For LEO Satellite Networks: Intelligent Interference Sensing and Signal Reconstruction Based on Blind Separation Technology

Chengjie Li ,Lidong Zhu ,Zhen Zhang

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

Abstract: In LEO satellite communication networks,the number of satellites has increased sharply,the relative velocity of satellites is very fast,then electronic signal aliasing occurs from time to time.Those aliasing signals make the receiving ability of the signal receiver worse,the signal processing ability weaker,and the anti-interference ability of the communication system lower.Aiming at the above problems,to save communication resources and improve communication efficiency,and considering the irregularity of interference signals,the underdetermined blind separation technology can effectively deal with the problem of interference sensing and signal reconstruction in this scenario.In order to improve the stability of source signal separation and the security of information transmission,a greedy optimization algorithm can be executed.At the same time,to improve network information transmission efficiency and prevent algorithms from getting trapped in local optima,delete low-energy points during each iteration process.Ultimately,simulation experiments validate that the algorithm presented in this paper enhances both the transmission efficiency of the network transmission system and the security of the communication system,achieving the process of interference sensing and signal reconstruction in the LEO satellite communication system.

Keywords: blind source separation;greedy optimization algorithm;interference sensing;LEO satellite communication networks;signal reconstruction

I.INTRODUCTION

In recent years,the integrated space-ground network has been rapidly developing,and the Low Earth Orbit(LEO) satellite communication networks has gained increasing attention.However,its shortcomings have also become evident.Such as due to the satellite movement speed is fast and the openness of communication channels,the phenomenon of electronic signal aliasing is also common,as described in Figure 1.These aliasing signals make the receiving ability of the signal receiver worse,signal separation and processing ability weaker,and the anti-interference ability of the communication system lower.The deterioration of this communication environment reduces communication efficiency and the security and confidentiality of network communication.Moreover,to optimize the transmission efficiency of the network transmission system while maintaining the security of the communication system,a configuration is employed where the number of receiving antennas is smaller than the number of source signals.then the number of rows in the matrix receiving the mixed signals is less than the number of columns.In light of this scenario,Blind Source Separation(BSS)technology can significantly enhance the processing performance and efficiency of the system[1,2].

To tackle the intricacies of the mentioned scenarios,experts and scholars have put forward the application of Blind Source Separation (BSS) theory to enhance the system’s electronic signal alignment performance.In 1986,P.Comon proposed a new BSS theoretical framework,which was based on output power error separation,resulting in a significant improvement in signal transmission performance[3].In 1989,Olivier Rossetto utilized a neural network for the BSS algorithm,further enhancing the accuracy of the technology [4].O.Yilmaz and S.Rickard were the first to employ binary time-frequency masks for blind separation [5].Anthony J.Bell introduced a self-organized blind separation algorithm,which maintains the maximization of information within the nonlinear unit network during implementation,ensuring statistical independence between signals and resulting in an effective separation [6].For sub Gaussian and super Gaussian mixed signals,T.Lee extended the Infomax algorithm to separate mixed signals,and effectively processed high-dimensional EEG data,separating brain command signals from line noise [7].BSS models are referred to as overdetermined,positivedetermined,and underdetermined when the observed signal number is greater than,equal to,or less than the source signal number,respectively [8].Most existing BSS algorithms,such as independent component analysis (ICA),assume that BSS models is positive-determined.However,in practice,underdetermined BSS problems frequently arise[9].As an illconditioned problem,underdetermined BSS has become a challenging issue in the field of blind signal processing[10].Currently,the solution to underdetermined BSS is typically based on the‘two-step method’concept,first estimating the mixing matrix from the observation signal,and then combining the estimated matrix with an optimization algorithm for source signal separation.The“two-step method”streamlines the research process and has significantly advanced the development of underdetermined BSS algorithms[8].In this paper,we aim to transforming the BSS problem into a sampling point data clustering problem,by exploiting the sparsity of signals.The greedy algorithm will be employed in this algorithm..

The greedy algorithm tends to converge towards a local optimum solution during the iterative process.J.A.Tropp has addressed the challenge of obtaining the global optimum solution from multiple local optimum solutions,but this approach is not suitable for wireless signal aliasing scenarios[11].The effectiveness of the greedy algorithm is greatly influenced by the choice of greedy strategy [12].Improving the performance of the greedy algorithm and the processing capacity of the system through the selection of an appropriate greedy strategy is a crucial aspect to consider in this paper.

The structure of this paper consists of six sections.The first section provides an overview of Sparse Component Analysis(SCA)method,along with its underlying principles of vector representation,and the evaluation metrics for the algorithm’s performance etc..Section II delves into the theoretical foundation of sparse signals and mathematical model of BSS.In Section III,the proposed sparse signals underdetermined greedy blind separation scheme is presented,including the details of theSCA,cost function construction,and sparse signals underdetermined greedy blind separation.Section IV focuses on the simulation analysis and the algorithm performance analysis,including performance discussion on signal processing and the low earth orbit satellite communication network security.Finally,in Section V,a summary is provided,along with objective and reasonable conclusions drawn for the algorithms proposed in this research.

II.BASIC MATHEMATICAL KNOWLEDGE RELATED TO THE ALGORITHM

In order to provide the rationality of the algorithm from a theoretical perspective,the mathematical model of the SCA method will be presented in this section.Firstly,the sparsity of the source signals is essential to ensure optimal separation performance.In cases where the signals are not sparse,they can be made so using a STFT,which is the Short-time Fourier Transform.Then,the theory of BSS is introduced as a statistical signal processing technique to separate mixed signals.The mathematical theory of BSS is detailed in Section B of this section.Finally,performance indices,including the “correlation coefficient” and“PI”,are introduced to measure the algorithm’s performance.These performance indices will be used in the later sections of the paper to measure the effectiveness and superiority of the proposed algorithm.

2.1 Sparse Representation Method(SRM)

SRM is a common step for dealing with underdetermined BSS.The mathematical expression of the SRM model is as follows,

in the above formula (1),εis a reconstruction error,Y={y1,y2,···yM} ∈Rn×Mis the matrix composed of original signals,X={x1,x2,···,xM}T ∈RK×Mis the matrix composed of sparse coefficients,‖xi‖0is the sparseness degree ofxi,is a dictionary,is the atom.In order to find a more suitable sparse matrix more easily,the dictionary usually uses an overcomplete dictionary,that is,,at this time,the equation is either infinite solution(Discriminant Theory of System of linear equations)[13].

In this article,Matching Pursuit (MP) algorithm is used to solve sparse coefficientsxi.AssumeD={d1,d2,d3}is the dictionary,-→OAis the original signal,the process of that is as follows,

(1) Project -→OAtod1,d2andd3respectively,and select the largest projectionis the residual vector,assumethe iteration ends,perform the second step(2);

According to the step(1)(2),the original signalis sparsely represented,τis the residual vector.The geometric framework of sparse representation is given in Figure 2.

Figure 2.Geometric framework of sparse representation.

2.2 Mathematical Model of BSS

The primary benefit of BSS technology lies in its capability to extract the original source signal solely from the mixed signal,even in situations where the parameters of both the source signal and transmission channel remain unknown.

Next,the principles of BSS technology will be elucidated from a theoretical standpoint.ConsiderNstatistically independent signals,their matrix representation isS(t)=[s1(t),···,sN(t)]T,transmitted through an unknown channelA,andMsensors that detect the observed signals,their matrix representation isX(t)=[x1(t),···,xM(t)]T.Then theS(t)is the source signal,theX(t) is the observed mixed signals.The mathematical representation of the entire transmission process is as follows:

In formula (3),X(t)=[x1(t),···,xM(t)]Tis aM-dimensional observed signal,which is a mixture ofNsource signals.S(t)=[s1(t),···,sN(t)]Tis anN-dimensional unknown source signal,N(t)=[n1(t),···,nM(t)]Tis aM-dimensional channel noise,andAis theM×Ndimensional transfer function matrix,which is determined by the communication channel.The Flow chart of BSS is given in Figure 3.

Figure 3.Flow chart of BSS.

The primary aim of BSS is to estimate the separation matrixWin situations with limited prior information,the mathematical model is as follows,

In the above formula (3),Y(t) is a matrix composed of estimated signals from the source signal (transmit signals),expressed asY(t)=[y1(t),···,yM(t)]T,which is aM-dimensional,and the process of BSS is finished.

2.3 Performance Index of Blind Separation Algorithm

In this paper,there are two indexes to measure signal processing;one is “correlation coefficient” (cc),and the other is“PI”.In the following section,we will briefly introduce these two performance indicators.

(1)correlation coefficient(cc)

To assess the advantages of a BSS algorithm,the“cc”is commonly used as a benchmark for evaluating its performance.The aim is to determine the proximity between the estimated separated source signal sample points and the actual source signal sample points[14].The“cc”is defined as follows,

In formula(4),yian estimated separated signal,sjis a actual source signal.

(2)PI

AssumeG=WA,as expressed in formula(3),Ais theM×Ndimensional transfer function matrix,Wis the calculated separation matrix.To evaluate the separation effect,the channel interference measurement error criterion is built base on the global performance estimation matrixG.The mathematical model of“PI”is as follows[15],

in formula (5),thegijis the (i,j)th element of the global performance estimation matrixG.

III.INTERFERENCE SENSING AND SIGNAL RECONSTRUCTION BASED ON BSS

According to the characteristics of wireless network signal transmission,we aim to solve the problem of wireless network signal transmission from the physical layer,improve signal processing efficiency,and enhance wireless network security.

3.1 Optimized Sparse Principal Component Analysis(Optimized-SPCA)

Sparse Principal Component Analysis(SPCA)is proposed to address the disadvantage of Principal Component Analysis (PCA) in which it is unable to explain the features corresponding to each principal component.In this paper,by sparsifying the principal component coefficients in PCA,the main components are highlighted.The original variables are approximated using linear regression,andL1andL2regularization terms are added on top of the approximating function to obtain sparse loadings.The specific cost function is as follows[16]:

in formula(6),‖?‖F(xiàn)representsFrobenius-norm,‖?‖prepresentsLp-norm,andkis the number of principal components,A ∈Rp×krepresents nonsparse loadings.

Equation (6) represents the cost function of the algorithm.To obtain its optimal solution,an alternative algorithm is used,that is,first fixAto solveB,and then fixBto solveA.Given any matrixA,AAT=I,andis orthogonal matrix,then

assume theAis confirmed,substitute the formula(7)into the formula (6),then the formula (6) can be expressed as the follows[17],

3.2 Construct Cost Function of Intelligent Interference Sensing

In low orbit satellite communication networks,the presence of numerous satellites,high mobility,and the openness of satellite communication channels make interference detection a challenging task.This paper builds two cost functions to accomplish the goal mentioned above.Those two cost function pairs form a two-dimensional coordinate system in which the mixed signal is separable.

We calculate two cost functions for each sample data,which are defined as follows[18].

(1)Construct Cost Functionρi

The Construct Cost Functionρiis defined as

In this research,the symboldijrepresents the Euclidean distance calculated between the sample pointsiandj.Thedcis the cutoff distance,which satisfies the following formula,

then,according to the formula (9) and formula (10),the value ofρican be calculated.

(2)Construct Cost Functionδi

The Construct Cost Functionδiis defined as

whereδirepresents the minimum distance separating sample pointifrom any other sample points with higher density.

(3)Construct Cost Functionxi

After the definitions ofρiandδi,xiis defined based onρiandδi.usingxias the training data set of a greedy algorithm can better realize the optimization performance of a greedy algorithm,that is,xiis the ratio ofρiandδi,

then,the valuexiis the objective value of the greedy algorithm.

3.3 Greedy Blind Source Separation Algorithm(GBSSA)

Derived from the execution process of the algorithm presented in partA,the sparse representation of the mixed signals is obtained.Similarly,following the execution process of the algorithm in partB,the classification results of the sampled points of the mixed sparse signals are obtained.Next,the GBSSA will be executed.Assume that the sampling point set of sparse signals isN,N={N1,...,Nr}andN1∪N2∪...∪Nr=N,Ni ∩Nj=?(i=j).In each data setNi,i=1,2,...,r,theGAwill be executed[19].With the objective of discovering the optimal solution,the following cost functions will be iterated[19],

In eachNi,according to the formula(13),the optimal solution will be given,but it is only local optimal.To ensure the attainment of the global optimal solution,the algorithm incorporates the K-means algorithm for reclassification after every 10 iterations,preventing the risk of being trapped in local optimality.At last,the global optimal solution will be found inNi(Ni ?N),and

IV.SIMULATION RESULTS

The preceding content proposes a novel intelligencedriven blind separation algorithm for the LEO satellite communication networks.The above processing process ensures the security and privacy of the wireless networks.The proposed algorithm’s performance will be presented in the following sections.

In the simulation experiments of this paper,the parameter settings are based on Hongyan LEO satellite system,with an orbital altitude of approximately 1100 kilometers.In order to assess the algorithm’s feasibility,UBSS is conducted on experimentally generated frequency hopping signals that exhibit sparsity.

4.1 Signal Processing Performance

The performance of signal processing will be verified in this subsection.The following are the experiment’s parameters[20].

In the case of underdetermined blind separation,there are three source signals and two receiving antennas;based on the actual transmission scenario,the parameter settings for the communication system are presented in Table 1,

Table 1.Simulation parameters.

This proposed algorithm in Section III can solve the UBSS problem.From the Table 1,the mixed signal consists of three transmitted signals,with a total of two receiving antennas.The waveform of the transmitted signals is partitioned into three segments,as depicted in Figure 4.The objective of this algorithm is to effectively extract the individual signals from the mixed signals in a wireless network system,subsequent to their transmission through the actual communication channel.As a result of having two receiving antennas,the temporal representation of the mixed signals upon reception is divided into two segments,which are illustrated in Figure 5.

Figure 4.The primary signals.

Figure 5.The received signals.

Once the set of sampling points for the mixed signals is obtained,the novel GBSSA described in Section III will be applied.This algorithm aims to restore the mixed signals depicted in Figure 5 into three distinct signals,as shown in Figure 6.As anticipated,the waveforms displayed in Figure 4 exhibit a high degree of similarity to those depicted in Figure 6.

Figure 6.The separated signals.

4.2 Performance Discussion on Signal Processing

The proposed algorithm is an optimized version of the greedy algorithm,addressing the limitation of the original greedy algorithm’s tendency to converge to local optima.This enhanced algorithm has been success-fully applied in the BSS process,demonstrating its effectiveness.To assess the efficiency of the algorithm put forward in this research,the “cc” and “PI” are employed as evaluation metrics.The mathematical expressions for these metrics are provided in equations(4)and(5)within the paper[21,22].

Figure 7 shows the experimental results using the correlation coefficient to measure mixed signal separation performance.According to Figure 7,the separation performance of mixed signals improves as SNR increases.When SNR is equal to 10,the separation performance has been significantly improved.Consequently,it can be inferred that the algorithm put forward in this research exhibits a significant capability for signal separation.Simultaneously,our algorithm surpasses theK-means BSS algorithm in terms of separation performance,and it also demonstrates enhanced stability compared to the algorithm presented in this paper[23-25].

Figure 7.The separation performance experiment 1.

To provide a comprehensive evaluation of the algorithm’s performance in this research,the PI is employed as an additional metric for measuring the separation performance.During the course of this simulation experiment,a comparison is made between the proposed algorithm and the DBSCAN BSS algorithm.The experimental results,depicted in Figure 8,illustrate the outcomes of this comparative analysis.The algorithm’s efficacy in signal separation put forth in this paper exhibited superior results compared to the DBSCAN BSS algorithm(Figure 8)[26-28].Furthermore,our proposed algorithm exhibits an enhanced convergence speed,achieving faster convergence compared to DBSCAN BSS.

Figure 8.The Separation Performance Experiment 2.

4.3 Performance Discussion on the LEO Satellite Communication Network Security

The algorithm presented in this paper can potentially improve signal processing performance and network transmission security.Consequently,the LEO satellite communication network security will be discussed in this subsection.Additionally,an encryption algorithm is used in the signal transmission process to improve network communication security[29].

The test environment is the server virtualization platform,and the hardware configuration of the virtual environment is given as follows[30].In addition to the parameters set at the signal physical layer,the parameters in Table 1 are set during wireless signal transmission net.

(1)Throughput

Throughput refers to the quantity of data that can be successfully transmitted within a specific time frame.It serves as a crucial metric for evaluating network performance.The magnitude of throughput is primarily influenced by the network equipment’s internal and external hardware capabilities,as well as the efficiency of the algorithm employed.In cases where the internal and external network hardware of the network equipment remains constant,the efficiency of the algorithm becomes a crucial factor affecting the network throughput[30,31].

This subsection involves conducting two sets of experiments,wherein the internal and external network hardware remains consistent across both groups.The sole distinction between these experiments lies in the choice of algorithms employed.

In Figure 9,the solid red line indicates the throughput over time with the algorithm put forth in this paper,and the blue dotted line indicates the throughput over time without the proposed algorithm.From Figure 8,after using the algorithm in this paper,the algorithm’s convergence speed is faster than without the proposed algorithm,and throughput has also been improved.In other words,the network’s throughput is not reduced while improving the signal processing capacity,improving the system’s spectral efficiency.

Figure 9.Throughput over time.

(2)Invulnerability analysis of the wireless network

The ability of the network to resist attacks is another critical indicator to measure the network.The standard method to measure the invulnerability of the network is whether the network can generally communicate when the network node is attacked.Parameter settings are shown in Table 2.

Table 2.Simulation parameters.

After improving wireless networks’signal processing capability,network invulnerability has also improved in this paper.In other words,it increases network processing capacity and ensures wireless net-work security.To measure the invulnerability of the wireless network,the connectivity performance analysis of network(E)is used.The formula ofEis given in formula(14),

wherelijis the shortest path between nodeiand nodej,and the above formula can measure the overall network connectivity when the network is attacked in any case[14].

The experimental results are shown in Figure 10.In Figure 10,the solid red line indicates the response of wireless networks without any optimization algorithm of signal processing when attacked.The network performance declines rapidly after being attacked.The blue dotted line indicates that the DE (Differential Evolution) algorithm is used in signal processing.The pink dotted line indicates that the PSO (Particle Swarm Optimization) algorithm is used in signal processing.The presence of the black dotted line on the graph serves as an indicator that the algorithm put forth in this paper leads to an improvement in wireless network performance[32].From Figure 10,the invulnerability of the wireless network with the algorithm put forth in this paper is significantly improved and is better than the DE algorithm and PSO algorithm.

Figure 10.Figure.10 Invulnerability analysis of the wireless network.

From Figure 9 and Figure 10,the algorithm put forth in this paper not only improves the throughput of the wireless network but also improves the invulnerability of the wireless network,which is very valuable.

V.CONCLUSION

We have proposed to improve the capability of interference sensing and signal reconstruction in the LEO satellite communication networks by using the greedy sparse optimization UBSS in this paper.The algorithm in this paper solves the problem of signal aliasing from the physical layer,which improves the efficiency of signal transmission,and the security of wireless networks.Moreover,the approach demonstrates commendable performance with limited prior information,successfully achieving the objective of conserving network resources.In the initial stage,we provide a comprehensive overview of the signal thinning technique,encompassing the categorization and practical implementation of clustering algorithms.Following that,we delve into the principle of UBSS and the model utilized for achieving satisfaction of sparse signals.In conclusion,leveraging the inherent traits of wireless networks,a greedy sparse UBSS technique is employed to effectively separate sparse signals even in uncertain conditions.The effectiveness demonstrated by this approach is subsequently evaluated to assess its effectiveness.Ultimately,the simulation outcomes demonstrate the commendable performance and practicality of the algorithm proposed in this paper.

ACKNOWLEDGEMENT

This work is supported by National Natural Science Foundation of China (62171390),Central Universities of Southwest Minzu University (ZYN2022032,2023NYXXS034) and the State Scholarship Fund of the China Scholarship Council(NO.202008510081).