Rocket detection using passive radar – challengesand solutions

Mateusz MalanowskiWarsaw University of Technology

Institute of Electronic SystemsWarsaw, Poland

Email: m.malanowski@elka.pw.edu.pl

Krzysztof BorowiecWarsaw University of Technology

Institute of Electronic SystemsWarsaw, Poland

Email: k.borowiec@elka.pw.edu.pl

Stanislaw RzewuskiRS Technologies Sp. z o.o.

Warsaw, PolandEmail: srzewuski@rstechologies.pl

Abstract—In the paper selected aspects of rocket detectionwith the use of passive radar are analyzed. The bistatic radarcross-section of a rocket is calculated using electromagneticsimulator. Next, the radar equation for passive radar is analyzedtaking into consideration the radiation patterns of the transmitterantenna. Limitations of integration time are also discussed. Thetheoretical analysis is supplemented with measurement results –the processing results of a rocket observed with a DVB-T basedpassive radar are shown and analyzed.

I. INTRODUCTION

Passive radar is used primarily for detection of airbornetargets, mainly aircraft [1], [2], [3]. Other types of targetsof interest include cars, helicopters, pedestrians and ships [4],[5], [6], [7]. Passive radar is also used for target imaging [8],[9], [10] and ionospheric observations [11]. In this paper wefocus on using passive radar for observation of rockets [12],[13]. The rockets under consideration are amateur experimentaland hobby rockets launched from the ground surface. Typicallength of such a rocket is from 1 m to 3 m. Both sub- andsuper-sonic rockets are of interest.

Rocket detection detection and tracking is a challengingtask. First problem is the radar cross-section (RCS) of therocket. It is not as small as in case of small drones, but notas large as of passenger aircraft. Rocket detection can be alsosignificantly influenced by the transmitter illumination as thetarget can fall in the null of the transmitter radiation pattern.Other challenge is high maneuverability of the target. Rocketstend to move very fast and accelerate rapidly. From this pointof view, the classical signal processing algorithms applied incase of other types of targets, may prove to be inadequate incase of rockets.

In the first part of the paper we analyze the RCS ofthe rocket using electromagnetic solver (CST Studio). Next,the radar equation for passive radar is reviewed with specialemphasis on the radiation patterns of the transmitter antenna.At the end of the paper, results of measurements are presentedshowing some of the typical problems encountered duringdetection of rockets.

II. DETECTION RANGE

A. RCS analysis

The RCS calculations for the rocket were performed usingCST (Computer Simulation Technology) Studio software [14].

Fig. 1. 3D model of the rocket in the CST Studio. Incident wave planemarked with red rectangle

A 3D model of the rocket used in the simulations is shown inFig. 1. The length of the rocket is 270 cm, and its diameter is12 cm. The simulated rocket has metallic surface. The rocketwas positioned vertically (along the z-axis) and illuminatedfrom the side (along the x-axis). The incident wave plane ismarked with red rectangle in Fig. 1.

The calculations were performed for the frequency of680 MHz (similar to the one used in the measurements) andhorizontal polarization (typical for DVB-T transmitters). Fig. 2shows the elevation cross-section of the calculated bistaticRCS. The angle θ = 0◦ corresponds to the view from the top(nose of the rocket), whereas θ = 180◦ is the view from thebottom (engine of the rocket). Two maxima can be observedin the pattern at θ = +90◦ and θ = −90◦. The first onecorresponds to the back scattering, where the incidence andreflection angles are the same. This it the monostatic case fromthe point of view of radar. The RCS value for this case is equalto 8.4 dBsm (decibels with respect to square meter), which is6.9 m2. The other maximum corresponds to forward scatteringscenario, when the angle between the incidence and reflectedwave is close to 180◦. In this case, the RCS reaches valueclose to 4 dBsm (2.5 m2). Apart from the two main lobes, theRCS is at the level of approximately −10 dBsm (0.1 m2).

As the rocket shape can be roughly approximated by athin tall cylinder, the maximum RCS can be estimated as (formonostatic case) [15]:

σmax =2πrh2

λ(1)

Fig. 2. Calculated RCS in the elevation plane

Fig. 3. 3D visualization of calculated RCS

where r is the cylinder radius, h is the cylinder height and λis the wavelength. For the considered rocket case r = 6 cmand h = 270 cm, which results in value of σmax equal to7.94 dBsm (6.2 m2) for frequency of 680 MHz. This is veryclose to the result obtained from the CST Studio simulation,approximately equal to 8 dBsm for back scattering (monostaticcase).

Fig. 3 shows full 3D pattern. The observed shaped is highlysymmetrical with respect to the z-axis. For this reason theazimuth cross-sections of the patterns are almost uniform. Thisresults form the fact that the rocket is highly symmetrical withrespect to the z-axis (the only exception are four stabilizers atthe end of the rocket).

Concluding the RCS simulations it can be stated that theRCS of a rocket observed from the boresight is relatively high– almost 10 dBsm in the considered case. When the rocket isobserved from the bottom or the top, the RCS is substantiallyreduced – to the value of −10 dBsm.

B. Range equation

Consider bistatic range equation, rearranged to express theminimum detectable RCS σdet [2]:

σdet =SNRmin(4π)3R2

1R22NfkTrL

PtGt(φ, θ)Grλ2T(2)

where SNRmin is the minimum signal-to-noise ratio requiredfor detection, R1 is the transmitter-target range, R2 is the

target-receiver range, Nf is the receiver noise figure, k is theBoltzmann constant, Tr is the receiver noise temperature, Lare the system losses, Pt is the maximum transmitted power,Gt(φ, θ) is the transmit antenna radiation pattern, Gr is thereceiver antenna gain λ is the wavelength and T is the inte-gration time. It was assumed that the receiver bandwidth andsignal bandwidth are the same, hence there is no bandwidthdependency in (2) (the bandwidth in integration gain BT andnoise power kTrB cancel each other).

For simplicity, often the transmitter antenna radiation pat-tern is assumed to be omnidirectional. In practice, however,this is far from true, and can significantly impact the radarperformance. In case of azimuth plane, transmitters are oftendesigned to radiate approximately with the same strengthin all directions, therefore the assumption on omidirectionalradiation is justified. However, in the elevation plane the beamis relatively narrow, which allows the radiated power to befocused in the direction of receivers that are placed on theground. Typically, the antennas are built using several radiatingelements stacked in the vertical direction. Based on thoseassumptions, a simple model for radiation pattern can beformulated as:

Gt(φ, θ) =sin(πLv

λ sin(θ))

πLv

λ sin(θ)(3)

where φ is the azimuth angle, θ is the elevation angle (0◦corresponds horizontal direction here), Lv is the vertical sizeof the antenna. The pattern (3) is omnidirectional in theazimuth direction, and has sin(x)/x shape typical for apertureswith rectangular current distribution. Typically the elementsare spaced by λ/2, then the length of the antenna can berecalculated to effective aperture length Lv = (Nv − 1)λ/2,where Nv is the number of radiating elements.

In Fig. 4 the azimuth cross-section of the detectable RCScalculated using (2) with trasnmitter radiation pattern (3) isplotted for different altitudes of the target. The calculationswere performed for a representative set of DVB-T-based pas-sive radar: SNRmin = 12 dB, Nf = 10 dB, Tr = 290 K,L = 10 dB, Pt = 100 kW, Gr = 5 dBi, fc = 600 MHzand T = 50 ms. It was assumed that the antenna consistsof Nv = 16 vertical radiating elements with λ/2 spacing.The transmitter is assumed to be at the ground level and theelevation tilt of the antenna is 0◦. The black contour indicatesthe level of 0 dBsm. The rings surrounding the transmittercorrespond to nulls of the elevation radiation pattern. Thesize and width of the rings increases with target altitude.This results from the fact that the same angular width of thepattern lobe corresponds to larger distance at higher altitudes.The shape of the ring is not symmetrical with respect to thetransmitter, as the detectable RCS is influenced by the Cassiniovals – shapes characteristic for the bistatic range equation(which result from the R2

1R22 term in the bistatic equation).

In Fig. 5 the elevation cross-section of the detectable RCSis shown. The observed fan shape corresponds to the elevationradiation pattern. As can be seen, in the presented examplearound 3 km above the receiver a null can be expected.

Presented results clearly indicate that when the observedtarget is changing its altitude, the detection capabilities of theradar can vary significantly. Even if the target is flying at

Fig. 4. Azimuth cross-section of detectable RCS (color-coded values in dBsm) for a target at altitude of 500, 1000, 2000 and 5000 m

Fig. 5. Elevation cross-section of detectable RCS (color-coded values indBsm)

a constant altitude, is can fall into a null of the transmitterradiation pattern, and that will prevent it from being detected.In case of a rocket launched from the ground and flying straightup this can mean that the rocket will disappear from the radarat certain altitudes and geographical coordinates.

III. NUMERICAL RESULTS

In this section we show results of processing of measureddata collected during observation of a rocket launch. Therocket under consideration is shown in Fig. 6. The rocket nameis Strega and it had been designed by rocket enthusiast DamianMayer. The rocket is 2.3 m in length and 8084 mm in diameter.It has three stabilizers. Everything except the rocket nose/headis made from aluminum 6060 alloy.

The data was collected using DVB-T-based passive radar.The transmitter used for target illumination was operating atthe frequency of 634 MHz in horizontal polarization. Thetransmitter was located 77 km from the receiver. The launchsite was located 200 m from the receiver. The rocket was flyingalmost vertically. The fact that the transmitter was far awayfrom the launch site resulted in rocket being illuminated fromthe boresight, similar as in the electromagnetic simulations ofRCS. The fact that the launch site was close to the receivermeans that as the rocket climbed, the elevation angle θ at whichthe rocket was observed by the radar approached 180◦ rapidly(compare Fig. 2).

In Fig. 7 the crossambiguity function is shown with rocketecho visible. Each of the plots corresponds to different inte-gration time, equal to 25 ms, 50 ms, 100 ms and 200 ms,respectively. The bistatic velocity resolution ∆V depends on

Fig. 6. Picture of a rocket launch

the integration time T according to:

∆V =λ

T(4)

For this reason increase in the integration time corresponds toproportional decrease of the velocity resolution. In the figurethis an be seen as the echo becomes narrower in case of 50 msintegration time in comparison to 25 ms integration time. Ifthe integration time is increased too much, the echo starts tospread across velocity because the target is accelerating. Thiscan be visible in the last plot for integration time equal to200 ms.

The presented result suggests that target acceleration canbe a serious problem when longer integration time are desired.This is only partially true. If a traditional crossambiguityfunction is calculated that does not take target accelerationinto account (see (5)), echo spreading and thus power loss canbe expected.

Ψ(R, V ) =

T/2∫−T/2

xe(t) · x∗r(t− R

c

)· exp

(j2π

λV t

)dt, (5)

where R is the bistatic range, V is the bistatic velocity, xr(t)is the reference signal and xe(t) is the surveillance signal.

If, on the other hand, extended crossambiguity functionis applied [16], [17], [18], [19], increase in integration timecan not only provide higher echo power, but also informationon target acceleration can be obtained. The crossambiguityfunction definition can be extended in the following way:

ΨA(R, V,A) =T/2∫

−T/2

xe(t) · x∗r(t− R

c

)· exp

(j2π

λ

(V t+

At2

2

))dt, (6)

where A is the bistatic acceleration. By examining whichacceleration A provides maximum crossambiguity value, thetarget bistatic acceleration can be estimated. The extendedcrossambiguity (6) can be calculated effectively by apllying

Fig. 8. Acceleration resolution vs. integration time

finite impulse response to a classical crossambiguity function(5). For details see [18], [19].

Let us analyze the influence of the integration time onacceleration resolution. The acceleration resolution can becalculated as:

∆A =λ

T 2(7)

An example of acceleration resolution calculated according to(7) for 600 MHz is shown in Fig. 8. As can be seen, thedependency on T 2 is very strong. For integration times in theorder of tens of milliseconds the acceleration resolution is verypoor. Only when the integration time reaches values of severalhundreds of milliseconds, the resolution reaches values in theorder of 10 m/s2. The acceleration resolution is connected tothe acceleration estimation accuracy. In practice, the estimationaccuracy can be much better than resolution – usually at leasone order of magnitude.

The dependency of acceleration measurement accuracy onthe integration time is illustrated in Fig. 9 on the measuredecho of rocket. The plot shows the acceleration cross-sectionof the crossambiguity function (6), i.e. ΨA(R0, V0, A), whereR0, V0 are bistatic range and bistatic velocity of the targetecho, respectively. For the shortest integration time (25 ms)the target amplitude is almost independent of the accelerationvalue assumed during calculations. For 50 ms a maximumappears indicating target bistatic acceleration in the rangeof 300-400 m/s2. In the case of 100 ms integration timethe maximum becomes higher and sharper. A more preciseacceleration estimation can be obtained. Other important effectis also visible. The classical crossambiguity function (5) iscalculated for A = 0 m/s2. In the case of 100 ms integrationtime that would correspond to almost 3 dB of losses. Forthe longest integration time, equal to 200 ms, the accelerationprofile does no longer have a sharp peak. This indicates thatfor such long integration time the acceleration changes, andthe assumed signal model with target acceleration is no longervalid.

IV. CONCLUSION

In the paper selected aspects of rocket detection have beenanalyzed. The electromagnetic simulations of the RCS showed

Fig. 7. Crossambiguity function for integration time equal to 25 ms, 50 ms, 100 ms and 200 ms

Fig. 9. Acceleration cross-section of the extended crossambiguity functionfor rocket echo for different integration times

that the rocket is reflecting strongly when illuminated from theboresight. As the rocket climbs, it is observed from the bottom,where the RCS is significantly lower (20 dB lower than themaximum in the analyzed case).

The analysis of the elevation patterns of the transmittershowed that capability of the radar to detect target can stronglydepend on its altitude. This results form the fact that typicallythe transmitter antennas are designed to focus emitted power ina narrow beam pointed toward the earth surface. As a result, theairspace is illuminated to a large extent through the sidelobesof the elevation radiation pattern.

The measurement results confirmed expected behavior ofthe rocket – its acceleration is very high and can lead toecho spreading for higher values of integration times. Thiseffect can be not only reduced, but in addition the accelerationmeasurement can be obtained.

ACKNOWLEDGMENT

The authors would like to thank Damian Mayer for provid-ing information on his rocket, and Andrzej Chwastek from thePolish Rocket Society for providing rocket launch photograph.

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