Knowledge-Based Generalized Side-Lobe Canceller for Ionospheric Clutter Suppression in HFSWR

13 Pages·2017·5.37 MB·English

remote sensing
TechnicalNote
Knowledge-Based Generalized Side-Lobe Canceller
for Ionospheric Clutter Suppression in HFSWR
XinZhang1,2,DiYao1,QiangYang1,2,YingningDong1,2andWeiboDeng1,2,*
1 SchoolofElectronicsInformationEngineering,HarbinInstituteofTechnology,92#WestDazhiStreet,Harbin
150001,China;[email protected](X.Z.);[email protected](D.Y.);[email protected](Q.Y.);
[email protected](Y.D.)
2 CollaborativeInnovationCenterofInformationSensingandUnderstandingatHarbinInstituteof
Technology,Harbin150001,China
* Correspondence:[email protected];Tel.:[phone]
Received:30October2017;Accepted:12January2018;Published:13January2018
Abstract: Highfrequencysurfacewaveradar(HFSWR)hasbeensuccessfullydevelopedforearly
warningandremotesensing. However,theionosphericclutterisadifficultchallengethatcanmake
HFSWRsysteminefficient. TheGeneralizedSide-lobeCanceller(GSC)hasbeenprovedtobean
effectivealgorithmforcluttersuppressionintheory,butitsuffersfromtheperformancedegradation
forsomenon-idealconditionsinpractice. Themostintolerableshortcomingisthesignaltonoise
ratio(SNR)losscausedbytheresidualsignalinthesecondarydata. Inthispaper,aknowledge-based
GSC(KB-GSC)methodhasbeenproposedviaanadaptivesinglenotchfilterdesigntorejectthe
residualsignalforreducingtheSNRloss. Thefeasibilityandavailabilityhasbeendemonstratedby
measureddata.
Keywords: HFSWR;ionosphericclutter;GSC;knowledgebased
1. Introduction
Highfrequencysurfacewaveradar(HFSWR)canprovidethecapabilitiesoftargetsmonitoring
and ocean remote sensing over the horizon (OTH) by transmitting HF vertical polarization
electromagneticwaveworkingon3MHz–30MHz[1]. However,itworksonthecongestedHFband
andfacesthecomplicatedelectromagneticenvironmentwhichincludesclutter(suchasseaclutterand
ionosphericclutter),directionalinterference(suchasradiointerference)andtheinterferencefromthe
universeandatmosphere[2].
Ionospheric clutter which is the echo reflected from the ionosphere is the most complex type
ofclutterforHFSWR[3–5]. Italwayshasstrongenergyandcoversawideregionatafardistance.
In this case, it may cause the HFSWR blind for detecting weak targets over the horizon. As such,
suppressingtheionosphericclutterforweaktargetdetectionoverthehorizoninHFSWRhasdrawn
muchattention.
AlargenumberofeffectshavebeenappliedtoHFSWR[6–8]andafewalgorithmsormethods
havebeenproposedforionosphericcluttersuppressionrecently. However,furtherdiscussiontomeet
therealoperatingenvironmentisstillrequired. Thegeneralizedside-lobecanceller(GSC),whichis
alsonamedasthestandardcoherentside-lobecancellationtechnique(CSLC)[9,10],hasbeenproved
to be an effective method in theory, for noise, co-channel communication, and interference in the
side-lobe[11–17]. BasedonGSC,Wanhasmadegreatcontributionbyconstructingareceivingarray
which consists of a main antenna for receiving echo including signal of interesting (SOI), clutter,
interference and noise and several auxiliary antennas for obtaining the information of clutter and
interferenceforcluttersuppressioninHFSWR[18,19]. However,theproposalofWan’sconstruction
is with only one degree of freedom and it is designed for ocean remote sensing, not for the target
RemoteSens.2018,10,104;doi:10.3390/rs10010104 www.mdpi.com/journal/remotesensing
RemoteSens.2018,10,104 2of13
detection. Thus,thereisalimitationfortargetdetectionduetothelimiteddegreeoffreedom,asthere
isonlyonemainantenna,especiallyinthedensetargetscene.
In this paper, we focus on the target detection, which are submerged in Es-layer ionospheric
clutterwhichoftencomesoutwhentheradarworkingfrequencyisinthe3–5MHzrange[20]. There
aretwochallengestobattle: oneisthatthefreedomofarrayshouldbeincreasedfordensetargets
scene;theotheristhatseveralpracticalconditionsinthepracticalHFSWRsystemshouldbeconcerned
carefully. Aimingatthesetwochallenges,thispaperiscomposedasfollows: firstly,theframeworkof
theGSCmethodisintroducedinSection2,includingtheGSCmethodandGSCbasedonthevirtual
slidingsubarraymethodforgreaterfreedomofthearray. Thepracticalproblemisalsoanalyzedin
thissection. AimingatthepracticalproblemanalyzedinSection2,aknowledge-basedGSCmethod
withanadaptivespacefilterisproposedinSection3andtheavailabilityisdemonstratedinSection4
withthemeasureddata. Finally,conclusionsaregiveninSection5.
2. GeneralizedSide-LobeCanceller
TheGSCisproposedbyGriffiths[11]anddevelopedforadaptivenoisecancellationbyJablon[10]
and non-stationary hot-clutter cancellation by Abramovich [12]. It has been further analyzed and
developedintotheionosphericcluttersuppressioninHFSWRforoceanremotesensingbyWan. Inthis
section,weintroducetheGSCmethodandamodifiedGSCmethodbasedonavirtualslidingsubarray
forgreatersystemfreedom.
2.1. InstructionofGSC
Assumption: thek-thsampleofechox(k)receivedbyaN-elementuniformlineararray(ULA)
isthesumofthreecomponents,asshowninEquation(1): s(k)indicatestheSOI,c(k)indicatesthe
interferenceandclutter,andn(k)indicatesthenoise:
x(k) =s(k)+c(k)+n(k) (1)
InHFSWR,thenoisecanbetreatedasGaussiandistributednoise,whichisuncorrelated,andthe
√
SOIcanbeexpressedass(k) = NA(k)a ,wherea isavectorwhichcontainsthedirectionofarrival
s s
(DOA)oftheSOI, A(k)istheamplitudeoftheSOIandNisthenumberofelements.
Thecorrelatedmatrixoftheechocanbeindicatedas
(cid:104) (cid:105)
Rx = E x(k)xH(k) = Nσs2asasH+Rc+n (2)
whereσs2 = |A(k)|2 isthepowerofthesignalandRc+n isthecovariancematrixoftheinterference,
clutter, and noise, which can be indicated as Rc+n = E(cid:2)c(k)cH(k)(cid:3)+σ2I where σ2 is the power of
thenoise.
AccordingtotheMinimumVarianceDistortionlessResponse(MVDR)[21],theoptimaladaptive
beamformingvectorwcorrespondingtoa canbeindicatedas:
s
R−1 a
w= c+n s (3)
aHR−1 a
s c+n s
Inthepracticalradarsystem,thecovariancematrixRc+ncannotbeobtainedinadvanceandithas
tobeestimatedbysecondarydata. TheGSCisaneffectivemethodutilizingtheestimatedcovariance
matrixtosuppresstheinterferencesandclutter. TheframeworkofGSCisshowninFigure1.
RemoteSens.2018,10,104 3of13
Remote Sens. 2018, 10, 104 3 of 13
x(k) y(k)
w
q
·
·
·
B w
a

Figure 1. The framework of the GSC
Figure1.TheframeworkoftheGSC.
The echo obtained via the receiving array is weighted by the static weights w , which is the
The echo obtained via the receiving array is weighted by the static weights wq, which is the
q
coefficients of digital beam forming (DBF) to keep the beam direction pointing at the SOI. The block
coefficientsofdigitalbeamforming(DBF)tokeepthebeamdirectionpointingattheSOI.Theblock
mmaattrrixixB Bi siws welle-ldl-edseigsnigendefdo rfoorb toabintainingitnhge tsheeco snedcaornyddaaryta dwaittah owuitththoeuSt OthI.ew SaOisI. thweaad iasp tthivee awdeaipgthivtse
vwecetiogrh,tws vheicchtoirs, wcahlcicuhla itse dcablcyultahteede sbtiym tahteio enstoimf tahtieonco ovfa trhiaen ccoevmaraiatrnixcef omraitnritxe rffoerr einncteerafenrdenccleu tatnerd
sculuptptreers ssuiopnp.rFeisnsaiollny., Fthineaolluyt,p tuhteo ofutthpeuGt oSCf thcaen GbSeCe xcapnre bsese edxpasre:ssed as:
yy(kk)=((ww −BBww))HHx(xk)k ((44))
qq aa
wq = (cid:16)1,ej2jλπ2ddsisninθ,ej2jλπ2·2d2dsisninθ,ej2λπj(2N−N1)d1sdinsinθ(cid:17)HH (5)
w 1,e  ,e  ，e   (5)
wheredistheintervaloftheadqjacentelements,λisthewavelengthofworkingfrequencyandθisthe
expectedbeampointingdirection.
wheIrne dth iiss tchaes ein,theorvwalt oofc athlceu aldatjeactehnet belloemckemntas,t rix Bisa tnhde twheavaedleanpgtitvhe owf weigorhktsinwg fraerqeutehnecyk eaynsdf or
a
tihse thpee refxoprmecatendc eboeafmth epGoiSnCti.nAg dpirroepcteirobnl. ockmatrixBcankeeptheSOIoutofsecondarydatawhich
benefiItns tthhies rceadsuec, thioonwo tfot hcaelScuNlRatelo tshse. block matrix B and the adaptive weights w are the keys for
(cid:104) (cid:105) a
LetJ= E |y(k)|2 ,theconstraintofMVDR[21]canberewrittenasanoptimizedproblem:
the performance of the GSC. A proper block matrix B can keep the SOI out of secondary data which
benefits the reduction of the SNR loss.
Let J  E yk2 , thmwei acnoJn=strmawiiannt( wofq M−VBDwRa )[H21R]xca(wn qbe− rBewwrai)tten as an optimized problem(6:)
whereR =x(k)xH(k)istheself-correlationmatrix. ForkeepingtheSNRlossminimized,R should
x minJ min(w Bw )HR (w Bw ) x
onlycontaintheinterferencesanwdclutter,wexcludqingtheaSOI.Txhusq,Rxcanabereplacedbythecovarian(6c)e
a a
matrixofinterferenceandclutterRc+n,whichcontainsalltheclutterandinterferenceinthesidelobe.
Twhhenerteh eRoxp=tixmikzedxwHeikght sisc athneb seeilnf-dciocrarteeldataios:n matrix. For keeping the SNR loss minimized, Rx
should only contain the interferences and clutter, excluding the SOI. Thus, R can be replaced by the
(cid:16) (cid:17)−1 x
covariance matrix of interference awnad= clutBteHrR cR+nB, whBicHhR cco+nntwaiqns all the clutter and interference( 7i)n
cn
the side lobe. Then the optimized weights can be indicated as:
2.2. GSCBasedonaVirtualSlidingSubarray
InEquation(7),theadaptivewweightsBwHaRforcBlutt1eBrsHuRpprewssio nareobtainedintheconstra(i7n)t
a cn cn q
ofEquation(6)inwhichthecovariancematrixRc+n impactstheperformanceofsuppression. Fora
betterestimationofthecovariancematrixRc+n,theSOImustnotbeinthesecondarydata. Through
d2i.v2i dGiSnCg Bthaesewd hono lae Vreircteuiavli nSglidairnrga ySuinbatorrsaeyv eralsubarraysanddesigningtheblockmatrixB,theSOI
canbeInr eEjeqcuteadtioinn t(h7e), stehceo anddaaprytivdea twa.eCigohntssi dwerin gfomr cullutit-ttearr sguetpdperetescstiioonn ,aarel aorbgteaidneegdr eine othfefr ceoendsotmraionft
a
thesystemisnecessary. Combiningtheabovetwoconsiderations,avirtualslidingsubarray(VSSA)is
of Equation (6) in which the covariance matrix R impacts the performance of suppression. For
proposed. Inthissection,theGSCbasedonavirtualcsnlidingsubarray(VSSA-GSC)isintroduced.
a beFttoerr aenstiNm-aelteiomne noft uthnei focormvarliiannecrea rmraayt,riixt isRdiv,i dtehde iSnOtoI Nm-uNst’ +n1ost libdei nign stuhbe asrercaoynwdahriyc hdaartea.
cn
formed by N’ elements, as shown in Figure 2. The block matrix for the i-th sliding subarray
Through dividing the whole receiving array into several subarrays and designing the block matrix B,
B,i = 1,2,··· ,N−N(cid:48)+1canbeformedbyaminimalP-normsinglenotchfilterwiththespace
thi e SOI can be rejected in the secondary data. Considering multi-target detection, a large degree of
responseshowninFigure3whereN=32,N’=12.
freedom of the system is necessary. Combining the above two considerations, a virtual sliding
subarray (VSSA) is proposed. In this section, the GSC based on a virtual sliding subarray (VSSA-
GSC) is introduced.
For an N-element uniform liner array, it is divided into N-N’+1 sliding subarray which are
formed by N’ elements, as shown in Figure 2. The block matrix for the i-th sliding subarray
Remote Sens. 2018, 10, 104 4 of 13
B,i1,2, ,NN'1 can be formed by a minimal P-norm single notch filter with the space
i
response shown in Figure 3 where N = 32, N’ = 12.
There are two beneficial features for obtaining secondary data by the minimal P-norm single
notch filter:
a) The width of the notch is almost equal to the width of the main lobe: the SOI in the main lobe
can be almost rejected and only the interferences and clutter are contained in the secondary data;
RemoteSens.2018,10,104 4of13
b) The side lobe of the filter is almost the same level with the side lobe: the interferences and clutter
can be well expressed in the secondary data.

B1 BN-N -1
B2 BN-N
B3 BN-N +1
Figure 2. The framework of virtual sliding subarray
Figure2.Theframeworkofvirtualslidingsubarray.
4040 DDBBFF
sisnignlgel en onotcthc hf ifltieltrer
2020
00
)BB)
d(esnopserresponse(d--24--004200
-6-060
-8--108-010 00 0 -5-050 00 5050 101000
anagnlgel(ed(degergeree)e)  
FFiigguurree 33.. SSppaaccee rreessppoonnsseess ooff DDBBFF aanndd aa ssiinnggllee nnoottcchh fifilltteerr wwiitthh NN == 3322 aanndd NN’’ == 1122.
The VSSA-GSC can be completed via the following steps:
There are two beneficial features for obtaining secondary data by the minimal P-norm single
(1). Design a minimal P-norm single notch filter with the coefficients c , j1,2, ,N' to be the
notchfilter: j
block matrix B. The output of the i-th block matrixu is expressed as Equation (8) and the output
i
(a) Thewidthofthenotchisalmostequaltothewidthofthemainlobe: theSOIinthemainlobecan
of the i-th VSSA v is expressed as Equation (9). All the VSSA outputs form the data matrix U
bealmostrejectediandonlytheinterferencesandclutterarecontainedinthesecondarydata;
(b) aTnhde dsiadtae vloebcetoorf tVheafisl etexrpirseasslmedo sint tEhqeusaatmioenlse v(1e0l)w ainthd t(h1e1)s; idelobe: theinterferencesandclutter
canbewellexpressedinthesecondarydata.
N'
u c x (k), i 1,2, ,N N'1 (8)
TheVSSA-GSCcanbecomipletedvjiaitjhefollowingsteps:
j0
(1). DesignaminimalP-normsinglenotchfilterwiththecoefficients c ,j = 1,2,··· ,N(cid:48) tobethe
j
N'
blockmatrixB.TheoutpvutofthweiH-thxblo(ckk),miatri1x,u2i,ise,xNpresNsed'a1s Equation(8)andtheout(p9u) t
i q,j ij
ofthei-thVSSAv isexpressedasEquation(9). AlltheVSSAoutputsformthedatamatrixU
i j0
anddatavectorVasexpressedinEquations(10)and(11);
ui =U∑N(cid:48) cujx1i+ju(k2),i =1,u2,N··N·',1NT− N(cid:48)+1 (10()8 )
j=0
V v v v T (11)
1 2 NN'1
N(cid:48)
(2). Calculate the self-correlatiovni =ma∑triwx qH,Rjxdi+ aj(nkd), tih=e c1r,o2s,s·-·co·r,rNela−tiNon(cid:48) +ma1trix R0 as Equations (1(29))
j=0
and (13);
(cid:104) (cid:105)T
U= u1Ru=2UU··H· uN−N(cid:48)+1 (1(21)0 )
d
(cid:104) (cid:105)T
V= v1 v2 ··· vN−N(cid:48)+1 (11)
(2). Calculate the self-correlation matrix R and the cross-correlation matrix R as Equations (12)
d 0
and(13);
R =UUH (12)
d
R =UV (13)
0
1
RemoteSens.2018,10,104 5of13
Remote Sens. 2018, 10, 104 5 of 13
(3). CalculatetheadaptiveweightswaasEquRationU(1V4) ; (13)
0
(3). Calculate the adaptive weights waas Equwaatio=n R(1−d41)R; 0 (14)
(4). FinallyobtaintheoutputofVSSA-GSCwbysubRtra1cRtio n,asshowninEquation(15); (14)
a d 0
(4). Finally obtain the output of VSSA-GyS(Ck )b=y s(uwbtr−acwtio)nH, axs( ks)hown in Equation (15); (15)
q a
yk(w w )H xk (15)
q a
TheframeworkofVSSA-GSCisshowninFigure4.
The framework of VSSA-GSC is shown in Figure 4.
w
q
V
·1 U
R
0
2
u1 wa y(k)
x(k)
B u R
· 2 d
N · ·
·
·
u
N-N +1

Figure4.TheframeworkoftheVSSA-GSC.
Figure 4. The framework of the VSSA-GSC
22..33. SSiimmuullaattiioonn ooff tthhee VVSSSSAA--GGSSCC
IInn tthhiiss sseeccttiioonn,,w weet rtyryt otov vereirfiyfyt htehee fefeffcetcivtievneensessos fotfh ethVe SVSSAS-AG-SGCSvCi avmia emaseuarseudredda tdaaotba toaibnteadinbeyd
abytr aai tlrHaiFl SHWFSRWsyRs tseymstewmit hwaith32 a- e3l2e-meleenmterencte rievcienigvianrgra ayrraanyd awndit hwaitshi ma usilmatuiolantitoarng teatrignejet cintejedcitnetdo itnhteo
mtheea msueraesdudreadta d.ata.
TThhee rraannggee--DDoopppplleerr ffrreeqquueennccyy mmaapp wwiitthh aa bbeeaamm ddiirreeccttiioonn ooff 00◦° ooff mmeeaassuurreedd ddaattaa iiss sshhoowwnn iinn
FFiigguurree 55 wwiitthh aa wwoorrkkiinngg ffrreeqquueennccyy ff00=5=.25 .M2HMzH, izn, iwnhwichhi cthhet hbeeabmeasm arsea dreesdigensiegdn ferdomfro -m30°− t3o0 3◦0t°o w3i0th◦
waR i3temh° oaiten 3St◦eenrisvn. a2te0l.r1 v8T,a 1hl0.e, T1t0hh4ee othreetoicre ftiircsfit-rosrtd-oerrd eBrraBgrgag fgrefqreuqeunecniecsie asraer e±0±.203.22362 6HHz zaacccocordrdiningg ttoo tthhee ccaarr6rr oiieef rr1 3
ffrreeqquueennccyy..D Duueet ototh tehceu rcruernrte,ntht,e tphrea cptricaacltificarsl t-foirrsdte-orrBdrearg gBrfaregqgu efrnecqieusenarceiessh iafrteed s.hIiofnteods.p hIoenriocscplhuettreirc
the algorithm described in Section 2.2, the targets in both situations are detected and the clutter in
acpluptetearr saparpoeuanrsd atrhoeu3n4dth thrae n3g4ethb rinaninget hbeind iinre tchtieo dniorefc2t1io◦na sofs h21o°w ans isnhoFwignu rien 5Fai,gbu.re 5a,b.
situation b is suppressed effectively, as shown in Figure 6a,b.
We consider two situations with the injected target to testify that the VSSA-GSC framework can
make the SOI loss minimal and suppress the clutter at a maximum level:
Situation a : a visible target is injected into the non-clutter region to testify that the VSSA-GSC
framework can make the SOI loss minimal;
Situation b : an invisible target is injected into the clutter region and it is submerged with the
clutter to testify that the VSSA-GSC framework can suppress the clutter at a maximum level.
The details of the injected targets with constant speed are listed in Table 1.
Table 1. The information of the injected targets.
Situation Range Bin Doppler Frequency (Hz) Angle (Degree) SCR/SNR (dB)
a 42 −0.39 9 SNR = 35
b 34 (a) − 0 . 3 9 9 (b) SCR = −5

FiFgiugruere5 .5.R Raannggee-D-Doopppplelerrf rfereqquueennccyym maapp:: (a(a)) rarannggee-D-Doopppplelerr mmaapp wwitihtht htheeb beaeammp pooinintitninggt oto2 12◦1;°;
(Ibn()b sa) inatgunlgaelt-eiDo-Donpo app,l petlhreemr rmaep aipsin nintoh t eihoe3n 43ot4hsthpra hrnaegnregiceb cibnliu.nt ter in the area where the target is injected. In situation
b, the target is injected into the Es-layer ionospheric clutter and the power is 5 dB stronger than the
ionospheric clutter, but the SCR is not enough for detection. For signal processing, each VSSA is
formed by 12 elements with the response shown in Figure 3 and 21 VSSAs are obtained. Following

(a) (b)
Figure 6. Doppler frequency profile: (a) visible target without clutter; (b) target submerged with
clutter
2.4 Practical Problems
According to the previous simulation, VSSA-GSC is effective for suppressing the clutter in the
side lobe. However, some practical factors must be considered carefully in the practical system, such
as if the direction of the target is mismatched with the direction in which the beam is pointing.
Commonly, the beams of DBF point to several fixed directions which are designed elaborately
due to the working frequency and the aperture of the receiving array. However, in the practical
situation, targets emerging just at the direction the beam is pointing occurs with low probability.
Under this consideration, the performance of VSSA-GSC is analyzed when a target emerging form
between the adjacent beams in this section.
As shown in Figure 3, the depth of the notch is degraded seriously when the target is not at the
direction in which the beam is pointing, which can lead to the SNR loss for strong targets in the trail
HFSWR system as described above. An experiment is carried out in this section to analyse the
relationship of SNR loss via the difference between the depth of the notch and input SNR when the
input SNR is 30 dB. As shown in Figure 7, the SNR loss decreases as the difference decreases. In order
to guarantee the SNR loss less than 3 dB, the depth of the notch has to be 7 dB deeper than the input
SNR.
RemoteSens.2018,10,104 6of13
Remote SeWnse. 2c0o1n8s, i1d0e, 1r0t4w osituationswiththeinjectedtargettotestifythattheVSSA-GSCframeworkcan 6 of 13
maketheSOIlossminimalandsuppresstheclutteratamaximumlevel:
the algoSriittuhamtio dneas:carivbiesdib lien tSaregcettioisn in2j.e2c, ttehdei ntatorgthetesn ionn b-coluthtt esritrueagtioionntso aterset idfyettehcattetdh eaVndSS tAh-eG cSlCutter in
situfraatmioenw bo risk scuanppmraeksesetdhe eSffOeIcltoivsselmy,i naism sahl;own in Figure 6a,b.
Situationb: aninvisibletargetisinjectedintotheclutterregionanditissubmergedwiththe
cluttertotestifythattheVSSA-GSCframeworkcansuppresstheclutteratamaximumlevel.
ThedetailsoftheinjectedtargetswithconstantspeedarelistedinTable1.
Table1.Theinformationoftheinjectedtargets.
Situation RangeBin DopplerFrequency(Hz) Angle(Degree) SCR/SNR(dB)
a 42 −0.39 9 SNR=35
b 34 −0.39 9 SCR=−5
Insituationa,thereisnoionosphericclutterintheareawherethetargetisinjected. Insituation
b,thetargetisinjectedintotheEs-layerionospheric clutterandthepoweris5dBstrongerthanthe
ionospheric clutter, but the(aS)C R is n o t e n o u g h fo r d e tect ion. F or si gnal(pbr)o cessing, each VSSA is
formedby12elementswiththeresponseshowninFigure3and21VSSAsareobtained. Following
Figure 5. Range-Doppler frequency map: (a) range-Doppler map with the beam pointing to 21°;
thealgorithmdescribedinSection2.2,thetargetsinbothsituationsaredetectedandtheclutterin
(b) angle-Doppler map in the 34th range bin
situationbissuppressedeffectively,asshowninFigure6a,b.

(a) (b)
FigFuigreu r6e.6 .DDoopppplleerr ffrreeqquueenncycyp rpofirolef:il(ea:) v(ais)i bvleistiabrlgee ttwarigtheotu wtciltuhtoteur;t (bcl)utattregre;t s(ubb) mtaerrggeedt wsuitbhmcleurtgteer.d with
clutter
2.4. PracticalProblems
2.4 Practical Problems
Accordingtotheprevioussimulation,VSSA-GSCiseffectiveforsuppressingtheclutterinthe
sidAeclcoobred. Hinogw teov tehr,es opmreevpioraucst isciamlfuaclatotirosnm, uVsStSbeAc-oGnSsCid eisre edffceacretifvuell yfoinr sthueppprraecstsicianlgs ythstee mcl,ustutechr in the
sidaes liofbthe.e Hdiorewcteivonero, fstohmeeta prgreatcitsicmalis fmacattochrse dmwuistth bthe ecdoinrseicdtieorneidn cwahreicfhultlhye ibne tahme ipsrpaocitnictianlg s.ystem, such
Commonly,thebeamsofDBFpointtoseveralfixeddirectionswhicharedesignedelaboratelydue
as if the direction of the target is mismatched with the direction in which the beam is pointing.
totheworkingfrequencyandtheapertureofthereceivingarray. However,inthepracticalsituation,
Commonly, the beams of DBF point to several fixed directions which are designed elaborately
targetsemergingjustatthedirectionthebeamispointingoccurswithlowprobability. Underthis
due to the working frequency and the aperture of the receiving array. However, in the practical
consideration,theperformanceofVSSA-GSCisanalyzedwhenatargetemergingformbetweenthe
situation, targets emerging just at the direction the beam is pointing occurs with low probability.
adjacentbeamsinthissection.
Under this consideration, the performance of VSSA-GSC is analyzed when a target emerging form
As shown in Figure 3, the depth of the notch is degraded seriously when the target is not at
bettwheeednir tehctei oandjiancwenhti cbheathmesb iena mthiiss speocitniotinn.g , which can lead to the SNR loss for strong targets in
theAtsr asihloHwFSnW inR Fsiygsuterme 3a,s tdhees dcreipbethd aobf otvhee. nAontcehx pise rdimegernatdisedca srerireidouosultyi nwthheisns tehceti otanrtgoeat nisa lnyoset at the
dirtehcetiroenla itnio wnshhiicpho tfhSeN bRelaomss ivsi apothinetdinifgfe,r wenhciecbhe ctwane elneatdhe tod etphteh SoNftRh elonsost cfhora sntdroinnpgu ttaSrNgeRtsw ihne tnhe trail
HFtShWe iRn psuytsSteNmR iass3 0dedsBc.riAbsedsh oawbonvien. FAignu reex7p,etrhime SeNntR ilso scsadrreicerdea soeust aisnt htehidsi fsfeercetniocne dteoc raenaaselys.se the
relationship of SNR loss via the difference between the depth of the notch and input SNR when the
input SNR is 30 dB. As shown in Figure 7, the SNR loss decreases as the difference decreases. In order
to guarantee the SNR loss less than 3 dB, the depth of the notch has to be 7 dB deeper than the input
SNR.
RemoteSens.2018,10,104 7of13
InordertoguaranteetheSNRlosslessthan3dB,thedepthofthenotchhastobe7dBdeeperthanthe
Remote Sens. 2018, 10, 104 7 of 13
inputSNR.
Remote Sens. 2018, 10, 104 7 of 13

Figure 7. The relationship of SNR loss via difference between the depth of notch and inputted target
Figure 7F.i gTuhree 7r.elaTthieonreslhatiipo nosfh iSpNoRf SloNsRs lvoisas dviiaffderifefenrceen cbeebtwetweeenen ththee ddeepptthh ooff nnootctchha nadndin ipnupttuetdted target
SNR
SNR targetSNR.
For the ideal situation, as simulated in Section 2.3, the injected targets in Table 1 are just
For theF oirdtheeali dseiatlusaittuiaotnio,n ,aass ssiimmuulaltaedteidn Sienc tiSonec2t.i3o,tnh e2i.n3je, cttehdet airngjeetsctinedT abtalerg1eatres juinst eTmaebrlgein g1 are just
emerging from the direction in which the beam is pointing. In this analysis, we adjust the direction
fromthedirectioninwhichthebeamispointing. Inthisanalysis,weadjustthedirectionofthetarget
emerging from the direction in which the beam is pointing. In this analysis, we adjust the direction
of tthoem taakregetht etota mrgaetkeem thereg teafrogremt ebmetweregeen ftohremad bjaectewnetebnea tmhes aanddjatcheenpt abraemametse rasnodf tthheet paragreatmareetethrse of the
of the target to make the target emerge form between the adjacent beams and the parameters of the
tar3g4etth arraen gtheeb i3n4,tfdh =ra−n0g.3e9 bHinz,, afdd =i r−ec0t.i3o9n Hofz2, 0a◦ wdiirthecatnioSnN oRf =201°5 dwBi.thF oarnf uSrtNhRer d= e1sc5r idpBti.o nF,otrh efurther
targetd easbrceera impthtsieoo nf3,D 4ttBhhFe nbraeeanarmgtehs e obifni nDje,c BtfeFd d =nt ea−ar0gr. e3tth9ae r Hein1zj8e,◦ catae nddd it2ra1er◦cgteainto danrt eho e1f 8in2°j 0ea°cn tedwd 2itt1ah°r gaaentndi s StihNneaR idn i=jre ec1ctt5eiod nd tBaorf. g2Fe0ot◦ ris fiunr ath er
descrdipirtweiochtniico,h ntih soeaf 21b◦0es°ah wmifthsfir coohmf iDsth aBe F1b°e snahmeiafptr o ftrihnotemin i gtnhajeet c2b1tee◦adamn td apraog2ine◦stt ihnaifrgte fa r1to 8m2°1 t°ah aennbdde a2am1 2°p° saohninidftti n ftgrhoaemt i1 n8th◦je.ecA btseedsahm otaw prnogientt iins gi n a
directaito 1inn8 °oF. fiAg 2us0r se°h 3wo,wthhinec dihne ipFsti hga uo1fr°ens o3ht,ic tfhht iefsr d−oem1p0t .8hth8 oedf Bbnewoathcmehn ips2 o◦−i1ins0st.8ihn8ifg tde Bdat fw r2oh1me° ntah 2ne°d bi sea as m2h°ipfsthoeiidnf ttfi rnforgmoamn tdh te−h be1e 6ba.9em2a dmpBo ipnotiinngti ng
when1◦ isshiftedfromthebeampointing. WiththisblockmatrixB,thesignaloftargetcannotbe
at 18°a. nAds − s1h6o.9w2 nd Bin w Fhiegnu 1re° i3s, s thhieft dede pfrtohm o fth neo btecahm is p −o1i0n.t8in8g d. BW withh ethni s2 b° liosc skh mifatetrdix f rBo,m th eth seig bneaal mof tpaorginetti ng
rejectedthoroughlyanditiscontainedinthesecondarydataobtainedbytheVSSA.Inthiscase,the
and −c1a6n.9n2o td bBe wrehjeecnte d1° t hiso srhouifgtehdly f arondm i tt hise c boenatamin pedo iinnt tinheg .s eWcoitnhd tahryis d baltoac okb mtaainteridx b By, tthhee V siSgSnAa. lI onf t htaisr get
targetinthemainbeamiscancelledbytheoutputoftheVSSAasshowninFigure8.
cannocta sbee, trheeje tcatregde tt hino trhoeu mghaliyn baenadm i ti sis c aconcnetlaleinde bdy i tnh eth oeu stpecuot nodf tahrey VdSaStAa oabs tsahionwedn biny Ftihgeu VreS 8S. A. In this
case, the target in the main beam is cancelled by the output of the VSSA as shown in Figure 8.

FFiigguurree 88.. DDoopppplelerrf rferqeuqeunecnycpyr pofirolefsilwesi twhDithB FDaBnFd aVnSdS AV-SGSSAC-.GSC

To enhance the performance of VSSA-GSC, one key is optimizing the block matrix B to reject the
ToenhancetheperformanceofVSSA-GSC,onekeyisoptimizingtheblockmatrixBtorejectthe
Figure 8. Doppler frequency profiles with DBF and VSSA-GSC
sigsnigaln aolf otfhteh teatragrgete taass tthhoorroouugghhllyy aassp poosssisbilbel.e.
To 3e.nKhnaonwclee dthgee- BpaesrefdorVmSSaAn-cGe SoCf VSSA-GSC, one key is optimizing the block matrix B to reject the
signa3l .o Kf nthoew tlaedrggeet- Baass tehdo VroSuSgAh-lGyS aCs possible.
AimingattheproblemilluminatedinSection2.4,aknowledge-basedVSSA-GSC(KB-VSSA-GSC)
isdevelopedforbetterdetectionofthetargetsubmergedinionosphericclutterinthischapter.
Aiming at the problem illuminated in Section 2.4, a knowledge-based VSSA-GSC (KB-VSSA-
GSC) is developed for better detection of the target submerged in ionospheric clutter in this chapter.
3. Knowledge-Based VSSA-GSC
The main idea of KB-VSSA-GSC is the single notch filter design adaptively based on two kinds
Aofi mknionwg laedt gthe:e s ypsrtoembl epmar aimlluemterisn aantedd t hien eSneecrtgiyo no f 2th.4e, satr konngoewstl etadrggee-t bdaesteecdt eVd SwSiAth-oGuSt Can (yK cBlu-VtteSrS A-
GSC)s iusp dperveseslioopne. d for better detection of the target submerged in ionospheric clutter in this chapter.
The principle of adaptive single notch filter (ASNF) design follows two points:
The main idea of KB-VSSA-GSC is the single notch filter design adaptively based on two kinds
Point a: the width of the notch should be wider than the width of the major beam according to
of knowledge: system parameters and the energy of the strongest target detected without any clutter
the system parameters.
suppression.
Point b: the depth of the notch should be deeper than the energy of the strongest target in the
The principle of adaptive single notch filter (ASNF) design follows two points:
looking direction.
Point a: the width of the notch should be wider than the width of the major beam according to
the sy stem parameters.
Point b: the depth of the notch should be deeper than the energy of the strongest target in the
looking direction.
RemoteSens.2018,10,104 8of13
The main idea of KB-VSSA-GSC is the single notch filter design adaptively based on two
kinds of knowledge: system parameters and the energy of the strongest target detected without
anycluttersuppression.
Theprincipleofadaptivesinglenotchfilter(ASNF)designfollowstwopoints:
Pointa: thewidthofthenotchshouldbewiderthanthewidthofthemajorbeamaccordingto
thesystemparameters.
Pointb: thedepthofthenotchshouldbedeeperthantheenergyofthestrongesttargetinthe
Remote Sens. 2018, 10, 104 8 of 13
lookingdirection.
Therefore,theframeworkoftheKB-VASS-GSCalgorithmisshowninFigure9. Inthisframework,
Therefore, the framework of the KB-VASS-GSC algorithm is shown in Figure 9. In this
apre-detectionmoduleCandanASNFdesignmoduleAareaddedintotheVSSA-GSCframework.
framework, a pre-detection module C and an ASNF design module A are added into the VSSA-GSC
Inthenextsubsectionsthedetailsoftheinnovativemodulesareintroduced.
framework. In the next subsections the details of the innovative modules are introduced.
1
2 x(k) d0(k) y(k)
w
q
·
·
·
R
0
KB d1 wa
C A B d R
2 d
·
·
·
dN-N’+1
FFigiguurree9 9..F Frraammeewwoorrkko offK KBB-V-VSSSSAA-G-GSSCC.
33..11. PPrree--DDeetteeccttiioonn ffoorr KKnnoowwlleeddggee
TThhee ttaasskk ooff tthhiiss mmoodduullee iiss ttoo oobbttaaiinn tthhee SSNNRR ooff tthhee ssttrroonnggeesstt ttaarrggeett ddeetteecctteedd wwiitthhoouutt aannyy cclluutttteerr
ssuupppprreessssiioonn.. TThhee mmaaxxiimmuumm eenneerrggyyi isst trreeaatteedda asst thheek knnoowwleleddggeef foorrt htheeA ASSNNFFd deessigignn..
TThheeC CeellllA AvverearaggininggC ConosntsatnatnFt aFlasleseA AlalramrmR aRteat(eC (AC-AC-FCAFRA)R[2) 2[,2223,]2m3] emtheotdhohda shbaese bnepenro pvreodvteodb teo
abne eafnfe ecftfivecetmiveet mhoedthfoodr pforer -pdreet-edcetitoenc.tiTohne. Tdheeta dilestaoiflsC oAf- CCAFA-CRFaAreRt ahraet tohfaat colfa ass cilcaaslsaiclgaol railtghomritahnmd iatnisd
nito itst hneotc othnec ecronncpeorinn tpoofintht iosf pthapise pr.aIpnetrh. iIsnc tahsies, ciatsise,n iot tisd neosct rdibeesdcriinbetdh iisns tehcitsi osne.ction.
UUttiilliizziinngg tthhee CCAA--CCFFAARRa allggoorriitthhmmb byys seettttiinngga at thhrreesshhoollddw whhiicchhi iss3 3.5.5t tiimmeesst thhaatto off tthhee cceellll mmeeaann
vvaalluuee,,o onnllyyt thheet taarrggeettssw witithhh higighhS SNNRRc caannb beed deetteecctteedd..i inn tthhiiss ccaassee,, oonnee ooff tthhee ffaaccttoorrss ffoorr AASSNNFF ddeessiiggnn
wwhhiicchhi sist thheem maaxximimuummS SNNRRi siso obbtatainineedd..
3.2. AdaptiveSingleNotchFilterDesign
3.2 Adaptive Single Notch Filter Design
TThhee mmoosstt iimmppoorrttaanntt kkeeyy ooff KKBB--VVSSSSAA--GGSSCC iiss hhooww ttoo ddeessiiggnn tthhee AASSNNFF.. IInn tthhiiss sseeccttiioonn,, aa nnoovveell
aaddaappttiivvee nnoottcchh fifilltteerr iiss pprrooppoosseedd bbaasseedd oonn ssppaattiiaall ttiimmee ssyymmmmeettrryy aanndd FFoouurriieerr sseerriieess eexxppaannssiioonn..
CCoonnssiiddeerriinngg tthhaatt HHFFSSWWRR ssyysstteemm ooppeerraattiinngg aatt ffrreeqquueennccyy ff0 wwitihtha annN Ne elelemmeennttu unniiffoorrmm lliinneeaarr aarrrraayy
0
(ULA),thebeamformingoftheechocanbeexpressedas:
(ULA), the beamforming of the echo can be expressed as:
FF(θ) =N∑−N11aan(θ0)·e−ejλ2/πjd2s/dinsiθn·nn=N∑N−11aan(θ0)·e−ejλ2j/πd2/sdinsinθ·ndnd·d1d1 ((1166))
n=0 n 0 n=0 n 0
n0 n0
wwhheerreed di sist thheed disistatanncceeb beetwtweeeennn neeigighhbboorriningge elelemmeenntstsa annddλ is tihse thwea wvealvenelgetnhg.th.
Furthermore,thediscreteFourierseriesoftheechocanbeexpressedas:
Furthermore, the discrete Fourier series of the echo can be expressed as:
NN 2
YY(kk)=∑yy(n∆nt)t·e−ej2Mπj·Mkn∆kntfstfs ((1177))
n=1
n1
where t is time sampling interval , f is sampling frequency, and M is the number of frequency
s
components.
According to the definition of discrete Fourier series and the similarity between Equations (16)
and (17), the relationship between space frequency and angle is given by Equation (18):
sin 1 sin f sin
f '    0 (18)
/d d  c
Based on experiential formula, the main-lobe width is expressed as:
RemoteSens.2018,10,104 9of13
where ∆t is time sampling interval ,f is sampling frequency, and M is the number of
s
frequencycomponents.
AccordingtothedefinitionofdiscreteFourierseriesandthesimilaritybetweenEquations(16)
and(17),therelationshipbetweenspacefrequencyandangleisgivenbyEquation(18):
sinθ 1 sinθ f ·sinθ
f(cid:48) = · = = 0 (18)
λ/d d λ c
Basedonexperientialformula,themain-lobewidthisexpressedas:
c
θ =51.05· (19)
m (N−1)·d·f
0
InsertingEquation(19)into(18),thespacefrequencyisobtainedby:
(cid:16) (cid:17)
f ·sin 51.05· c
f(cid:48) = 0 (N−1)·d·f0 (20)
m c
AccordingtoEquation(20)andFourierseriesexpansion, thespatialresponsefunctionofthe
proposedANSFisexpressedasEquation(21):
(cid:40)
H(ejω(cid:48)) = e−jω(cid:48)a ωc(cid:48) ≤ |ω(cid:48)| < π (21)
0 0≤ |ω(cid:48)| < ω(cid:48)
c
whereω(cid:48) =2πf(cid:48) isthespacefrequency,ω(cid:48) isthecut-offfrequency. ω(cid:48) isthespatialpass-bandcut-off
c p
frequency,ω(cid:48) isthespatialstop-bandcut-offfrequency. Inanidealsituationω(cid:48) = ω(cid:48) = ω(cid:48),thenotch
s c s p
filter would acquire optimal performance. However, under the real situation, we can only get ω(cid:48)
p
whichisclosetoω(cid:48) owingtothelimitofthearrayaperture;Rightnow,weexpectω(cid:48) = (ω(cid:48) +ω(cid:48))/2.
s c s p
Aimingtoensurethatthepass-bandofthespacenotchfilterisnolessthanthemain-lobewidth,ω(cid:48)
s
shouldmeetω(cid:48) =2πf(cid:48) .
s m
The unit impulse response [24] of the proposed spatial notch filter is expressed as shown in
Equation(22)
sin[π(n(cid:48)−a)] sin[ω(cid:48)(n(cid:48)−a)]
 − c n(cid:48) (cid:54)= a
h(n(cid:48)) = π(n(cid:48)−a) π(n(cid:48)−a) (22)
1− ωc(cid:48) n(cid:48) = a
π
wherea = (N(cid:48)−1)/2,andN’istheorderofthefilter.
Implementingthespatialnotchfilterneedsthenumberoftheantennaelements. Thecoefficients
ofthefilterportrayanevensymmetry,sothat,N’istheoddnumberandcanbegivenbyEquation(23),
owingtotheempiricalformula[24]:
 
A−8
N(cid:48) =  (cid:12) (cid:12) (23)
2.285(cid:12)(cid:12)ω(cid:48)p−ωs(cid:48)(cid:12)(cid:12)
where(cid:100)x(cid:101)istheceilingofx,and Aandω(cid:48) mustbenolessthanthemaximumSNRdetectedbythe
s
CA-CFARinthepre-detectionofthemonitoringregionandmain-lobewidthseparately,whichensures
avoidingtheproblemrevealedinSection2.4,whileω(cid:48) needstobeadjustedaccordingtothepractical
p
elementsappropriately. Inthepracticalsystem,theFourierseriesistruncatedbythelimitedelements
Remote Sens. 2018, 10, 104 10 of 13
RemoteSens.2018,10,104 I ( 1[12n' /(N' 1)]2) 10of13
w(n')  0 ,0 n'  N' 1 (24)
I ()
N’,whichbringsabouttheGibbsphenomen0on,andthenextremelydegradestheperformanceofthe
filter. Forthereason,aKaiserwindowwhichisexpressedasEquation(24)isemployed.
whereI ( ) is the First Class Zero-order Modified Bessel Function,  is a variable parameter for
0
(cid:113)
the selecting the main beam widIt(hβ an1d− [s1i−de2 nl(cid:48)o/b(Ne (cid:48)a−tt1e)n]2u)ation. Consequently, the modified unit
w(n(cid:48)) = 0 ,0≤ n(cid:48) ≤ N(cid:48)−1 (24)
impulse response of the spatial notch filter isI d(βe)veloped as Equation (25)
0
where I0(·)istheFirstClassZero-ordher(Mno'd)ifiehd(Bne's)se*lwFu(nnc't)io n,βisavariableparameterforthe (25)
d
selectingthemainbeamwidthandsidelobeattenuation. Consequently,themodifiedunitimpulse
Ther eosrpdonesre ooff AthNesSpFa tiaNln'o, twchhfiiclther isis adlesvoe tlohpee nduasmEbqeura toiofn e(l2e5m) ents in VSSA, is calculated by Equation
(23) which depends on the maximum SNhR( nA(cid:48)) a=nhd( nt(cid:48)h)e∗ ww(ind(cid:48))th of main-lobe ' . In theory(,2 5th) e length
d s
N' can affeTcht ethored emroafxAimNSuFmN n(cid:48),uwmhicbheirs oalfs odtehteencutimnbge rtaorfgeleetms eanntsdin thVeSS mA,aixsicmalcuumlat endubmyEbqeura otifo nin(2te3)rferences
suppreswsehdic. hTdheipse nmdseaonnst htehmata xiNmu' mshSoNuRldA abned ltahregwerid itfh mofomraei nt-alorgbeetωs s(cid:48).nIenedth etoor yb, teh edleetnegctthedN (cid:48)and N'
can affect the maximum number of detecting targets and the maximum number of interferences
should be smaller if more interferences need to be suppressed. In this case, the lengthN'should be
suppressed. ThismeansthatN(cid:48) shouldbelargerifmoretargetsneedtobedetectedandN(cid:48) shouldbe
designedsm baallseerdif omno rtehein steyrsfeteremnc erseqnueeidretmobeenstus.p pressed. Inthiscase,thelength N(cid:48) shouldbedesigned
Accboarsdedinogn thtoe styhstee mmreeqausiurermeden tds.ata parameters used in Section 2, and considering that the
maximum SANcRco rodfin tghteo tshuesmpeeacstuerded tdaartgaeptasr ainm ettheres museadinin lSoebceti oins 23,5a nddBco, nwsihdeicrihn gisth tahteth eoumtapxuimt uomf the pre-
SNRofthesuspectedtargetsinthemainlobeis35dB,whichistheoutputofthepre-detectionmodule,
detection module, the space responses of the proposed ASNF is shown in Figure 10, where the filter
thespaceresponsesoftheproposedASNFisshowninFigure10,wherethefilterorderisN(cid:48) =12and
order isthNe'e=xp1e2ct eadnadng tlehaet teenxupaetciotnedis −an4g7.l2e2 daBtt.eTnhueactoimonp airse d−s4p7a.c2e2r edspBo.n Tsehree scuoltmsopfathreedA SsNpFaacned response
results osfi ntghlee nAoStcNhFfil taenrsdc hsoinsegnlein nFoigtuchre f3ilatreerssh cohwonsiennF iignu rFeig10u.rIet c3a narbee sseheonwfronm inF iFguigreu1r0e t1h0at. AItS cNaFn be seen
from Figisumreu c1h0b tehttaert tAhaSnNthFe sisin mgleuncohtc bhefitltteerr ftohraanbs othluete slyinregjelect innogtmchai nfi-llotebre ifnofro rambastoiolnuatenldyr erteajiencintigng main-
theside-lobeinformationasmuchaspossible.
lobe information and retaining the side-lobe information as much as possible.

FiguFreig 1u0re. 1S0p.aScpea creersepspoonnsseess ooff DDBBFFa nadntdw towsion gslienngoltec hnfiolttcehrs .filters
4. ResultsoftheMeasuredData
4. Results of the Measured Data
Theexperimentsarecarriedoutinthissectiontoverifytheprecedingframeworkusingmeasured
data as shown in Figure 8 (Section 2.3). For one simulated target at beam direction ϕ = 20◦,
The experiments are carried out in this section to verify the preceding framework using
f = −0.3878 Hz, and the 34th range bin are injected into the measured data. The adjoining
measurebddea dmastaof aths esshyostwemn ainre F1i8g◦aunrde 281 ◦(S.Uectitliiozinn g2V.3S)S. AF-oGrS oCnwei sthimouutAlaNteSdF, tthaerginejet catet dbteaargmet disirceancctieollned  20o
, f  0a.s3t8h7e8ioHnzos,p ahnerdic tchleu t3te4rthis rcaanncgeell ebdi.nO aprpeo isnitjee,cKteBd-V iSnStAo -tGhSeC mweitahsaur1e2d-o rddaetraA. STNhFe caadnjomiankineg beams
d
the injectedtargetvisible as theionospheric clutter issuppressedand the SCRis improved 14 dB,
of the system are 18°and 21°. Utilizing VSSA-GSC without ANSF, the injected target is cancelled as
respectively,asshowninFigure11.
the ionospheric clutter is cancelled. Opposite, KB-VSSA-GSC with a 12-order ASNF can make the
injected target visible as the ionospheric clutter is suppressed and the SCR is improved 14 dB,
respectively, as shown in Figure 11.