Liu et al. EURASIP Journal on Wireless Communiations and Networking (016) 016:1 DOI 10.1186/s13638-015-0498-8 RESEARCH Modeling and analyzing interferene signal in a omplex eletromagneti environment Chun-tong Liu, Rong-jing Wu, Zhen-xin He *, Xiao-feng Zhao, Hong-ai Li and Peng-zhi Wang Open Aess Abstrat Eletroni jamming is the key tehnology of eletroni ountermeasure, for whih models and simulations are studied on noise jamming, deeption jamming, and haff jamming. In the noise jamming, the simulation analysis of radio frequeny noise jamming is onduted and the theoretial models of other forms of noise jamming are built. The simulation analysis of range-gate pull off (RGPO) is arried out in the deeption jamming. In addition, theoretial modeling and simulation analysis of haff jamming are arried out with the Monte Carlo method. Simulation results show that the models are orret and an be used to simulate the statistial harateristis of haff jamming. With the development and wide appliation of eletroni tehnology, radar, ommuniation, navigation, and IFF signals onstitute a omplex eletromagneti environment. It is a must to study eletroni jamming tehnology in the omplex eletromagneti environment, whih will play an indispensable role in the onstrution of information team and vitory in the ountermeasure of information tehnology. Keywords: Eletromagneti environment, Eletroni jamming, Mathematial model, Simulation analysis 1 Introdution The Gulf war and the Kosovo war show that the eletroni ountermeasure kiks off and exists in the whole proess of war, affeting the war proess and pattern, whih is the mainstream and a signifiant feature of information warfare [1]. Radar jamming andanti-jammingabilityhavebeomethekeyfators in the eletroni ountermeasure. The detetion and intentional eletroni interferene of launh task of the foreign spy satellites are inevitable to affet the eletromagneti safety of the launh site, whih seriously threatens the spae launh task of eah ountry []. In omplex eletromagneti environments, the eletromagneti interferene has greatly damaged the performane of the guidane equipment. Guidane equipment under eletromagneti interferene annot be properly guided and lose targets. Therefore, it is signifiant to study eletromagneti interferene in a omplex eletromagneti environment, whih will play an indispensable role in the onstrution of information team and vitory in the ountermeasure of information tehnology. It also has pratial signifiane in anti-interferene researh for guidane equipment. * Correspondene: hezhenxin1986@16.om Xi an Researh Institute of High Tehnology, Xi an ity, Shaan Xi Provine 71005, China Eletroni attak is the fighting fore whih an destroy the target diretly by the ative use of an eletromagneti spetrum or diretional energy. Eletroni attaks against radar inlude non-destrutive ations and destrutive ations. Non-destrutive ation is to redue or offset the operational effetiveness of enemy radar by using suppressing jamming and deeption jamming [3]. The development of eletroni jamming and antijamming tehnology has brought unpreedented hallenges to the guidane equipment. Radar jamming redues the lethality of the guidane equipment yet improves the survival ability of the target [4]. The new strategy should be proposed in air defense guidane equipment system to meet the urrent eletroni warfare needs after arefully studying the development of airborne eletroni ountermeasure tehnology [5]. At present, there have been a large number of researhes onerning the eletroni interferene, but most of them are based on a ertain kind of interferene. The researh sope is relatively sattered and laks omprehensive interferene analysis and model study [6]. This paper analyzes the theory of mathematial modeling and simulation of ommon types of eletroni jamming, whih will play an important role in the identifiation of enemy eletroni jamming and eletroni jamming to enemies. It has important pratial signifiane in the urrent 015 Liu et al. Open Aess This artile is distributed under the terms of the Creative Commons Attribution 4.0 International Liense (http://reativeommons.org/lienses/by/4.0/), whih permits unrestrited use, distribution, and reprodution in any medium, provided you give appropriate redit to the original author(s) and the soure, provide a link to the Creative Commons liense, and indiate if hanges were made.
Liu et al. EURASIP Journal on Wireless Communiations and Networking (016) 016:1 Page of 9 form of eletroni warfare tehnology and pushes forward the researhes of radar anti-jamming tehnology. Classifiation and mathematial model of radar jamming Eletroni ountermeasure is an ation where both sides interfere with the equipment s usage of the eletromagneti spetrum and eletromagneti information and attak the other side and their equipment by using eletromagneti energy or diretional energy; in the meantime, it guarantees equipment normal funtion and personnel s safety [7]. Radar ountermeasure and ounter-ountermeasure is one of the important ontents of eletroni warfare. The interferene of radar is mainly lassified into bakground and artifiial interferene, and the latter is the fous of our study. Artifiial interferene an be lassified into ative jamming and passive jamming. Ative jamming an be further lassified into the suppression of jamming and deeption jamming aording to the priniple of interferene signal. Under the omplex eletromagneti environment, how to analyze the jamming effet is of great value [8]. The mathematial modeling and analysis of ommon jamming signals are disussed in the following parts..1 Radio frequeny noise jamming Masking jamming is used to over or flood useful signals by using noise or jamming signals similar to noise and to prevent radar from deteting targets. Its basi priniples are as follows: internal noise and external noise exist in any radar, detetion of radar targets is onduted in these noises, and the detetion is based on a ertain probability riterion. Radio frequeny noise jamming is one of the effetive ways of masking jamming. The radio frequeny (RF) noise jamming an be obtained by diret amplifiation of mirowave noise, and its mathematial model an be expressed as follows: u j ðþ¼u t n ðþ t os ω j t þ ϕðþ t ð1þ where u n (t) satisfies the Rayleigh distribution and ϕ(t) satisfies uniform distribution in [0,pi], u n (t) and ϕ(t) are independent of eah other, and ω j is the arrier frequeny and it is a onstant. The noise is a power signal and its power is limited, but the energy is unlimited. So the power spetrum is used to express its frequeny harateristis. Its power spetral density expression is 8 σ >< f f G j ðþ¼ f Δf j Δf j j ðþ >: 0 others where σ is the average power of noise, Δf j is the interferene bandwidth, and f j is the enter frequeny of RF noise jamming. If the medium frequeny of the reeiver Fig. 1 Simulation flow hart of RF noise has a retangular feature, after the radio frequeny noise is reeived by the reeiver, the output interferene signal of the medium-frequeny amplifier is still narrowband Gauss noise, and its power spetrum G j (f) is as follows: G j ðþ¼h f j 8 i ðþ f j G j ðf f i Þ >< σ i jf f ¼ Δf i j Δf r i >: 0 others ð3þ where f i is the enter frequeny of the reeiver and Δf r is the medium bandwidth of the reeiver. The orrelation funtion of the RF noise an be obtained aording to Fourier transform relation between the orrelation funtion and the power spetrum density Fig. Time-domain wave of band-limited RF noise
Liu et al. EURASIP Journal on Wireless Communiations and Networking (016) 016:1 Page 3 of 9 Fig. 3 Envelope distribution and phase distribution of RF noise jamming. a The envelope obeys the Rayleigh distribution. b The phase obeys the uniform distribution funtion of the signal. The orrelation funtion of the RF noise satisfies R i ðþ¼ τ Z 0 G i ðþosπfτdf f ¼ σ sinπδf r τ i osπδf πδf r τ i τ ð4þ After the linear detetor, the Gauss white noise distribution beomes Rayleigh distribution P i ðu v Þ ¼ U v σ v U v σ e v; U v > 0 ð5þ where σ v ¼ k σ (k is the amplifiation fator of the linear detetor). In pratie, the RF noise signals and radar signals are often simultaneously entered into the radar reeiver and build the model for the mixed signals of both. Set target eho signal as single-frequeny signal, and then st ðþ¼u s osðw 0 tþ ð6þ The expression of the mixed signals of the output signal of the reeiver and the noise is u j ðþþst t ðþ¼u n ðþ t os ω j t þ ϕðþ t þ us osðw 0 tþ ¼ u i ðþ t osðω i t þ ϕðþ t Þ ð7þ where u i (t) is the amplitude of the synthesized signal and the probability distribution is the rie distribution.. Range-gate pull off Range-gate pull off (RGPO) an be applied to radar systems of different ranging systems. Its basi priniple is to make radar traking systems trak interferene signal whose distane is gradually farther away from the target position and then to make radar fail to apture target position information. RGPO an be roughly divided into three stages: stop delay period, towing period, and termination period. In the first period, jammers amplify and forward signals quikly to make time delay differene between the target eho and itself short enough to enter the radar range gate; due to its higher power of interferene signal, the range gate annot lok the exat interferene signal. When the Fig. 4 Autoorrelation funtion of RF noise Fig. 5 Power spetral density of RF noise
Liu et al. EURASIP Journal on Wireless Communiations and Networking (016) 016:1 Page 4 of 9 Fig. 6 Performane simulation of eho with RF noise when u s /σ i = 0.1. a Time-domain waveform. b Power spetral density stop delay period ends or when the range gate loks interferene signal, it omes to the seond period, towing period. In this period, time delay of a jammer s forwarding signal is gradually extended to inrease distane between the interferene signal and target signal in a range dimension. Beause the range gate is loked in the interferene signal, the target has been dragged out of the range gate gradually. Then the hange rule of time delay of the interferene signal an be expressed as dτ(t)/dt = v(t), where τ(t) andv(t) are the towing distane and towing speed, respetively. Finally, when the target is dragged out of the range gate, it omes to the termination period, in whih the jammer is turned off or stops forwarding the interferene signal, and the radar returns bak to the searh state beause there is no signal within the range gate. Based on the analysis of the target eho model, the target eho signal reeived by the reeiver an be obtained by st ðþ¼a s exp jðω þ ω d Þ t Rt ðþ ð8þ The signal of RGPO satisfies Jt ðþ¼a j exp jðω þ ω d Þ t Rt ðþ Δt j ðþ t ð9þ where A s is the signal amplitude of the real target; A j is the amplitude of the interferene signal and A j >A s ; ω is the arrier frequeny of the radar; ω d is the Doppler frequeny; R(t) is the real distane of the target; Δt j (t) is the delay time of the signal of RGPO ompared with the normal eho signal of the target and it hanges with time; and C is the speed of light. Assuming that the target is moving at a onstant speed, when adopting the linear or paraboli dragging ways, the distane funtion of the false target an be expressed as follows: where R is the distane of the target; V 1 is the veloity of the target; V is the towing speed of the linear towing; and a is the towing aeleration of the paraboli towing. Aording to the priniple of radar delay ranging, the distane hange of the interferene signal is onverted into time delay and we an obtain 8 0 0 t < t 1 ðstop delayperiodþ >< v Δt j ðþ¼ t ðt t 1 Þor a ðt t 1 Þ t 1 t < t ðtowing periodþ >: jamming off t 1 t < t ðtermination periodþ ð11þ.3 Chaff jamming Chaff jamming takes advantage of a large number of randomly distributed metalli satterers whih are put into the air to produe sattering wave and interferes with radar [9]. Chaff jamming is widely used in eletroni warfare beause of its simple manufaturing, low ost, and strong appliability. The onventional haff sattering mehanism is resonant sattering, so it has a narrow band. It will inrease omplexity to use broadband. The Monte Carlo method for the stohasti problems mainly onsists of three steps: the first step is to build model of problems; the seond step is to ondut statistial experiments; and the third step is to solve the problem based on the experimental results. When analyzing haff eho power, we regard eah haff as a single unit and only onsider the first refletion. Assuming that the eho signal delay is known, the ehoes of all haff units are superimposed together to get the haff loud eho. Based on the above assumptions, the haff loud eho signal an be treated as a random sampling of zero-mean R j ðþ¼ t 8 < R þ v 1 t 0 t < t 1 ðstop delay periodþ R þ v 1 t 1 þ v ðt t 1 Þ or R þ v 1 t 1 þ at t ð 1 Þ t 1 t < t ðtowing periodþ : jamming off t 1 t < t ðterminaton periodþ ð10þ
Liu et al. EURASIP Journal on Wireless Communiations and Networking (016) 016:1 Page 5 of 9 Fig. 7 Performane simulation of eho with RF noise when us/σi = 1. a Time-domain waveform. b Power spetral density omplex Gauss stohasti proess. Statistial integral form of the haff loud eho signal is as follows: rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Z X S 0 ðt Þ ¼ S i ðt t ÞÞ ð1þ t dz ðt Þ where Si(t) is the radar emission signal, S(t) is the radar reeipt signal, is the speed of light; t0 is the eho delay; (t0/) is the average power of the haff loud refletion, and Z(t) is a zero-mean omplex Gaussian random proesses and it satisfies E[ dz(t) ] = dt. The average power of the haff loud refletion is derived as Z X λ G t ðiþ ρ σ λ= expð γ ÞdV t ¼ Pt 3 R4 ð4π Þ E S 0 ðf 1 ÞS 0 ðf Þ ¼ S i ðf 1 ÞSi ðf Þ Z exp½ πiðf 1 f Þt ð15þ Based on simple sattering theory, the frequeny response to haff loud an be expressed as Z S ðf Þ ¼ rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi X expð πift Þ t dz ðt Þ ð13þ where A is the volume of haff loud. The mean value of the eho power is as follows: Z 1 1 X E js 0 ðt Þj ¼ ð14þ t dt js i ðt t Þj Fourier transform on both sides of the equation an be used to get autoorrelation funtion ð16þ Chaff loud eho an be obtained by onvolution between the emission signal and response to haff loud. While it orresponded to the frequeny domain, its frequeny response is the produt of both S 0 ðf Þ ¼ S i ðf ÞS ðf Þ A X t dt ð17þ The simulation method is used to solve the frequeny response to haff loud. Let X(T) and Y(T) be two zeromean real normal proesses. So the zero-mean omplex Gauss stohasti proess is desribed as Z ðt Þ ¼ X ðt Þ þ iy ðt Þ Then, Fig. 8 Performane simulation of eho with RF noise when us/σi = 10. a Time-domain waveform. b Power spetral density ð18þ
Liu et al. EURASIP Journal on Wireless Communiations and Networking (016) 016:1 Page 6 of 9 The above formula is substituted into the haff loud frequeny response, and the disrete proessing is used to get S ðnδf Þ ¼ XN 1 exp πi nm N m¼0 þ inð0; δtþ r ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi X mδt 1 ½N ð 0; δt Þ ð1þ The above equation an be used to express the haff loud eho signal in the frequeny domain, and the orresponding signal form in the time domain an be obtained after Fourier inverse transform. Fig. 9 Algorithm flow hart of distane deeption jamming E jdzðþ t j ¼ E jd½xðþþiy t ðþ t j ¼ de X ðþþy t ðþ t ¼ dfd½xðþ t þdy ½ ðþ t g ð19þ For E[ dz(t) ]=dt, the zero-mean omplex Gauss random proess an be expressed as Zt ðþ¼ 1 ½Nð0; t ÞþiN ð 0; t Þ ð0þ 3 Computer simulation analysis 3.1 RF noise jamming simulation We design MATLAB program for RF noise and arry out omputer simulations. The simulation parameters are set as follows: the sampling frequeny is 80 MHz; the bandwidth of the band-pass filter is 8 MHz; and the noise figure is 1.1. A simulation flow hart is showninfig.1. Simulation results are shown in Figs. and 3. It an be seen from the graph that the envelope of the RF noise obeys the Rayleigh distribution and the phase obeys the uniform distribution, whih is onsistent with the theoretial analysis. Through the filter, autoorrelation funtion and power spetrum density funtion of the RF noise are shown in Figs. 4 and 5. It an be seen that Fig. 10 Simulation of distane deeption jamming
Liu et al. EURASIP Journal on Wireless Communiations and Networking (016) 016:1 Page 7 of 9 power spetral density shows the filter shape through a band-pass filter and autoorrelation funtion shows harateristis of a single-frequeny signal, whih is onsistent with the theoretial analysis. Respetively, u s /σ i = 0.1; 1; 10, the omputer simulation results of the signal superimposed with noise are shown in Figs. 6, 7, and 8. It an be seen that the output amplitude of the reeiver under RF noise jamming shows the following distribution. Eho signals magnitude is no longer the original form of a retangular pulse under the influene of RF noise jamming and varies around the average potential of noise. As the interferene power inreases, the signal is submerged in the noise interferene and it annot be deteted and identified. 3. RGPO simulation Assume that the arrier frequeny of the radar emission signal is 8 MHz, the pulse repetition frequeny is 3 khz, the duty ratio is 1/4, the sampling frequeny is 80 MHz, and the range gate is towed at a onstant speed. The simulation parameters are as follows: R = 4 km, V 1 = 0 m/s, t 1 = 0.3 ms, t = ms, V =10 6 m/s, and jamming to signal ratio is 1 db. A flow hart of deeption jamming simulation algorithm is shown in Fig. 9. Figure 10 shows that the interferene signal is formally exatly the same as the target signal exept amplifiation of amplitude before 0.3 ms. They both have the same time delay ompared to the emission signal, about 7 μs whih is onsistent with the target distane. Distane towing begins at 0.3 ms, and then the interferene signal and the target signal differ. Compared with the emission signal, time delay of the interferene signal is gradually inreased within eah pulse period and the delay of target signal remains unhanged, so the distane between the interferene signal and the target signal beomes larger, whih is onsistent with the theoretial analysis. It verifies the validity of the simulation model. 3.3 Chaff jamming simulation Assuming haff is uniformly distributed in a 150-mdiameter sphere, there is a total of 1.5 10 8 dipoles. Phase enoding signal emitted by radar is simulated at a medium frequeny of 55 MHz and an algorithm flow hart of simulation is shown in Fig. 11. It an be seen from Fig. 1 that the normalized amplitudes satisfy Rayleigh distribution; phases satisfy uniform distribution within ( pi, pi); spetrum broadens to a ertain extent around 55 MHz. Power spetrum satisfies the Gauss distribution whose mean value is about 55 MHz. Therefore, the simulation results are onsistent with the statisti harateristis of haff eho. Fig. 11 Algorithm flow hart of haff jamming Computer simulations of RF noise jamming, RGPO, and haff jamming are arried out in this paper. Aording to the results of omputer simulation, the simulation ahieves the expeted goal and orretly reflets the mathematial model. By omparing the simulation results of the different parameters, the related interferene proess an be simulated. In the simulation of RF noise jamming, the proess is simulated that the useful signal is submerged by the noise signal and annot be deteted or identified. The simulation harateristis of the envelope and phase of the noise signal are onsistent with the theoretial analysis. The results of RGPO simulation and haff jamming simulation are the same as what is expeted. 4 Conlusions For new radar eletroni systems and new ommuniation equipment that ontinue to emerge, the orresponding eletroni ountermeasure tatis tehnology has also been rapidly developed. To meet the objetive requirements of
Liu et al. EURASIP Journal on Wireless Communiations and Networking (016) 016:1 Page 8 of 9 Fig. 1 Simulation of haff loud eho. a Normalized one-dimensional range image. b Amplitude distribution. Phase distribution. d Spetrum harateristi. e Power spetrum harateristi the eletroni warfare theory researh and pratial testing, many eletroni warfare simulation systems have been produed at home and abroad with the help of the rapidly developed modeling theory and omputer network tehnology. Therefore, it is urgent for eletroni ountermeasure researhers to omprehend and master the system simulation tehnology in time [10]. We analyzed the mathematial model of the ommon eletroni interferenes in a omplex eletromagneti environment and onduted omputer simulation of RF noise jamming, RGPO, and haff jamming. Simulation analyses verify the validity of the mathematial model of the eletroni interferene. This study will be helpful in further study on the eletroni interferene and suppression. Competing interests The authors delare that they have no ompeting interests. Aknowledgements This work is partially supported by the National Nature Siene Foundation of China under Grant 414040 and the Nature Siene Foundation of Shannxi Provine under Grant 015JM418. Reeived: 9 September 015 Aepted: 15 Deember 015
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