A cross‐eye jammer based on a phase‐conjugating (PC) retrodirective array is proposed. Such PC cross‐eye jammers eliminate the delay inherent in traditional Van‐Atta (VA) cross‐eye jammers and induce errors in radars that use the same antenna beam for transmission and reception, while VA cross‐eye jammers do not. Validated simulations are provided to confirm the effectiveness and retrodirective properties of the PC cross‐eye jammer.https://ietresearch.onlinelibrary.wiley.com/journal/1350911xhj2021Industrial and Systems Engineerin

Du Plessis, W.P. (Warren Paul)

UPSpace at the University of Pretoria

Phase-conjugating retrodirectivecross-eye jammingW.P. du Plessis✉ELECTA cross-eye jammer based on a phase-conjugating (PC) retrodirectivearray is proposed. Such PC cross-eye jammers eliminate the delayinherent in traditional Van-Atta (VA) cross-eye jammers and induceerrors in radars that use the same antenna beam for transmission andreception, while VA cross-eye jammers do not. Validated simulationsare provided to confirm the effectiveness and retrodirective propertiesof the PC cross-eye jammer.Introduction: Glint is a naturally-occurring phenomenon that affects allradar systems and can cause large angular errors [1–5]. Cross-eye jamm-ing is an electronic attack (EA) technique that seeks to artificially recreatethe conditions under which glint causes large angular errors [6–13]. Theprimary benefits of cross-eye jamming are that it is one of only a smallnumber of countermeasures capable of generating an angular error andits origin in glint means that it should affect all radar systems.The two main challenges to implementing cross-eye jamming are thehigh jammer-to-signal ratio (JSR) required as a result of the signal can-cellation that arises from the conditions corresponding to a large angularerror, and the extremely fine tolerances required [8–15]. The tolerancerequirements arise because a radar needs to in a narrow angular regionto experience a significant angular error. This narrow angular regionmeans that a retrodirective implementation is required to direct theregion of large angular error towards an incoming radar signal.Retrodirective cross-eye jamming is traditionally based on atwo-antenna Van-Atta (VA) retrodirective array [16]. However, thisimplementation has a number of additional drawbacks with thejammer return appearing some distance behind the jammer antennas,and radars that use the same antenna beam for transmission and recep-tion experiencing no angular error [7, 11, 17].Basing a cross-eye jammer on a phase-conjugating (PC) retrodirectivearray [18, 19] offers the possibility of overcoming both of these draw-backs [20]. This approach is considered below and compared to the tra-ditional VA retrodirective cross-eye jammer to demonstrate its potential.Retrodirective arrays: A retrodirective array automatically transmits asignal in the direction of an incoming signal, thereby removing theneed to explicitly steer the transmitted signal. This retrodirective prop-erty is achieved by ensuring that the signals transmitted by an array ofantennas add in phase in the direction of the incoming signal. Thetwo approaches to achieving this phase coherence in the direction ofan incoming signal are described below.An example of a VA retrodirective array is shown in Figs. 1a and b[16]. The antennas in a VA array are connected in pairs so that thesignal received by one antenna is retransmitted by the other antennain the pair. Additionally, all antenna pairs share the same midpoint asshown in Fig. 1a, and the feed networks of all antenna pairs haveequal phase shifts shown in Fig. 1b.The significance of the common centre point for all pairs of antennasin a VA array is shown in Fig. 2a. When rotated around a point halfwaybetween the antennas (l1 = l2), the distance that one antenna movescloser to an incoming plane wave is equal to the distance the otherantenna in the pair moves further from the incoming plane wave(l3 = l4). The result is that the total distance the plane wave propagatesto and from each pair of antennas is a constant over all rotations becausethe signal received by one antenna is transmitted by the other.The return from a VA array appears to originate from the position atthe common centre of the antenna pairs, but at a range behind that theposition corresponding to half the delay between the antenna pairs.The return is thus behind the physical location of the VA array andmay even be in a separate radar range gate to the platform mountingthe VA array. This range separation makes it relatively simple to separatethe repeater return from the return of the platform it is mounted on – aproblem compounded by the fact that electromagnetic (EM) waves pro-pagate slower in cables and waveguides than in air [21].PC arrays use a common phase reference to compensate the phases at theantennas as shown in Figs. 1c and d. The transmitted signal phase is thenegative of the received phase relative to the reference phase (the conjugateof the signal in phasor representation), thereby compensating for the phaseshifts due to the position differences relative to a phase front [18, 19].RONICS LETTERS 30th September 2020 Vola bc dFig. 1 Retrodirective array structuresa VA array front view: note the common centre of all antenna pairsb VA array back view: note the equal-length feed networksc Phase-conjugating array front view: note the arbitrary antenna layoutd Phase-conjugating array back view: note the common phase referencea bl3l 1l 2l4θφ1φ1–φ1–φ2φ221φ20000Fig. 2 Principles underlying retrodirective arraysa Rotating a pair of antennas around its centre does not change the total distance aretransmitted wave propagates in a VA arrayb Transmitted signals add in phase at the reference plane in a PC arrayThe operating principle of a PC array is shown in Fig. 2b. The phaseshifts from a reference point on the incoming plane wave to two anten-nas are f1 and f2 at antennas 1 and 2, respectively. Transmitting signalswith the negatives of these phases (−f1 and −f2) will cause the trans-mitted signals to be phase at the plane-wave reference point because thephase shift to that plane is compensated by the phases of the transmittedsignals (−f1 + f1 = 0 = −f2 + f2). The use of a common phasereference for all antennas in a PC array effectively achieves the situationdepicted in Fig. 2b by substituting a common phase reference for acommon reference plane.Retrodirective cross-eye jamming: Analyses of glint have shown that alarge angular error is induced in radar systems that receive two signalswhich have equal amplitudes and a phase difference of 180° [1–5].These conditions correspond to signal cancellation and are the reasoncross-eye jamming requires high (JSR).Retrodirective cross-eye jamming is traditionally based on thetwo-antenna VA retrodirective implementation shown in Fig. 3 (e.g.[6–13]), with two patents describing such systems being filed in 1958[22, 23]. The only change to a VA array necessary to create a retrodir-ective cross-eye jammer is to shift the signals in one direction throughthe jammer by 180° (i.e. a  1 and f  180° in Fig. 3).The major advantage of VA cross-eye jammers is that all sharedaspects of the propagation path, including all the components, apartfrom the portions in the box in Fig. 3, are identical, so their effectscancel. This cancellation simplifies the practical implementation ofsuch systems by avoiding the need to match shared components.. 56 No. 20 pp. 1079–10821e j0ae jφFig. 3 VA retrodirective cross-eye jamming implementationThe main drawback of the use of the VA retrodirective implemen-tation for cross-eye jamming is the delay caused by signals having totravel from one antenna to the other before retransmission as outlinedabove. Cross-eye jammers create larger angular errors as the spacingbetween the jammer antennas increases, with typical antenna spacingsvarying from 10 to 20 m [12]. This delay will mean that the Van-Attacross-eye jammer return be 5 to 10 m behind its antennas in even thebest case. However, transmission lines and waveguides propagatesignals slower than the speed of light in air [21], practical considerationsincrease the required lengths of transmission lines and waveguides, andany processing required by the jammer will further increase the delay,and thus, the apparent range of the jammer return. This apparentrange offset is the motivation for using leading-edge tracking as a coun-termeasure to cross-eye jamming [10], even though leading-edge track-ing does not directly influence the angular error caused by a cross-eyejammer.A further drawback of a VA retrodirective cross-eye jammer is that noangular error is induced in any radar that uses the same antenna beam fortransmission and reception, including the sum channel of a monopulseradar [7, 11, 17]. This is clearly a significant consideration as it limitsthe threats that can be countered using VA cross-eye jamming andsuggests that relatively simple countermeasures are possible.The use of PC arrays to implement retrodirective cross-eye jamming,as shown in Fig. 4, has not previously been proposed. Extending PCarrays to cross-eye jamming can again be achieved by changing thephase of one of the two signals transmitted by a retrodirective arrayby 180° (i.e. ax  1, fx  −2f1, ay  1, and fy  −2f1 + 180°in Fig. 3).axejφx ayejφyFig. 4 Proposed PC retrodirective cross-eye jamming implementationThe primary benefit of a PC cross-eye jammer is that the delay inherentin a VA cross-eye jammer is eliminated. An additional benefit is thatangular errors will also be induced in radars that use the same antennabeam for transmission and reception. This is not true for a VA cross-eyejammer as the signal received by one antenna is transmitted by the other.However, the signal received by each antenna is transmitted by thatantenna in a PC cross-eye jammer, and this condition corresponds directlyto the conditions that cause glint, which affects all radar systems.Simulations: Simulations were performed to compare the performanceof VA and phase-comparison cross-eye jammers. The parameters usedare listed below and are representative of cross-eye jamming against amissile threat to the aircraft or ship (e.g. [7, 11, 24]):† 10 GHz carrier frequency,† 1 km engagement range (r = 1 000 m),† 10 m jammer baseline (dc = 10 m),† 2.54 wavelength separation of the radar antenna elements (dr =2.54l) to give a radar sum-channel beamwidth of approximately 10°,† 30° jammer-rotation angle (uc = 30°),† jammer-amplitude match of 0.5 dB (a = 0.9441), and† jammer phase difference of 175° (f = 175°).The geometric parameters are defined in Fig. 5.ELECTRONICS LETTERS 30th SThe simulations were performed with the nec2c version 1.3implementation of the Numerical Electromagnetics Code (NEC) [25]because the use of a full-wave electromagnetic simulator means thatall propagation effects are accounted for. Horizontal dipoles of length0.4860 wavelengths with 21 segments were used to model both thephase-comparison monopulse antenna elements and the jammer anten-nas. Horizontal dipoles were used to minimise the coupling in theradar and jammer systems as end-on dipoles have low coupling [26],and their length was chosen to minimise the imaginary component oftheir input impedance.rd rd cθrθcFig. 5 Geometry of a cross-eye jamming engagement with the monopulseradar antenna elements on the left denoted by circles and the jammer anten-nas on the right denoted by blocksA first simulation was performed with the two radar dipoles excitedwith 1-V sources at their centre segments to create a sum-channel trans-mission. The signals received by the jammer antennas were determinedfrom the resulting voltages at centre segments of the jammer dipoles.These received jammer signals were then used to determine the signalsthat would be transmitted by the jammer. The voltages at the centre seg-ments of the jammer antennas were then set to these jammer transmissionsignals, and a second simulation was performed. The resulting voltagesat the two radar dipoles were then combined to form the sum- anddifference-pattern returns, after which monopulse processing was per-formed [4]. This two-step approach mimics a pulsed radar and allowsthe small voltages at the jammer due to transmission from the radar tobe determined without needing to separate small received signals fromlarge transmitted jammer signals and vice versa.The first task was to validate the accuracy this approach to simulatingretrodirective targets. The results for both VA and PC retrodirectivebeacons were considered, and as shown in Fig. 6, the results correspondto a target at a radar rotation of zero (ur = 0°) as expected. A simulatedVA cross-eye jammer was then compared to theoretical results that havebeen experimentally validated [7, 11, 17]. The monopulse indicatedangles for the theoretical and simulated results are seen to agree extre-mely well in Fig. 6. The proposed simulation approach is thus shownto be accurate.The next task is to demonstrate that a PC cross-eye jammer induceslarge angular errors in the threat radar. The indicated angle due to thePC cross-eye jammer is seen to be large in Fig. 6a, with the indicatedangles at zero radar rotation being 2.86° and 1.88° in the VA and PCcases respectively, while the jammer antennas are positioned at+0.25°.Now that the PC cross-eye jammer has been shown to induce largeangular errors, the final task is to show that the jammer is retrodirectiveby rotating the jammer and confirming that the induced indicated angleremains high. This is done in Fig. 6b, where the indicated angle due tothe phase-comparison cross-eye jammer is shown to be high over a widerange of jammer rotations.The major differences between the VA and PC cross-eye jammers inFig. 6 are the non-monotonic variations with radar rotation and asymme-try with jammer rotation in the PC case. These effects are believed to bedue to the differing ranges to each of the jammer antennas leading todifferent path losses. The previously-noted sensitivity of cross-eyejamming to parameters such as amplitude matching, coupled to ther−4 amplitude variation of radar systems with range means that evensmall range differences can be significant. Additional study is necessaryto resolve this question. A similar effect cannot occur in a VA cross-eyejammer as both signals travel along identical paths, just in differentdirections, so the path losses are equal.The final point to confirm is that a PC cross-eye jammer will inducean angular error in a radar that uses the same antenna beam for trans-mission and reception. This is shown in Fig. 7, where the sum-channelreturns for all cases except the PC cross-eye jammer have their peaks at aeptember 2020 Vol. 56 No. 20 pp. 1079–1082radar rotation of zero. The condition corresponds to accurate tracking ofthe retrodirective system (the absence of an angular error), as expected[7, 11, 17]. By comparison, the maximum return from the PC cross-eyejammer is not at a radar rotation of zero, but rather at −3.22°, which isthe same angle where the indicated angle is zero in Fig. 6a. As an aside,it is noted that this agreement with experimentally-validated results pro-vides further validation of the simulation approach used.–15–10–5051015–15 –10 –5 0 5 10 15NNN Nindicated angle, °indicated angle, °radar rotation, °beacon (VA)beacon (PC)theory (VA)jammer (VA)jammer (PC)a–101234–30 –20 –10 0 10 20 30jammer rotation, °beacon (VA)theory (VA)jammer (VA)beacon (PC)jammer (PC)bFig. 6 Indicated angle induced in a monopulse radar by VA and phase-conjugating (PC) beacons and cross-eye jammers. The letters ‘N’ on thetop and the right axes indicate the positions of the first sum-channel nulls.The two beacon cases are indistinguishablea Radar is rotated with the jammer at a 30° angle (uc = 30°)b Jammer is rotated with the radar pointing towards the jammer (ur = 0°)–20–15–10–505–15 –10 –5 0 5 10 15N Nnormalised sum-channel return, dBradar rotation, °jammer (PC)jammer (VA)beacon (PC)beacon (VA)Fig. 7 Normalised sum-channel returns for VA and PC beacons and cross-eye jammers. The letters ‘N’ on the top axis indicate the positions of thefirst sum-channel nulls. All cases apart from the phase-conjugating cross-eyejammer case are indistinguishable and show no angular errorConclusion: Retrodirective cross-eye jammers based on PC retrodirec-tive arrays are proposed. Traditional retrodirective cross-eye jammersare based on the VA arrays leading to disadvantages related to thedelay inherent in such systems and their inability to induce angularerrors in radars that use the same antenna beam for transmission andreception. Both of these drawbacks are shown to be overcome by PCcross-eye jamming, with validated simulations confirming this.ELECTRONICS LETTERS 30th September 2020 Vol© The Institution of Engineering and Technology 2020Submitted: 19 June 2020 E-first: 10 August 2020doi: 10.1049/el.2020.1818One or more of the Figures in this Letter are available in colour online.W.P. du Plessis (University of Pretoria, Pretoria 0002, South Africa)✉ E-mail: wduplessis@ieee.orgReferences1 Howard, D.D.: ‘Radar target angular scintillation in tracking andguidance systems based on echo signal phase front distortion’. Proc.Nat. Eng. Conf., vol. 15, 1959. reprinted in Radars, Vol. 4, RadarResolution & Multipath Effects, David K. 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Phase‐conjugating retrodirective cross‐eye jamming

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Phase‐conjugating retrodirective cross‐eye jamming

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