Analysis of an Ultra High Resolution Wideband False

Target Technique

M. Attygalle, D. Dissanayake, P. Hall, K. Hue and K. Brown

Defence Science and Technology Group

Edinburgh, SA, 5111, Australia

manik.attygalle@dst.defence.gov.au

Abstract—The paper presents a novel ultra-wideband (6

GHz), high resolution (0.16 ps) true time delay range-velocity

gate pull off (RVGPO) deception technique that is effective

against modern threat waveforms. It utilizes fractional sample

delays that increase the effective sample rate by up to three

orders of magnitude. The paper presents theoretical discussion

and experimental results of the time domain waveform and

spectrum generated by this high resolution technique, that show

the spurious Doppler signals generated are significantly lower (by

more than 30 dB) than that of a conventional sample delay based

implementation.

Keywords—electronic attack, digital RF memory, electronic

countermeasures, fractional delay

I. INTRODUCTION

A radio frequency (RF) electronic attack (EA) system or jammer is typically employed to deny or degrade radar target information and inject false targets into the radar system [1]. One of the most simple and effective (against modern threat waveforms) RF EA techniques that may be implemented in digital RF memory (DRFM) based deception jammers, is a true time delay (TTD) coordinated range and velocity gate pull-off (RVGPO) deception technique. True time delay techniques are effective against different waveform types, including low probability of intercept (LPI) radar signals with frequency and waveform agility, and are much simpler to implement than other techniques because they do not need to detect the received signal and extract signal parameters. The technique relies on the principle of delaying the captured input signal progressively in a true time fashion that achieves both velocity and range pull off synchronously, thus making the radar tracker follow the false target instead of the real target.

A DRFM based EA system uses an analogue to digital converter (ADC) to sample the incoming signal, then digitally processes the signal according to the countermeasure techniques to be implemented (in this case progressively delaying the signal) and retransmits the signal using a digital to analogue converter (DAC). A RF down/up converter is utilized to down and up convert the radar RF signal to baseband or an intermediate frequency before digitization as shown in Fig. 1. One limitation of this technique comes from the discrete nature of the delays that are limited by the resolution of the sampling and quantization [2-3]. Even with high speed sampling in modern ADCs/DACs, this effect results in spurious signals in

retransmitted signal that can be used by electronic protection schemes to discriminate false targets from real ones [3-4]. This effect can be exacerbated when emulating slow moving targets where the required time delays can be relatively small.

We have developed an ultra-high resolution wideband deceptive jammer system in a DRFM that is capable of implementing a high resolution range-velocity gate pull-off technique suitable for a range of EA application. The system uses fractional sample delays [5], to achieve wideband high-resolution time delays and increases the effective sampling rate by up to 3 orders of magnitude in order to achieve the required time resolution. This paper analyses the performance of this technique in terms of the time domain waveform and spectral purity in achieving RVGPO of a LPI radar waveform. In this implementation the 12 Gsps sampling rate of the system is increased by 512 times to an effective sampling rate of 6144 Gsps with a time resolution of (0.16 ps). The experimental results obtained from the DRFM EA system is compared against simulation results of a conventional DRFM based implementation at the original sample rate of 12 Gsps. The paper is organized as follows. Section 2 presents the theory for discrete RVGPO and discusses the effect of discrete delays on the signal spectrum while Section 3 presents the time domain and spectral analysis of the novel technique, showing that the Doppler spurious signals generated by this techniques are significantly lower (by more than 30 dB) compared to the conventional case.

II. ANALYTICAL DISCUSSION OF TRUE TIME DELAY

RVGPO

In this section the effect of the discrete delays imparted on a radar signal is discussed mathematically. A radar signal with

ADC

DAC

FPGA

(TTDRVGPO

Algorithm)

~

Fig. 1. Functional block diagram of digital true time delay RVGPO

system. (FPGA – field programmable gate array).

periodic pulses over the coherent processing interval (CPI) can be written as

𝑠�𝑡 = 𝑟𝑒𝑐𝑡 𝑡

𝜏 ∗ 𝛿�𝑡 − 𝑛𝑇

∞

𝑛=−∞

. 𝑟𝑒𝑐𝑡 𝑡

𝑁𝑇 .𝑤�𝑡

(1)

where T is pulse repetition period, N is the number of

pulses in the CPI, is the pulse width, and w(t) is the radar

waveform at the carrier frequency. Here depicts the convolution operation.

The rectangular function rect(t) is defined as

𝑟𝑒𝑐𝑡�𝑡 = 1, -1

2< t ≤

1

2

0, 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒

(2)

The first half of (1) depicts the pulse train and the second rectangular function puts a time window over the CPI. This function is finally multiplied by the respective waveform used, w(t) [6].

The radar waveform is given by the following: (3) for a pulsed continuous wave (CW) and (4) for an up-chirped pulsed linear frequency modulation (LFM) signal respectively.

𝑤𝐶𝑊�𝑡 = 𝐴𝑒2𝜋𝑓𝑐𝑡 (3)

𝑤𝐿𝐹𝑀�𝑡 = 𝐴𝑒2𝜋 𝑓𝑐𝑡+12𝛼𝑡2 , 0 ≤ 𝑡 ≤ 𝜏 (4)

Where, fc is the carrier frequency and is the chirp rate of the LFM signal.

Consider the pulse train function over the CPI

𝑓�𝑡 = 𝑟𝑒𝑐𝑡 𝑡

𝜏 ∗ 𝛿�𝑡 − 𝑛𝑇

∞

𝑛=−∞

. 𝑟𝑒𝑐𝑡 𝑡

𝑁𝑇

(5)

The spectrum of this signal can be written as [6]

𝐹�𝑓 = 𝜏𝑁 𝑠𝑖𝑛�𝜋𝜏𝑚𝑓𝑟

𝜋𝜏𝑚𝑓𝑟.𝑠𝑖𝑛 𝜋𝑁𝑇�𝑓 − 𝑚𝑓𝑟

𝜋𝑁𝑇�𝑓 − 𝑚𝑓𝑟

∞

𝑚=−∞

(6)

The spectrum of the pulse train consists of discrete spectral components spaced by fr = 1/T, the pulse repetition frequency (PRF). The Fourier transform of the CPI rectangular function produces a sinc function of width 1/NT at each delta function. The pulse rectangular function produces a sinc function of

width 1/ that forms the envelope of all the spectral components.

Now the spectrum of the radar signal at the carrier frequency

𝑠�𝑡 = 𝑓�𝑡 .𝑤�𝑡 (7)

is given by

𝑆�𝑓 = 𝐹�𝑓 ∗ 𝑤�𝑓 (8)

Now consider a pulsed CW case with A=1 given below

𝑠�𝑡 = 𝑟𝑒𝑐𝑡 𝑡

𝜏 ∗ 𝛿�𝑡 − 𝑛𝑇

∞

𝑛=−∞

. 𝑟𝑒𝑐𝑡 𝑡

𝑁𝑇 . 𝑒2𝜋𝑓𝑐 𝑡

(9)

In the pulsed CW case the spectrum of the radar signal is spectrum of f shifted to the respective carrier frequency and is given by [7]

𝑆�𝑓 = 𝐹�𝑓 − 𝑓𝑐

= 𝜏𝑁 𝑠𝑖𝑛�𝜋𝜏𝑚𝑓𝑟

𝜋𝜏𝑚𝑓𝑟.𝑠𝑖𝑛 𝜋𝑁𝑇�𝑓 − 𝑚𝑓𝑟 − 𝑓𝑐

𝜋𝑁𝑇�𝑓 − 𝑚𝑓𝑟 − 𝑓𝑐

∞

𝑚=−∞

(10)

The pulsed LFM case will follow similar argument but with a finite bandwidth signal as opposed to a single carrier frequency. Fig. 2 shows the power spectral density of a pulsed

LFM signal with 20 MHz chirp bandwidth and PRI of 100 s. The inset shows a zoomed view near 10 MHz frequency showing the two spectral components separated by the 10 kHz PRF.

After true time delay, the delayed version of the signal Sd(t) in time domain can be given by

𝑆𝑑�𝑡 = 𝑟𝑒𝑐𝑡 𝑡

𝜏 ∗ 𝛿 𝑡 − 𝑛𝑇 − 𝑑�𝑡

∞

𝑛=−∞

× 𝑟𝑒𝑐𝑡 𝑡

𝑁𝑇 . 𝑒𝑗2𝜋𝑓𝑐 𝑡−𝑑�𝑡

(11)

Where d(t) is the delay function, and in the ideal case the delayed signal will be continuous linear function given by

𝑑𝐼�𝑡 = 2𝑣𝑡/𝑐 (12)

Where v is the velocity pull off rate and c is speed of light. Note in this discussion, any delays and Doppler shifts due to actual target movements relative to radar are ignored.

Fig. 3 shows the true time delay of the waveform against time for a RVGPO at a constant velocity of 10 m/s. In the non-ideal discrete case, the delay function is a stair step function with the step resolution equal to either the sampling rate (when the delay is achieved on a sample by sample basis) shown in dotted blue line or fractional sample rate (when the delay is achieved at a fractional sample rate) shown in solid red line. In this case the number of fractional delays is equal to 512 (effective sample rate of 6144 Gsps). As shown in Fig. 3, the stair-step delay function with a large number of fractional

10 kHz

Am

plit

ud

e (d

B)

Fig. 2. Spectrum of a pulsed LFM signal with a 10 MHz bandwidth and

40 s pulse width and a PRI of 100 µs. Inset shows two individual

spectral components separated by the 10 kHz PRF.

delays will be closer to the ideal case relative to the function at the original sample rate (12 Gsps).

Mathematically, the stair-step delay function during the CPI can be given by

𝑑𝑆�𝑡 = 𝑇𝑑 𝑛. 𝑟𝑒𝑐𝑡 𝑡 −

𝑐𝑇𝑑2𝑣

𝑛 −𝑐𝑇𝑑4𝑣

𝑐𝑇𝑑2𝑣

∞

𝑛=−∞

(13)

This can be rearranged to give

𝑑𝑆�𝑡 = 𝑇𝑑 . 𝑟𝑒𝑐𝑡 𝑡 −

2

∗ 𝑛. 𝛿�𝑡 − 𝑛

∞

𝑛=−∞

(14)

Where = cTd/2v is the update rate of the delay and Td is delay increment. Note, for the sample delay, Td ~ 83 ps and for the fractional delay, Td ~ 0.16 ps.

Typically, the time delay introduced on the pulse profile is negligible compared to the pulse width and therefore we can approximate the delayed signal given in (11) as

𝑆𝑑�𝑡 =

𝑟𝑒𝑐𝑡 𝑡

𝜏 ∗ 𝛿�𝑡 − 𝑛𝑇

𝑁

𝑛=0

𝑟𝑒𝑐𝑡 𝑡

𝑁𝑇 . 𝑒𝑗2𝜋𝑓𝑐 𝑡−𝑑�𝑡

(15)

The spectrum of the signal now is

𝑆𝑑�𝑓 = 𝐹�𝑓 ∗ 𝑊′�𝑓 (16)

Where w’(t) is the phase delayed waveform function

𝑤′�𝑡 = 𝑒𝑗2𝜋𝑓𝑐 𝑡−𝑑�𝑡 = 𝑒𝑗2𝜋𝑓𝑐𝑡 . 𝑒− 𝑗2𝜋𝑓𝑐𝑑�𝑡 (17)

and

𝑊′�𝑓 = 𝛿�𝑓 − 𝑓𝑐 ∗ 𝑃�𝑓 = 𝑃�𝑓 − 𝑓𝑐 (18)

Therefore the spectrum of the discrete delayed signal will be F convolved with P, (p(t) is the phase delay function), shifted to the carrier frequency of the signal.

Using (14) we can write p(t) as

𝑝�𝑡 = 𝑒−𝑗2𝜋𝑓𝑐 .𝑇𝑑 . 𝑟𝑒𝑐𝑡

𝑡−𝛾2𝛾 ∗ 𝑛 .𝛿�𝑡−𝑛𝛾 ∞

𝑛=−∞

(19)

This can be rearranged to give [7]

𝑝�𝑡 = 𝑟𝑒𝑐𝑡 𝑡 −

𝛾2

𝛾 ∗ 𝑒

−𝑗2𝜋𝑓𝑐 .𝑇𝑑 1𝛾 𝑡

. 𝛿�𝑡 − 𝑛𝛾

∞

𝑛=−∞

(20)

and the spectrum of p(t) is given by

𝑃�𝑓 = 𝑒−𝑗𝜋𝑓𝛾𝑠𝑖𝑛�𝜋𝑓𝛾

𝜋𝑓𝛾 𝛿 𝑓 −

2𝑣𝑓𝑐𝑐

−𝑛

𝛾

∞

𝑛=−∞

(21)

In the case of an ideal delay, the carrier frequency, fc, in the

original signal can be replaced by fd = fc 2vfc/c, indicating that the initial spectrum will be shifted by the ideal Doppler frequency. When the delay is not ideal or is a stair step function, the spectrum observed in Fig. 2 will have additional spectral components according to the summation in (21). Compared with the spectrum of the original signal given in (10), the stepwise delayed signal will have additional frequency

components separated by 1/ = 2v/cTd. For example, when the sampling rate is 12 Gsps and induced velocity of 10 m/s, the additional discrete components will be separated by 800 Hz as shown in Fig 4(a). With the use of 512 fractional delays, this separation will be more than 400 kHz.

III. RESULTS & DISCUSSION

This section compares the experimentally generated results of the ultra-high resolution DRFM system, that implements the

(b)

(a)800 Hz

Am

plit

ud

e (

dB

)A

mp

litu

de

(d

B)

Fig. 4. Power spectral density of the time delayed waveform at a rate of

10 m/s velocity. (a) Simulated at 12 Gsps sampling resolution and (b)

experimentally measured fractional delay implementation.

Fig. 3. Time delay for RVGPO at a constant 10 m/s velocity for the ideal

(solid blue), sample by sample (dotted blue) and fractional sample (red)

implementations.

fractional delay RVGPO technique, to simulated results of a conventional sample based true time delay RVGPO technique. Comparisons are made in terms of the spectral purity in the time domain waveform, Doppler spectrum and range Doppler map generated by a threat stimulator. A Curtiss-Wright CHAMP-WB-DRFM digital board that has a Xilinx Virtex 7 FPGA, which has integrated Tektronix 12 Gsps ADC (8 bit) and DAC (10 bit) modules [8], is used in the implementation. The results presented here are at a nominal carrier frequency of 1 GHz, processed at a sample rate of 100 MHz. The waveform used is a pulsed LFM signal with 20 MHz linear chirp, a PRI of

100 s and a pulse width of 40 s. The CPI was 256 pulses long or 25.6 ms. In order to show the effectiveness of the technique in different application scenarios, the false target was pulled-off at a constant 10 m/s velocity using the true time delay technique.

Fig. 4 shows the power spectral density of the RVGPO signal with (a) delay step size equivalent to the ADC sample rate of 12 Gsps, and (b) the experimentally measured signal through the DRFM using a fractional delay implementation with an equivalent sample rate of 6144 Gsps. A hamming window was used on the time domain waveform. The figures show a zoomed view of two line spectral components separated by 10 kHz (the PRF) near the 1 GHz frequency of the 20 MHz

LFM signal with a 100 s PRI, analogous to the inset in Fig. 2. In both cases the 10 m/s coordinated RVGPO technique

implemented would, in an ideal case, have a 67.4 Hz Doppler

shift. However, even at the high sampling rate of 12 Gsps, significant spurious signals are observed in the waveform as shown in Fig. 4(a). These spurs are separated by 800 Hz, as expected. In the fractional delay implementation shown in Fig. 4(b), these spurs are almost completely removed.

Fig. 5 shows the in-phase (solid blue) and quadrature (dotted red) components of the waveform along the slow time dimension across multiple PRIs for: (a) when the signal is delayed at the sample rate; and (b) when the signal is delayed at the fractional sample rate. Here the signal delayed at the sample rate is simulated, while the signal delayed at the fractional sample rate is experimentally measured. No windowing is used in making the measurements. The waveforms clearly show the phase rotation due to the Doppler frequency shift with the former figure clearly showing the effects of the finite ‘relatively slower’ sample rate.

In order to observe the effects in the frequency domain, the respective power spectral densities of the waveforms against the slow time dimension are plotted in Fig. 6. The power spectral density in Fig. 6(a), when the signal is delayed at the sample rate of 12 Gsps, show significant spurious frequency components that are only 20 dBc down from the expected Doppler frequency. On the other hand, Fig. 6(b) shows that the experimentally measured signal that is delayed at the fractional

sample rate has spurious Doppler frequencies at less than 50 dBc. The fractional delay implementation has much

(b)

(a)

Fig. 6. Power spectral density of the waveform along the slow time

dimension. (a) Simulated at 12 Gsps resolution and (b) experimentally

measured at the effective fractional sample rate of 6144 Gsps.

(b)

(a)

Fig. 5. IQ waveform against slow time dimension over the 256 PRIs.

(a) Simulated at 12 Gbps resolution and (b) experimentally measured at

the effective fractional sample rate of 6144 Gsps.

better Doppler spectral characteristic close to that of an ideal signal scenario with more than 30 dB reduction in the spurious signals.

Fig. 7 show range-Doppler maps for the above scenario with 256 pulse CPI for (a) simulated signal at 12 GHz sample rate (81.33 ps delay resolution) and (b) experimentally measured signal at an equivalent 6144 GHz sample rate (0.16 ps delay resolution). Blackman windows are used in the range-Doppler maps. We observe the signal that is delayed at the sample rate has significant additional Doppler peaks creating ‘ghost’ targets, while the fractional delay implementation shows a significant reduction in this unwanted effect.

IV. CONCLUSION

The paper presented a novel ultra- high resolution (0.16 ps) true time delay range-velocity gate pull off (RVGPO) deception technique that is effective against modern threat waveforms. It utilizes fractional sample delays that increase the effective sample rate by up to three orders of magnitude. The paper presented a theoretical analysis and experimental results of the time domain waveform and spectrum generated by this high resolution technique. The results clearly showed the effectiveness of the true time fractional delay RVGPO implementation, and show that realistic target behavior can be achieved with the ultra-high resolution DRFM system. The technique is both frequency and waveform agnostic and will be effective against next generation waveforms that are wideband and agile.

ACKNOWLEDGMENT

The authors would like to thank Dr. Anthony Szabo for valuable feedback.

REFERENCES

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[3] M. Greco, F. Gini, A. Farina and V. Ravenni, “Effect of phase and range gate pull-off delay quantisation on jammer signal”, IEE Proc. Radar, Sonar and Navigation, Vol. 153, No. 5, Oct 2006, pp. 454-459.

[4] D. Gold and H. Ur, “Method for reduction of harmonics, caused by coarse quantisation, suitable for digital radio frequency memory”, IEE Elec. Lett. Vol. 29, No. 4, 1993, pp. 411-412.

[5] T.I. Laakso, V. Valimaki, M. Karjalainen, U.K. Laine, “Splitting the unit delay: Tools for fractional delay filter design”, IEEE Signal Processing Magazine, 1996, pp. 30-60.

[6] G. W. Stimson, “Introduction to airborne radar”, 2nd Ed, SciTech Publishing Inc., 1998.

[7] S. D. Berger, “The spectrum of a digital radio frequency memory linear range gate stealer electronic attack signal”, IEEE Trans. on aerospace & Elec. Sys., Vol. 39, No. 2, Apr. 2003.

[8] http://www.curtisswrightds/products/cots-boards/fpga-cards/drfm/

(b)

(a)

Fig. 7. Range-Doppler maps for RVGPO signals. (a) Simulated at 12

Gsps resolution and (b) experimentally measured at the fractional

sample rate of 6144 Gsps.