ZHOU Zhe－shuai(周哲帅)，WU Han－ping(吴汉平)

(Electronic Engineering Institute of PLA，Hefei 230037，Anhui，China)

Introduction

Air attack and anti－attack become important operational modes in modern warfare.In order to destroy the important military targets of blue side，red side sends bombers and fighters close to its region.The blue side launches surface－to－air missiles(SAM)to shot the aircrafts after discovering the air fleet of red side.In order to protect aircrafts effectively，the red side must disturb the guidance radar of blue side to reduce the kill probability of missile.In this paper，efficiency evaluation and tactics calculation of radar decoy jamming［1］are studied to easily select the correct tactical parameters of radar decoy.

1 Effectiveness Evaluation of Guidance Radar Jammed by Radar Decoy

1.1 Shot Times of Missile in Jamming Conditio n

For the jammed guidance radar，reduction of actual detection range makes a corresponding reduction of the missile launch distance［2］.Without considering the ammunition consumption，when aircraft fleet flies into the actual launch zone of fire units，the shot times of missile can be expressed as

(a)If Dfs≥Dfsminand SAM shots the target from front hemisphere(head－on attack)or rear hemisphere(trailing attack)only，Qj=1;

(b)If Dfs≥Dfsminand the missile shots the target from front and rear hemispheres，Qj=2;

(c)If Dfs＜ Dfsmin，Qj=0.

1.2 One-shot Kill Probability of Missile in Decoy Jamming

The aircraft releases the decoy to disturb the guidance.SAM will be deceived and fly to the centroid A of decoy and aircraft，if the decoy and aircraft are both in the resolution cell of radar，as shown in Fig.1.

Fig.1 Sketch of radar decoy jamming

From proportional relationship，the distance djbetween the aircraft and centroid can be easily expressed as

where σjis the effective radar cross section(RCS)of reflector beam in a decoy，njthe number of reflector beams in a decoy，σcthe RCS of aircraft，d the distance between target and decoy，βjthe attenuation coefficient of radar moving－target selection system to decoy reflected signal［4］.

Assume that the hitting point moves along the connection of aircraft and decoy only，if the guidance radar is jammed by decoy.In order to ensure the missile can damage the target，the distance between the target and hitting point(x，y)must be less than the kill radius，then one－shot kill probability on aircraft of SAM can be written as

where Rris the kill radius of missilethe synthetic root－mean－square error(RMSE)of SAM，αjthe component of RMSE caused by jamming，taking(0.3 ～0.4)djgenerally，αrthe RMSE of the missileitself，

1.3 Synthetic Damage Ability of Missile in Jamming Condition

The influence of jamming on the synthetic kill probability is the ultimate expression of the influence on the synthetic damage ability.The reductions of shot and one－shot kill probability lead to low synthetic kill probability of SAM.According to the probability formula，the synthetic kill probability on aircraft of SAM fire unit in its entire shooting period can be expressed as

2 Tactics Calculation for Decoy Jamming

2.1 Number of Anti-radar Reflector Beams in Single Decoy

The suppression coefficient［5］of passive jamming on guidance radar can be written as

where Jsdenotes the necessary effective energy jamming－to－signal ratio(JSR)accessing into guidance radar receiver under certain defensive probability Wn，and can be expressed as

The effective critical condition［6］of passive jamming is that the suppression coefficient just equals to the ratio of the effective RCS of anti－radar reflector beams to the effective RCS of target，namely

Combined Eq.(5)and Eq.(7)，njcan be expressed as

2.2 Continuous Release Time Interval of Antiradar Reflector Beams

The jamming effect of decoy on guidance radar depends upon the heading angle qrof aircraft［7］，and different qrlead to different release time interval of anti－radar reflector beams.Two instances are discussed below.

Fig.2 Sketch of radar distance automatic tracking

(a)If －30°≤qr≤30°or 150°≤qr≤210°，the decoy mainly affects the distance automatic tracking system of radar，as shown in Fig.2.The aircraft should release the decoy in the distance resolution cell of guidance radar.According to the geometry in Fig.2，the time that aircraft fly over the distance resolution cell can be written as

where c=3.0 ×108m/s denotes the propagation velocity of electromagnetic wave，τ the radar’s pulse width in μs，VCthe aircraft’s speed in m/s.

Considering that the aircraft needs to release njreflector beams within tD，thus，the release time interval tjDcan be expressed as

(b)If 30°＜qr＜150°or 210°＜qr＜330°，the decoy mainly affects the direction automatic tracking system of guidance radar，as shown in Fig.3.

Fig.3 Sketch of radar direction automatic tracking

According to the geometry in Fig.3，the time of releasing one radar decoy can be written as

where θadenotes the radar’s beam width in degree.

Considering that the aircraft needs to release njanti－radar reflector beams within tK，so the release time interval tjKcan be expressed as

Generally，the aircraft releases the anti－radar reflector beams continuously during its flight，the release time interval tjcan be written as

2.3 Total Consumption of Anti-radar Reflector Beams

When the aircraft flies over the SAM damage zone，the needed number of decoy njΣdepends upon to the performance of SAM fire unit.According to Eq.(1)，we have

where VΣis the approach velocity between the aircraft and missile，and

VΣ=Vr+VCcos qr，where Vris the SAM’s velocity in m/s，VCthe aircraft’s velocity in m/s.

It can be seen from Eq.(8)that the needed antiradar reflector number of releasing one decoy is nj，thus，combined Eq.(14)，the total consumption NΣof anti－radar reflector beams when the aircraft flies over the SAM damage zone can be expressed as

3 Numerical Example

3.1 Scenario Assumptions and Parameters

Suppose the red side sends multiple bombers(VC=250 m/s)to bomb valuable target on the blue side，which are equipped with type A decoy release device and some type B jamming projectiles.In order to ensure successful bombing，the red side carries out decoy jamming to the ground air－defense fire control and guidance radar of blue side.The release device can salvos 2，3 or 6 jamming projectiles or continuously launch 6 jamming projectiles in the release time interval of 0.05，0.1 or 0.5 seconds.For the blue side，after its warning radar discovers the aircrafts，the command center issues the launch instructions，and the guidance radar controls one SAM to try to shot down the aircraft of red side.All parameters are listed in Tab.1.

Tab.1 Simulation parameters

3.2 Results and Analyses

According to the known parameters，the synthetic RMSE of jammed SAM=12.6 m，under the condition of RMSE component αj=0.4dj，can be found out，and then one－shot kill probability of SAM Pkj=0.704 can be calculated from Eq.(4).Compared with the kill probability Pk=0.8 of single missile without jamming，the kill probability Pkjdecreases when SAM is jammed.

The bombers need to release anti－radar reflector beam continuously in order to protect themselves effectively.The number of anti－radar reflector beams in a decoy，release time interval and total consumption in defensive probability Wn=0.8 can be found out as follows.

It can be easily obtained form Eq.(6)that the effective JSR Jsin the input of ground guidance radar receiver is 4，and then from Eq.(8)，the number of anti－radar reflector beams in a decoy is 2.The results show that the release device of type A has to volley 2 jamming projectiles to form a radar decoy.

Also，it can be found out from Eq.(10)and Eq.(12)that，if qr=120°，the continuous release time interval tjKof reflector beams is 0.56 sec，and if qr=180°，the continuous release time interval tjDof reflector beams is 0.24 sec.

From Eq.(14)，it can be seen that the needed number njΣof decoys when the aircraft fly over the SAM damage zone is 3.Finally，the total consumption NΣof type B jamming projectiles is 6 from Eq.(15).

The relationship between heading angle qrand release time interval of reflector beam is shown in Fig.4.It can be seen that the maximum release time interval is no more than 1s in any heading angle，which is far less than the missile’s launch cycle of 40 s.Thus，the change of heading angle does not affect the continuity of releasing anti－radar reflector beams.

Fig.4 Relationship between heading angle and time interval

Based on the calculation results shown above，in order to ensure SAM is deceived and the defensive probability of aircraft reaches to 80%，as the release device of type A has to volley 3 times and release 2 jamming projectiles of type B in each 0.56 s.

4 Conclusions

The kill efficiency of missile under decoy jamming condition is investigated form three aspects，the shot times，kill probability and synthetic damage ability.The tactics calculation method of releasing decoy under certain defensive probability is given also.Finally，the calculation results of numerical example are analyzed.The achievement has significance for the operational efficiency evaluation，airborne weapon equipment and tactics application in air attack warfare.

［1］CHEN De－feng，GAO Mei－guo，FU Xiong－jun，et al.Effect of parameters detection error to SAR deception jamming［J］.Transactions of Beijing Institute of Technology，2009，29(7):639－643.(in Chinese)

［2］TANG Zheng，GAO Xiao－guang，ZHANG Ying.Research on the model evaluating the efficiency of the airborne active self－defense jamming system［J］.Systems Engineering and Electronics，2008，30(2):236 －239.(in Chinese)

［3］CUI Xiao－bao.Introduction to air force combat simulation［M］.Beijing:Blue Sky Press，2001:260－290.(in Chinese)

［4］HU Xiao－hui.The calculation method of battle and strategy for EW［M］.Beijing:Airforce Command Collegy，2002.(in Chinese)

［5］QI Deng－feng.Tactical calculation method research of radar jamming［D］.Hefei:Electronic Engineering Institute，2009.(in Chinese)

［6］SHAO Guo－pei，CAO Zhi－yao，et al.Electronic warfare operational effectiveness analysis［M］.Beijing:The Publishing House of PLA，1998:169－170.(in Chinese)

［7］LI Yun－jie，ZHANG Yan－bin，GAO Mei－guo.Parameters design of pull－off deceptive jamming to terminal guidance radar［J］.Journal of Beijing Institute of Technology，2010，19(3):362－366.(in Chinese)