Effective Methods and Performance Analysis on Data Transmission Security with Blind Source Separation in Space-Based AIS

Chengjie Li,Lidong Zhu,Zhongqiang Luo,Zhen Zhang,Ying Yang

1 The Key Laboratory for Computer Systems of State Ethnic Affairs Commission,School of Computer Science and Technology(Southwest Minzu University),Chengdu 610000,China

2 National Key Laboratory of Science and Technology on Communications(University of Electronic Science and Technology of China),Chengdu 610000,China

3 Sichuan University of Science&Engineering,Zigong,China

4 College of Computer Science(Sichuan University),Chengdu 610000,China

Abstract:In space-based Automatic Identification Systems(AIS),due to high satellite orbits,several Ad Hoc cells within the observation range of the satellite are vulnerable to interference by an external signal.To increase efficiency in target detection and improve system security,a blind source separation method is adopted for processing the conflicting signals received by satellites.Compared to traditional methods,we formulate the separation problem as a clustering problem.Since our algorithm is affected by the sparseness of source signals,to get satisfactory results,our algorithm assumes that the distance between two arbitrary mixed-signal vectors is less than the doubled sum of variances of distribution of the corresponding mixtures.Signal sparsity is overcome by computing the Short-Time Fourier Transform,and the mixed source signals are separated using the improved PSO clustering.We evaluated the performance and the robustness of the proposed network architecture by several simulations.The experimental results demonstrate the effectiveness of the proposed method in not only improving satellite signal receiving ability but also in enhancing space-based AIS security.

Keywords:space-based automatic identification systems;tolerance rough set;particle swarm optimization;invulnerability performance

I.INTRODUCTION

With the rapid development in space technology,satellite communication has become one of the most important and promising information transmission technologies because of its wide coverage,large communication capacity,good mobility,and strong transmission capacity.

In shore-based systems,due to the influence of communication distance and communication facilities,ships in far-sea areas are difficult to supervise,but this challenge can be effectively solved by a spacebased Automatic Identification System(AIS).However,because of the high satellite orbit,multiple Ad Hoc cells are present in the observation range that could easily be interfered by external signals.To improve the signal detection efficiency and enhance system security,the signal processing capacity must be improved.The framework is shown in Figure.1[1,2].Based on the scenario in Figure 1,space-based AIS has been an important research subject in recent years[3–5].Qianyun Zhang proposed the possibility of passive AIS signal localization with low Earth orbit satellite con-stellations is investigated,which provides a more reliable vessel position determination[6].Fabio Maggio investigated using DBF onboard AIS satellites with the objective to increase the SINR(Signal to Interference plus Noise Ratio)so that the number of decoded AIS messages can be increased[7,8].Lars J.Foged discussed the design of array elements,from breadboard to engineering model(TRL4),manufacturing and validation campaigns at single element and array level[9].

Figure 1.Framework of space-based AIS.

Figure 2.Framework of BSS model.

In space-based AIS,since the satellite power and processing capacities are constrained,blind source separation theory and technology can be used to achieve better separated results,save more spectrum resources,and enhance the security of space-based AIS[10,11].In this paper,in order to improve the invulnerability of the network,a novel technique based on blind source separation is proposed,which solves the security problem from the physical layer,falls under the category of the cyberspace endogenous safety and security[12].

Blind signal separation(BSS)aims to separate the unobserved source signals from multiple observed mixed signals based on the statistical characteristics of the source signal[13].The biggest advantage of BSS is that the source signal can be separated without occupying additional system resources,thus,the frequency spectrum utilization efficiency is improved.The matrix form of BSS is described as follows[14,15],

here,Y(t)=[y1(t),y2(t),···,yM(t)]Tis the received mixed signal,A(t)=[a1(t),a2(t),···,aM(t)]is the mixed matrix,⊗is the matrix convolution,X(t)=[x1(t),x2(t),···,xN(t)]is the unobserved source signals,N(t)is the noise.The framework of BSS model is given in Figure 2.

Figure 3.(a)The original sample data.(b)The data has been classified two clusters duo to two received sensors.(c)The output sample data after tolerance rough set technique.

Since BSS is based on the statistical characteristics of observed signals,the BSS problem can be transformed into the classification problem of signal sampling data.In order to get better separation effect,the basic assumptions of the problem are as follows:(1)The original signals are all zero-mean signals and are statistically independent of each other.If the probability density function of the original signalsi(t)ispi(si),then the probability density function ofs(t)is(2)The source signal can only have one Gaussian distribution.When there is more than one Gaussian distribution,the mixed signal is not separable.In this paper,improved Particle Swarm Optimization(PSO)is used as a blind separation technique[16].

PSO was proposed by Eberhart and Kennedy in 1995,that is a stochastic optimization technique based on population[17].The advantages of PSO are that the optimized function is not required to be continuous or differentiable and converges quickly.But the disadvantages of PSO should not be ignored.The disadvantages of it can be summarized into the following two aspects:(1)The influence of the interference signal is relatively large,when the interference signal power is high,it is difficult to get accurate results;(2)For a function with multiple local extremum points,it is easy to fall into the local extremum points,can not obtain the correct results.In this paper,for the first disadvantage,the sample data is reduced prior to improved BSS using the tolerance rough set technique;For the second disadvantage,an novel BSS algorithm with improved PSO is given.

The paper is organized as follows.In Section II,the preparatory work is given,it is the basis knowledge of all algorithms in this paper;Section III introduces all algorithms implementation process,including sampled data preprocessing with tolerance rough set technique,the improved PSO algorithm and the algorithm flowchart;In Section IV,we present the details of the algorithm properties discussions,including optimization analysis,stop iterative criteria analysis,convergence characteristics analysis and algorithm robustness;In Section V,algorithm properties simulation discussions are present,including the comparative experiment of effect and invulnerability analysis of the space-based AIS network;at last a short conclusion is provided in Section VI.

II.PREPARATORY WORK

In this section,we introduce the related preparatory work of the improved BSS method.

2.1 Tolerance Rough Set Technique

The signals received by the sensors are mixed and contain interference signals.To avoid unnecessary computing costs and improve the algorithm accuracy,the sample data is reduced prior to improved BSS using the tolerance rough set technique[18].Tolerance rough set theory is used to classify data with tolerance relationships.Some definitions are given as follows:

If the sample data is reduced using the tolerance rough set technique,the K-means clustering algorithm is necessary.

2.2 Existing K-Means Clustering Algorithm

K-means clustering algorithm is a cluster analysis algorithm with iterative solution.The algorithm process can be summarized as: K objects were randomly selected as the initial clustering center,then the distance between each object and its clustering center is calculated,assign each sample to the closest clustering center,after each sample allocated,the cluster center will be recalculated according to the existing objects,the conditions for the iteration end is that no(or minimum number of)samples are reassigned to different clusters or no(or minimum number of)cluster centers change again[19].As a general rule,in K-means clustering algorithm,the Euclidean distance measurement is used.The Euclidean distances among every sample is described as below[20]:

here,α=(α1,α2,...,αn),β=(β1,β2,...,βn),1≤p ＜∞.

III.ALGORITHM EXECUTION PROCESS

In this section,the algorithm execution process will be introduced.

3.1 Cost Function of the Received Signal In Space-based AIS

In space-based AIS,assuming that containsNcAd Hoc cells within the observation range of a satellite,each Ad Hoc cell contains a base station(BS)multiplexing the same frequency band,and each BS containsnantennas andksingle antenna mobile stations,then the signal from thei-th BS can be expressed as[21],

wheresik(t)is the signal from the kth mobile station in thei-th cell,wikis a beam forming factor.The received signal can be expressed as,

wherenik(t)is the additive noise,in Eq.(6),the first item is a useful signal,the second item is the interference signal within the Ad Hoc cell,the third item is the interference signal between Ad Hoc cells.Then the SINR(Signal to Interference plus Noise Ratio)can be expressed as[22],

To improve the quality of the received signal,according to the Eq.(7),the cost function can be described as,

whererikis the threshold of theSINRik.But the cost function Eq.(8)is non-convex,we can convert it into a convex function by second order cone programming(SOCP).The converted convex function expression is as follows,

The detailed conversion process can be found in the appendix.[23].

In order to reduce the impact of interference signals,reduce the time and computational complexity of signal processing,the sampled data preprocessing with tolerance rough set technique is introduced in the following subsection.

3.2 Sampled Data Preprocessing with Tolerance Rough Set Technique

In actual signal transmission,two sensors are available.The sample data is computed using the Short-Time Fourier Transform(STFT),and the received mixtures are represented by[Y(t,f),Y(t,f)]T.Yi(t,f)is described as follows:

wherey(t)is the received mixing signal,andh(τ-t)is the Hamming window function.

From the above process,unobservable mixed vectors could emerge from these clusters of mixtures.Since the local optimal condition may reduce the performance of the traditional method,the effect of BSS is not satisfied if the sampled data is directly used.Thus,to enhance BSS performance and handle more advanced conditions,preprocessing with the K-means clustering algorithm is required.

K-means clustering algorithm classifies or clusters objects based on attributes or features into several groups.The grouping is implemented by minimizing the sum of squares of distances between every datum and the corresponding cluster center,as shown in Eq.(11),

whereµiis the mean vector ofSicluster.Note thatµi,(i= 1,2,···,N)is the cluster center and stands for the general feature of the corresponding class.

According to the specific circumstance in this study and based on the theory discussed in Section 2.1,the sparse sample data of the observed signal can be reduced.Table(1)provides the steps of data reduction process.

Table 1.Steps of data reduction process.

Table 2.Robustness of proposed algorithm compared with other algorithms.

3.3 Improved PSO

In the above subsection,to get the effective data,the sample data is preprocessed with tolerance rough set technique before BSS.In the following subsection,the improved PSO is discussed.

PSO is an optimization algorithm designed by simulating the movement of birds in a flock,each particle has two properties: velocityvand positionx,the velocityvrepresents the speed of movement,and the positionxrepresents the direction of movement.PSO gets the optimal solution through iteration,in each iteration,the particle updated itself by tracking two extreme valuespiandgi,the evolution equation is as follows[24],

3.4 Update Two Extreme Values

In the above iterative process,the updating of extreme valuespifor each initial sampling point is as calculated as follows[26]:

whereTCiis the object function evaluated at the position of the initial sampling pointi.In addition,giis set as the best estimation position in iterationk+1 in.

The proposed algorithm has better performance and less complexity after undergoing the tolerance rough set technique.The description of the system model is as follows,1)To avoid unnecessary computing costs and improve the algorithm accuracy,the sample data is reduced prior to improved BSS using the tolerance rough set technique;2)To improve the quality of the received signal,complete the optimization of the system model according to the Eq.(8)and Eq.(9);3)To separate the mixed signals,the improved PSO is used.The detailed performance analysis is described in Section 4.

After performing the implementation and updating processes,the cluster centers can now be generated.Every remaining sampling point is assigned to the cluster based on the nearest cluster center.The algorithm flowchart is displayed in Figure 4[27].

Figure 4.Algorithm flowchart.

Figure 5.The process of searching for the optimum value before using the tolerance rough set technique.

Figure 6.The process of searching for the optimum value after using the tolerance rough set technique.

IV.ALGORITHM PROPERTIES DISCUSSIONS

In this section,we investigate the properties of our proposed algorithm,such as implementation strategies,convergence characteristics,robustness.

4.1 Optimization Analysis

The sampled data are processed using the tolerance rough set technique to reduce time complexity and improve the stability of the algorithm(to be discussed in 4.4).Figure 5 shows the search process for the optimum value before using the tolerance rough set technique.In the figure,there are multiple local optimal values present,which would require additional time and computations in the search process due to redundant data.Figure 6 presents the search process for the optimum value after implementing the tolerance rough set technique;Only one optimal value is present.Due to the significant reduction in redundant data,time and computational complexities are reduced in the search process[28].

Figure 7.The separation performance comparison with improved BSS algorithm with PSO under different K.

4.2 Stop Iterative Criteria Analysis

The accuracy of the algorithm can be controlled according to actual needs.Pearson’s correlation coefficient will be used as the decision condition for the termination of the algorithm.The algorithm will be terminated if the Pearson’s correlation coefficient value is more than a cutoff valuer0.The Pearson’s correlation coefficient is expressed as[29]:

4.3 Convergence Characteristics Analysis

The improved BSS with PSO after tolerance rough set technique performs considerably better.To evaluate and compare the convergence performance of the improved BSS with PSO,theEctvalue was calculatedusing the formula[30]:

From the results shown in Figure 7,the algorithm in this paper has better convergence speed than Classical Searching and Averaging Method BSS Algorithm,Kmeans Clustering BSS and JADE.

4.4 Robustness Analysis

In the following subsequent sections,the robustness of the proposed algorithm is discussed.In this paper,to measure the robustness of the algorithm,Pearson’s correlation coefficient value in Eq.(18)is used as a measure[31].The Pearson’s correlation coefficient cutoff valuer0=0.95.If the value ofr0＞0.95 is acceptable,the value ofr0＜0.95 is unacceptable.In the same number of experiments,the algorithm in this paper is effective,robust and the experimental results have a small deviation.The robustness analysis is presented in Table(2).

In Table(2),running 100 experiments,the number ofr0＞0.95 is 97,88,86,90 respectively.Even if the time consumption of the proposed algorithm in this paper is not minimal,the robustness of it is the optimal.If making a trade-off between time spent and robustness,the proposed algorithm in this paper is the most efficient.

4.5 Time Complexity Analysis

In the following subsequent sections,the time complexity of the proposed algorithm is discussed.In the traditional PSO algorithm,the number of particles remains the same in each iteration.Assume that the number of particles in stepiisNi(i= 1,2,...,mis the maximum number of iterations),and the time of each iteration for each particle isTT,then the traditional PSO algorithm time complexity isN×m×TT.In this paper,the sample data is reduced with the tolerance rough set technique,the number of particles decreases with each iteration,that isN1＞N2＞...＞Nm,and the time of each iteration for each particle isTD,then the time complexity of the proposed algorithm in this paper is.

V.ALGORITHM PROPERTIES SIMULATION DISCUSSIONS

In the following simulation,the performance of blind source signal separation and the space-based AIS network are discussed.The system parameters used in the experiment were Inter(R)Core(TM)i3-3240 CPU@3.40GHz.The various experimental parameters are summarized in Table(3).In the simulation,the signal in the time-frequency domain was separated from the mixed signals[32].The sample data after the tolerance rough set technique had better separation performance effect.Every sampling point was assigned to the nearest neighbor cluster using the proposed algorithm.The classification results are displayed in Figure 8.The horizontal and vertical axes in the figure are calculated using Eq.(10).

Table 3.Simulation parameters.

As shown in Figure 8,the data has been preprocessed,and as expected,the classification results showed three groups.

Figure 8.The sampling points has been classified into three groups.

5.1 The First Comparative Experiment of Separation Effect

Figure 9 shows the waveforms of the sent source signals.We need to separate each object signal from the received mixed signals.Here,we consider two channels to simulate actual signal transmission.Figure 10 shows the received mixed signal waveforms after Gauss channel transitions.

Figure 11 shows the final BSS waveforms after the proposed algorithm is performed.Visually,the generated object signals Figure 11)are similar to the initial object signals(Figure 9).We compared these signals using objective evaluation and,for comparison,evaluated the separation performance of the JADE algorithm using Pearson’s correlation coefficient.The results are shown in Figure 12,where the Pearson’s correlation coefficient is calculated using Eq.(18)[33].

Figure 9.The sent source signals waveforms.Three sent source signals are considered.

Figure 10.The received mixed signal waves after gaussian channels.Two gaussian channels are considered.

As shown in Figure 12,the proposed method can efficiently separate blind source signals and perform much better than the classical JADE algorithm.Our results suggest that the JADE algorithm is more sensitive to noise than the proposed algorithm[34].

Figure 11.Blind source separation waveform with the proposed improved BSS algorithm with PSO.

Figure 12.The separation performance comparison with JADE algorithm under different SNR.

Figure 13.Blind source separation result,the algorithm in this article has a better performance than classical based on the ratio matrix clustering algorithm.

5.2 The Second Comparative Experiment of Effect

From the previous section,the BSS algorithm of adjacent satellite interference has a satisfying separation effect.We then analyze the separation effect using the error performance analysis as another evaluation criterion.In the error performance analysis,we compared the separation performance with the classical Based on the Ratio Matrix Clustering Algorithm,where the PI value is used.The formula is defined as[35]:

whereAis the mixed matrix,andis the estimation mixed matrix.As shown in Figure 13,the blind source signals can be efficiently separated with the proposed algorithm.The proposed algorithm also had better performance than the classical Based on the Ratio Matrix Clustering Algorithm.

Figure 14.Invulnerability analysis of the space-based AIS network with the proposed algorithm.

5.3 Invulnerability Analysis of the Spacebased AIS Network with the Proposed Improved Algorithm

The proposed algorithm not only improves the satellite signal receiving ability but also increases space-based AIS security.To better assess the security of the spacebased AIS network using the proposed algorithm,we conducted an invulnerability analysis of the network under random attack.Using the experimental parameters in Table 3.the cost function,which measures the connectivity of a network under random attack,is calculated using the formula[30]:

wherelijis the distance of nodeiand nodej.

As shown by the test results in Figure 14,the invulnerability performance of the proposed network architecture under random attack had significantly improved and is comparatively better than the DE(Differential Evolution algorithm)network optimization and PSO(Particle Swarm Optimization)network optimization.The results show that as the number of nodes increased,the network’s vulnerability also increased and that the proposed network architecture decreased more slowly than the others.

VI.CONCLUSION

In this paper,we proposed a novel signal separation approach to solve data transmission security using BSS.First,we get the original data by computing the Short-Time Fourier Transform(STFT)for each observation.Second,we preprocess the original data using the tolerance rough set technique to get high-efficiency data for better separation performance,reduced computational complexity and improve network security performance.Third,signal processing optimization model is discussed,and a convex function by second order cone programming(SOCP)is presented.In the PSO,to get a more accurate result,mading an assumptionand in the process of iterative solution,the Euler differential equation is introduced.

At last,the algorithm performances are discussed from many aspects,such as optimization analysis,stop iterative criteria analysis,convergence characteristics analysis,robustness analysis,invulnerability analysis etc..The experiment results show that the proposed algorithm in this paper is highly effective and performed much better than other BSS algorithms.The proposed approach in this paper enhanced satellite signal receiving ability and increased space-based AIS security.

ACKNOWLEDGEMENT

This work was supported by National Natural Science Foundation of China(No.61821001)and This work is fully supported by Natural Science Foundation of China Project(61871422),Science and Technology Program of Sichuan Province(2020YFH0071),National Natural Science Foundation of China under Grant(61801319),in part by Sichuan Science and Technology Program under Grant(2020JDJQ0061),(2021YFG0099),in part by the Sichuan University of Science and Engineering Talent Introduction Project under Grant(2020RC33),Innovation Fund of Chinese Universities under Grant(2020HYA04001).and Technology Key Project of Guangdong Province,China(2019B010157001).

APPENDIX

The cost function Eq.(22)is a non-convex,we can convert it into a convex function by second order cone programming(SOCP),the constraint condition can be converted to the following,

wherehiis the ith channel vector,the vectorwikhave a phase rotation,it’s equivalent to adding a constraint condition to Eq.(22),