Modeling and realization of real time electronic countermeasure simulation system based on SystemVue

Xiao-rong Tong

College of Computer, Weinan Normal University, Weinan 714099, China

Keywords:Electronic countermeasure system Real-time property System modeling SystemVue Simulation Signal processing Transparent computing

ABSTRACT In this paper, we proposed a new design scheme of real time electronic countermeasure simulation system. This paper mainly expounds the modeling and realization methods of each part of the whole simulation system,and the real-time property of system has been lucubrated.Electronic countermeasure simulation system is the key part of military training of individuals; it can also allow the realistic evaluation of the performance of modern equipments and techniques. As a proof, we have drawn up a series of simulation scenarios,such as radar electronic reconnaissance simulation scenario,to explain the feasibility and the superiority of our modeling scheme in this paper.

1. Introduction

Electronic countermeasure(ECM)is becoming the main combat pattern in modern warfare, so that, it has been valued by a lot of research institutions, and related research achievements of electronic countermeasure have been proposed to the world. Simulation technology is widely applicable in modern electronic countermeasure field,such as a variety of radar simulation systems[1-5], equipment evaluation simulation systems[6-8], and so on.Electronic countermeasure simulation system(ECSS)is a big part of modern simulation system nowadays,it has provided a simulation platform for realistic evaluation of the equipments and the realistic training of individuals[9].So it is necessary to establish a set of full functional ECSS with high stability.In 1988,Klass[10]proposed the application prospects of electronic countermeasure and the related digital signal processing methods.In 2000,Aatre[11],furthermore,proposed the importance of electronic countermeasure for modern warfare. In 2014, Poisel [12] focused on the electronic countermeasure receivers. With the rapid development of electronic technology and computer technology, electronic countermeasure has become a hotspot in the field of modern military. Nowadays,many military related research institutions spend a lot of manpower and material resources to study on electronic countermeasure campaign tactics and related signal processing algorithms,and the significant results of EW have been proposed both in battle tactics and signal processing. But as we can see, most of research achievements above are based on the huge cost of investment,so in this paper, we use simulation technology to establish a ECSS for reducing the cost of research. Definition of simulation is the creation of an artificial situation or stimulus that causes an outcome to occur as though a corresponding real situation or stimulus were presented [13].

Today, there are a series of ECSS modeling and realization methods have been proposed. Hansen [14] has proposed a cost effective method to simulation for electronic countermeasure in 2014,the modeling method of ECSS has been studied in his paper.Satish [15] and his team concentrated their focus on RF front end which is equipped on the front of fighters, and the simulation basically realized the functions of RF front. Lan [16] analyses the C4ISR (Command, Control, Communications, Computers, Intelligence,Surveillance and Reconnaissance)system and its application in modern countermeasure, and some simulation experiments have been carried out based on their proposed simulation system.Liu [17] studied the rotating cross-eye jamming in the electronic countermeasure,the its impact of the electronic countermeasure is evaluated in the literature [17]. Xiao [18] and his team established the radar simulation system based on HLA (High Level Architecture).But there are more or less defects in the simulation systems above,such as low real time performance,poor system simulation degree and unpleasant simulation platform compatibility. In order to solve the problems, we choose the SystemVue software as the simulation platform which can improve the fidelity and the compatibility of simulation system. Real time property can be improved by changing system structure, this is one of the innovation points of this paper.

In this paper, ECSS involves complex signal environment generation (CSEG) unit, electronic countermeasure (ECM) unit and simulation system evaluation(SSE)unit,and the whole simulation system emulates the electronic countermeasure between radars and reconnaissance aircraft.CSEG unit is used to produce complex signal environment,it includes the simulation of radar transmitting signals, interference and clutters. ECM unit can be seen as an electronic countermeasure receiver, which can intercept mixed signals,analysis signal component and estimate the threat level of each radar source signal.In ECM unit, there are three parts: signal intercept module,parameters estimation module and signal sorting module. SSE unit evaluates the operating results of the ECSS. And the distributed architecture is used in the whole ECSS, so there is another question about real-time property of ECSS. In this paper,we change the structure of the simulation system with the principle of transparent computing [19], and the real time performance of the system is improved by using the structure advantages of the transparent computing.

2. Simulation structure

In this paper,ECSS consists of CSEG unit,ECM unit and SSE unit.CSEG unit involves radar signal emitter module, antenna module,clutter & jamming generation module and angle calculation module. ECM unit involves signal intercept judgment module, signal parameter estimation module and signal sorting module. SSE unit involves error evaluation module and simulation unit status assessment module [20]. The whole structure of ECSS is shown in Fig.1.

In Fig.1, we can see the system structure clearly. To emphasize an important point, the module in Fig. 1 represents the function module and does not represent the number of modules. That is to say,we can increase or reduce the appropriate module according to our needs. We can conclude the system simulation as three steps:

First step.CSEG unit generates mixed radar signals,and radiation in a direction which is calculated by angle calculation module.Clutter and jamming parameters are generated by Clutter & jamming generation module in the same time. The mixed signal is transmitted to ECM unit in the form of a signal matrix.

Second step.ECM unit processes the mixed signal by three functional modules, estimation results transmitted to CSEG reservoir in SSE unit, it includes PDWs of each radar signal and source number. The state, including algorithm performance and simulation time,of ECM unit and CSEG unit are transmitted to the SSE unit in the same time.

Third step. Compared the original data of simulation scenario with simulation results of CSEG unit and ECM unit in two reservoirs and the final assessment report is acquired in SSE unit. The report includes simulation unit status,simulation time of each simulation unit and the error evaluation of signal processing algorithms.

In addition,the largest advantage of this structure is that each of modules runs independently, so that, a unit parameter can be changed without affecting the other unit. For example, it can be expanded by increasing the number of CSEG units,and other units are unchanged. So we say that the structure of the ECSS is more flexible, and make it better adapted than others.

In order to realize the real-time simulation of the system, the whole simulation system is connected based on 100 MHz ethernet.Considering the independence of data from different signal sources,each signal generating module of the signal generating unit is allocated to a computer; the environment simulation unit is allocated to a computer;and the alarm unit is allocated to a computer.Because of the large number of signals and the huge amount of data, the network cannot transmit the signal data in real time,resulting in delay, slowing down the response time of the system,and reducing the fidelity of the simulation system.

Fig.1. Structure of ECSS.

Transparent computing model is composed of server and terminal. Users make requests to the server through the network.According to the request,the server sends instructions to the users,and the terminal held by the users generates the resources needed by the users. This computing model enables users to choose resources according to their interests and needs, and reduces the waste of resources; at the same time, servers are only used for storage, not for storage.

Engaged in application calculation, improved user response speed.This mode can also be understood as providing instructions to the remote end, providing hardware locally, obtaining remote technical instructions according to user needs, and generating corresponding data locally.The advantage of this method is that the remote end does not need to provide all the data needed by the user, and guides the user's local hardware to generate corresponding data through instructions, which greatly reduces the amount of data transmitted and shortens the response time.

By comparing the mode structure of transparent computing with the structure of the simulation system,we can find that there are some similarities between them.

2.1. Signal generating unit and server

Both the signal generator and the server provide the original data to the whole system or network. The server transmits a large amount of data stored by the server to the user through the network; the signal generator is the source of the simulation system, and also provides the source signal and transmits it to the signal receiver of the simulation system through the network line for further processing.

2.2. Alarm unit and terminal

Radar warning unit and terminal play the role of receiving and processing data in the system or network. By receiving the data transmitted by the signal generator or server and processing it according to the need, the expected purpose can be achieved.

2.3. Signal eigenvalues and technical instructions

Signal eigenvalues and technical instructions are the transmission media of the system or network.In the simulation system,the signal eigenvalue is used as the transmission medium to transmit to the receiver, and then the receiver restores the signal according to the eigenvalue. Finally, the source signal is generated at the receiver.

3. Simulation units modeling

3.1. ECM unit modeling

In this section, we mainly discussed the modeling method of ECM simulation unit.ECM unit mainly uses ‘mathlang’modules to achieve the function of ECM, therefore, the most important is the signal processing algorithms in the modeling of ECM unit. The following is a detailed analysis of the signal sorting algorithm and signal parameter estimation algorithm.

3.1.1. Signal sorting algorithm

Given M-dimension mixing vectorx（t）= ［x1（t），x2（t），…xM（t）］Tand N-dimension source vectors（t）= ［s1（t），s2（t），…sN（t）］T.

wherex（t）= ［x1（t），x2（t），…xM（t）］Tis the sensor observations,A is aM×Nfull rank mixing matrix andn（t）= ［n1（t），n2（t），…nN（t）］Tis the additive Gaussian white noise with zero mean. The sensor observations are converted into time-frequency(TF)domain by Short Time Fourier Transformation (STFT):

wherex（t，f）,s（t，f） andn（t，f） are the STFT ofx（t）,s（t） andn（t）respectively.

Def.1.TF support point

Def.2.TF single source point

In the TF plane,ifsi（t，f）≫sk（t，f）,we consider that at（t，f）point,there only existsi（t，f）, point （t，f） is the TF single source point ofsi（t，f）.

Suppose the TF single source point's assemblage of signalsk（t）isSo observed signal of any point in the assemblage can be described as

Ignore the noise, Eq. (4) is simplified to

Calculating each channel and themchannel TF ratio

Bringing Eq. (5) into Eq. (6), we obtain

Eq.(7)indicates that if point（t，f）is one TF single source point of signalsk（t）,the TF ratio is constant.So we can get the estimation of vector via detecting all TF single source points. The estimation of vector is

whereLkis the number of single source points. If we consider the array noise, ω is not a constant, but mixed signal has obvious clustering characteristics, we can statistically detect single source points.

Considering array noise, the matrix of TF ratio becomes a complex matrix.So we take the real part and the imaginary part into the histogram statistics respectively to get the matrix. Firstly, extract the real and imaginary parts of each element in the matrix. Then,divide the real and imaginary parts intoM1andM2groups respectively. The column vector corresponding to each group becomes sub-matrix.At last,remove the sub-matrix which number of column less thanK1andK2,and the rest of sub-matrix represent toRjkandIjk. So the time-frequency single source points assemblage corresponding toRjkandIjkis come from one radar source signal.

Whenm=1,the corresponding matrix of time-frequency ratio is

Eq. (8) becomes

Then work out the autocorrelation matrix of the mixed signal,the autocorrelation matrix is

And the singular value decomposition ofis computed through [21]

whereUis a unitary matrix corresponding to the singular value matrixS, andU= ［u1，u2，…uM］.

From the above, only one signal exists at the time-frequency single source point, and combining with the characteristics of singular value decomposition, if there is one signal, the feature vector corresponding to the maximal eigenvalue in the singular value matrixSis the estimation of mixed vector.So the estimation of mixed vector is

whereuSmaxis a vector corresponding to the maximal eigenvalue in unitary matrixU.

All above is just the situation ofm=1,so we should change the value ofmfrom 1 toM,repeat the above process,then all the mixed vector can be worked out.

The estimation method of vector need go through all the value ofm,the result is that the vectors of mixed matrixAare estimated too many times. In order to estimateA, we must clustering all the estimated vectors. But in the context of radar reconnaissance, the number of clustering is unknown, traditional clustering methods are not applicable. A new clustering method based on k-means clustering algorithm is proposed to solve this problem. Specific steps are as follows:

Step. 1Suppose the maximal number of clustering iscmax,clustering the estimated vectors toccategory,c∈｛1，2，…，cmax｝.So mixed matrixAcan be worked out asthe problem becomes how to determine the number of clustering centersc.

Step. 2According to literature [22], a verification technology is presented for calculating the number of clustering centers.

Def. 3.compaction between category.

The expression of compaction is

where ψiis theicategory; σ is mean square error of each mixed matrix estimation, and σ is

So compaction define the separability of estimated mixed matrix,lower degree of compaction represents better clustering result.

Adjusting Eq.(14),the large value ofscat（c）must be classified as one category, naturally the others must be classified as different category.

Step. 3Determine the objective function. Regard the ‘distance’between different clustering centers as objective function.

Def.4.The ‘distance’ between different clustering centers.

Define the “distance” to measure the degree of separation, the expression is

wheredmaxanddmaxrespectively represent the maximum and minimum ‘distance’ between different clustering centers. When the value ofdis（c） achieves maximum value, the numbercis the best classification number,so that the estimation of mixed matrixAis the best estimation. The specific steps are shown in Table 1.

3.1.2. Parameters estimation algorithm

First, under the cyclic correlation transformation, Eq. (1)becomes

After singular value decomposition,Abecomes

whereUsis signal subspace, andUnis noise subspace. Eq. (18)becomes

The specific estimation algorithm is similar to proposed method in literature[23],the difference between them is spatial spectrum.In this paper, the spatial spectrum is

Table 1 Signal sorting method based on detection of time-frequency signal source point.

whereais the vector of mixing matrixA,uis the vector of subspace matrix. And the specific steps are shown in Table 2.

3.2. CSEG unit modeling

In this section, we mainly discussed the modeling method of CSEG simulation unit.CSEG unit is mainly modelled by three model layers, which includes track layer, antenna layer and signal layer.The following is a detailed analysis of modeling method of each layer of CSEG unit [33].

3.2.1. Track layer modeling

Track layer is responsible for generating the track information of each platform, including route (location information), speed, acceleration, etc. In the CSEG unit modeling, there are radar platforms, target platforms and receiver platforms. It needs to be explained that the target platform is the radar warning receiver platform,so the target platform and the platform of receiver are the same.According to the simulation scheme,the radar platforms are still in the ground, and the radar warning receiver platform is moving in the air[24].SystemVue modules are used to establish the radar platform module and the target module (radar warning receiver module), as shown in Fig. 2.

As we can see in Fig.2,the inputs of two modules are roll angle(Roll), pitch angle (Pitch) and heading angle (Yaw). These three angles are the Euler angle,which is used to describe the angle of the rigid body and the scattering area of the target. For the radar platform, the input is zero, the output of radar platform is coordinate information of the target area and the target. A space rectangular coordinate system based on radar platform is established,the heading angle is defined as ψ,the pitch angle is defined as θ and the roll angle is defined as φ. The rotation matrix is defined as

In Eq.(23),Rint1/nvis the rotation matrix of the moving platform and the Z axis,Rint2/nvis the rotation matrix of moving platform and the X axis,Rb/int2is the rotation matrix of the moving platform and Y axis. We can obtain the position of any point in the trajectory of the moving target by using the three-rotation matrix, and the attitude of target is obtained in the same time.After seeking out the air attitude, we can settle the scattering cross section (RCS) of the target platform at the moment.As the target platform's RCS varies with time goes by,it is usually treated as a statistical variable in the field of radar detection and described by probability density function (PDF) [25]. According to the simulation results of literature[25], the RCS of the target platform is modelled by the PDF of lognormal distribution, and the definition PDF of lognormal distribution is

In Eq. (24), σ is the target RCS, μ is the mean value andSis standard deviation. We can get the RCS information of the target platform by modeling the Euler angle.In the different requirements of system simulation,it can be directly used to define the scattering area of the target by RCS parameters in the target platform module.The specific parameters setting of the two modules are shown in Tables 3 and 4.

The position information is defined by longitude, latitude and altitude. The coordinates of radar platform are determined by the simulation thought, the coordinates of target platform are determined according to the default route. The inputs, including coordinate information of radar platform and target's scattering area,are used to guide the radar transmit antenna to produce angle information in antenna layer.

3.2.2. Antenna layer modeling

The antenna layer is responsible for solving the angle between the main beam of radar signals and the target, including the elevation angle and azimuth angle. The modeling principle of the antenna layer is described based on establishment of space rectangular coordinate system in Fig. 3.

As we can see in Fig.3,the point target in the projection ofxoyplane isPxy. The radar platform coordinates (BLH coordinates) are carried out according to literature [26] firstly. The principle is as follows. Assuming the coordinates of radar platform is （Xr，Yr，Zr）.

Table 2 Parameters estimation method based on joint block diagonalization.

Fig. 2. Radar & target platform.

Table 3 Parameters setting of radar platform module.

Table 4 Parameters setting of target platform module.

Fig. 3. Mathematical model of main beam irradiation of radar antenna.

In Eq. (25),Nis the vertical circle radius, and the calculation formula is as follows.

In Eq. (26),ais the semimajor axis of earth ellipsoid ande2=（a2-b2）/a2,bis the semi minor axis of earth ellipsoid. And Eq.(26) can be used to convert the radar platform and the target platform to the geodetic coordinates, then the antenna azimuth angle and the elevation angle can be obtained through Eq.(27)and Eq. (28).

In Eq.(27),Dis the distance between radar platform and targetsetting of the antenna module is shown in Table 5.

In Table 5, the input parameters include the coordinateinformation of the three platforms (from the track layer) and the angle information. According to the mathematical principle of the above, the azimuth angle and elevation angle are calculated, and the angle data are input to the signal layer. In the CSEG unit modeling, the radar platform has no inclination angle, so that the angle information of the radar platform is zero and the angle information of the antenna in radar platform is zero.The platform of radar platform and target platform is a point platform,which is not considered in the angle of the platform itself.

Table 5 Inputs and outputs of antenna module.

3.2.3. Signal layer modeling

The signal layer is responsible for generating the radio frequency (RF) signal, it is also the key of the CSEG unit modeling.After the signal is generated,the signal is transmitted out,and the signal is mixed in the air through the clutter and jamming. Radar signal generation is based on the operating principle of the radar transmitter, including the design of the signal generator module,filter, mixer, amplifier and other corresponding module, the final realization of the radar RF signal[34].Module settings are shown in Fig. 4.

As we can see in Fig. 4, the radar signal generator module is a linear frequency modulation(LFM)signal,after two times of mixing by mixers and the signal frequency is increased to meet the requirements of the RF. Two amplifiers are used to improve the transmit power of the radar signal.Radar signal generation module can produce not only the linear frequency modulation signal but also can produce other signals like continuous wave signal,pseudorandom code phase modulation signal, nonlinear frequency modulation signal, can according to think in different form of a radar platform, set up different forms of radar signal. In the signal generation module, the signal pulse width, pulse repetition period,bandwidth, etc. can be adjusted according to the formation of complex radar signal. Take the linear frequency modulation signal as an example,the radar signal generation module parameters are shown in Table 6.

According to the predetermined set of the content, the specific radar signals are set up combining with the linear frequencymodulation signal parameters setting in Table 6. Radar frequency signal generating unit, which is shown in Fig. 4, forms a radar transmitting signal. In the whole simulation modeling, a radar signal generating unit is a radar platform (because the receiver is not considered),and the simulation process is independent.In the radio frequency generating unit,the filter is designed according to the specific model of the radar transmitter, and the filter parameters are shown in Table 7.

Table 6 Linear frequency modulation signal generation parameter.

The filter includes low pass,high pass,band-pass and band stop filter,and the filter's shape includes IIR and FIR two kinds[27-28],including ‘Bessel’, ‘Butterworth’, ‘Chebyshev I’, ‘Chebyshev II’,‘Elliptic’and ‘Tuned Synchronously’.For FIR filter design,including‘Parks-McClellan’,‘Gaussian’,‘Cosine Raised’and ‘Window’.For the specific style of these filters are not one introduced.In the modeling of the CESG unit, we choose different pass filters to form different center frequency. When the radar radio frequency signal isgenerated, the signal data is transmitted to the radar transmitting antenna, and then, signal is transmitted out. The transmitting antenna module is made up of a radar antenna transmitting module,which is needed to explain the difference between the antenna module and the antenna module.In the antenna layer,the antenna is mainly carried on the coordinate transformation, and the antenna is based on the signal data generated by the radar signal.The signal layer of the transmit antenna module parameters information is shown in Table 8.

Table 7 Filter parameters.

Fig. 4. Design of radar RF signal generating.

The input of the transmit antenna module includes [29]: the radar signal data,the target direction angle,the azimuth angle and the elevation angle between radar platform and the target. In the process of system simulation,the angle of the beam emitted by the transmitting antenna is zero; the radar signal data is the radio frequency signal data generated by the radar signal generation unit;the azimuth angle and the elevation angle are the target angle information. After the signal is transmitted, the signal is inputted to the echo signal, and the echo signal is generated by the echo generating module to generate the echo signal of the target.Modules are shown in Fig. 5.

It should be emphasized that the radar echo generation module(RADAR_EchoGenerator) is based on the relationship between the input signal and the position (distance) of the target platform,including the amplitude attenuation and time delay of the signal in the transmission process.In the background of this paper,the radar signal receiver is in the same position with the target platform, so the echo signal can be considered as a signal to the target platform.The signalu（t） is generated by the radar platform.

In Eq.(29),a（t）is the signal amplitude;φ（t）is the initial phase of the signal. After antenna module, the RF signals（t） is generated.

After the radar signal is transmitted to the target, the signal is changed to

In Eq. (31),R（t） is the distance function between the radar platform and the target platform;σ is the target scattering section area; andcis the speed of light. The propagation attenuation coefficientkis defined as

In Eq. (32),Gis the antenna gain, λ is the wavelength,Ris the distance between the target and the radar signal at the moment.By Eq. (31), we can obtain the radar signal which is after time delay and attenuation, and the signal is the signal environment of the target platform.

Above for the track layer, antenna layer and signal layer were modeling method just for one radar platform and one target platform, we can increase the number of each module, if the specific requirements, just according to the modeling method of repeat, it will not repeat here.

4. Simulation experiments

This section mainly elaborates on the tests of the proposed ECSS to demonstrate the rationality and feasibility of the design scheme.The ECSS provides a new controllable virtual platform for military training,and also a test platform for the proposed signal parameter estimation and signal sorting methods. In this section, the main tests performed on the ECSS pertain to the electronic countermeasure performance of the simulation system. The theoretical derivation is validated through experimental results to verify the rationality of the design scheme.

Before analyzing the tests performed on the ECSS,it is necessary to set the context of the tests. The ECSS is divided into red, white and blue parts,the red part being a fighter combat simulation unit,the white part being the director of combat simulation, while the blue part is an air defense combat simulation unit.

4.1. Electronic reconnaissance simulation scenario

Let us assume that the blue part has recently adjusted the deployment of defensive positions, for the purpose of strengthening the air defense force available.In order to obtain air defense system equipment configuration information as quickly as possible from the blue part,the headquarters of the red part decided on the implementation of electronic reconnaissance on their part to obtain the relevant information in an effective manner.

The blue part is an air defense combat simulation unit, the configuration of which includes a brigade command, two antiaircraft artillery battalions and an anti-aircraft missile camp. Each anti-aircraft artillery battalion consists of three artillery units,while each successive level artillery unit includes eight batteries,one radar and one command vehicle; each missile battalion is equipped with one radar, two mobile missile launcher units, and one command vehicle. The commander of the battalion and the brigade's command communicate over the Internet to achieve information transmission; the radar functions as the eyes of the combat unit,used to survey the airspace and guide the deployment of the combat weapons.

The red part is a fighter combat simulation unit;it includes one aircraft, which is equipped with one radar warning receiver. According to the implemented scenario,the blue part uses the aircraft as a vanguard to carry out reconnaissance missions,the purpose of which is to obtain as much as relevant information as possible regarding radar emissions.

Table 8 Transmit antenna parameters.

Fig. 5. Signal echo generating modules.

The white part simulates the commander, who issues the necessary orders to both the red and the blue part to ensure the smooth running of the exercise.

At the beginning of the simulation, according to the red part's operational command orders, the fighter plane take off and flies according to a predetermined path flight,until it enters an airspace where the No.1, No. 2, No. 4 and No. 7 surveillance radars detect target for the first time,and the relevant information is reported to the air defense brigade headquarters, while the blue part changes its operational status and all its radars start to look for the target.When the white part issues the order to the blue part to locate the target, this simulation experiment begins, and the relevant measurement of the simulation time is set to zero.

This test of the simulation system evaluates the process of deploying electronic countermeasures from the moment the simulation time is equal to zero.The following will be described in detail in comparison with the parameters of the weapon platform.

In Table 9, the radar sources' configuration is shown, in which‘AG’ is the abbreviation for ‘Antiaircraft Gun’; ‘GM’ is the abbreviation for ‘Guided Missile’. Numbers 1 to 6 are the anti-aircraft battalion's radar emitters, while 7 to 9 correspond to guided missile radar sources.The coordinates consist of the longitude,latitude and altitude.The radar warning receiver configuration is shown in Table 10.

4.2. System interface test

According to the simulation scenario, the blue part consists of nine radar platforms, while the red part consists of one aircraft platform.At the top-level design of the simulation system interface,we can only see the red and blue parts and the relevant information exchanged between the platforms,while the details of the platform cannot be displayed.Using the SystemVue software for the process of top-level design, we simplified the design to allow users of the top-level interface to clearly visualize the concepts, and better comprehend the events and concepts of the simulation.The actual top-level interface designed for the simulation is shown in Fig. 6.

As we can see in Fig.6,in the interface designed for this test,we can clearly see the red and blue parts of the ECSS configuration.Theinterface depicts the outermost level of the simulation platform's characteristics. The aircraft platform interface is located at the bottom of Fig.6.In order to represent the aircraft platform module,a signal processing module is used reflected in the design,but in the actual combat simulation test interface [30,31], three signal processing not visible to the user are located in the bottom-level design of the aircraft platform.Before the start of the simulation test,there are some known data parameters, such as the target's tracking information, RCS (Radar Cross Section), and so on. No information about the blue part is known available to the red part [32]. The corresponding bottom-level design is shown in Fig. 7.

Table 9 Radar deployment of blue part.

Fig.7 shows the bottom-level design of each module of both the red and blue parts in the simulation system during its testing.The corresponding diagrams for the red and blue parts were implemented in SystemVue software's environment.Fig.7(a),(b),and(c)are the blue part's air defense radar position modeling modules,including the radar signal generation unit and each radar platform's coordinate position information; Fig. 7(d) is the aircraft model of the red part,including the signal acquisition and signal parameters estimation modules, the underlying signal sorting module and aircraft tracking coordinate sets.Fig.7 reflects all simulated aspects for each module design and parameter settings. The pulse descriptor words(PDW)of the blue part are presented in Table 11.

The purpose is to process the mixed radar signals intercepted from the air and eventually obtain the pulse descriptor words of each radar signal. The test results obtained during the simulation test are described and analyzed in the following subsection.

4.3. System test results and analysis

This section mainly analyzes the test results of the ECSS.The test platform was set up according to the simulation scenario presented above.

The blue part generated the radar signals aimed towards the airspace at the beginning of the simulation test, according to the parameters' settings. The number of signals which can be intercepted by the ECM unit is 5, respectively, Radar_1, Radar_2, Radar_4, Radar_7. Taking into account the parameters of the transmitted signal, the transmitting signals of the 4 radars were detected as shown in Fig. 8.

Fig.8 shows the radar signals echoes of the blue part.Because of the different signal parameters and the different platform coordinates,the radar signal echoes are detected at different angle by the ECM unit. The blue lines in the figure indicate the signal envelope.

After the source signals of the blue part are generated,the signal is transmitted out by the antenna module and the signal is transmitted to the front of the ECM unit.The radar signals are randomly mixed by using the mixing matrix.So,according to the system test operation, the final iteration of the hybrid matrix is the complex random matrix shown below:

Table 10 Flight & radar warning receiver deployment of red part.

Fig. 6. System Interface design.

Fig. 7. Bottom-level designs of the simulation units.

In Eq. (33), ‘T’ denotes the transpose of the matrix. The mixed matrix is obtained by multiplying the source signal matrix with the mixed matrix. Each row of the matrix represents the mixed signal data required to be processed by the receiver.The basic parameters of the SystemVue software environment simulation were set according to the previous section.The number of sampling points of the radar signal data obtained by the simulation was 9991.

When the echo signals are generated,the radar signals detected from the different coordinates are transmitted to the ECM unit,and the angle of arrival of each signal is detected,as shown in Table 12.

Table 12 shows the results of the detection of the angle of arrival of the various echoes, which will be used to estimate the angle of arrival of the actual radar signal. After the signal has intercepted,the signal parameters, which are related to the number of the echoes and the signal arrival angle estimation, are obtained. The results are shown in Fig. 9.

Fig. 9 shows the results of the mixed signal spatial spectrum from the -90 to 90°, as obtained using SystemVue software.Fig. 9(a) shows the results obtained using a step size of 2 deg; (b)are the results of a 1 deg step size;(c) are results obtained using a 0.1 deg. As the step size decreases, the simulation duration increases, so the search step cannot be too small, otherwise the simulation time will be very long,and will not correspond to realtime applications.Therefore,the estimated value of the signal DOA chosen is of an appropriate order of magnitude,which in our case,the estimation step size was 0.1°.

When the DOA of the mixed signal has been estimated, the mixed signal is fed into the signal sorting section,and the data are fed into the signal to estimate the number of source signals. The radar signal is separated from the mixed signal and the principle of the algorithm is no longer according to the signal sorting method based on the time frequency dominant region detected by the preamble. After the signal sorting module, the estimate of the mixed matrix will be the following:

Fig. 7. (continued).

Comparing the original mixed matrix with the mixed matrix estimate,it is evident that the estimation results are different from those of the original matrix.However,it can be shown that a certain column vector of the estimated matrix is linearly related to a column vector in the original matrix. It should be noted that the real parts will be different for different values of the column vector,that is,the general will not appear.Therefore,the final signal recovered will be different in amplitude than source signal. The specific recovery method is as follows.

The source signals are recovered by using the generalized inverse of the matrix

In Eq.(35),the generalized inverse matrix of the mixed matrix is obtained for the generalized inverse of the mixed matrix. The mixed matrix is estimated by full rank decomposition.

In Eq. (36), the matrix is of full rank, and can be obtained through elementary transformations. It can also be written as

Finally, the pulse of the source signal is obtained by recovering the original signal, as shown in Table 13.

Fig. 7. (continued).

Fig. 7. (continued).

Table 11 PDWs of each radar signal.

As we can see in Table 13, the final output signal pulse description words are obtained by the simulation system, and the estimation accuracy of the radar signals obtained using the fighter platform (red part) is higher than that of the blue part. Therefore,we can conclude that the red part is the “winner”of this electronic countermeasure simulation. The simulation results demonstrate the feasibility of the design and implementation of ECSS.

The final and the original signal pulse descriptor words are different in terms of the sequence and signal amplitude.This is due to the introduction of the blind signal separation method;the radar signal pulse description words of the sequence are different and the estimated signal amplitude is also changed, due to the inherent characteristics this method. As the radar warning system is concerned with the accuracy of the pulse descriptor words of the radar signal, the change of the order and magnitude is not considered significant.

5. Conclusions

A signal parameter estimation algorithm, a signal sorting algorithm and an alarm effciiency test were presented for simulation system modeling. For the testing of the algorithm, a clear testing scenario was defnied and a corresponding test platform was designed.The test was conducted in order to examine two aspects of the proposed algorithm: its feasibility and its superiority compared to existing methods. The feasibility of the proposed method was proved through the analysis of the experimental results.The superiority of the proposed signal processing algorithm was demonstrated through a comparison with traditional signal processing methods. During the testing of the simulation system,its alarm performance was also analyzed. The test system was divided into three parts: red, white, and blue three parts. The test results were analyzed using SystemVue software environment,and the feasibility of the system was proved.

Fig. 8. Radar signal echoes of the blue part.

Table 12 DOAs of radar signals of blue part.

Fig. 9. The results of mixed signal spectrum estimation.

Table 13 The results of PDWs.

Acknowledgements

This work was supported by Scientific Research Program Funded by Shaanxi Provincial Education Department (Program No.18JK0286), and Weinan Science and Technology Initiatives Fund program(Program No.2019JCYJ-2-6),and Teaching Reform Project of Weinan Normal University (Program No. JG201704), Industry-University-Cooperation Education Project of the Ministry of Education of China (Program No. 201702030020, 201801082110);Weinan Normal University’s Characteristic Discipline Construction Project Electronic Information (Computer Technology) Master’s Degree Point Construction Project(18TSXK06).And thank Dr Cheng Cheng for providing SystemVue software platform for simulation.