& 0.37& 0.105\\ 0.018& 0.37& 1& 0.37& 0.018\end{array}\right]$$

(71)

$$R_4=\left[\begin{array}{ccccc}0.002& 1& 0.002& 0& 0\\ 0.64& 0.37& 0.001& 0& 0\end{array}\right]$$

(72)

The first-level FCE sets $B_1$, $B_2$, $B_3$, and $B_4$ are calculated using Equations (16), (44), and (62)–(65), respectively.

$$B_1=[0.096,0.56,0.74,0.213,0.108]$$

(73)

$$B_2=[0.238,0.32,0.472,0.012,0]$$

(74)

$$B_3=[0.475,0.748,0.867,0.37,0.016]$$

(75)

$$B_4=[0.321,0.685,0.002,0,0]$$

(76)

The single-factor evaluation matrix $R$ (Equation (77)) for the two-level FCE is derived from Equations (45) and (66)–(69).

$$R=\left[\begin{array}{ccccc}0.096& 0.56& 0.74& 0.213& 0.108\\ 0.238& 0.32& 0.472& 0.012& 0\\ 0.475& 0.748& 0.867& 0.37& 0.016\\ 0.321& 0.685& 0.002& 0& 0\end{array}\right]$$

(77)

The two-level FCE set $B$ (Equation (71)) is obtained by combining Equations (47), (60), and (70).

$$\begin{array}{l}B=[0.417,0.148,0.278,0.157]•\left[\begin{array}{ccccc}0.096& 0.56& 0.74& 0.213& 0.108\\ 0.238& 0.32& 0.472& 0.012& 0\\ 0.475& 0.748& 0.867& 0.37& 0.016\\ 0.321& 0.685& 0.002& 0& 0\end{array}\right]\\ =(0.258,0.582,0.60,0.193,0.049)\end{array}$$

(78)

Based on the calculation results of Equation (78),

Table 7. Evaluation scores.

Comparative Experiment	V1-PA-1	V1-PA-2	V1-PC	V2-PC	V2-PB
Evaluation score	0.258	0.528	0.60	0.193	0.049
Class	bad	good	good	bad	bad

lists the detailed evaluation scores.

4.2. Discussion and Analysis

4.2.1. Sensitivity Analysis of Weights Change

The TOPSIS and AHP sensitivity analyses to weight variations are discussed in this section.

(1)

Only the TOPSIS method was employed for weight calculation.

As described in Section 2.2, the TOPSIS method requires raw evaluation indicator data for weight determination. However, when calculating weights for the criterion layer ($U_1$, $U_2$, $U_3$, and $U_4$), the TOPSIS method cannot be directly applied because these criteria inherently lack raw data. This limitation demonstrates that the TOPSIS method is unsuitable for the multi-level index system structure shown in Figure 8.

(2)

Only the AHP method was employed for weight calculation.

As outlined in Section 2.1, the AHP method typically requires the construction of an initial judgment matrix based on expert experience for weight calculation. For determining weights of the criterion layer, only one initial judgment matrix needs to be constructed. However, determining sub-criterion layer weights requires four initial judgment matrices, increasing subjective judgments. This multi-matrix construction process introduces additional subjective judgments, consequently increasing uncertainty in the evaluation results.

4.2.2. Communication Performance Analysis

This section analyzes the bit error rate (BER) of the vehicular voice communication system and its correlation with overall communication performance from both simulation and experimental perspectives. As a key metric for evaluating communication quality, the BER value directly reflects the system’s communication performance.

In terms of simulation modeling, a complete voice communication link model was developed using the Simulink platform (Figure 9). For experimental validation, field tests were conducted to measure the BER and signal-to-noise ratio (SNR) of vehicular voice communication under all evaluation scenarios. The test setup is illustrated in Figure 10.

The results (

Table 8. BER measurement values.

Comparative Experiment	V1-PA-1	V1-PA-2	V1-PC	V2-PC	V2-PB
BER	$8.25\times {10}^{-4}$	$7.73\times {10}^{-5}$	$6.47\times {10}^{-5}$	$8.83\times {10}^{-4}$	$9.21\times {10}^{-4}$
SNR (dB)	5.36	6.13	6.51	5.88	4.94

and Figure 11) show that (1) the mean relative error (MRE) between simulated and measured BERs is 16.37%; (2) the MER between simulated and measured SNRs is 12.85%.

4.2.3. EMC Analysis

This section investigates the correlation between the BER of the vehicular voice communication systems and their evaluation scores, and further examines the inherent relationship between these parameters and overall EMC. The results (Table 8 and Figure 12) show the following:

(1)

All experimental schemes

A comparative performance analysis was conducted across all schemes. The results consistently demonstrate a correlation between the evaluation score and BER. The main trends are as follows: The EMC of the system in Scheme 3 is superior to that of other schemes, while Scheme 5 consistently exhibits the poorest EMC performance.

(2)

Same-Position, Same-Vehicle control experiment group (V1-PA-1 vs. V1-PA-2)

A comparative performance analysis was conducted between Schemes 1 and 2. Scheme 1 achieved an evaluation score of 0.258 with a measured BER of $8.25\times {10}^{-4}$, while Scheme 2 obtained an evaluation score of 0.582 with a measured BER of $7.73\times {10}^{-5}$. Comprehensive analysis indicates that Scheme 2 exhibits superior EMC performance.

(3)

Different-Position, Same-Vehicle control experiment group (V2-PC vs. V2-PB)

A comparative performance analysis was conducted between Schemes 4 and 5. Scheme 4 achieved an evaluation score of 0.193 with a measured BER of $8.83\times {10}^{-4}$, while Scheme 5 obtained an evaluation score of 0.049 with a measured BER of $9.21\times {10}^{-4}$. Comprehensive analysis indicates that Scheme 4 exhibits superior EMC performance.

(4)

Same-Position, Different-Vehicle control experiment group (V1-PC vs. V2-PC)

A comparative performance analysis was conducted between Schemes 3 and 4. Scheme 3 achieved an evaluation score of 0.60 with a measured BER of $6.47\times {10}^{-5}$, while Scheme 4 obtained an evaluation score of 0.193 with a measured BER of $8.83\times {10}^{-4}$. Comprehensive analysis indicates that Scheme 3 exhibits superior EMC performance.

(5)

Different-Position, Different-Vehicle control experiment group (V1-PC vs. V2-PB and V1-PA-1 vs. V2-PC)

A comparative performance analysis was conducted between Schemes 3 and 5. Scheme 3 achieved an evaluation score of 0.60 with a measured BER of $6.47\times {10}^{-5}$, while Scheme 5 obtained an evaluation score of 0.049 with a measured BER of $9.21\times {10}^{-4}$. Comprehensive analysis indicates that Scheme 3 exhibits superior EMC performance.

A comparative performance analysis was conducted between Schemes 1 and 4. Scheme 1 achieved an evaluation score of 0.258 with a measured BER of $8.25\times {10}^{-4}$, while Scheme 4 achieved an evaluation score of 0.193 with a measured BER of $8.83\times {10}^{-4}$. Comprehensive analysis indicates that Scheme 1 exhibits superior EMC performance.

5. Conclusions

This study proposed a TOPSIS–AHP and fuzzy comprehensive evaluation method to evaluate the EMC of vehicular wireless communication systems. Using high-resolution satellite remote sensing images, urban geographic data were collected to build an accurate city model. A communication link model was established, considering key factors like building occlusion and diffraction loss for urban radio propagation analysis. Key EMC performance indicators were identified in terms of three dimensions: communication quality, anti-interference capability, and transmission reliability. A hierarchical evaluation model (target, criterion, and sub-criterion layers) was developed, with weights determined using TOPSIS (quantitative) and AHP (qualitative) methods. The system’s EMC performance was then evaluated using FCE. The findings provide critical insights for optimizing vehicular communication systems and improving urban intelligent transportation efficiency. Overall, this study proposes an improved practical framework for performance evaluation and enhancement of wireless communications in complex urban environments, thereby providing sustainable support for vehicular R&D and urban transportation planning.