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Design of less-detectable RADAR waveforms using stepped frequency modulation and coding
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Procedia Computer Science 00 (2018) (20 000–000
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Procedia Computer Science 143 (2018) 39–47
8th International Conference on Advances in Computing and Communication (ICACC (ICACC-2018) 8th International Conference on Advances in Computing and Communication (ICACC (ICACC-2018)
8th International Conference on Advances in Computing and Communication (ICACC-2018)
Design of less-detectable detectable RADAR waveforms using stepped Design of less-detectable detectablemodulation RADAR waveforms frequency and codingusing stepped frequency modulation and coding
a
Vignesh Raa,Shanmugha Sundaram G Aa,b,* ,Soman K Paa a,b,* Vignesh R ,Shanmugha Sundaram G A ,Soman K P
Center For Computational Engineering And Networking(CEN), Networkin Amrita School of Engineering-Coimbatore, Amrita Vishwa Vidyapeetham, India Center For Computational Engineering And Networking(CEN), Networkin Amrita School of Engineering-Coimbatore, Amrita Vishwa Vidyapeetham, India b Department Of Electronics And Communications Engineering, Engineering Amrita School of Engineering - Coimbatore, Amrita Vishwa Vidyapeetham, India b Department Of Electronics And Communications Engineering, Engineering Amrita School of Engineering - Coimbatore, Amrita Vishwa Vidyapeetham, India a
Abstract Abstract Radar signal generation and processing techniques are developing with an aim of reducing interference and signal interception interception. Signal signal jamming and signal have become emerging areas of interest in of thereducing field of radar engineering. So there is a nneed Radar generation anddetection processing techniques are developing with an aim interference and signal interception interception. for design and development of new waveforms which are lessareas detectable by the less susceptible to jamming jamming. Signal jamming and signal detection have become emerging of interest in hostile the fieldreceiver of radarand engineering. So there is a nneed In the work here, Frequency Waveform (SFW) SFW) is by modulated with phase and modulation techniques such as for design andmentioned development of Stepped new waveforms which are less detectable the hostile receiver less susceptible to jamming jamming. Barker codes mentioned and nd polyphase to improve the Waveform complexity(SFW) and to isreduce the detectability waveform techniques thus increasing In the work here,codes Stepped Frequency SFW) modulated with phaseofmodulation such the as bandwidth of waveform and limiting transmitted power of the pulse compression techniques. The SFW Barker codes and nd polyphase codes tothe improve the complexity andwaveform to reduce by theusing detectability of waveform thus increasing the considered of here is generated d having step size.power Pulse compression technique is employed here in order to generate bandwidth waveform and limitingvarying the transmitted of the waveform by using pulse compression techniques. Thea pulse SFW having a range of shorter varying pulse and transmitted of longer pulse. The modulatedhere waveform have considered hereresolution is generated d having step size. Pulsepower compression technique is employed in ordercharacteristics to generate a pulse been studied andresolution analyzed of using ing ambiguity functions of the power waveform. having a range shorter pulse and transmitted of longer pulse. The modulated waveform characteristics have been studied and analyzed using ing ambiguity functions of the waveform. © 2018 The Authors. Published by Elsevier B.V. © 2018 The Authors. Published by Elsevier B.V. This is an open accessPublished article under the CC BY-NC nd/4.0/) © 2018 The Authors. by Elsevier B.V.NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/ This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) Selection review under responsibility of the scientific committee of the 8th International Conference on Advances in This is an and openpeer-review access article under the CC BY-NC NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/ nd/4.0/) Selection and peer-review under responsibility of the scientific committee of the 8th International Conference on Advances in Computing and Communication (ICACC-2018). Selection and peer-review review under responsibility of the scientific committee of the 8th International Conference on Advances in Computing and Communication (ICACC-2018). Computing and Communication (ICACC-2018). Keywords: SFW,, Phase modulation, Pulse compression, Ambiguity Function, Less detectable waveform Keywords: SFW,, Phase modulation, Pulse compression, Ambiguity Function, Less detectable waveform
*
Corresponding author. SIERS Research Laboratory, Amrita School of Engineering - Coimbatore, Amrita Vishwa Vidyapeetham, India. T Tel.: Corresponding author. SIERS Research Laboratory, Amrita School of Engineering - Coimbatore, Amrita Vishwa Vidyapeetham, India. T Tel.: E-mail address: [email protected] +91-422-268-5000: fax: +91-422-268-6274. E-mail address: [email protected] 0509 © 2018 The Authors. Published by Elsevier B.V. 1877-0509 This is0509 an open access under the CC BY-NC-ND NDB.V. license (https://creativecommons.org/licenses/by-nc-nd/4.0/) ( © 2018 Thearticle Authors. Published by Elsevier 1877-0509 Selection review under responsibility of theND scientific of the 8th International International Conference on Advances in Computing and This is an and openpeer-review access article under the CC BY-NC-ND licensecommittee ( (https://creativecommons.org/licenses/by-nc-nd/4.0/) Communication (ICACC-2018). Selection and peer-review review under responsibility of the scientific committee of the 8th International International Conference on Advances in Computing and Communication (ICACC-2018).
*+91-422-268-5000: fax: +91-422-268-6274.
1877-0509 © 2018 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) Selection and peer-review under responsibility of the scientific committee of the 8th International Conference on Advances in Computing and Communication (ICACC-2018). 10.1016/j.procs.2018.10.349
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R Vignesh et al. / Procedia Computer Science 143 (2018) 39–47 Vignesh R et al. / Procedia Computer Science 00 (2018) 000–000
1. Introduction The short duration pulse train waveforms have been widely equipped with military radars in the past[1]. These pulses have high peak to average power ratio without any phase or frequency modulations which makes them easily susceptible to electronic support measures, electronic attack, and radar warning receivers. For the survival of these enemy attacks complex radar waveforms are designed in order to reduce detection and identification of passive intercept receiver devices. These waveforms are termed as low probability of interception (LPI) waveforms [1, 2]. The LPI technique is based on a property of emitter due to its wide bandwidth, low power, varying frequency, and other attributes make interception of radar difficult [3,7]. The characteristics of the target are determined with help of radar by transmitting known signal and receiving the echo signal scattered by the target. The echo signal plays a major role in information extraction and processing of waveform at receiver side [4]. The maximum unambiguous range determines the pulse repetition interval (PRI) of radar waveform[14]. Range resolution is the ability of radar to classify targets correctly based on the desired range of the targets. Range resolution is inversely related to pulse bandwidth of waveform. Preservation of high range resolution can be achieved by usage of stepped frequency waveforms (SFW). In order to reduce the detectability of these waveform phase modulation techniques, frequency modulation techniques and various spread spectrum techniques are employed [5,13]. Wideband modulation techniques are generally employed to improve the complexity of the waveform. The commonly used wideband modulation techniques include frequency modulation techniques such as Linear frequency modulation (LFM), Non-Linear frequency modulation (NLFM) and phase modulation techniques such as Barker codes, Frank codes, Polyphase codes [8-10]. The probability of detection and probability of interception is dependent on the input SNR (signal to noise ratio) at interceptor [3, 4]. Generally, SFW of uniform step size and wide bandwidth are employed for generating radar waveform with good range resolution. Here SFW of varying frequency step size is considered in the pretext of increasing the complexity and detecting the target with good range resolution [6,12]. In this paper, the performance of pulse compression techniques is compared with the help of ambiguity function also called as uncertainty function and two-dimensional autocorrelation function[9,11]. The time-bandwidth product of various waveforms is also compared. Ambiguity function effectiveness is generally measured using two measurements namely peak sidelobe ratio (PSLR) and integrated sidelobe ratio (ISLR). The effectiveness of phase modulated SFW is compared with previous existing waveforms such as rectangular waveform, uniform linear frequency waveform (LFM) and the detectability performance is analyzed. The delay and Doppler characteristics of the waveform are also analyzed using ambiguity function. The rest of the paper is as follows: Section II describes Frequency modulated pulse compression. Section III describes Phase modulated pulse compression. Section IV describes the proposed technique of modulating stepped waveform with P1 code. Section V describes the results and discussion. Finally in section VI conclusion is done. 2. Frequency Modulated Pulse Compression Modulation is a technique used to increase the transmission bandwidth of the waveform [9]. The transmitted waveform received as echo when matched filtered at the receiver side is used to extract range information about the target. Frequency modulation is a technique in which the frequency varies with time either uniformly or nonuniformly in order to obtain highly suppressed sidelobes, so that pulse compression achieved is good[15]. Consider a rectangular pulse having single frequency with no modulation. Figure 1 shows the autocorrelation function of the rectangular waveform. It is clear from the plot that the waveform after performing matched filtering at receiver side the output occupies a particular time period. This delay area occupied by the waveform ambiguity
R Vignesh al. / Procedia Computer Science 143 000–000 (2018) 39–47 Vignesh R et al. /etProcedia Computer Science 00 (2018)
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Fig. 1. Autocorrelation of rectangular pulse
plot indicates that two or more targets are distinguishable only when they are separated by a delay of particular time period occupied in the plot. 2.1 Uniform SFW SFW is a type of frequency modulation technique for generating a high range resolution profile. A sequence of N pulses with fixed pulse repetition frequency (PRF) and the varying carrier frequency is transmitted by SFW radar. Each set of N pulses is called coherent processing interval (CPI) or burst. The frequency of each pulse in the sequence is increased uniformly from one pulse to another by a fixed step size (∆f). The frequency of the first pulse is taken as carrier frequency (f0) and the subsequent pulse has a difference of step size (∆f) from the preceding pulse as shown in Figure 2. The received signal is sampled and spectral weighting is applied to reduce the sidelobe levels. The quadrature component for each burst is stored and IDFT is applied to find out the range profile of the corresponding burst. Thus for n-th transmitted pulse in sequence, with n=0, 1, 2…N-1, the carrier frequency (fn) of the waveform for the n-th step is given by [10]:
fn f 0 nf
(1)
Each pulse in SFW can be modulated using any modulation scheme. If the transmitted waveform for the n-th pulse is:
S 1 t A1cos[2 ( f 0 n)t ]
(2)
Then the received signal from the target after a time delay of 2R/c is given as [10]:
S 2 t A2 cos[2 ( f 0 n) t 2 R / c ]
(3)
Where R is Target Range in meters, c is propagation speed in meter per second and N is number of steps or pulses Range resolution (∆R) of SFW is determined from the overall bandwidth [8,14].
R c / 2 N f
(4)
From equation (4) it can be understood that the range resolution of SFW can be increased by increasing number of pulses in the sequence or frequency step size. The unambiguous range window (Ru) of stepped fm waveform is given by: Ru c / 2f (5)
R Vignesh et al. / Procedia Computer Science 143 (2018) 39–47 Vignesh R et al. / Procedia Computer Science 00 (2018) 000–000
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Fig. 2. Stepped frequency modulated waveform.
From equations (4) and (5) it noted that the frequency step size of the SFW plays an important role in determining the unambiguous range and range resolution. Figure 2 shows SFW with linearly increasing step size. Frequency step size is generally chosen to be approximately half the inverse of pulse width (τ):
f 1/
(6)
2.2. Non- Uniform SFW Non-uniform SFW is designed by replacing the constant step size (∆f) parameter of SFW. For the generation of a less detectable waveform, two main parameters are to be considered; they are waveform bandwidth and modulation type. SFW have high bandwidth. In order to make stepped waveform more complex and difficult to detect the frequency step size of the waveform is set to vary accordingly either uniformly or non-uniformly based on the information provided at the transmitter end. The non-uniform stepped waveform is modulated with LPI waveforms such as the Frank codes [9],P1, P2, P3, P4 codes etc.. in order to reduce the sidelobes which helps in increasing the stealthiness and to implement pulse compression in SFW for generating shorter pulse with less transmitted power required for transmission of longer pulse [15]. 3. Phase Modulated Pulse Compression Phase modulated pulse compression is a technique in which the phase of the signal is varied with time. Phase modulation is done to increase the bandwidth of the signal. One simple way is to use binary phase shift with the code sequence. But the random sequence is not effective as the amplitude varies for each sidelobe. So Barker codes were introduced which gives equal amplitude sidelobes [11]. 3.1. Barker codes Barker codes belong to binary phase coded pulse compression technique with a phase shift of 00 and 1800 [11]. These codes don’t have random sequences and only particular combinations which give equal amplitude sidelobes are considered. The largest combination available is 13bits.The main advantage of this code is that no amplitude weighting is needed to suppress sidelobes. The possible combinations of Barker code and the PSLR value for these combinations are listed in Table 1. These PSLR values were obtained when there is no Doppler shift and no delay introduced in autocorrelation process.
R Vignesh et al. / Procedia Computer Science 143 (2018) 39–47 Vignesh R et al. / Procedia Computer Science 00 (2018) 000–000
a
43 5
b Fig.3. (a) Doppler cut of 5-bit Barker code; (b) Ambiguity function of 5-bit Barker code
The Barker bit combinations are employed for choosing the step size of nonuniform SFW. Here 5-bit combinations are taken. This result in a total of 25=32 combinations of different frequencies, but not all combinations can be selected. The main advantage of barker is combinations having equal amplitude sidelobes. The combinations used for selecting step size are 11101, 10101,11011,11100,11111 which have equal sidelobes. The main drawback of barker code is that pulse compression is achievable up to a maximum of 13 bits. The amount of pulse compression achievable is directly related to the number of sub-pulses. The Doppler cut and ambiguity function of Barker code having 5bit combinations are shown in Figure 3(a) and 3(b) Table 1.Barker codes with existing PSLR value.
Code Length 2 3 4 5 7 11 13
Code Elements 10,11 110 1101,1110 11101 1110010 11100010010 1111100110101
PSLR(dB) -6.0 -9.5 -12.0 -14.0 -16.9 -20.8 -22.3
3.2. Polyphase codes Polyphase codes use harmonically related phases based on certain fundamental phase increment. Frank, P1, P2 are derived from step approximations, while P3 and P4 codes are derived from uniform frequency modulated waveforms. The codes have N2 elements and so they can produce higher compression ratios than Barker code. The selection of the length of polyphase codes is an important factor [9].The phase of the i-th element of the j-th group of P1 code is given as:
* N 2 j 1 * j 1 N i 1 N
i, j
(7)
where i denotes N samples per frequency, and j denotes N frequency steps. The length of P1 code should always be even. The pulse width (τ) i.e. longer pulse is divided into N smaller sub-pulses called chip width Tc. Each sub-pulse can be binary. P1 code is used for double sideband detection. The Doppler response of P1 code at matched filter output is shown in Figure 4(a). It is noticed that the sidelobes of the P1 code are not of equal amplitude as that of Barker. The null occurs at 1 microseconds which states that the delay between two or more targets should be more than 1 microseconds for correct classification and detection of targets. The relationship between delay and Doppler frequency shift as a function of detected power is shown in
R Vignesh et al. / Procedia Computer Science 143 (2018) 39–47 Vignesh R et al. / Procedia Computer Science 00 (2018) 000–000
44 6
a
b Fig.4. (a) Doppler cut of P1 code; (b) Ambiguity function of P1 code
Figure 4(b). It states that the detection of targets is accurate within the region of higher power concentration where delay and Doppler values are zero and it decreases with reduction in power. 4. Phase coded non-uniform SFW SFW is known for high range resolution, while P1 code is known for LPI properties [6,11]. So a new waveform has been developed by modulating the SFW with polyphase (P1) codes. This waveform is expected to possess both properties of the stepped waveform and polyphase codes such as high range resolution and less detectability. The varying step size is fixed to various combinations by the user. Thus the user alone can retrieve the information about the radar transmitter waveform from the received echo signal, while the jammer or interceptor have little probability to identify and acquire the radar signals, having been entirely unaware of the frequency combinations used. The performance of the waveform is analyzed by means of ambiguity function. 4.1. Ambiguity Function The ambiguity function is defined as the absolute value of matched filter output envelope. The input signal to the filter is a Doppler shifted version of the return signal, to which the filter is matched. The ambiguity function is given as [9,11]:
| X ( , fd ) ||
s(t )*(t ).exp( j 2 f t )dt | d
(8)
Where s(t) denotes transmitted signal, τ denotes delay and fd denotes frequency shift In any radar system, two measurements are mainly used for measuring the effectiveness of the ambiguity function: the PSLR and ISLR. The former indicates the ability of radar to detect weak targets. It is associated with the probability of false alarm in particular range bin due to the presence of a target in neighboring range bin [9]:
l arg est _ sidelobe PSLR dB 20*log mainlobe _ peak
(9)
ISLR is a measure of how much energy is leaking from the main lobe of impulse response function of the target. It is the measure of energy distributed in sidelobes [9]:
ISLR(dB) 10* log (
sidelobe 2 ) mainlobe _ peak 2
(10)
R Vignesh et al. / Procedia Computer Science 143 (2018) 39–47 Vignesh R et al. / Procedia Computer Science 00 (2018) 000–000
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5. Results and Discussion An important inference of pulse compression signal is obtained with the help of the ambiguity function [9]. Ambiguity is similar in characteristics to matched filtering at the radar receiver side. The SFW is generated with an
a
b Fig .5. (a) Delay cut of SFW with constant
f
; (b) Doppler cut of SFW with constant
f
unambiguous range of 30 km, a range resolution 150 m. Hence, the sample rate will be fs=2MHz, with a pulse width of 5microseconds, and a pulse repetition frequency (PRF) of 5MHz.The number of frequency elements considered is 5, so there is 4 frequency step size. Figure 5(a) explains that the targets should be separated by at least a range equivalent of 0.2MHz for correct classification of targets.
a
b Fig . 6. (a) Ambiguity of SFW with constant
f
; (b) Spectrogram of SFW with constant
f
The detection of targets corresponding to the radial velocity of the target is depicted in Figure 5(b). The first null occurred at 10 microseconds, which is the delay necessary between targets for correct identification. The delay as a function of Doppler characteristics is plotted in Figure 6(a) and shows that target detection is good in the area where the signal power concentration is more. Figure 6(b) shows that the frequency step size increases uniformly. In the case of stepped waveform with constant frequency step size that is shown in Figures 5 and 6, the frequency step size (∆f) increases linearly. The range that has been defined between two targets is 0.1 MHz for better identification, and the delay between targets should be more than 1 ms for correct target detection. The case of stepped waveform with varying frequency step size is explained in Figures 7 and 8. The area of concentration where target detection is good is depicted in Figure 7(a), while Figure 7(b) shows the spectrogram for SFM with varying step size used to improve the complexity and stealthiness of the waveform. The SFW with varying step size is further phase modulated with the P1 code to improve the low probability of intercept characteristics of waveform thereby improving the bandwidth of the waveform by phase modulation. The first null
R Vignesh et al. / Procedia Computer Science 143 (2018) 39–47 Vignesh R et al. / Procedia Computer Science 00 (2018) 000–000
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occurs at 0.05 MHz in the frequency-shift Doppler domain and at 0.5 ms in the time delay domain. The unambiguous range and delay between the targets are reduced in the modulated waveform compared to the normal stepped waveform.
a
b Fig . 7. (a) Ambiguity of SFW with varying
f
a
; (b) Spectrogram of SFW with varying
f
b Fig . 8. (a) Ambiguity of P1 modulated SFW with varying
f
; (b) Spectrogram of P1 modulated SFW with varying
f
The detection of a radar target is good only in a particular region where power concentration is more, as inferred from Figure 8(a), while Figure 8(b) shows spectrogram of modulated SFW. When comparing among the results in Figures 7 and 8 it becomes evident that the power concentration for phase modulated waveform is greater. From the ambiguity function delay and Doppler cut the PSLR value for modulated waveform have been determined; the PSLR has been found to be -4.152 dB for the phase modulated waveform. The time-bandwidth product, that determines the amount of pulse compression in a waveform, has been chosen for modulating the waveform as having a value of 5. The bandwidth of modulated waveforms is more, thus increasing the SNR on the radar receiver side, and making the signal less detectable by the jammer. The results shown in Figures 5 - 8 compare favorably in terms of the delay, Doppler and ambiguity functions with previous studies performed using phase coded waveforms [11] and other conventional radar waveforms such as rectangular waveforms [1][10] and chirp waveforms [10], for constant and varying f . It is also observed that the ambiguity function obtained for phase modulated stepped frequency waveform has better range resolution compared to other waveforms along with low probability of intercept. 6. Conclusions The conventional pulsed radar waveforms have been subjected to pulse compression techniques such as waveform modulation and coding. These methods result in tandem enhancements to radar sensitivity and range resolution for dynamic targets. The characteristics of the phase modulated waveform are analyzed with the help of
R Vignesh et al. / Procedia Computer Science 143 (2018) 39–47 Vignesh R et al. / Procedia Computer Science 00 (2018) 000–000
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ambiguity functions Doppler plot and delay plot. The stepped waveform complexity is increased by using varying step size and is then modulated with an LPI code such as P1, thus decreasing the detectability and improving the stealthiness of radar waveforms. From the analysis of the ambiguity functions plots, it becomes apparent that the modulated waveform has good Doppler and delay characteristics along with a low probability of interception. References [1] Merrill, I. S. (2001). "Introduction to radar systems." Third Edition,Mc Grow-Hill., 7, 10. [2] Lange, J. B. (2012).”The Relative Nature of Low Probability Of Detection”,Radar.Defence R&D, Canada-Ottawa. [3] Ankarao, V., Srivatsa, S., and Sundaram, G. A. (2017).”Evaluation of pulse compression techniques for X-band radar systems.”, In: Wireless Communications, Signal Processing and Networking (WiSPNET), International Conference.,IEEE:1287-1292. [4] Weeks, G. D., Townsend, J. K., and Freebersyer, J. A. (1998). "A method and metric for quantitatively defining low probability of detection." In: Military Communications Conference. MILCOM 98. Proceedings., IEEE, 3, 821-826. [5] Paulose, A. (1994). "High radar range resolution with the step frequency waveform." Naval postgraduate school, Monterey ,CA., Master’s Thesis. 104. [6] Axelsson, S. R. (2007)."Analysis of random step frequency radar and comparison with experiments." IEEE Transactions on Geoscience and Remote Sensing, 45(4), 890-904. [7] Pace, P. E. (2009). "Detecting and classifying low probability of intercept radar." Second Edition , Artech House. [8] Srivatsa, S., and Sundaram, G.A. (2017). "PAM4-Based RADAR Counter-Measures in Hostile Environments." In: The International Symposium on Intelligent Systems Technologies and Applications, Springer, Cham., 390-400. [9] Jennison, B. K. (2003). "Detection of polyphase pulse compression waveforms using the Radon-ambiguity transform." IEEE Transactions on Aerospace and Electronic Systems, 39(1), 335-343. [10]Mahafza, B. R. (2005). "Radar Systems Analysis and Design Using MATLAB " Second Edition. Chapman and Hall/CRC. [11]Farnane, K., Minaoui, K., Rouijel, A., and Aboutajdine, D. (2015, November)."Analysis of the ambiguity function for phase-coded waveforms." In: Computer Systems and Applications (AICCSA), IEEE/ACS 12th International Conference of IEEE, 1-4. [12]Levanon,N. (2002).”Stepped-frequency pulse-train radar signal”.IEE proceedings-Radar,Sonar and Navigation,149(6),297-309. [13]Ning, B., Li, Z., Guan, L., and Zhou, F. (2017). "Probabilistic frequency-hopping sequence with low probability of detection based on spectrum sensing." IET Communications, 11(14), 2147-2153. [14]White, P. (2013) “Radar Waveforms for A&D and Automotive Radar.” White Paper., Rohde-Schwarz instruments. [15]Sachin, A. R., Ambat, S. K., and Hari, K. V. S. (2017).” Analysis of intra-pulse frequency modulated, low probability of interception, radar signals.” Sadhana, 42(7), 1037-1050.
ScienceDirect ScienceDirect
Procedia Computer Science 00 (2018) (20 000–000
Available at Science www.sciencedirect.com Procedia online Computer 00 (2018) (20 000–000
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Procedia Computer Science 143 (2018) 39–47
8th International Conference on Advances in Computing and Communication (ICACC (ICACC-2018) 8th International Conference on Advances in Computing and Communication (ICACC (ICACC-2018)
8th International Conference on Advances in Computing and Communication (ICACC-2018)
Design of less-detectable detectable RADAR waveforms using stepped Design of less-detectable detectablemodulation RADAR waveforms frequency and codingusing stepped frequency modulation and coding
a
Vignesh Raa,Shanmugha Sundaram G Aa,b,* ,Soman K Paa a,b,* Vignesh R ,Shanmugha Sundaram G A ,Soman K P
Center For Computational Engineering And Networking(CEN), Networkin Amrita School of Engineering-Coimbatore, Amrita Vishwa Vidyapeetham, India Center For Computational Engineering And Networking(CEN), Networkin Amrita School of Engineering-Coimbatore, Amrita Vishwa Vidyapeetham, India b Department Of Electronics And Communications Engineering, Engineering Amrita School of Engineering - Coimbatore, Amrita Vishwa Vidyapeetham, India b Department Of Electronics And Communications Engineering, Engineering Amrita School of Engineering - Coimbatore, Amrita Vishwa Vidyapeetham, India a
Abstract Abstract Radar signal generation and processing techniques are developing with an aim of reducing interference and signal interception interception. Signal signal jamming and signal have become emerging areas of interest in of thereducing field of radar engineering. So there is a nneed Radar generation anddetection processing techniques are developing with an aim interference and signal interception interception. for design and development of new waveforms which are lessareas detectable by the less susceptible to jamming jamming. Signal jamming and signal detection have become emerging of interest in hostile the fieldreceiver of radarand engineering. So there is a nneed In the work here, Frequency Waveform (SFW) SFW) is by modulated with phase and modulation techniques such as for design andmentioned development of Stepped new waveforms which are less detectable the hostile receiver less susceptible to jamming jamming. Barker codes mentioned and nd polyphase to improve the Waveform complexity(SFW) and to isreduce the detectability waveform techniques thus increasing In the work here,codes Stepped Frequency SFW) modulated with phaseofmodulation such the as bandwidth of waveform and limiting transmitted power of the pulse compression techniques. The SFW Barker codes and nd polyphase codes tothe improve the complexity andwaveform to reduce by theusing detectability of waveform thus increasing the considered of here is generated d having step size.power Pulse compression technique is employed here in order to generate bandwidth waveform and limitingvarying the transmitted of the waveform by using pulse compression techniques. Thea pulse SFW having a range of shorter varying pulse and transmitted of longer pulse. The modulatedhere waveform have considered hereresolution is generated d having step size. Pulsepower compression technique is employed in ordercharacteristics to generate a pulse been studied andresolution analyzed of using ing ambiguity functions of the power waveform. having a range shorter pulse and transmitted of longer pulse. The modulated waveform characteristics have been studied and analyzed using ing ambiguity functions of the waveform. © 2018 The Authors. Published by Elsevier B.V. © 2018 The Authors. Published by Elsevier B.V. This is an open accessPublished article under the CC BY-NC nd/4.0/) © 2018 The Authors. by Elsevier B.V.NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/ This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) Selection review under responsibility of the scientific committee of the 8th International Conference on Advances in This is an and openpeer-review access article under the CC BY-NC NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/ nd/4.0/) Selection and peer-review under responsibility of the scientific committee of the 8th International Conference on Advances in Computing and Communication (ICACC-2018). Selection and peer-review review under responsibility of the scientific committee of the 8th International Conference on Advances in Computing and Communication (ICACC-2018). Computing and Communication (ICACC-2018). Keywords: SFW,, Phase modulation, Pulse compression, Ambiguity Function, Less detectable waveform Keywords: SFW,, Phase modulation, Pulse compression, Ambiguity Function, Less detectable waveform
*
Corresponding author. SIERS Research Laboratory, Amrita School of Engineering - Coimbatore, Amrita Vishwa Vidyapeetham, India. T Tel.: Corresponding author. SIERS Research Laboratory, Amrita School of Engineering - Coimbatore, Amrita Vishwa Vidyapeetham, India. T Tel.: E-mail address: [email protected] +91-422-268-5000: fax: +91-422-268-6274. E-mail address: [email protected] 0509 © 2018 The Authors. Published by Elsevier B.V. 1877-0509 This is0509 an open access under the CC BY-NC-ND NDB.V. license (https://creativecommons.org/licenses/by-nc-nd/4.0/) ( © 2018 Thearticle Authors. Published by Elsevier 1877-0509 Selection review under responsibility of theND scientific of the 8th International International Conference on Advances in Computing and This is an and openpeer-review access article under the CC BY-NC-ND licensecommittee ( (https://creativecommons.org/licenses/by-nc-nd/4.0/) Communication (ICACC-2018). Selection and peer-review review under responsibility of the scientific committee of the 8th International International Conference on Advances in Computing and Communication (ICACC-2018).
*+91-422-268-5000: fax: +91-422-268-6274.
1877-0509 © 2018 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) Selection and peer-review under responsibility of the scientific committee of the 8th International Conference on Advances in Computing and Communication (ICACC-2018). 10.1016/j.procs.2018.10.349
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R Vignesh et al. / Procedia Computer Science 143 (2018) 39–47 Vignesh R et al. / Procedia Computer Science 00 (2018) 000–000
1. Introduction The short duration pulse train waveforms have been widely equipped with military radars in the past[1]. These pulses have high peak to average power ratio without any phase or frequency modulations which makes them easily susceptible to electronic support measures, electronic attack, and radar warning receivers. For the survival of these enemy attacks complex radar waveforms are designed in order to reduce detection and identification of passive intercept receiver devices. These waveforms are termed as low probability of interception (LPI) waveforms [1, 2]. The LPI technique is based on a property of emitter due to its wide bandwidth, low power, varying frequency, and other attributes make interception of radar difficult [3,7]. The characteristics of the target are determined with help of radar by transmitting known signal and receiving the echo signal scattered by the target. The echo signal plays a major role in information extraction and processing of waveform at receiver side [4]. The maximum unambiguous range determines the pulse repetition interval (PRI) of radar waveform[14]. Range resolution is the ability of radar to classify targets correctly based on the desired range of the targets. Range resolution is inversely related to pulse bandwidth of waveform. Preservation of high range resolution can be achieved by usage of stepped frequency waveforms (SFW). In order to reduce the detectability of these waveform phase modulation techniques, frequency modulation techniques and various spread spectrum techniques are employed [5,13]. Wideband modulation techniques are generally employed to improve the complexity of the waveform. The commonly used wideband modulation techniques include frequency modulation techniques such as Linear frequency modulation (LFM), Non-Linear frequency modulation (NLFM) and phase modulation techniques such as Barker codes, Frank codes, Polyphase codes [8-10]. The probability of detection and probability of interception is dependent on the input SNR (signal to noise ratio) at interceptor [3, 4]. Generally, SFW of uniform step size and wide bandwidth are employed for generating radar waveform with good range resolution. Here SFW of varying frequency step size is considered in the pretext of increasing the complexity and detecting the target with good range resolution [6,12]. In this paper, the performance of pulse compression techniques is compared with the help of ambiguity function also called as uncertainty function and two-dimensional autocorrelation function[9,11]. The time-bandwidth product of various waveforms is also compared. Ambiguity function effectiveness is generally measured using two measurements namely peak sidelobe ratio (PSLR) and integrated sidelobe ratio (ISLR). The effectiveness of phase modulated SFW is compared with previous existing waveforms such as rectangular waveform, uniform linear frequency waveform (LFM) and the detectability performance is analyzed. The delay and Doppler characteristics of the waveform are also analyzed using ambiguity function. The rest of the paper is as follows: Section II describes Frequency modulated pulse compression. Section III describes Phase modulated pulse compression. Section IV describes the proposed technique of modulating stepped waveform with P1 code. Section V describes the results and discussion. Finally in section VI conclusion is done. 2. Frequency Modulated Pulse Compression Modulation is a technique used to increase the transmission bandwidth of the waveform [9]. The transmitted waveform received as echo when matched filtered at the receiver side is used to extract range information about the target. Frequency modulation is a technique in which the frequency varies with time either uniformly or nonuniformly in order to obtain highly suppressed sidelobes, so that pulse compression achieved is good[15]. Consider a rectangular pulse having single frequency with no modulation. Figure 1 shows the autocorrelation function of the rectangular waveform. It is clear from the plot that the waveform after performing matched filtering at receiver side the output occupies a particular time period. This delay area occupied by the waveform ambiguity
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Fig. 1. Autocorrelation of rectangular pulse
plot indicates that two or more targets are distinguishable only when they are separated by a delay of particular time period occupied in the plot. 2.1 Uniform SFW SFW is a type of frequency modulation technique for generating a high range resolution profile. A sequence of N pulses with fixed pulse repetition frequency (PRF) and the varying carrier frequency is transmitted by SFW radar. Each set of N pulses is called coherent processing interval (CPI) or burst. The frequency of each pulse in the sequence is increased uniformly from one pulse to another by a fixed step size (∆f). The frequency of the first pulse is taken as carrier frequency (f0) and the subsequent pulse has a difference of step size (∆f) from the preceding pulse as shown in Figure 2. The received signal is sampled and spectral weighting is applied to reduce the sidelobe levels. The quadrature component for each burst is stored and IDFT is applied to find out the range profile of the corresponding burst. Thus for n-th transmitted pulse in sequence, with n=0, 1, 2…N-1, the carrier frequency (fn) of the waveform for the n-th step is given by [10]:
fn f 0 nf
(1)
Each pulse in SFW can be modulated using any modulation scheme. If the transmitted waveform for the n-th pulse is:
S 1 t A1cos[2 ( f 0 n)t ]
(2)
Then the received signal from the target after a time delay of 2R/c is given as [10]:
S 2 t A2 cos[2 ( f 0 n) t 2 R / c ]
(3)
Where R is Target Range in meters, c is propagation speed in meter per second and N is number of steps or pulses Range resolution (∆R) of SFW is determined from the overall bandwidth [8,14].
R c / 2 N f
(4)
From equation (4) it can be understood that the range resolution of SFW can be increased by increasing number of pulses in the sequence or frequency step size. The unambiguous range window (Ru) of stepped fm waveform is given by: Ru c / 2f (5)
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Fig. 2. Stepped frequency modulated waveform.
From equations (4) and (5) it noted that the frequency step size of the SFW plays an important role in determining the unambiguous range and range resolution. Figure 2 shows SFW with linearly increasing step size. Frequency step size is generally chosen to be approximately half the inverse of pulse width (τ):
f 1/
(6)
2.2. Non- Uniform SFW Non-uniform SFW is designed by replacing the constant step size (∆f) parameter of SFW. For the generation of a less detectable waveform, two main parameters are to be considered; they are waveform bandwidth and modulation type. SFW have high bandwidth. In order to make stepped waveform more complex and difficult to detect the frequency step size of the waveform is set to vary accordingly either uniformly or non-uniformly based on the information provided at the transmitter end. The non-uniform stepped waveform is modulated with LPI waveforms such as the Frank codes [9],P1, P2, P3, P4 codes etc.. in order to reduce the sidelobes which helps in increasing the stealthiness and to implement pulse compression in SFW for generating shorter pulse with less transmitted power required for transmission of longer pulse [15]. 3. Phase Modulated Pulse Compression Phase modulated pulse compression is a technique in which the phase of the signal is varied with time. Phase modulation is done to increase the bandwidth of the signal. One simple way is to use binary phase shift with the code sequence. But the random sequence is not effective as the amplitude varies for each sidelobe. So Barker codes were introduced which gives equal amplitude sidelobes [11]. 3.1. Barker codes Barker codes belong to binary phase coded pulse compression technique with a phase shift of 00 and 1800 [11]. These codes don’t have random sequences and only particular combinations which give equal amplitude sidelobes are considered. The largest combination available is 13bits.The main advantage of this code is that no amplitude weighting is needed to suppress sidelobes. The possible combinations of Barker code and the PSLR value for these combinations are listed in Table 1. These PSLR values were obtained when there is no Doppler shift and no delay introduced in autocorrelation process.
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a
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b Fig.3. (a) Doppler cut of 5-bit Barker code; (b) Ambiguity function of 5-bit Barker code
The Barker bit combinations are employed for choosing the step size of nonuniform SFW. Here 5-bit combinations are taken. This result in a total of 25=32 combinations of different frequencies, but not all combinations can be selected. The main advantage of barker is combinations having equal amplitude sidelobes. The combinations used for selecting step size are 11101, 10101,11011,11100,11111 which have equal sidelobes. The main drawback of barker code is that pulse compression is achievable up to a maximum of 13 bits. The amount of pulse compression achievable is directly related to the number of sub-pulses. The Doppler cut and ambiguity function of Barker code having 5bit combinations are shown in Figure 3(a) and 3(b) Table 1.Barker codes with existing PSLR value.
Code Length 2 3 4 5 7 11 13
Code Elements 10,11 110 1101,1110 11101 1110010 11100010010 1111100110101
PSLR(dB) -6.0 -9.5 -12.0 -14.0 -16.9 -20.8 -22.3
3.2. Polyphase codes Polyphase codes use harmonically related phases based on certain fundamental phase increment. Frank, P1, P2 are derived from step approximations, while P3 and P4 codes are derived from uniform frequency modulated waveforms. The codes have N2 elements and so they can produce higher compression ratios than Barker code. The selection of the length of polyphase codes is an important factor [9].The phase of the i-th element of the j-th group of P1 code is given as:
* N 2 j 1 * j 1 N i 1 N
i, j
(7)
where i denotes N samples per frequency, and j denotes N frequency steps. The length of P1 code should always be even. The pulse width (τ) i.e. longer pulse is divided into N smaller sub-pulses called chip width Tc. Each sub-pulse can be binary. P1 code is used for double sideband detection. The Doppler response of P1 code at matched filter output is shown in Figure 4(a). It is noticed that the sidelobes of the P1 code are not of equal amplitude as that of Barker. The null occurs at 1 microseconds which states that the delay between two or more targets should be more than 1 microseconds for correct classification and detection of targets. The relationship between delay and Doppler frequency shift as a function of detected power is shown in
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a
b Fig.4. (a) Doppler cut of P1 code; (b) Ambiguity function of P1 code
Figure 4(b). It states that the detection of targets is accurate within the region of higher power concentration where delay and Doppler values are zero and it decreases with reduction in power. 4. Phase coded non-uniform SFW SFW is known for high range resolution, while P1 code is known for LPI properties [6,11]. So a new waveform has been developed by modulating the SFW with polyphase (P1) codes. This waveform is expected to possess both properties of the stepped waveform and polyphase codes such as high range resolution and less detectability. The varying step size is fixed to various combinations by the user. Thus the user alone can retrieve the information about the radar transmitter waveform from the received echo signal, while the jammer or interceptor have little probability to identify and acquire the radar signals, having been entirely unaware of the frequency combinations used. The performance of the waveform is analyzed by means of ambiguity function. 4.1. Ambiguity Function The ambiguity function is defined as the absolute value of matched filter output envelope. The input signal to the filter is a Doppler shifted version of the return signal, to which the filter is matched. The ambiguity function is given as [9,11]:
| X ( , fd ) ||
s(t )*(t ).exp( j 2 f t )dt | d
(8)
Where s(t) denotes transmitted signal, τ denotes delay and fd denotes frequency shift In any radar system, two measurements are mainly used for measuring the effectiveness of the ambiguity function: the PSLR and ISLR. The former indicates the ability of radar to detect weak targets. It is associated with the probability of false alarm in particular range bin due to the presence of a target in neighboring range bin [9]:
l arg est _ sidelobe PSLR dB 20*log mainlobe _ peak
(9)
ISLR is a measure of how much energy is leaking from the main lobe of impulse response function of the target. It is the measure of energy distributed in sidelobes [9]:
ISLR(dB) 10* log (
sidelobe 2 ) mainlobe _ peak 2
(10)
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5. Results and Discussion An important inference of pulse compression signal is obtained with the help of the ambiguity function [9]. Ambiguity is similar in characteristics to matched filtering at the radar receiver side. The SFW is generated with an
a
b Fig .5. (a) Delay cut of SFW with constant
f
; (b) Doppler cut of SFW with constant
f
unambiguous range of 30 km, a range resolution 150 m. Hence, the sample rate will be fs=2MHz, with a pulse width of 5microseconds, and a pulse repetition frequency (PRF) of 5MHz.The number of frequency elements considered is 5, so there is 4 frequency step size. Figure 5(a) explains that the targets should be separated by at least a range equivalent of 0.2MHz for correct classification of targets.
a
b Fig . 6. (a) Ambiguity of SFW with constant
f
; (b) Spectrogram of SFW with constant
f
The detection of targets corresponding to the radial velocity of the target is depicted in Figure 5(b). The first null occurred at 10 microseconds, which is the delay necessary between targets for correct identification. The delay as a function of Doppler characteristics is plotted in Figure 6(a) and shows that target detection is good in the area where the signal power concentration is more. Figure 6(b) shows that the frequency step size increases uniformly. In the case of stepped waveform with constant frequency step size that is shown in Figures 5 and 6, the frequency step size (∆f) increases linearly. The range that has been defined between two targets is 0.1 MHz for better identification, and the delay between targets should be more than 1 ms for correct target detection. The case of stepped waveform with varying frequency step size is explained in Figures 7 and 8. The area of concentration where target detection is good is depicted in Figure 7(a), while Figure 7(b) shows the spectrogram for SFM with varying step size used to improve the complexity and stealthiness of the waveform. The SFW with varying step size is further phase modulated with the P1 code to improve the low probability of intercept characteristics of waveform thereby improving the bandwidth of the waveform by phase modulation. The first null
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occurs at 0.05 MHz in the frequency-shift Doppler domain and at 0.5 ms in the time delay domain. The unambiguous range and delay between the targets are reduced in the modulated waveform compared to the normal stepped waveform.
a
b Fig . 7. (a) Ambiguity of SFW with varying
f
a
; (b) Spectrogram of SFW with varying
f
b Fig . 8. (a) Ambiguity of P1 modulated SFW with varying
f
; (b) Spectrogram of P1 modulated SFW with varying
f
The detection of a radar target is good only in a particular region where power concentration is more, as inferred from Figure 8(a), while Figure 8(b) shows spectrogram of modulated SFW. When comparing among the results in Figures 7 and 8 it becomes evident that the power concentration for phase modulated waveform is greater. From the ambiguity function delay and Doppler cut the PSLR value for modulated waveform have been determined; the PSLR has been found to be -4.152 dB for the phase modulated waveform. The time-bandwidth product, that determines the amount of pulse compression in a waveform, has been chosen for modulating the waveform as having a value of 5. The bandwidth of modulated waveforms is more, thus increasing the SNR on the radar receiver side, and making the signal less detectable by the jammer. The results shown in Figures 5 - 8 compare favorably in terms of the delay, Doppler and ambiguity functions with previous studies performed using phase coded waveforms [11] and other conventional radar waveforms such as rectangular waveforms [1][10] and chirp waveforms [10], for constant and varying f . It is also observed that the ambiguity function obtained for phase modulated stepped frequency waveform has better range resolution compared to other waveforms along with low probability of intercept. 6. Conclusions The conventional pulsed radar waveforms have been subjected to pulse compression techniques such as waveform modulation and coding. These methods result in tandem enhancements to radar sensitivity and range resolution for dynamic targets. The characteristics of the phase modulated waveform are analyzed with the help of
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ambiguity functions Doppler plot and delay plot. The stepped waveform complexity is increased by using varying step size and is then modulated with an LPI code such as P1, thus decreasing the detectability and improving the stealthiness of radar waveforms. From the analysis of the ambiguity functions plots, it becomes apparent that the modulated waveform has good Doppler and delay characteristics along with a low probability of interception. References [1] Merrill, I. S. (2001). "Introduction to radar systems." Third Edition,Mc Grow-Hill., 7, 10. [2] Lange, J. B. (2012).”The Relative Nature of Low Probability Of Detection”,Radar.Defence R&D, Canada-Ottawa. [3] Ankarao, V., Srivatsa, S., and Sundaram, G. A. (2017).”Evaluation of pulse compression techniques for X-band radar systems.”, In: Wireless Communications, Signal Processing and Networking (WiSPNET), International Conference.,IEEE:1287-1292. [4] Weeks, G. D., Townsend, J. K., and Freebersyer, J. A. (1998). "A method and metric for quantitatively defining low probability of detection." In: Military Communications Conference. MILCOM 98. Proceedings., IEEE, 3, 821-826. [5] Paulose, A. (1994). "High radar range resolution with the step frequency waveform." Naval postgraduate school, Monterey ,CA., Master’s Thesis. 104. [6] Axelsson, S. R. (2007)."Analysis of random step frequency radar and comparison with experiments." IEEE Transactions on Geoscience and Remote Sensing, 45(4), 890-904. [7] Pace, P. E. (2009). "Detecting and classifying low probability of intercept radar." Second Edition , Artech House. [8] Srivatsa, S., and Sundaram, G.A. (2017). "PAM4-Based RADAR Counter-Measures in Hostile Environments." In: The International Symposium on Intelligent Systems Technologies and Applications, Springer, Cham., 390-400. [9] Jennison, B. K. (2003). "Detection of polyphase pulse compression waveforms using the Radon-ambiguity transform." IEEE Transactions on Aerospace and Electronic Systems, 39(1), 335-343. [10]Mahafza, B. R. (2005). "Radar Systems Analysis and Design Using MATLAB " Second Edition. Chapman and Hall/CRC. [11]Farnane, K., Minaoui, K., Rouijel, A., and Aboutajdine, D. (2015, November)."Analysis of the ambiguity function for phase-coded waveforms." In: Computer Systems and Applications (AICCSA), IEEE/ACS 12th International Conference of IEEE, 1-4. [12]Levanon,N. (2002).”Stepped-frequency pulse-train radar signal”.IEE proceedings-Radar,Sonar and Navigation,149(6),297-309. [13]Ning, B., Li, Z., Guan, L., and Zhou, F. (2017). "Probabilistic frequency-hopping sequence with low probability of detection based on spectrum sensing." IET Communications, 11(14), 2147-2153. [14]White, P. (2013) “Radar Waveforms for A&D and Automotive Radar.” White Paper., Rohde-Schwarz instruments. [15]Sachin, A. R., Ambat, S. K., and Hari, K. V. S. (2017).” Analysis of intra-pulse frequency modulated, low probability of interception, radar signals.” Sadhana, 42(7), 1037-1050.