Research ArticleMainlobe Jamming Suppression Using Improved FrequencyDiverse Array with MIMO Radar

Guang-ming Li,1,2 Qun Zhang ,1,2,3 Qi-yong Liu,4 Jia Liang,1,2 Dan Wang,1,2

and Feng Zhu5,6

1Information and Navigation College, Air Force Engineering University, Xi’an 710077, China2Collaborative Innovation Center of Information Sensing and Understanding, Xi’an 710077, China3Key Laboratory for Information Science of Electromagnetic Waves, Fudan University, Shanghai 200433, China493116 Unit of PLA, Shenyang 110000, China5National Defense University of PLA, Beijing 100091, China6Academy of Military Sciences of PLA, 100091, China

Correspondence should be addressed to Qun Zhang; zhangqunnus@gmail.com

Received 26 October 2018; Accepted 19 March 2019; Published 2 May 2019

Academic Editor: Antonio Lazaro

Copyright © 2019 Guang-ming Li et al. This is an open access article distributed under the Creative Commons Attribution License,which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Frequency diverse array (FDA) has attracted much attention in recent years due to its range-angle-dependent beampattern.Multiple-input multiple-output (MIMO) radar can offer waveform diversity to increase the virtual aperture length for azimuthcoherent focus processing in radar imaging. Combining the advantages of FDA and MIMO radar, FDA-MIMO radar can steermultiple beams to different targets in the same line of sight (LOS) of radar with different waveforms. In this paper, an improvedFDA model with the logistic map is proposed to get the aperiodic and range-angle uncoupling beampattern. Based on theproposed FDA, combining the FDA-MIMO radar, the waveform and chirp rate jitter techniques are adopted to mainlobejamming suppression. Simulation results show the effectiveness of the proposed method.

1. Introduction

Due to the all-day, all-weather, long-range capability, theinverse synthetic aperture radar (ISAR) has played a criticalrole in space surveillance. In situationswhere other radars dis-play only a single bright unidentifiablemoving pixel, the ISARimage is adequate to discriminate between various missiles,military aircraft, and civilian aircraft. In order to protect theimportant goals and regions of detection and observation, avariety of jamming techniques are designed against the ISARsystem. Sub-Nyquist sampling jamming against the ISAR sys-tem is studied in [1–4]. In [1], sub-Nyquist jamming is used tothe bistatic ISAR; by undersampling the intercepted signal ofISAR, multiple deceptive false targets will be induced and thereal targets will be emerged in false targets. Although ISARjamminghasgotasignificantprogress, thereareonlyrare stud-ies about ISAR anti-jamming. In [5], the ISAR anti-jamming

effect of planar array is analyzed, but this method can onlyeliminate the jamming signal from the sidelobe and is invalidfor the mainlobe jamming (MLJ).

Currently, phased-array radar and multiple-inputmultiple-output (MIMO) radar are two common radar sys-tems for target imaging [6]. Both phased-array radar andMIMO radar have their advantages and disadvantages, andphased-MIMO radar exploits the benefits of the phased-array andMIMO radars [7]. There are multiple advantages ofphased-MIMO radar, but the beampattern of phased-MIMOradar is just angle-dependent. In some electronic warfare sce-narios, e.g., when the jammer and targets are in the same LOSof radar, ISAR will receive both the jamming signal and targetecho. In this situation, the traditional electronic counter-countermeasure (ECCM) method, such as a spatial filteringmethod, will degrade greatly because the jamming signal hasa similar steering vectorwith the target echo. In order to detect

HindawiJournal of SensorsVolume 2019, Article ID 3948597, 12 pageshttps://doi.org/10.1155/2019/3948597

targets from MLJ, many techniques have been proposedrecently. MLJ suppression techniques on the monopulsesum-difference network have been studied in [8, 9]. Thesemethods can cancel MLJ by adaptive sum-difference channelcancellation, but restricted by the degree of freedom; and thesemethods just workwhen there is only oneMLJ.MultipleMLJscan be cancelled by adaptive arrays in [10, 11], but the shape ofthemainlobewould bedistorted greatly and themainlobe gainon target echoeswill become very small. The blockmatrix pre-processing (BMP) and eigen-projection processing (EMP)methods can solve the mainlobe deformation, mainlobe shift,and sidelobe elevation problem [12, 13], but BMP has highaccuracy requirement for thedirectionof jamming signal; oth-erwise, the effect ofMLJ suppressionwill degrade greatly. EMPmethoddoes not need for accurate estimation for the directionof MLJ, but eigenvalue decomposition and inverse matrixoperation increase the calculation cost seriously. There aremany improved methods in recent years [14–16], but whenMLJ is located close and even overlapped to the target, thesetechniques will be invalid. Considering the growing threats ofMLJ, new techniques need to be studied.

In recent years, frequency diverse array (FDA), whichfeatures flexible beam scanning ability, has attracted growingattention. The FDA was first introduced by Antonik et al. in[17], where a minor carrier frequency offset is employedacross the array elements. Different from phased array,FDA is capable of forming a range-angle-dependent beam-pattern, so FDA has the innate advantage in MLJ suppres-sion. Due to the range-angle-coupled beampattern, basicFDA is not desirable for application. And the beampatternof FDA can be influenced by the frequency offset, so manyfrequency shift methods are studied to eliminate the rangeperiodicity and decouple the range-angle-coupled response.In [18, 19], the frequency offset is controlled by logarithmicand sine law, respectively. The range-angle-coupled charac-ter has been overcome, but it has difficulties in forming highresolution beams.

Refer to phased-MIMO radar, FDA-MIMO radar hasbeen proposed in [20–23]. The essence of FDA-MIMOradar is dividing the transmit array into some subarrays.Each subarray adopts the operating mode of FDA radar,which can get coherent processing in range-angle dimen-sion with element level frequency shifting. And the signalemitted by each subarray is orthogonal or irrelevant. Com-pared with phased-MIMO radar, FDA-MIMO radar cantransmit different signals in the same LOS of radar with dif-ferent ranges, so it has the innate benefits in MLJ suppres-sion. A subspace projection-based sample selection methodis proposed in [24] to handle the pseudorandom distribu-tion false targets, and the jammings can be suppressed ade-quately even if they are in the mainlobe direction. The keypoints of FDA-MIMO radar are the character of FDA andstructure of FDA-MIMO radar, so in this paper, animproved FDA based on the logistic map is proposed toget the high-resolution range-angle-uncoupled beampat-tern. Then, the transmit array is divided into multiple sub-apertures according to the number of targets, and eachsubaperture operates in FDA mode. For each subaperture,the elements steer transmit beam in one of the targets’

directions and ranges. To avoid echo signal separation ofmultitargets, it is guaranteed that there is only one targetin each transmit beam by adjusting the subaperture divid-ing method. On the basis, orthogonal signals with differentchirp rates and waveforms are transmitted to the jammerand targets, respectively. The jamming signal is mismatchedwith reference signal and will be eliminated.

Compared with MLJ suppression based on the phased-array radar, the proposed method has three advantages: (1)according to the target and jamming characters, differentwaveforms will be transmitted to different targets even if theyare in the same LOS of radar; (2) the time sampling can bereplaced by spatial sampling; thus, the requirement of timeresource can be decreased and the real-time performancecan be increased; and (3) MLJ can be suppressed much easiercompared with the complex null steering algorithm inphased array.

Compared with the anti-jamming method based on theMIMO radar, the proposed method has two advantages:(1) it has higher SNR gain, which leads to better anti-jamming effect; and (2) because the waveform emitted byeach subaperture is orthogonal or irrelevant and there isonly one target in each beam, the separated orthogonal sig-nal obtained in the receiver will contain single target infor-mation; thus, the signal separation of multiple targets andjammers can be avoided.

The reminder of this paper is organized as follows. InSection 2, an improved FDA is proposed and the FDA-MIMO based on the improved FDA is introduced; exper-iments are given to demonstrate effectiveness in Section3. Finally, conclusion and following points are given inSection 4.

2. Model of Improved FDA-MIMO Radar

2.1. Model of Improved FDA. Assuming the basic FDA radaris a uniform linear array formed byMtransmit antennas anddefines the first element as reference. The transmit frequencyof the m-th element is

f m = f0 + m − 1 Δf , m = 1, 2,… ,M, 1

where f0 is the reference carrier frequency and Δf is the basicfrequency offset. In general, M − 1 Δf ≪ f0. For a targetlocated at θ, r in the far field, neglecting the high-orderphase term [25, 26], the transmit steering vector can beexpressed as

a θ, r = 1,⋯, exp −j2π M − 1

cΔf r − f0d sin θ

2

The array factor is

AF θ, r = 〠M

m=1exp −j

2π m − 1c

Δf r − f0d sin θ 3

2 Journal of Sensors

With frequency offset as formula (1), the beam of basicFDA is shown in Figure 1 [17].

The application of basic FDA is limited by the period-icity and coupling, which result in ambiguously positioningtargets in range-angle dimension. In [27], a new FDAstructure is proposed, the nonuniform FDA is exploitedas a transmitter to provide range-dependent transmittingbeampattern, and the uniform phased array is exploitedas a receiver to provide angle-dependent receiving beam-pattern. The key point of this FDA structure is the nonuni-form FDA, but this needs high accuracy of space betweenarray elements. Considering the cost and difficulties inachieving, we prefer to improve the beampattern by chang-ing the frequency offset in two ways: (1) increase the fre-quency offset and (2) change the frequency shift method.Because the frequency offset cannot be too large, or thesignal’s phase emitted by FDA is incoherent among ele-ments and cannot form the desired beam in the spatialdomain, in this paper, we propose a new frequency offsetshift method to achieve the range-angle decouple and highresolution of the beam.

The logistic map, one form of chaos theory, has attractedwide attention in recent decades. The sequence created by alogistic map has the similar distribution and probabilitycharacter with the white noise [28]. In this paper, we try tomake the FDA’s frequency offset shifted with the logisticmap, and the FDA proposed in this paper is called L-FDA.Figure 2 is the system sketch of L-FDA [29]. There areM ele-ments in a linear array, with a constant interelement spacingd. These array elements are located symmetrically along thex-axis; the original point of the x-axis is selected as the firstelement, and the coordinate of the m-th element is

xm = m − 1 d, m = 1, 2,… ,M 4

The transmitted waveform of each element is the same,but the carrier frequencies of different elements are randomlyassigned. The frequency offset of the m-th element is

Δf m+1 = μΔf m 1 − Δf m , m = 1, 2,… ,M 5

μ ∈ 0, 4 is the control parameters; when μ ∈ 3 5699456, 4 , the logistic map is in the chaotic region. The transmittedwaveform of m-th element can be expressed by

sm t = exp j2π f0 + Δf m t 6

Define the first element as reference, with the far-fieldassumption for angle θ and range r, L-FDA is utilized asthe transmit array; then, the signal that transmitted by them-th element is

srm t ; θ, r = sm t −r − xm sin θ

c

= exp j2π f0 + Δf m⋅ t −

r − xm sin θ

c,

7

where c is the wave propagation speed. The baseband signalthat transmitted by the m-th element is

Ψm θ, r = exp −j2πc

f0 + Δf m r − m − 1 d sin θ

8

The baseband samples Ψm θ, r of all elements canbe arranged to formulate a range-angle-dependent steer-ing vector:

Ψ θ, r = Ψ0 θ, r ,Ψ1 θ, r ,⋯,ΨM−1 θ, r =Ψ θ ⊙Ψ r ,9

Spec

tral

freq

uenc

y

…… (M−1) d

Spatial array element coordinate

01

……

M1

…… ……d d

d0

𝜃

Figure 2: System sketch of L-FDA.

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le (°

)

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Figure 1: Beampattern of basic FDA.

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where ⊙ is the Hadamard product.

Ψ θ = 1, exp j2π f0 + Δf2

cd sin θ ,⋯,

exp j2π f0 + Δf M

cd M − 1 sin θ

T

,

Ψ r = exp −j2πcf0r ⋅ exp −j

2πcΔf1r,⋯,−j 2π

cΔf Mr

T

10

The array factor is

AF θ, r = Ψ θ1, r1 ,⋯,Ψ θp, rp 11

The beam point to θ1, r1 is

P θ, r =w θ1, r1 ⋅AF θ, r , 12

where w θ1, r1 =ΨH θ1, r1 .In order to better illuminate the advantage of FDA in

mainlobe jamming suppression, the beampattern of phasedarray is discussed. Considering the following 4 cases, in case1, only echo signal is from 0° and there is no jamming signal;in case 2, echo signal and two jamming signals are from 0°,30°, and 60°, so the two jamming signals are both sidelobejamming; in case 3, the echo signal and two jamming signalsare from 0°, 3°, and 60°, so there is one MLJ and one sidelobejamming; and in case 4, the echo and two jamming signalsare from 0°, 0°, and 60° and the MLJ has the same directionwith real echo signal. The beamforming results are shownin Figure 3. Comparing Figures 3(a) and 3(b), we can get that

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Figure 3: Normalized beams of phased array: (a) θ = 0°; (b) θ = 0°, 30°, and 60°; (c) θ = 0°, 3°, and 60°; (d) θ = 0°, 0°, and 60°.

4 Journal of Sensors

the phased array can form nulling in sidelobe jamming direc-tion and real echo signal can be received effectively; fromFigure 3(c), we can get that when the phased array is usedto suppress MLJ, the mainlobe will drift and sidelobe willraise; from Figure 3(d), we can get that when the jammerand targets are overlapped in the same LOS of radar, themainlobe is seriously distorted.

MLJ suppression based on the phased array is achieved inthe receiver [10–16]. Next, the beamforming of improvedFDA proposed by this paper will be discussed to illuminatethat radar’s performance can also be improved from thetransmitter. Assuming there are three targets located at(10°, 10 km), (10°, 15 km) and (10°, 20 km), respectively, thecontrol parametersμ = 3 9, initial frequency offsetΔf1 = 5000

Hz,f0 = 10GHz, and the number of array elements is 100.Beamforming results of L-FDA are shown in Figure 4.

Comparing Figure 4 to Figure 1, we can see that beams ofFDA have been greatly improved. In Figure 4(a), three range-angle uncoupled mainlobe beams are formed in the desiredregion and the sidelobe is much lower than the mainlobe,so energy can be effectively focused on the desired area; inFigures 4(b) and 4(c), the 3 dB bandwidth of range anddimension is about 250m and 1°, respectively. Frequency off-sets of different antenna arrays are shown in Figure 4(d); wecan see that the frequency offset floats between 0 and 5 kHz;so, by the frequency offset shift method proposed in thispaper, this means ideal beampattern can be got through asmall frequency offset.

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Figure 4: (a) Normalized beams of the proposed FDA; (b) range dimension; (c) angle dimension; (d) frequency offset of differentantenna arrays.

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Compared with the basic FDA and phased array, the pro-posed FDA based on the logistic map has the following fouradvantages: (1) since the frequencies of different FDA ele-ments are random, the transmit signal will not be detectedaccurately and L-FDA has higher anti-jamming ability; (2)because frequencies of elements float around the initial fre-quency, the difference between the maximum and minimumfrequency offsets is much smaller than the basic FDA, whichreduces the bandwidth requirement on hardware and cost;(3) the resolution of L-FDA’s beam is much better than thebasic FDA; and (4) multiple ideal beams will be generatedin the direction of different targets, no signal will be transmit-ted or received in the uninterested area, and this will raise theefficiency of energy utilization.

2.2. FDA-MIMO Radar Based on the Improved FDA. Basedon the improved FDA, a new type of FDA-MIMO radaris put forward. Refer to the literature [30], the transmitarray of FDA-MIMO consists of K subarrays. All elementsof l-th subarray are used to coherently emit the signal φl t ,and a beam can be formed toward a certain direction andrange, e.g., direction and range of the target, as shown in

Figure 5. For a clearer comparison of FDA-MIMO andphased-MIMO radars, beams of phased-MIMO radars aredenoted by dashed lines and beams of FDA-MIMO radarsare denoted by solid lines. Different beams can be formedby different subarrays toward different directions or ranges.The data from beams (formed from different subarrays) inthe same direction and range contains the information ofthe same target; thus, these data can be used for coherentprocessing. And the data from beams in different directionsor ranges contain the information of different single target;thus, the information of each target can be obtained simul-taneously without signal separation.

The well-separated subarrays are used to form MIMOradar. Different waveforms transmitted by different subar-rays should be orthogonal. In this paper, the receiver is aphased array, which is made up of N antenna elements.In each FDA-MIMO radar, the signals transmitted fromsubarrays which formed toward the same direction anddistance are used to synthesize a signal toward the target.Therefore, for one target, each FDA-MIMO radar willtransmit a signal to observe it and each FDA-MIMO radarcan be treated as one transmitter.

Subarray 1 Subarray 4Subarray 2 Subarray 3

Figure 5: Illustration of the FDA-MIMO antenna array K = 4 .

Subarray 1 Phased arraySubarray 2 Subarray 3 Subarray 4

Figure 6: The model of FDA-MIMO.

6 Journal of Sensors

We combine the advantages of FDA and MIMO radar inrange-angle-uncoupled beampattern: coherent array gain,waveform diversity, better beamsteering performance, andhigh SNR gain; FDA-MIMO radar is applied to transmit dif-ferent signals to jammers and targets, respectively. We con-sider the co-located MIMO radar as showed in Figure 6(K = 4, N = 5). In Figure 6, the elements in each subarrayemits signals with the same envelop and the subarray isworked in FDA mode.

2.3. Imaging Based on the FDA-MIMO Radar. The signalemitted by the l-th subarray is

sl t = φl t exp j2πf lt , 0 ≤ t ≤ T , 13

where φl t is the signal’s envelop of the l-th subarray, f lis the carrier frequency of l-th subarray, and T is thepulse duration. The signals transmitted by different sub-arrays satisfy

Tsl t s

∗p t − τ = 0, l ≠ p, ∀τ, 14

where τ is time delay and the superscript ∗ denotes aconjugate operator.

The signals emitted by different subarrays are orthogonalor irrelevant. Considering the far-field situation, when signalis emitted by the m-th element of l-th subarray and receivedby the h-th element of receiving array, the round trip timedelay is

τl,m,h′ = τ0 + τl,m,h

= Rtl

c+ Rr

c−d1 m − 1 sin θ1 + d2 h − 1 sin θ2

c,

15

where Rtl and Rr are distances from the target to the firstelement of l-th subarray and receiving array, respectively,d1 and d2 is the element space of subarrays and phasedarray, respectively, θ1 and θ2 is the angle of FDA-MIMO and phased array, respectively, τ0 = Rtl + Rr /c isthe common time delay, and τl,m,h is the time delaybetween elements [21].

The receiving signal corresponding to τl,m,h′ is

srl,m,h t = φl t − τl,m,h′ ⋅ exp j2πf l t − τl,m,h′ 16

The receiving snapshot of FDA-MIMO radar can beexpressed as a vector:

xs = y1,1,1, y1,1,2,⋯,y1,1,N ,⋯,yK ,M,NT = ξb θ2 ⊗ a θ1, r ,

17

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Figure 7: (a) ISAR image with LFM signal. (b) ISAR image with SFCS signal.

Jammer

Target

Echo signal

Jamming signal

ISAR

Figure 8: The geometric relation diagram of MLJ.

7Journal of Sensors

where xs ∈ CKMN×1, the superscript T denotes the operationof transpose, a θ1, r ∈ CKM×1, and b θ2 ∈ CN×1. The expres-sion of a θ1, r and b θ2 is

a θ1, r = exp j2π f0 Rtl + Rr

c

1, exp −j4πΔfc

m − 1 Rtl + Rr ,⋯,

exp −j4πΔfc

M − 1 Rtl + Rr

T

⊙ 1, exp j2π f lcd1 m − 1 sin θ1 ,⋯,

exp j2π f lcd1 M − 1 sin θ1

T

≈ exp j2π f0 Rtl + Rr

c

1, exp −j4πΔfc

m − 1 Rtl + Rr ,⋯,

exp −j4πΔfc

M − 1 Rtl + Rr

T

⊙ 1, exp j2π d1λ0

m − 1 sin θ1 ,⋯,

exp j2π d1λ0

M − 1 sin θ1

T

,

b θ2 = 1, exp j2π d2λ0

sin θ2 ,⋯,

exp j2π N − 1 d2λ0

sin θ2

T

,

18

where λ0 is the wavelength corresponding to the referencecarrier frequency f0.

Due to the small frequency offset, there are some differ-ences between signals emitted by FDA and phased array,and the imaging results based on FDA need to be further

analyzed. Because LFM and SFCS signals are widelyapplied in ISAR imaging, the ISAR image of these two sig-nals based on the FDA radar will be discussed, respectively,in the following.

First, considering that the FDA-MIMO radar emits LFMsignal, the signal emittedby them-thelementof l-thsubarray is

sl,m t̂, tm = σrect t̂Tp

⋅ exp j2π f0 + m − 1 Δf t

+ 12 γt

2 ,  t̂ ≤Tp

2 , m = 1, 2,… ,M,19

whereTp is time width. So, signal emitted by l-th subarray canbe expressed by

sl t̂, tm = σrect t̂Tp

⋅ 〠M

m=1exp j2π f0 + m − 1 Δf t

+ 12 γt̂

2 ,  t̂ ≤Tp

2

20

The reference signal of l-th subarray is

sl,ref t = rect t̂ − 2Rref /c /Tref ⋅ exp j2πf l t −Rrefc

+ 12 γ t̂ −

Rrefc

2,  t̂ ≤

Tp

2 ,

21

where Rref is the distance between the target and l-th subarrayand Tref is the time width of reference signal.

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Figure 9: Sub-Nyquist sampling jamming: (a) theHRRPof Sub-Nyquist sampling jamming; (b) the ISAR imageof Sub-Nyquist sampling jamming.

Table 1: The chirp rates of signals transmitted to the jammer andtarget.

Chirp rate (Hz/s) Jammer Target

LFM 3 × 1013/6 × 1012 3 × 1014

SFCS 3 × 1013/6 × 1012

8 Journal of Sensors

Then, considering the FDA-MIMO radar emits SFCS sig-nal, the i-th subpulse emitted by m-th element of l-th subar-ray is

sl,m t̂, i = σrect t̂ − iTr

T1⋅ exp j2π f0 + iδf

+ m − 1 Δf t̂ − iTr + jθi

⋅ exp jπγ t̂ − iTr2 ,

  t̂ ≤T12 , m = 1, 2,… ,M, i = 0, 1,… ,N − 1,

22

where δf is the stepped frequency of SFCS signal, Tr is therepetition interval of subpulses, T1 is the time width of sub-pulse, γ is the chirp rate of subpulse, and θi is the initial phaseof i-th subpulse.

The SFCS signal emitted by l-th subarray can beexpressed as

sl t̂, i = σ 〠N−1

i=0〠M

m=1rect t̂ − iTr

T1⋅ exp j2π f0 + iδf

+ m − 1 Δf t̂ − iTr + jθi

⋅ exp jπγ t∧ − iTr2 ,  t̂ ≤

T12

23

For l-th subarray, assumed the first element’s signal asreference. The simulation parameters of L-FDA are identicalwith Section 2. The carrier frequency of ISAR is 10GHz, andbandwidth is 300MHz.

Figures 7(a) and 7(b) are images of FDA-MIMO radarwhen it emits LFM and SFCS signals, respectively. We canget that for L-FDA, the ISAR image can also be obtained assame as phased array, so FDA is feasible to ISAR imaging.

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Figure 10: Anti-jamming effect. (a) HRRP when the jamming chirp rate is one-tenth of the target echo; (b) HRRP when the jamming chirprate is fiftieth of the target echo; (c) ISAR image of jamming signal when the chirp rate is one-tenth of the target echo; (d) ISAR image ofjamming signal when the chirp rate is fiftieth of the target echo.

9Journal of Sensors

3. Experiments

In order to suppress the MLJ, we will emit different signals tothe target and jammer by the proposed FDA-MIMO radar inthe following. Because sub-Nyquist sampling jamming hasattracted much attention, theMLJ suppression effect is exam-ined by sub-Nyquist sampling jamming. And detailed princi-ple of sub-Nyquist sampling jamming is explained inreference [1].

The geometric relation between targets, jammer, andFDA-MIMO radar is shown in Figure 8; range and angleparameters of the targets and jammer can be obtained bythe method proposed in the literatures [21, 31]. The targetechoes and jamming signal can be discriminated by themethod proposed in [32]. In order to make full use ofrange-angle-dependent beampattern of the improved FDA,we consider transmitting different signals to the jammerand targets based on the pulse diversity theory. The signals

are altered in two aspects: (1) different waveforms (LFM orSFCS) are applied in the anti-jamming method and (2) chirprates of signals are jittered.

Following simulation results are utilized to validate theeffectiveness of the proposed anti-jamming method. First,the sub-Nyquist sampling jamming is presented when sig-nal is emitted by FDA-MIMO radar. Assumed the X-bandradar is operated at 10GHz, and bandwidth is 300MHz. Atotal of 108 pulses are transmitted within a coherent imageintegration time of 1 1268 × 10−6 s, and the sampling inter-val of sub-Nyquist is Ts = 8 3776 × 10−8 s; multiple decep-tive images are induced in Figure 9.

Assumed the FDA-MIMO system is constructed withMr = 2 transmitters, and the antenna number of receivingphased array is N = 100. Each transmitter is a FDA-MIMO radar with 100 elements. There is one target andone jammer located at (10°, 200 km) and (10°, 205 km) asshowed in Figure 8. Each transmitter is divided into K = 4

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Figure 11: Anti-jamming effect. (a) HRRP when the jamming chirp rate is one-tenth of the target echo; (b) HRRP when the jamming chirprate is fiftieth of the target echo; (c) ISAR image of jamming signal when the chirp rate is one-tenth of the target echo; (d) ISAR image ofjamming signal when the chirp rate is fiftieth of the target echo.

10 Journal of Sensors

subarrays with the fully overlapped method. The first twosubarrays are toward the jammer, and last two subarraysare toward the target.

In simulation, the carrier frequencies of signals transmittedto the target and jammer are 10GHz and 11GHz, respectively;the chirp rates of different waveforms are shown in Table 1.

Firstly, we just consider chirp rate jitter, which meansISAR emits LFM signal to both the jammer and the target.Figures 10(a) and 10(c) are the HRRP and ISAR images whenthe chirp rate of jamming signal is taken as 3 × 1013 Hz/s (thechirp rate of jamming signal is one-tenth of the target ech-oes); Figures 10(b) and 10(d) are the HRRP and ISAR imageswhen the chirp rate of jamming signal is 6 × 1012 Hz/s (thechirp rate of jamming signal is fiftieth of the target echoes).Compared with the jamming image in Figure 9, the HRRPand the ISAR image of jamming signal is blurred and thefalse targets cannot be formed successfully. But in the radarwork area, the jamming signal can also cause occlusion; thiswill affect the target recognition. This means just consideringthe chirp rate jitter cannot get well anti-jamming effect. Inthe following, besides chirp rate jitter, waveform diversity isalso considered in jamming suppression.

In the following, we consider the waveform changing andchirp rate jitter at the same time, Figure 11 shows the anti-jamming result when LFM signal transmits to the targetand SFCS signal transmits to the jammer. Figures 11(a) and11(b) are HRRP; Figures 11(c) and 11(d) are ISAR images.Compared to Figure 10, jamming is eliminated more thor-oughly. It means by combining the waveform changing andchirp rate jitter, jamming can be better suppressed comparedwith chirp rate jitter only.

4. Conclusion

In this paper, FDA-MIMO radar is applied to suppressMLJ. In order to overcome the periodicity and range-angle coupling of FDA’s beampattern, an improved FDAmodel based on the logistic map is proposed. Then, theFDA-MIMO based on the proposed FDA is introduced,and an anti-jamming method is proposed in this paper.With the advantage of FDA-MIMO radar, by transmittingdifferent signals to the target and jammer, the well MLJsuppression effect will be obtained easily without complexalgorithms. The simulation results demonstrate the effec-tiveness of the anti-jamming method.

Some in-depth work will be studied in the future on thefollowing points:

(1) Because the radar resource is limited, the resourcesaturation will be an important problem when thereare too many targets in the radar work area. In thiscase, the available subarrays and limited radar powerwill be not enough to be allocated for every target.Thus, reasonable and effective resource schedulingalgorithms are important for exploiting the benefitsof FDA-MIMO radar

(2) In this paper, we just consider the LFM and SFCS sig-nals to MLJ suppression. Waveform design has been

an effective measure for anti-jamming. If the signalstransmitted to the jammer and the target are welldesigned, jamming can be eliminated better. Thus,designing waveforms with well self-correlation andcross-correlation features is very important for themainlobe jamming suppression with FDA-MIMO

Data Availability

The data used to support the findings of this study areavailable from the corresponding author upon request.

Conflicts of Interest

The authors declare that there is no conflict of interestregarding the publication of this paper.

Acknowledgments

This work was supported in part by the National NaturalScience Foundation of China under Grant 61631019, YoungScientists Fund of the National Natural Science Foundationof China under Grant 61703412, and Natural Science Foun-dation Research Program of Shaanxi Province under Grant2018JM6072.

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