# Effectiveness Evaluation Method of Application of Mobile Communication System Based on Factor Analysis

^{*}

## Abstract

**:**

## 1. Introduction

_{ij}is the factor loading and its size indicates the importance of the common factor relative to the original indexes [47].

- We study an effectiveness evaluation method of mobile communication network design schemes and propose a design scheme for the evaluation and optimization of network plans.
- We propose an improved method of effectiveness evaluation based on factor analysis. It can not only effectively use the historical data but also greatly reduce the amount of data collection and calculation.
- We propose a decision preference setting method based on cluster analysis.

## 2. Evaluation Indices and Data Acquisition

#### 2.1. Evaluation Indexes

#### 2.2. Data Acquisition

#### 2.3. Data Preprocessing

_{cpl}represents the category of encryption algorithm, three different algorithms (DES, 3DES and AES) can be selected and the corresponding assigned value is from 1 to 3. α

_{cpl}represents the length of the encryption key, which can be selected as 56, 64, 128 and 256, and the corresponding values are assigned 1–4. t

_{cyc}represents the key update cycle and t

_{min}and t

_{max}represent the longest and shortest cycle of key update, which are 2 and 24 in this paper. ω

_{1}, ω

_{2}, ω

_{3}represent the weight of the three indexes, which can be artificially specified or obtained by AHP and other methods [49].

_{1}and ω

_{2}represent the weight of two types of networks, which can be artificially specified or obtained by AHP and other methods.

_{1}and ω

_{2}represent the weight of accuracy and delay, which can be artificially specified or obtained by AHP and other methods.

## 3. An Improved Effectiveness Evaluation Method Based on Factor Analysis

#### 3.1. Traditional Factor Analysis

#### 3.2. Analysis on the Importance of Evaluation Index

_{ij}is the load of the ith index on the jth factor, m is the number of factors and p is the number of original indexes.

#### 3.3. Correlation Analysis

#### 3.4. Simplified Algorithm Model

_{i}

^{*}.

_{i}

^{*}is the new normalized commonness of the index i, W

_{i}is the original normalized commonness of the index i and k is the number of simplified indexes.

## 4. Preference Strategy

#### 4.1. Analysis of Evaluation Results

- (1)
- First, n samples are regarded as one category;
- (2)
- The distance between categories is calculated;
- (3)
- Select the two categories with the smallest distance to merge into a new category;
- (4)
- Repeat steps 2 and 3 to reduce one category at a time until all samples become one category.

_{pq}between category G

_{p}and G

_{q}.

#### 4.2. Preference Selection Algorithm

- (1)
- According to the preference strategy (information transmission, network control, security protection and integration), perform cluster analysis on the evaluation results and obtain n-level data set (the number of grades can be specified by users based on the cluster analysis results);
- (2)
- Select the first two levels of the corresponding cluster analysis as initial ranking;
- (3)
- Delete schemes at the lower 2 levels among other preferences;
- (4)
- Output the remaining schemes in order as the result.

## 5. A Summary of the Evaluation Process

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

ADC | Availability Dependability and Capability |

MIML | Availability Dependability and Capability |

IDPS | Intrusion Detection and Prevention System |

DES | Data Encryption Standard |

3DES | Triple Data Encryption Standard |

AES | Advanced Encryption Standard |

AHP | Analytic Hierarchy Process |

KMO | Kaiser Meyer Olkin |

VoIP | Voice over Internet Protocol |

TOPSIS | Technique for Order Preference by Similarity to an Ideal Solution |

LTE-R Long | Term Evolution-Railway |

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Index Name | Index Definition | Abbreviation |
---|---|---|

Information encryption intensity | Average value of correlation coefficient between enciphered information and original information. | X1 |

Network throughput | The data transmission volume of the whole network per unit time. | X2 |

End to end average delay | The average value of the delay from the source node to the destination node. | X3 |

Network state perception | When the state of the network node changes, the accuracy and delay weighted value of the network management device perception changes. | X4 |

Timeliness of network adjustment | The time delay from the network adjustment instruction to the successful network adjustment | X5 |

Success rate of temporary network access | Success rate of temporary users. | X6 |

Voice interruption rate | The ratio of the number of voice communication interruptions to the total number of calls. | X7 |

Voice link building time | The average time of voice users from dialing to successful chain building. | X8 |

**Table 2.**Parameter value, factor score and comprehensive score of each participating unit after standardization.

Unit | X1 | X2 | X3 | X4 | X5 | X6 | X7 | X8 | Factor 1 | Factor 2 | Factor 3 | Total Points |
---|---|---|---|---|---|---|---|---|---|---|---|---|

1 | 1.960 | 2.493 | 1.909 | 3.130 | 2.297 | 3.084 | 0.361 | 1.699 | 0.602 | 2.938 | 1.639 | 1.644 |

2 | −0.098 | 0.347 | 0.861 | 0.871 | 2.063 | 0.860 | 1.613 | 0.689 | 0.534 | 1.392 | −0.947 | 0.582 |

3 | −0.112 | −0.950 | −0.779 | 0.729 | −0.257 | −0.807 | −0.360 | −0.394 | −1.006 | 0.429 | −0.216 | −0.339 |

4 | −0.197 | −0.445 | −1.058 | 0.051 | −0.725 | −0.516 | −0.759 | −0.795 | −0.983 | 0.024 | 0.006 | −0.437 |

5 | 0.348 | −0.222 | −1.041 | −0.682 | −0.864 | −0.598 | −0.687 | −0.395 | −0.409 | −0.756 | 0.551 | −0.364 |

6 | 0.328 | −0.635 | −0.351 | 0.338 | −0.977 | −0.485 | −0.640 | −0.631 | −0.679 | −0.174 | 0.485 | −0.285 |

7 | 0.009 | −0.654 | −0.669 | −0.155 | −1.062 | −0.680 | −0.402 | −0.645 | −0.533 | −0.520 | 0.138 | −0.408 |

8 | −0.098 | −0.910 | −0.816 | 0.107 | −1.051 | −0.656 | −0.526 | −0.792 | −0.859 | −0.227 | 0.001 | −0.474 |

9 | 0.225 | 2.570 | 3.203 | 2.014 | 1.127 | 2.794 | 1.182 | 2.292 | 2.235 | 1.270 | 0.490 | 1.570 |

10 | −0.141 | 0.008 | 0.218 | −0.416 | 0.907 | 0.001 | −0.491 | 0.124 | −0.115 | 0.262 | −0.075 | 0.030 |

11 | 0.876 | 1.508 | 1.352 | 1.778 | 2.748 | 1.563 | 1.137 | 1.260 | 0.622 | 2.179 | 0.169 | 1.111 |

12 | −0.563 | −0.985 | −0.101 | −1.277 | −0.665 | −0.442 | −0.668 | −0.709 | −0.267 | −0.868 | −0.297 | −0.493 |

13 | −0.276 | −0.102 | 0.964 | −0.548 | 0.252 | −0.386 | 0.656 | 0.544 | 0.942 | −0.678 | −0.337 | 0.120 |

14 | −1.366 | −1.066 | −0.773 | −1.791 | −0.866 | −0.848 | 0.015 | −0.833 | −0.126 | −1.254 | −1.226 | −0.737 |

15 | 1.098 | −0.259 | −0.424 | −0.135 | 0.445 | 0.362 | −0.473 | −0.278 | −0.528 | 0.331 | 0.796 | 0.024 |

16 | −0.438 | −1.009 | −1.039 | −0.404 | −0.632 | −1.101 | 0.715 | −0.894 | −0.453 | −0.517 | −0.852 | −0.548 |

17 | 0.262 | −0.815 | −0.427 | −0.934 | −0.549 | 0.032 | 0.351 | −0.693 | −0.065 | −0.674 | −0.088 | −0.292 |

18 | 0.040 | 0.006 | −0.192 | −0.125 | 0.091 | 0.567 | 0.784 | 0.073 | 0.277 | 0.042 | −0.324 | 0.084 |

19 | −1.156 | 2.052 | 1.680 | 0.470 | 0.638 | 1.131 | 3.425 | 3.399 | 3.521 | −0.596 | −1.410 | 1.130 |

20 | −1.297 | −0.379 | −0.152 | −0.828 | 0.208 | 0.056 | 1.226 | −0.023 | 0.495 | −0.313 | −1.621 | −0.180 |

21 | −2.394 | −0.215 | −0.063 | −0.915 | −0.921 | −0.691 | −0.367 | −0.620 | −0.057 | −0.696 | −1.614 | −0.570 |

22 | 0.309 | −0.485 | 0.452 | −0.074 | 0.374 | 0.664 | 0.223 | −0.105 | 0.027 | 0.267 | −0.015 | 0.107 |

23 | −0.398 | −0.387 | 0.035 | −0.389 | 0.093 | −0.069 | 0.032 | −0.443 | −0.164 | −0.029 | −0.460 | −0.168 |

24 | −0.423 | −0.930 | −0.510 | −0.864 | −0.469 | −0.704 | −1.085 | −0.497 | −0.643 | −0.529 | −0.085 | −0.501 |

25 | −0.074 | 0.616 | 0.073 | 0.258 | −0.783 | −0.398 | −0.089 | 0.034 | 0.245 | −0.429 | 0.309 | 0.010 |

26 | 3.238 | 0.921 | 0.925 | −1.137 | −1.059 | −0.820 | −0.884 | 0.924 | 1.411 | −2.383 | 3.598 | 0.415 |

27 | −0.725 | −0.431 | −0.770 | 0.179 | 0.487 | −0.204 | −0.409 | −0.527 | −0.965 | 0.782 | −0.761 | −0.289 |

28 | −0.056 | −0.188 | −0.689 | 0.181 | −0.438 | −0.412 | −1.147 | −0.778 | −1.033 | 0.247 | 0.296 | −0.326 |

29 | −0.094 | 0.959 | −0.442 | 0.302 | −0.532 | −0.406 | −1.303 | −0.551 | −0.648 | 0.130 | 0.646 | −0.131 |

30 | 0.187 | −0.183 | −0.814 | 0.634 | 0.142 | −0.622 | −1.146 | −0.131 | −1.063 | 0.606 | 0.411 | −0.188 |

31 | 1.026 | −0.231 | −0.562 | −0.366 | −0.022 | −0.270 | −0.284 | −0.303 | −0.317 | −0.258 | 0.793 | −0.096 |

Index | Nonrotation | After Rotation | ||||
---|---|---|---|---|---|---|

Factor 1 | Factor 2 | Factor 3 | Factor 1 | Factor 2 | Factor 3 | |

X1 | 0.320650 | 0.843998 | 0.287874 | 0.083278 | 0.162547 | 0.929873 |

X2 | 0.909567 | 0.120463 | 0.172870 | 0.725623 | 0.488718 | 0.326088 |

X3 | 0.911390 | −0.071196 | 0.242330 | 0.837270 | 0.401471 | 0.179513 |

X4 | 0.780331 | 0.293705 | −0.430681 | 0.228377 | 0.881250 | 0.227832 |

X5 | 0.827407 | −0.010898 | −0.395764 | 0.396441 | 0.826709 | −0.027115 |

X6 | 0.933679 | 0.030354 | −0.169476 | 0.586084 | 0.737937 | 0.115563 |

X7 | 0.656920 | −0.646705 | 0.113004 | 0.791305 | 0.218188 | −0.434478 |

X8 | 0.913760 | −0.152106 | 0.303287 | 0.903241 | 0.342474 | 0.130169 |

Index | Factor 1 | Factor 2 | Factor 3 |
---|---|---|---|

X1 | 0.044136 | −0.155257 | 0.789911 |

X2 | 0.243241 | −0.063296 | 0.219128 |

X3 | 0.360151 | −0.171547 | 0.122934 |

X4 | −0.347005 | 0.631644 | −0.022096 |

X5 | −0.219985 | 0.550707 | −0.218813 |

X6 | −0.021879 | 0.313877 | −0.050131 |

X7 | 0.382698 | −0.146096 | −0.376688 |

X8 | 0.437015 | −0.252909 | 0.101338 |

X1 | X2 | X3 | X4 | X5 | X6 | X7 | X8 | |
---|---|---|---|---|---|---|---|---|

H_{i} | 0.8980 | 0.8717 | 0.8944 | 0.8807 | 0.8413 | 0.9014 | 0.8625 | 0.9501 |

W_{i} | 0.1265 | 0.1228 | 0.1260 | 0.1240 | 0.1185 | 0.1270 | 0.1215 | 0.1338 |

W_{i} ^{*} | 0.2501 | -- | -- | 0.2452 | -- | -- | 0.2402 | 0.2501 |

X2 | X3 | X7 | X8 | |
---|---|---|---|---|

X2 | 1.0000 | 0.8494 | 0.4655 | 0.8770 |

X3 | 0.8494 | 1.0000 | 0.6019 | 0.8866 |

X7 | 0.4655 | 0.6019 | 1.0000 | 0.7204 |

X8 | 0.8770 | 0.8866 | 0.7204 | 1.0000 |

X4 | X5 | X6 | |
---|---|---|---|

X4 | 1.0000 | 0.7023 | 0.7688 |

X5 | 0.7023 | 1.0000 | 0.8149 |

X6 | 0.7688 | 0.8149 | 1.0000 |

Unit | Factor Total Score | Factor Ranking | Simplified Index Score | Simplify Sorting | Sort Difference |
---|---|---|---|---|---|

1 | 1.644 | 1 | 2.1178 | 1 | 0 |

2 | 0.582 | 5 | 0.8886 | 5 | 0 |

3 | −0.339 | 22 | −0.3680 | 20 | −2 |

4 | −0.437 | 25 | −0.5566 | 25 | 0 |

5 | −0.364 | 23 | −0.5136 | 23 | 0 |

6 | −0.285 | 18 | −0.3784 | 21 | 3 |

7 | −0.408 | 24 | −0.5300 | 24 | 0 |

8 | −0.474 | 26 | −0.5914 | 26 | 0 |

9 | 1.57 | 2 | 1.9360 | 2 | 0 |

10 | 0.03 | 10 | 0.0236 | 11 | 1 |

11 | 1.111 | 4 | 1.5177 | 3 | −1 |

12 | −0.493 | 27 | −0.6742 | 28 | 1 |

13 | 0.12 | 7 | 0.1394 | 9 | 2 |

14 | −0.737 | 31 | −0.9431 | 31 | 0 |

15 | 0.024 | 11 | 0.0410 | 10 | −1 |

16 | −0.548 | 29 | −0.6078 | 27 | −2 |

17 | −0.292 | 20 | −0.3476 | 19 | −1 |

18 | 0.084 | 9 | 0.1539 | 8 | −1 |

19 | 1.13 | 3 | 1.4659 | 4 | 1 |

20 | −0.18 | 16 | −0.1548 | 14 | −2 |

21 | −0.57 | 30 | −0.7751 | 30 | 0 |

22 | 0.107 | 8 | 0.1690 | 7 | −1 |

23 | −0.168 | 15 | −0.1948 | 15 | 0 |

24 | −0.501 | 28 | −0.6824 | 29 | 1 |

25 | 0.01 | 12 | −0.0421 | 12 | 0 |

26 | 0.415 | 6 | 0.2849 | 6 | 0 |

27 | −0.289 | 19 | −0.3079 | 18 | −1 |

28 | −0.326 | 21 | −0.4422 | 22 | 1 |

29 | −0.131 | 14 | −0.2590 | 17 | 3 |

30 | −0.188 | 17 | −0.2417 | 16 | −1 |

31 | −0.096 | 13 | −0.1267 | 13 | 0 |

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**MDPI and ACS Style**

Jia, G.; Zhou, J.
Effectiveness Evaluation Method of Application of Mobile Communication System Based on Factor Analysis. *Sensors* **2021**, *21*, 5414.
https://doi.org/10.3390/s21165414

**AMA Style**

Jia G, Zhou J.
Effectiveness Evaluation Method of Application of Mobile Communication System Based on Factor Analysis. *Sensors*. 2021; 21(16):5414.
https://doi.org/10.3390/s21165414

**Chicago/Turabian Style**

Jia, Guohui, and Jie Zhou.
2021. "Effectiveness Evaluation Method of Application of Mobile Communication System Based on Factor Analysis" *Sensors* 21, no. 16: 5414.
https://doi.org/10.3390/s21165414