# Modeling and analyzing interference signal in a complex electromagnetic environment

- Chun-tong Liu
^{1}, - Rong-jing Wu
^{1}, - Zhen-xin He
^{1}Email author, - Xiao-feng Zhao
^{1}, - Hong-cai Li
^{1}and - Peng-zhi Wang
^{1}

**2016**:1

https://doi.org/10.1186/s13638-015-0498-8

© Liu et al. 2015

**Received: **29 September 2015

**Accepted: **15 December 2015

**Published: **4 January 2016

## Abstract

Electronic jamming is the key technology of electronic countermeasure, for which models and simulations are studied on noise jamming, deception jamming, and chaff jamming. In the noise jamming, the simulation analysis of radio frequency noise jamming is conducted and the theoretical models of other forms of noise jamming are built. The simulation analysis of range-gate pull off (RGPO) is carried out in the deception jamming. In addition, theoretical modeling and simulation analysis of chaff jamming are carried out with the Monte Carlo method. Simulation results show that the models are correct and can be used to simulate the statistical characteristics of chaff jamming. With the development and wide application of electronic technology, radar, communication, navigation, and IFF signals constitute a complex electromagnetic environment. It is a must to study electronic jamming technology in the complex electromagnetic environment, which will play an indispensable role in the construction of information team and victory in the countermeasure of information technology.

## Keywords

## 1 Introduction

The Gulf war and the Kosovo war show that the electronic countermeasure kicks off and exists in the whole process of war, affecting the war process and pattern, which is the mainstream and a significant feature of information warfare [1]. Radar jamming and anti-jamming ability have become the key factors in the electronic countermeasure. The detection and intentional electronic interference of launch task of the foreign spy satellites are inevitable to affect the electromagnetic safety of the launch site, which seriously threatens the space launch task of each country [2]. In complex electromagnetic environments, the electromagnetic interference has greatly damaged the performance of the guidance equipment. Guidance equipment under electromagnetic interference cannot be properly guided and lose targets. Therefore, it is significant to study electromagnetic interference in a complex electromagnetic environment, which will play an indispensable role in the construction of information team and victory in the countermeasure of information technology. It also has practical significance in anti-interference research for guidance equipment.

Electronic attack is the fighting force which can destroy the target directly by the active use of an electromagnetic spectrum or directional energy. Electronic attacks against radar include non-destructive actions and destructive actions. Non-destructive action is to reduce or offset the operational effectiveness of enemy radar by using suppressing jamming and deception jamming [3].

The development of electronic jamming and anti-jamming technology has brought unprecedented challenges to the guidance equipment. Radar jamming reduces the lethality of the guidance equipment yet improves the survival ability of the target [4]. The new strategy should be proposed in air defense guidance equipment system to meet the current electronic warfare needs after carefully studying the development of airborne electronic countermeasure technology [5]. At present, there have been a large number of researches concerning the electronic interference, but most of them are based on a certain kind of interference. The research scope is relatively scattered and lacks comprehensive interference analysis and model study [6]. This paper analyzes the theory of mathematical modeling and simulation of common types of electronic jamming, which will play an important role in the identification of enemy electronic jamming and electronic jamming to enemies. It has important practical significance in the current form of electronic warfare technology and pushes forward the researches of radar anti-jamming technology.

## 2 Classification and mathematical model of radar jamming

Electronic countermeasure is an action where both sides interfere with the equipment’s usage of the electromagnetic spectrum and electromagnetic information and attack the other side and their equipment by using electromagnetic energy or directional energy; in the meantime, it guarantees equipment normal function and personnel’s safety [7]. Radar countermeasure and counter-countermeasure is one of the important contents of electronic warfare. The interference of radar is mainly classified into background and artificial interference, and the latter is the focus of our study. Artificial interference can be classified into active jamming and passive jamming. Active jamming can be further classified into the suppression of jamming and deception jamming according to the principle of interference signal. Under the complex electromagnetic environment, how to analyze the jamming effect is of great value [8]. The mathematical modeling and analysis of common jamming signals are discussed in the following parts.

### 2.1 Radio frequency noise jamming

Masking jamming is used to cover or flood useful signals by using noise or jamming signals similar to noise and to prevent radar from detecting targets. Its basic principles are as follows: internal noise and external noise exist in any radar, detection of radar targets is conducted in these noises, and the detection is based on a certain probability criterion.

*u*

_{n}(

*t*) satisfies the Rayleigh distribution and

*ϕ*(

*t*) satisfies uniform distribution in [0,2pi],

*u*

_{n}(

*t*) and

*ϕ*(

*t*) are independent of each other, and

*ω*

_{j}is the carrier frequency and it is a constant.

*σ*

^{2}is the average power of noise, ∆

*f*

_{j}is the interference bandwidth, and

*f*

_{j}is the center frequency of RF noise jamming. If the medium frequency of the receiver has a rectangular feature, after the radio frequency noise is received by the receiver, the output interference signal of the medium-frequency amplifier is still narrowband Gauss noise, and its power spectrum

*G*

_{j}(

*f*) is as follows:

*f*

_{i}is the center frequency of the receiver and ∆

*f*

_{r}is the medium bandwidth of the receiver. The correlation function of the RF noise can be obtained according to Fourier transform relation between the correlation function and the power spectrum density function of the signal. The correlation function of the RF noise satisfies

*k*is the amplification factor of the linear detector).

In practice, the RF noise signals and radar signals are often simultaneously entered into the radar receiver and build the model for the mixed signals of both.

*u*

_{i}(

*t*) is the amplitude of the synthesized signal and the probability distribution is the rice distribution.

### 2.2 Range-gate pull off

Range-gate pull off (RGPO) can be applied to radar systems of different ranging systems. Its basic principle is to make radar tracking systems track interference signal whose distance is gradually farther away from the target position and then to make radar fail to capture target position information.

RGPO can be roughly divided into three stages: stop delay period, towing period, and termination period. In the first period, jammers amplify and forward signals quickly to make time delay difference between the target echo and itself short enough to enter the radar range gate; due to its higher power of interference signal, the range gate cannot lock the exact interference signal. When the stop delay period ends or when the range gate locks interference signal, it comes to the second period, towing period. In this period, time delay of a jammer’s forwarding signal is gradually extended to increase distance between the interference signal and target signal in a range dimension. Because the range gate is locked in the interference signal, the target has been dragged out of the range gate gradually. Then the change rule of time delay of the interference signal can be expressed as *dτ*(*t*)/*dt* = *v*(*t*), where *τ*(*t*) and *v*(*t*) are the towing distance and towing speed, respectively. Finally, when the target is dragged out of the range gate, it comes to the termination period, in which the jammer is turned off or stops forwarding the interference signal, and the radar returns back to the search state because there is no signal within the range gate.

*A*

_{s}is the signal amplitude of the real target;

*A*

_{j}is the amplitude of the interference signal and

*A*

_{j}

*> A*

_{s};

*ω*

_{c}is the carrier frequency of the radar;

*ω*

_{d}is the Doppler frequency;

*R*(

*t*) is the real distance of the target; Δ

*t*

_{j}(

*t*) is the delay time of the signal of RGPO compared with the normal echo signal of the target and it changes with time; and

*C*is the speed of light.

*R*is the distance of the target;

*V*

_{1}is the velocity of the target;

*V*

_{2}is the towing speed of the linear towing; and

*a*is the towing acceleration of the parabolic towing. According to the principle of radar delay ranging, the distance change of the interference signal is converted into time delay and we can obtain

### 2.3 Chaff jamming

Chaff jamming takes advantage of a large number of randomly distributed metallic scatterers which are put into the air to produce scattering wave and interferes with radar [9]. Chaff jamming is widely used in electronic warfare because of its simple manufacturing, low cost, and strong applicability. The conventional chaff scattering mechanism is resonant scattering, so it has a narrow band. It will increase complexity to use broadband. The Monte Carlo method for the stochastic problems mainly consists of three steps: the first step is to build model of problems; the second step is to conduct statistical experiments; and the third step is to solve the problem based on the experimental results.

When analyzing chaff echo power, we regard each chaff as a single unit and only consider the first reflection. Assuming that the echo signal delay is known, the echoes of all chaff units are superimposed together to get the chaff cloud echo.

*S*

_{i}(

*t*) is the radar emission signal,

*S*(

*t*) is the radar receipt signal,

*c*is the speed of light;

*t*

_{0}is the echo delay; ∑(

*ct*

_{0}/2) is the average power of the chaff cloud reflection, and

*Z*(

*t*) is a zero-mean complex Gaussian random processes and it satisfies

*E*[|

*dZ*(

*t*)|

^{2}] =

*dt*.

*A*is the volume of chaff cloud. The mean value of the echo power is as follows:

The simulation method is used to solve the frequency response to chaff cloud. Let *X*(*T*) and *Y*(*T*) be two zero-mean real normal processes.

*E*[|

*dZ*(

*t*)|

^{2}] =

*dt*, the zero-mean complex Gauss random process can be expressed as

The above equation can be used to express the chaff cloud echo signal in the frequency domain, and the corresponding signal form in the time domain can be obtained after Fourier inverse transform.

## 3 Computer simulation analysis

### 3.1 RF noise jamming simulation

It can be seen from the graph that the envelope of the RF noise obeys the Rayleigh distribution and the phase obeys the uniform distribution, which is consistent with the theoretical analysis.

*u*

_{ s }/

*σ*

_{ i }= 0.1; 1; 10, the computer simulation results of the signal superimposed with noise are shown in Figs. 6, 7, and 8. It can be seen that the output amplitude of the receiver under RF noise jamming shows the following distribution. Echo signals’ magnitude is no longer the original form of a rectangular pulse under the influence of RF noise jamming and varies around the average potential of noise. As the interference power increases, the signal is submerged in the noise interference and it cannot be detected and identified.

### 3.2 RGPO simulation

*R*= 4 km,

*V*

_{1}= 0 m/s,

*t*

_{1}= 0.3 ms,

*t*

_{2}= 2 ms,

*V*

_{2}= 10

^{6}m/s, and jamming to signal ratio is 12 dB. A flow chart of deception jamming simulation algorithm is shown in Fig. 9.

### 3.3 Chaff jamming simulation

^{8}dipoles. Phase encoding signal emitted by radar is simulated at a medium frequency of 55 MHz and an algorithm flow chart of simulation is shown in Fig. 11.

Computer simulations of RF noise jamming, RGPO, and chaff jamming are carried out in this paper. According to the results of computer simulation, the simulation achieves the expected goal and correctly reflects the mathematical model. By comparing the simulation results of the different parameters, the related interference process can be simulated.

In the simulation of RF noise jamming, the process is simulated that the useful signal is submerged by the noise signal and cannot be detected or identified. The simulation characteristics of the envelope and phase of the noise signal are consistent with the theoretical analysis. The results of RGPO simulation and chaff jamming simulation are the same as what is expected.

## 4 Conclusions

For new radar electronic systems and new communication equipment that continue to emerge, the corresponding electronic countermeasure tactics technology has also been rapidly developed. To meet the objective requirements of the electronic warfare theory research and practical testing, many electronic warfare simulation systems have been produced at home and abroad with the help of the rapidly developed modeling theory and computer network technology. Therefore, it is urgent for electronic countermeasure researchers to comprehend and master the system simulation technology in time [10]. We analyzed the mathematical model of the common electronic interferences in a complex electromagnetic environment and conducted computer simulation of RF noise jamming, RGPO, and chaff jamming. Simulation analyses verify the validity of the mathematical model of the electronic interference. This study will be helpful in further study on the electronic interference and suppression.

## Declarations

### Acknowledgements

This work is partially supported by the National Nature Science Foundation of China under Grant 41404022 and the Nature Science Foundation of Shannxi Province under Grant 2015JM4128.

**Open Access**This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

## Authors’ Affiliations

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