research article research on polarization cancellation of...

Research ArticleResearch on Polarization Cancellation of NonstationaryIonosphere Clutter in HF Radar System

Xingpeng Mao Hong Hong Weibo Deng and Yongtan Liu

School of Electronic and Information Engineering Harbin Institute of Technology Harbin Heilongjiang 150001 China

Correspondence should be addressed to Xingpeng Mao mxphiteducn

Received 25 April 2014 Revised 20 August 2014 Accepted 9 September 2014

Academic Editor Hang Hu

Copyright copy 2015 Xingpeng Mao et alThis is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Oblique projection polarization filter (OPPF) can be applied as an effective approach for interference cancellation in high-frequencysurface wave radar (HFSWR) and other systems In order to suppress the nonstationary ionosphere clutter further a novel OPPFbased clutter suppressing scheme is proposed in this paperThe polarization and nonstationary characteristic of the clutter are takeninto account in the algorithms referred to as range-Doppler domain polarization suppression (RDDPS) and the range-time domainpolarization suppression (RTDPS) method respectively The RDDPS is designed for weak ionosphere clutter and implemented inthe range-Doppler domain directly whereas the RTDPS algorithm is designed to suppress the powerful ionosphere clutter with amultisegment estimation and suppression scheme About 15ndash23 dB signal to interference ratio (SIR) improvement can be exceptedwhen using the proposed method whereas the targets can be more easily detected in the range-Doppler map Experimental resultsdemonstrate that the scheme proposed is effective for nonstationary ionosphere clutter and is proven to be a practical interferencecancellation technique for HFSWR

1 Introduction

By exploiting the long-range propagation of vertically polar-ized electromagnetic wave in the band of 2ndash15MHz high-frequency surface wave radar (HFSWR) is able to receive ves-sel and low-flying aircraft echoes over the horizon Howeverthe signal environment of high-frequency (HF) band is farfrom satisfactoryThe powerful shortwave radio interferenceionosphere clutter and industrial interference that dominatethe pure receiver noise in the HF band cause a significantlimit of detection capability Ionosphere clutter which is oftenobserved to mask multiple successive range and Dopplercells is one of the main interference sources In some casesthe power of the clutter is so high that even the target echoesare overwhelmed resulting in poor detection and trackingperformance [1 2]

Adaptive beamforming schemes have been developedby using the space information of ionosphere clutter [3ndash5] However when the target is overlapped by ionosphereclutter from the same or close direction such approaches arenot ideal According to the fact that the echoes of targetsarriving along the surface of ocean used to be vertically

polarized while ionosphere clutter is elliptically polarizedpolarization filtering can be applied to improve the HF radarperformance By utilizing the polarization difference betweenthe target and the clutter polarization filter can be usedto suppress interference [6ndash9] However a severe loss ofcoherent integration occurswhen a conventional polarizationfilter is applied to coherent systems such as HFSWR as anadditional amplitude andor phase distortion of the targetsignal will be introduced In order to solve this problemnull phase-shift polarization filter (NPPF) [10] is proposedand then extended to a frequency domain null phase-shiftmultinotch polarization filter in [11 12] Such improvementeffectively keeps the temporal coherence of the target withincoherent integration time (CIT) and successfully paved a wayfor the application of polarization filtering in HFSWR Toimprove the flexibility and convenience oblique projectionpolarization filter (OPPF) [13] is further proposed to dealwith nonorthogonal signals Successful experimental evalu-ation of OPPF for suppressing shortwave radio interferencein HFSWR is reported in [14]

However the ionosphere clutter cancellation methodwhich meets the requirement of practical HFSWR system

Hindawi Publishing CorporationInternational Journal of Antennas and PropagationVolume 2015 Article ID 631217 12 pageshttpdxdoiorg1011552015631217

2 International Journal of Antennas and Propagation

is still an open issue as the ionosphere clutter is usuallynonstationary In this paper two types of clutter cancel-lation approaches are given to suppress the nonstationaryionosphere clutter The range-Doppler domain polarizationsuppression (RDDPS) is designed for weak ionosphere clutterand performed in the range-Doppler domain while therange-time domain polarization suppression (RTDPS) isdesigned for strong ionosphere clutter The procedure ofclutter polarization estimation and clutter suppression insegments for the RTDPS is emphasized in our research Andthe segmentation parameter optimization is also discussed indetail to obtain a balance between the clutter cancellation andthe target restoration The specific utilization of RDDPS orRTDPS depends on the type of the clutter at the correspond-ing range cell

The remainder of this paper is organized as follows InSection 2 the design of OPPF is introduced and the impacton the performance of the OPPF by the estimation error isanalyzed The nonstationary ionosphere clutter cancellationscheme is proposed in Section 3 whereas the applications ofRDDPS and RTDPS are discussed in detail in Section 4Thenthe experimental performance evaluation of the proposedscheme is given in Section 4 Finally the conclusions aredrawn in Section 5

2 Oblique Projection Polarization Filter

21 Received Signal Model Suppose the received wavefrontis a completely polarized wave and its polarization angleand polarization angle difference are 120574 and 120578 respectivelyIgnoring the absolute phase the incident signal E(119905) can bedescribed by Jones vector as in [10] as

E (119905) = [ 119878 (119905) cos 120574119878 (119905) sin 120574 exp (119895120578)]

= [cos 120574

sin 120574 exp (119895120578)] 119878 (119905) = a119878 (119905) (1)

where 119878(119905) cos 120574 is the horizontally polarized componentof E(119905) while 119878(119905) sin 120574 exp(119895120578) is the vertically polarizedcomponent of E(119905) Vector a is defined as the polarizationsteering vector of E(119905) and

a = [ cos 120574sin 120574119890119895120578] (2)

22 OPPF and Error Analysis Suppose the polarizationsteering vectors of the target and interference are a119878 and a119868respectively If the two steering vectors satisfy a119878 = a119868 acorresponding polarization oblique projection operator canbe constructed by [13]

H = a119878(aH119878 Pperpa119868a119878)minus1aH119878 Pperpa119868

(3)

where Pperpa119868 = E minus a119868(aH119868 a119868)minus1aH119868 and E represents the unit

matrixThe fundamental property of this polarization oblique

projection operator can be given as

Ha119878 = a119878 Ha119868 = 0 (4)

The scalar form of (4) can be given as

(Adagger119878H) a119878 = 1 (Adagger119878H) a119868 = 0 (5)

where Adagger119878 = (aH119878 a119878)minus1aH119878

Usually the received signal is a linear combination of thetarget E119878(119905) = a119878119878(119905) interference E119868(119905) = a119868119868(119905) and noisen(119905) According to (4) the output of the OPPF can be givenas

E119878 (119905) = H (E119878 (119905) + E119868 (119905) + n (119905))

= Ha119878119878 (119905) +Ha119868119868 (119905) +Hn (119905)

= E119878 (119905) +Hn (119905)

(6)

When scalar form is required the filtering process can berewritten as

119878 (119905) = Adagger119878H (E119878 (119905) + E119868 (119905) + n (119905))

= Adagger119878Ha119878119878 (119905) + Adagger119878Ha119868119868 (119905) + A

dagger119878Hn (119905)

(7)

According to (5) (7) can be simplified as

119878 (119905) = 119878 (119905) + Adagger119878Hn (119905) (8)

Equations (6) and (8) indicate that the interference canbe completely cancelled and the target is restored withoutdistortion when the polarization steering vectors of the targetand interference which are utilized to build the subspaces ofdesired ranges and null spaces are estimated accurately

If the estimation accuracy is uncertain in order toanalyze the performance loss of OPPF that was caused bythe estimation error the mean square error (MSE) of thetarget can be defined as MSE = E119878(119905) minus 119878(119905)2F where119878(119905) is the recovered signal of the target 119878(119905) and E(sdot) and sdot F denote themathematical expectation and the Frobeniusnorm Substituting (7) into MSE the general form of MSE ofthe target 119878(119905) can be given as

MSE = E 10038171003817100381710038171003817Adagger119878Ha119878119878 (119905) + A

dagger119878Ha119868119868 (119905) + A

dagger119878Hn (119905) minus 119878 (119905)10038171003817100381710038171003817

2

F

(9)

where H = a119878(aH119878 Pperpa119868 a119878)minus1aH119878 P

perpa119868 Adagger119878 = (a

H119878 a119878)minus1aH119878 a119878 and

a119868 are the real polarization steering vectors of the targetand the interference and a119878 and a119868 are the estimated valuesrespectively

Supposing the target signal interference and noise areuncorrelated (9) can be simplified as

MSE = |119909|21205902119904 +1003816100381610038161003816119910100381610038161003816100381621205902119894 + |119911|

21205902 (10)

where

119909 = Adagger119878Ha119878 minus 1 (11)

119910 = Adagger119878Ha119868 (12)

119911 = radic1

sin2120595 (13)

120595 = arccos (10038161003816100381610038161003816aH119878 a11986810038161003816100381610038161003816) (14)

International Journal of Antennas and Propagation 3

And 1205902119878 1205902119868 and 120590

2 are the power of the target interferenceand noise respectively Define 119909 and 119910 as the coefficients of1205902119878 and 120590

2119868 The error analysis of the MSE will be discussed in

three cases as follows

221 MSE without Estimation Error a119878 = a119878 a119868 = a119868Supposing the polarization steering vectors of the target andthe interference are both accurately estimated according to(11) and (12) we have119909 = 119910 = 0TheMSEgets to itsminimumas

MSE = |119911|21205902 (15)

222 MSE with Target Estimation Error a119878 = a119878 a119868 = a119868In this case we have 119909 = 0 and 119910 = 0 which indicates thatthe interference can be completely suppressedwhile the targetis restored with distortion Then the MSE can be simplifiedfrom (10) as

MSE = |119909|21205902119878 + |119911|21205902 (16)

Ignoring the noise term the MSE is mainly determinedby 119909 and1205902119878 According to the properties of oblique projection[15] it is beneficial to decompose vector a119878 into two specificcomponents the component that locates in the subspacespanned by a119878 and the one which lies in the subspace spannedby a119868 Therefore a119878 can be decomposed as

a119878 = (120572 + 120573) a119878 + ]a119868 (17)

where

120572 =aH119878 a119878

(1003816100381610038161003816aH11987810038161003816100381610038161003816100381610038161003816a1198781003816100381610038161003816)

120573 =(1003816100381610038161003816a11986810038161003816100381610038162aH119878 d minus a

H119878 a119868a

H119868 d)

(1003816100381610038161003816a119878100381610038161003816100381621003816100381610038161003816a11986810038161003816100381610038162minus aH119878a119868aH119868 a119878)

] =(1003816100381610038161003816a11987810038161003816100381610038162aH119868 d minus a

H119868 a119878a

H119878 d)

(1003816100381610038161003816a119878100381610038161003816100381621003816100381610038161003816a11986810038161003816100381610038162minus aH119878a119868aH119868 a119878)

d = a119878 minus 120572a119878

(18)

According to [13] the first part in (17) which locates inthe target subspace will be reserved as a whole whereas thesecond part will be cancelled by H to null Substituting (17)into (11) 119909 can be rewritten as

119909 = Adagger119878H ((120572 + 120573) a119878 + ]a119868) minus 1 = 120572 + 120573 minus 1 (19)

Therefore (16) can be rewritten as

MSE = 1003816100381610038161003816120572 + 120573 minus 1100381610038161003816100381621205902119878 + |119911|

21205902 (20)

Equation (20) indicates that theMSE ismainly affected bythe term of |120572 + 120573 minus 1|21205902119878 which is the product of the targetpower 1205902119878 and its corresponding coefficient 119909 The lower theestimation accuracy of targetrsquos polarization state is the largerthe value of 119909will be and the MSE increases However whenthe target is estimated with no error (20) will be identical to(15)

223 MSE with Interference Estimation Error a119878 = a119878 a119868 =

a119868 Supposing the target signal is accurately estimated whilethe interference is not we have Adagger119878Ha119878 = 1 and Adagger119878Ha119868 = 0which makes 119909 = 0 119910 = 0 In this case the target is perfectlyrestored while the interference is partly suppressed by OPPFDecomposing vector a119868 into two specific components wehave

a119868 = (1205721015840+ 1205731015840) a119868 + ]

1015840a119878 (21)

where

1205721015840=

aH119868 a119868(1003816100381610038161003816aH11986810038161003816100381610038161003816100381610038161003816a1198681003816100381610038161003816)

1205731015840=(1003816100381610038161003816a11987810038161003816100381610038162aH119868 d minus a

H119868 a119878a

H119878 d1015840)

(1003816100381610038161003816a119868100381610038161003816100381621003816100381610038161003816a11987810038161003816100381610038162minus aH119868 a119878aH119878 a119868)

]1015840 =(1003816100381610038161003816a11986810038161003816100381610038162aH119878 d minus a

H119878 a119868a

H119868 d1015840)

(1003816100381610038161003816a119868100381610038161003816100381621003816100381610038161003816a11987810038161003816100381610038162minus a119868a119878aH119878 a119868)

d1015840 = a119868 minus 1205721015840a119868

(22)

Substituting (21) into (12) 119910 can be rewritten as

119910 = Adagger119878H (1205721015840+ 1205731015840) a119868 + A

dagger119878H]1015840a119878 = V1015840 (23)

The MSE can be simplified as

MSE = 10038161003816100381610038161003816]101584010038161003816100381610038161003816

21205902119868 + |119911|

21205902

= 1205902119878 (

10038161003816100381610038161003816]101584010038161003816100381610038161003816

2

SIR+|119911|2

SNR)

(24)

where SIR = 12059021198781205902119868 and SNR = 1205902119878120590

2 refers to the signal tonoise ratio (SNR)

Equation (24) demonstrates that the interference cannotbe suppressed completely when it is estimated with errorThe degree of interference suppression is determined by thecomponent (1205721015840 + 1205731015840)a119868 in (21) The smaller the estimationdeviation is the larger this component will be and theperformance of OPPF will be better

Moreover fixing the SIR and SNR and the power of thetarget according to (14) it can be noticed that the part of|119911|21205902 in (15) (20) and (24) will increase and the MSE will

become larger when the polarization state of the target andthe interference are getting close

3 Polarization Cancellation forIonosphere Clutter

To apply an OPPF in ionosphere clutter cancellation it isnecessary to accurately estimate the polarization state of thetarget and the ionosphere clutter so that the clutter canbe suppressed to the maximum whereas the target can beeffectively restored With regard to the nonstationary charac-teristic of the ionosphere clutter the polarization estimationmethods and ionosphere clutter cancellation scheme shouldbe properly designed


31 Polarization and Nonstationary Characteristic of Iono-sphere Clutter Ionosphere clutter which is a kind of self-generated interference inHFSWR is the radar signals reflect-ing back from the ionosphere The polarization plane of theelectromagnetic wave is usually rotated by the ionospherealong the radio propagation path which makes the highpower vertically polarized radar signals change into ellipti-cally polarized ones However the echoes of targets arrivingalong the surface of ocean remain vertically polarized Evi-dent difference between the elliptical polarized ionosphereclutters and the vertically polarized target signals can befound in the dual-polarized HFSWR That is the power ofthe horizontally polarized component of ionosphere clutter isclose to that of the vertically polarized part or even strongerHowever the power of the horizontally polarized componentof the target echoes propagating along the ocean surface isquite weak compared with that of the vertically polarizedcomponent [16 17]

Affected by the irregular activities of the free electronsand charged ions the electron concentration of the iono-sphere is unstable which leads to the nonstationary featureof the ionosphere clutter [3] The following characteristics ofthe ionosphere clutter are usually observed

(1) The ionosphere clutter is not stable in a CIT and itsduration time varies from several pulse periods to thewhole CIT

(2) In each single pulse some clutters occupy less rangecells whereas some occupy more

(3) The nonstationary feature also leads to the differentfrequency spread in Doppler spectrum some clutterslocate inmultiple successive Doppler cells while someexist in fewer Doppler cells

(4) The ionosphere clutter is usually elliptically polarizedbut its polarization state is unstable in the whole CIT[5] As a result it behaves as a partially polarized wavein a long time observation

32 Nonstationary Ionosphere Clutter Polarization Cancella-tion Scheme According to the characteristics of ionosphereclutter discussed above a novel OPPF based polarizationcancellation scheme for nonstationary ionosphere clutter isproposed Figure 1 gives the basic structure of this schemeIn Figure 1 the raw data is pretreated first to obtain thepolarization information of the clutters and the targets whichis necessary for building the RDDPS or RTDPS then thesignals are filtered in range or range-Doppler domain andthe output of the filter will be utilized to perform rangeand Doppler processing in RTDPS or given as the resultin RDDPS respectively Five steps are needed to finish theclutter cancellation

(1) Because of the weak power of radar echoes rangeprocessing andDoppler processing need to be carriedout first Range-Doppler maps are generated fromthe raw data of each horizontal and vertical channelrespectively

(2) The state of all the samples in the range-Dopplermap is then estimated including the power value and

Rawdata

Signalestimation

Signalclassification

Clutter typeidentification and

filter selection

Doppler processingRange processing

RTDPS RDDPSor

Composed range-Doppler map

Ionospheric cluttercancellation

Pretreatment

Range cell = 1 end

Figure 1 Structure of ionosphere clutter cancellation scheme

polarization parameters By using the basic charac-teristic of the signals in the range-Doppler map thetarget and other clutters such as ground clutter oceanclutter and ionosphere clutter can be preliminarilyseparated and classified

(3) Based on the power estimation the type of ionosphereclutter is identified cell by cell in range domain Thespecific utilization of RDDPS or RTDPS at each rangecell is determined by the clutter type at each range cell

(4) RDDPS and RTDPS algorithms designed for dif-ferent types of ionosphere clutter will be used tosuppress the clutter The former one is designed forthe ionosphere clutter with low power and the filter-ing process is carried out in range-Doppler domaindirectly The latter one is designed for powerfulclutter and the filtering process is mainly carried outin the range-time domain In a practical HFSWRsystem the two types of ionosphere clutter mayexist simultaneously and locate at different rangecells Therefore the selection of RDDPS or RTDPS isdecided by the clutter type at the corresponding rangecell Because of the adaptive scheme in this part anoptimal filtering effect can be obtained

(5) After all the range cells are treated with the procedurein (4) the final range-Doppler map is composedfor RDDPS whereas a range-Doppler processing isneeded for RTDPS to obtain the final range-Dopplermap

33 Pretreatment As drawn in Figure 1 pretreatmentincludes the range-Doppler processing the signal parametersestimation signal classification determination of ionosphereclutter type and the selection of filtering method Differentfrom conventional processing in a dual-polarized HFSRWsystem the radar raw data of both the horizontal polarizationchannel and vertical polarization channel are recordedsimultaneously Then range-Doppler map of each channelcan be obtained respectively Then the power value andpolarization state of all the signals in the range-Dopplermap can be estimated and stored After all the signals are


classified the target (big enough or separated from theclutter) groundocean clutter and ionosphere clutter willbe separated apart Suppose the range-Doppler map iscomposed by 119869 range cells and 119877 Doppler cells The samplesof the vertical and horizontal polarization channel at thecurrent range-Doppler cell (119895 119903) are defined as 119881(119895 119903) and119867(119895 119903) where 1 le 119895 le 119869 and 1 le 119903 le 119877 respectively Theestimation values of the power value 119889(119895 119903) polarizationangle 120574(119895 119903) and polarization angle difference 120578(119895 119903) ofrange-Doppler cell (119895 119903) can be given as

119889 (119895 119903) = radic(119881 (119895 119903))2+ (119867 (119895 119903))

2

120574 (119895 119903) = arctan (abs (119881 (119895 119903))abs (119867 (119895 119903))

)

120578 (119895 119903) = angle (119881 (119895 119903)) minus angle (119867 (119895 119903))

(25)

where angle() is the function to obtain the complex phase of119881(119895 119903) and119867(119895 119903)

After the parameters have been estimated all the signalswill be classified Firstly a power value gate is set by 119889119871to reduce the impact of noise All the samples that satisfy119889(119895 119903) ge 119889119871 are determined to be valid while the othersamples are considered to be noise Secondly the oceanclutter can be separated by utilizing the relationship betweenthe radar transmitting frequency and the Braggs frequency[18] Thirdly by using the polarization characteristic of theionosphere clutter a polarization angle gate 120574119871 is furtherdefinedThose valid samples that satisfy 120574(119895 119903) le 120574119871 are deter-mined as ionosphere clutterwhile the others are considered asechoes returning along the ocean andor the mixed signal Inthis way the target ocean clutter and ionosphere clutter arepreliminarily separated from each other in the range-Dopplermap

The ionosphere clutter is checked cell by cell For therange cells that ionosphere clutter exists in polarizationcancellation scheme will be applied In order to decide whichpolarization filtering algorithm will be taken define functionFn of which the logic is set to 1 0 If Fn = 1 RDDPSalgorithm is chosen if Fn = 0 RTDPS algorithm will beapplied

The criterion of algorithm selection is based on the rela-tionship of the power between the target and the ionosphereclutter At the corresponding range cell if themaximumvalueof the ionosphere clutter power is smaller than the averagepower of the target the clutter is considered to be weak andFn = 1 On the contrary the clutter is considered to bestrong and Fn = 0 Suppose the set of power values of allthe ionosphere clutters and targets at the corresponding rangecell are defined as119863119868 and119863119878 respectively Fn can be specifiedas

Fn = 1 max (119863119868) lt mean (119863119878)0 max (119863119868) ge mean (119863119878)

(26)

However in certain range cells the target may be nonex-istent the value of Fn in (26) will be uncertain Therefore

11

Ω

Rang

e cel

ls

Doppler cells

Lj

J

R

Figure 2 Diagrammatic illustration of RDDPS

considering the Bragg scattering lines have the similar polar-ization characteristic with the target (26) can be modified as

Fn = 1 max (119863119868) lt max (119863Bragg119871 119863Bragg119877)

0 max (119863119868) ge max (119863Bragg119871 119863Bragg119877) (27)

where 119863Bragg119871 and 119863Bragg119877 are the power value of left andright Braggs at the current range cell respectively

34 Range-Doppler Domain Polarization Suppression Toillustrate the potential advantages of range-Doppler domainsuppression three main aspects are given as follows

(1) Due to the time-frequency invariance of the signalrsquospolarization characteristic [12 19] the estimation ofthe signalrsquos polarization parameters can be performedin range-Doppler domain

(2) In range-Doppler domain the power of each signalcan be concentrated on limited range and Dopplercells respectively which significantly increases theSNR and interference to noise ratio (INR) In thisway the polarization estimation accuracy of both thetarget and the clutter will be improved effectively Asmentioned in Section 2 the improvement of estima-tion accuracy is beneficial for the clutter suppressionand the restoration of the targets as well

(3) In range-Doppler domain the multiple clutters andtargets can be isolated in different cells providing apossibility of individual polarization estimation andsuppression for each clutter and the polarizationdegree of the signals is improved

Based on the analysis above polarization filtering inrange-Doppler domain is considered to be more suitableto process the ionosphere clutter with weak power Theimproved SIR and INR will significantly enhance the estima-tion accuracy and the performance of the filter

The illustration of RDDPS is drawn in Figure 2 Suppos-ing there are some ionosphere clutters existing at the rangecell 119895 a range-Doppler window (119871timesΩ) is first set in the range-Dopplermap (119869times119877) as shown in Figure 2 In the center of thewindow is the clutter area to be processed The polarizationstate of clutters at the range cell 119895 will be estimated in theadjacent cells as the characteristic of the ionosphere clutterin the neighbor range-Doppler is similar [3]


In the range-Doppler window the polarization estima-tion is performed cell by cell in range for 119871 times In eachrange cell the samples that have the maximum power valueare used for polarization estimation To avoid the influenceof target-like signal the range-Doppler domain data in thewindow are excluded with the target and groundoceanclutter In this way a sum of 119871 polarization parametersis obtained and the corresponding 119871 OPPF operators aregenerated Ignoring the noise and supposing there are 119876clutters at range cell 119895 the composite input signal E(119895 120596) canbe expressed as

E (119895 120596) = E119878 (119895 120596) + E119868 (119895 120596)

= E119878 (119895 120596) +119876

sum

119902=1

E119868119902 (119895 120596)

= a119878119878 (119895 120596) +119876

sum

119902=1

a119868119902119868119902 (119895 120596)

(28)

where 120596 is the Doppler frequency E119878(119895 120596) and E119868(119895 120596) arethe target and the ionosphere clutters at range cell 119895 andE119868119902(119895 120596) is the 119902th clutter of E119868(119895 120596) where a119878 a119868119902 119878(119895 120596)and 119868119902(119895 120596) are the polarization steering vector and range-Doppler spectrum of the target and the 119902th clutter E119868119902(119895 120596)respectively

For simplicity suppose 119871 = 119876 and the generated 119871OPPF operators have one-to-one correspondence with the 119876clutters Specifically the 119897th OPPF operator H119897 is generatedto suppress the 119902th clutter when 119897 = 119902 According to (3)the corresponding OPPF operator can be given as H119897 =a119878(aH119878 P

perpa119868119897a119878)minus1aH119878 P

perpa119868119897 119897 = 1 2 119871 According to (6) the

output of 119897th OPPF at range cell 119895 can be expressed as

Y119897 (119895 120596) = H119897E (119895 120596)

= H119897(a119878119878 (119895 120596) + a119868119897119868119897 (119895 120596)

+

119897minus1

sum

119902=1

a119868119902119868119902 (119895 120596) +119876

sum

119902=119897+1

a119868119902119868119902 (119895 120596))

= E119878 (119895 120596) +H119897119876

sum

119902=1119902 =119897

E119868119902 (119895 120596)

(29)

where Y119897(119895 120596) is the 119897th range-Doppler spectrum in whichthe 119897th ionosphere clutter E119868119897(119895 120596) is completely suppressed

Equation (29) indicates that the 119897th clutterE119868119897(119895 120596) can beeffectively cancelled byH119897 while the rest of 119876 minus 1 clutters arestill left in Y119897(119895 120596) Obviously when all OPPF operators areapplied to E119868(119895 120596) in turn 119871 filtering results will be obtainedand only the clutter that matches a119868119897 will be suppressed tothe maximum Suppose all the clutters are not overlappingwith each other in the Doppler spectrum In order to obtaina composite result from the above 119871 filtering results logicproduct process [12] which reserves the smallest points in

Doppler spectrum from the 119871 filtering results can be appliedTherefore all the 119876 ionosphere clutters will be suppressedsimultaneously in theDoppler spectrumMoreover as shownin (29) the target E119878(119895 120596) can be completely restored in eachfiltering result In this way the logic product process willnot influence E119878(119895 120596) in the final result And the output ofRDDPS YRDDPS(119895 120596) can be expressed as

YRDDPS (119895 120596) =119877

sum

119903=1

120575 (120596 minus 120596119903)119871

min119897=1(H119897E (119895 120596)) (30)

where 120596119903 is the Doppler frequency of Doppler cell 119903When the actual number of the clutters is less than 119871

(119871 gt 119876) which is the most common situation for RDDPSthe amount of estimated parameters is more than the amountof clutters Clearly for some clutters their polarizationstate will be estimated for more than once in the range-Doppler window And the corresponding filtering resultswill be similar Note that the OPPF which is generated bythe estimated parameters approaching the real values willsuppress the clutter deeper the recovered YRDDPS(119895 120596) infact can be considered as an optimized result of the 119871 filteroutputs

35 Range-Time Domain Polarization Suppression Thescheme of RDDPS takes advantage of the characteristic ofthe ionosphere clutter in range-Doppler domain and henceis suitable for ionosphere clutter cancellation of low powerin HFSWR However the nonstationary characteristic ofionosphere clutter will degrade the performance of RDDPSas a result of the decline of clutterrsquos polarization degree Tosolve this problem another scheme which is referred to asrange-time domain polarization suppression (RTDPS) isproposed

Rather than estimating the polarization state in a CITthe nonstationary characteristic of ionosphere clutter can berelaxed when the clutter is observed under a smaller timescale By dividing the time domain data into many segmentsthe polarization degree in each segment can be improvedThus for a RTDPS data segmentation is performed prior tothe estimation and filtering process The range-Doppler mapis used to find the position (range and Doppler frequency)of the clutter and the polarization state of the clutter isestimated in the corresponding range-Doppler cell of eachsegment whereas the filtering process is performed in therange-time domain To guarantee the estimation accuracy ahigher INR is required to compensate the decreased coherentintegration time in each segment That is why the RTDPS ismore suitable for suppressing the strong ionosphere cluttersFor the case of single clutter in the corresponding range cellRTDPS is applied in themode of single-notchmode whereasa multinotch filtering mode of RTDPS will be taken whenmore clutters exist It is necessary to emphasize that the notchis in the Doppler domain rather than in the polarizationdomain which is completely different from the definition in[12]

351 Single-Notch RTDPS As shown in Figure 3 the single-notch RTDPS contains the following parts setting of notch


in Doppler domain time domain segmentation polarizationestimation and clutter suppressing in each segment and thefinal time domain data reconstruction

Based on the results of the pretreatment step a Dopplernotch is set first to cover the region of several successiveDoppler cells where the ionosphere clutter locates In thisway the polarization steering vector of the ionosphere cluttercan be estimated from the samples in the Doppler notchAfter being processed by RTDPS the ionosphere clutter inthis area will be suppressed heavily forming a ldquonotchrdquo in theDoppler spectrum

After the Doppler notch has been set the time domaindata is divided into 119875 segments In each segment Dopplerprocessing and polarization estimation are carried out togenerate the corresponding OPPF operator As shown inFigure 3 the ionosphere clutters in the Doppler notch will besuppressed by the OPPF within each segment It should benoticed that the polarization estimation is finished inDopplerdomain whereas the filter is used in time domain

Suppose the sum of time domain samples at the currentrange cell 119895 is119873 and the number of segments is 119875 (suppose119873can be exactly divided by 119875) The ionosphere clutter E119868(119895 119899)can be described as

E119868 (119895 119899) =119875

sum

119901=1

E119868119901 (119895 119899) 119873 (119901 minus 1)

119875lt 119899 le

119873119901

119875 (31)

where E119868119901(119895 119899) is the clutter in segment 119901 in range-timedomain

In each segment it is convenient to decompose E119868119901(119895 119899)into the completely polarized componentE119868 CP119901(119895 119899) and thecompletely unpolarized component E119868 UP119901(119895 119899) E119868(119895 119899) canbe rewritten as

E119868 (119895 119899) =119875

sum

119901=1

(E119868 CP119901 (119895 119899) + E119868 UP119901 (119895 119899))

=

119875

sum

119901=1

(a119868119901119868119901 (119895 119899) + E119868 UP119901 (119895 119899))

119873 (119901 minus 1)

119875lt 119899 le

119873119901

119875

(32)

where a119868119901 and 119868119901(119895 119899) are the polarization steering vectorand the corresponding time domain data of the completelypolarized component E119868 CP119901(119895 119899)

Meanwhile the highly polarized target E119878(119895 119899) can bedescribed as

E119878 (119895 119899) =119875

sum

119901=1

E119878119901 (119895 119899) =119875

sum

119901=1

a119878119878119901 (119895 119899)

119873 (119901 minus 1)

119875lt 119899 le

119873119901

119875

(33)

Time domain samples at the current range

Setting notch in Doppler domain

Segmentation of time domain data

Doppler processing Doppler processing Doppler processing

Polarizationestimation



Segment 1 Segment 2 Segment Pmiddot middot middot

Reconstruction of processed time domain data

Clutter suppressionin time domain



Doppler processing

Processed Doppler spectrum at the current range

OPPF operator OPPF operator OPPF operator


Figure 3 Principle of single-notch RTDPS

where a119878 is the polarization steering vector of the target and119878119901(119895 119899) is the corresponding time domain data of E119878119901(119895 119899) insegment 119901 respectively

Then the OPPF operators of each segment can beobtained as H119901 = a119878(aH119878 P

perpa119868119901a119878)

minus1aH119878 Pperpa119868119901 where P

perpa119868119901 = I minus

a119868119901(aH119868119901a119868119901)minus1aH119868119901 and 119901 = 1 2 119875 According to (6) the

filtering process of single-notch RTDPS can be given as

E119878 (119895 119899) =119875

sum

119901=1

H119901 (E119878119901 (119895 119899) + E119868119901 (119895 119899))

=

119875

sum

119901=1

H119901a119878119878119901 (119895 119899) +H119901a119868119901119868119901 (119895 119899)

+H119901E119868 UP119901 (119895 119899)

=

119875

sum

119901=1

a119878119878119901 (119895 119899) +H119901E119868 UP119901 (119895 119899)

= E119878 (119895 119899) +119875

sum

119901=1

H119901E119868 UP119901 (119895 119899)

(34)



Pretreatment

Setting multiple notches in Doppler domain

Single-notchRTDPS

for clutter 1

Single-notchRTDPS

for clutter 2

Single-notchRTDPS

for clutter M

Notch 1 Notch 2 Notch Mmiddot middot middot

Logic product


Processed Dopplerspectrum 1


Processed Dopplerspectrum M

Figure 4 Principle of multinotch RTDPS

After the Doppler processing the final output of single-notch RDTPS can be expressed as

YRTDPS single (119895 120596) = FFT[E119878 (119895 119899) +119875

sum

119901=1

H119901E119868 UP119901 (119895 119899)]

(35)

The second component in (35) is the completely unpo-larized part of the ionosphere clutter which will be kept asstochastic noise Meanwhile the completely polarized partdescribed as the first component in (32) can be completelycancelled when a119894119901 is accurately estimated

By dividing the range-time domain data into segmentsthe estimation and suppression scheme is performed inseparate segments and the polarization degree of the iono-sphere clutter in each segment can be increased As aresult the estimation accuracy of the clutterrsquos polarizationwill be improved and the clutter can be suppressed morecompletely as the completely unpolarized part is unable to besuppressed

352 Multinotch RTDPS Multinotch RTDPS is imple-mented for more clutters at the current range cell as drawnin Figure 4 The quantity and distribution state of the iono-sphere clutters at the current range cell are estimated in thepretreatment step After the locations and sizes of theDopplernotches are decided single-notch RDTPS is implemented foreach clutter And the final Doppler spectrum is generated bythe logic product process

Supposing the sum of ionosphere clutters is 119872 119872filtering results can be obtained by utilizing single-notchRTDPS shown in (35) Supposing all the clutters are not

overlapping with each other in the Doppler spectrum theresult of multinotch RTDPS YRTDPS multi(119895 120596) can be given as

YRTDPS multi (119895 120596)

=

Rsum

119903=1

120575 (120596 minus 120596119903)119872

min119898=1

(YRTDPS single119898 (119895 120596))(36)

where 119872 and 119873 represent the number of clutters andthat of the time domain samples at the current range cell119895 respectively 120596119903 is the frequency of Doppler cell 119903 andYRTDPS single119898(119895 120596) is the output of the single-notch RTDPSfor the119898th clutter

353 Clutter Polarization Estimation within Each SegmentSupposing the width of the Doppler notch is 119870 the param-eters of the samples in this Doppler notch are defined as(120574119868119896119901 120578119868119896119901 119889119868119896119901) 119896 isin [1 119870] where the first and secondparameters are the polarization angle and angle differenceand the third parameter is the power value of the sample Tobe clear the subscript of 119868 denotes the ionosphere clutter 119896 isthe serial number of the Doppler notch and 119901 represents theserial number of the current segment respectively

For each segment the polarization steering vector of theionosphere clutter within theDoppler notch can be estimatedby

a119868119901 (120574119868ℎ119901 120578119868ℎ119901) = [[

cos 120574119868ℎ119901sin 120574119868ℎ119901 exp (119895120578119868ℎ119901)

]

]

(37)

where119889119868ℎ119901 = max [119889119868119896119901] 119896 ℎ isin [1 119870] (38)

The estimated values are determined by the sample thathas the maximum power within the Doppler notch


170 172 174 176 178 180 182 184 186 188 19010

15

20

25

30

35

40

Doppler cells in the notch

Pola

rizat

ion

angl

e

p = 1p = 4p = 7

p = 17p = 35

Figure 5 Selection of polarization parameters in Doppler notch

Derived from the experimental HFSWR data Figure 5gives polarization angles in segments 1 4 7 17 and 35when total 40 segments are used The horizontal axisis the Doppler cells whereas the vertical axis is thepolarization angle By using the definition in (38) thesamples of the maximum power in the 5 segments areselected and marked with ellipses as shown in Figure 5According to (37) the polarization steering vectors ofeach of the corresponding segments can be estimated asa1198681(1205741198681761 1205781198681761) a1198684(1205741198681744 1205781198681744) a1198687(1205741198681797 1205781198681797)a11986817(12057411986817917 12057811986817917) and a11986835(12057411986817535 12057811986817535) respective-ly

354 Set of Segment Numbers In Figure 5 an obviousfluctuating which is caused by the nonstationary polarizationcharacteristic of the ionosphere clutter can be found whereasa plain curve is expected to suppress the clutter with differentDoppler frequency together within the notch

To improve the polarization stationarity or the polariza-tion degree of the clutter in each segment more segmentsnumber should be used As given in Figure 6 the variance ofpolarization angle distribution of the clutter decreases whenthe segment number increases However more segmentsindicate shorter time in coherent integration and result inmore estimation error which degrades the performance ofthe filter

Therefore a satisfied performance of clutter cancellationcan be only obtained by properly selecting the number of timedomain segment There is a trade-off between the improve-ment of polarization degree and reduction of estimationerror which should be balanced in practical application

4 Experimental Performance Evaluation

To evaluate the performance of the proposed method exper-imental data of a dual-polarized HFSWR in the east coastalregion of China [20] are utilized The HFSWR is installedby Harbin Institute of Technology and is equipped with

20 40 60 80 100 1200

20

40

60

80

100

120

140

Section number

Pola

rizat

ion

angl

e dist

ribut

ion

varia

nce

Figure 6 Polarization stationarity under different segment num-bers

50 100 150 200 250minus80

minus75

minus70

minus65

minus60

minus55

minus50

minus45

minus40

minus35

minus30

Doppler cells

Pow

er (d

B)

OriginalP = 25

P = 40P = 60

Figure 7 Clutter cancellation performance by different segmentnumbers

eight-element vertically polarized receiving antenna arrayand two mutual-orthogonal horizontal polarized antennas tocarry out various experiments of interference cancellation

41 Segmentation Setting of RTDPS Set a group of successivenotches that cover the ionosphere clutters region locating inDoppler cells 132ndash195 at the range cell 157 Figure 7 gives theoriginal Doppler spectrum and the outputs of the RTDPSby using 25 40 and 60 segments respectively The averagepower of the four curves in the region is minus48 dB minus61 dBminus64 dB and minus66 dB respectively It can be found that theclutter can be suppressed effectively and the suppressedcapability depends on the segment number used The SIRimprovement is about 13 dB 16 dB and 18 dB when thesegment number is 25 40 and 60 respectively

In each segment the target signal with an ideal polariza-tion will be recovered without any distortion However thepolarization of some targetsmay be differentwith an ideal oneand a distortion of amplitude and phase will be introduced


in these segments As a result the targets (or Braggs) are alsosuppressed when the segment number increases (see Dopplercell 200 in Figure 7)

Therefore while the segmentation of RTDPS improvesthe performance of clutter cancellation the coherent inte-gration of the targets with polarization mismatching will beinfluenced Then the segment number should be balancedbetween the clutter suppressing and target restoration In oursimulation the segmentation number is set as

119875opt = 40 (39)

42 Ionosphere Clutter Cancellation Figure 8 gives the resultof two typical types of ionosphere clutter suppression atthe range cell 69 by the RDDPS and RTDPS respectivelyIn Figure 8 the blue dashed line is the original Dopplerspectrum whereas the black solid line and the red dotted lineare the results of RDDPS and RTDPS respectively In orderto evaluate the effectiveness of the clutter cancellation and thetarget preservation a synthetic target is also added to the rawdata which locates in the range cell 69 Doppler cell 32 withthe power of minus22 dB

In Figure 8 the peak at theDoppler cell 64with the powerof minus36 dB (64 minus36 dB) is the left Bragg peak and the one atthe Doppler cell 198 with the power of minus30 dB (198 minus30 dB) isthe right Bragg peak of the ocean clutter whereas the peaks ataround (80 minus41 dB) (83 minus33 dB) (118 minus45 dB) (172 minus31 dB)and (177 minus25 dB) are the signals of the targets At the currentrange cell the ionosphere clutter is weak andmasks almost allthe Doppler cells In Figure 8 the power of the backgroundnoise of RDDPS and RTDPS degrades to about minus73 dB andminus66 dB respectively and the SIR improvement is about 14 dBfor RDDPS and 7 dB for RTDPS No matter what methodsare used the targets and Braggs can be well restored and thepeaks are clearer after process

Figure 9 gives the results of RDDPS and RTDPS at therange cell 158 respectively A synthetic target is also addedto the raw data which locates in the Doppler cell 32 withthe power of minus42 dB Different from the range cell 69 theionosphere clutter occupying Doppler cells 110ndash190 revealshigher power value (minus44 dB in average) of which the maxi-mumpower is as high asminus35 dBwhich is 9 dBhigher than thetarget signal (94 minus44 dB) In Figure 9 the targets at Dopplercells 94 and 32 are completely restored independent of themethod However the background noise of RDDPS andRTDPS in Doppler cells 110ndash190 is about minus59 dB and minus66 dBrespectively indicating a better performance of RTDPS

Figure 10 gives the original range-Doppler map and thefinal result The same as in Figures 8 and 9 two synthetictargets at range cells 69 and 158 are added to the raw dataTo be specified a light blue line is attached and divides theoriginal range-Doppler map into two parts The ionosphereclutter is estimated to be stronger than the targets and Braggsin the upper part so Fn = 0 andRTDPS is applied in the rangecells 156ndash200 whereas Fn = 1 in the lower part of the mapand the RDDPS is utilized in the rest of range cells Processedwith the proposed method the weak ionosphere clutter thatmasks range cells 25ndash155 is suppressed close to the power ofbackground noise and the SIR improvement is about 15 dB

minus90

minus80

minus70

minus60

minus50

minus40

minus30

minus20

minus10

RDDPSRTDPS

Synthetic target

50 100 150 200 250Doppler cells

Original

Pow

er (d

B)

Figure 8 Results of RDDPS and RTDPS at range cell 69

minus90

minus80

minus70

minus60

minus50

minus40

minus30

minus20

RDDPSRTDPS

Synthetic target

50 100 150 200 250Doppler cells

Original

Pow

er (d

B)

Figure 9 Results of RTDPS at range cell 158

in average Meanwhile the powerful ionosphere clutters thatcover range cells from 156 to 180 are also suppressed while theSIR improvement is about 22 dB in average As a result all thetargets are more clear and easier to be detected and trackedin the range-Doppler map

5 Conclusion

In this paper a novel ionosphere clutter cancellation schemeis proposed Two types of ionosphere clutter cancellationmethods RDDPS and RTDPS are designed based on thetheory of OPPF RTDPS is suitable in dealing with powerfulionosphere clutter whereas the RDDPS performs a stablefiltering effect to suppress the clutter of low power Theselection of RDDPS or RTDPS algorithm is determined by


20

40

60

80

100

120

140

160

180

50 100 150 200 250Doppler cells

Rang

e cel

ls

(dB)

minus110

minus100

minus90

minus80

minus70

minus60

minus50

minus40

minus30

minus20

minus10

0

Synthetictargets

(a)

20

40

60

80

100

120

140

160

180

50 100 150 200 250Doppler cells

Rang

e cel

ls

(dB)

minus110

minus100

minus90

minus80

minus70

minus60

minus50

minus40

minus30

minus20

minus10

0

Synthetictargets

(b)

Figure 10 The original and the processed range-Doppler map

the clutter type at the corresponding range cell Combiningthe RDDPS and RTDPS together the ionosphere clutters canbe suppressed deeply Theoretical analysis and experimentalresults demonstrate that the proposed scheme is valid andthe SIR can be increased more than 15 dB It is indicated thatthe proposed method may serve as a suitable method forionosphere clutter cancellation in a practical HFSWR system

Conflict of Interests

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

Acknowledgment

This project is sponsored by the National Natural ScienceFoundation of China (no 61171180)

References

[1] H C Chan ldquoCharacterization of ionospheric clutter in HFsurface wave radarrdquo Defence RampD Canada-Ottawa TechnicalReport DRDC Ottawa TR 2003

[2] W Shen B-Y Wen Z-L Li X-J Huang and J Yang ldquoIono-spheric measurement with HF ground wave radar systemrdquoChinese Journal of Radio Science vol 23 no 1 pp 1ndash5 2008

[3] X Guo H Sun and T S Yeo ldquoInterference cancellationfor high-frequency surface wave radarrdquo IEEE Transactions onGeoscience and Remote Sensing vol 46 no 7 pp 1879ndash18912008

[4] H-T Su and Z Bao ldquoAdaptive HF-communication interferencemitigation in HF-GWRrdquo Chinese Journal of Radio Science vol18 no 3 pp 270ndash274 2003

[5] G A Fabrizio A B Gershman and M D Turley ldquoRobustadaptive beamforming for HF surface wave over-the-horizonradarrdquo IEEE Transactions on Aerospace and Electronic Systemsvol 40 no 2 pp 510ndash525 2004

[6] A J Poelman ldquoVirtual polarisation adaptationmdasha method ofincreasing the detection capability of a radar system throughpolarization-vector processingrdquo IEE Proceedings of Communi-cations Radar and Signal Processing vol 128 no 5 pp 261ndash2701981

[7] M Gherardelli D Giuli and M Fossi ldquoSuboptimum adaptivepolarisation cancellers for dual-polarisation radarsrdquo IEE Pro-ceedings Part F Communications Radar and Signal Processingvol 135 no 1 pp 60ndash72 1988

[8] G Y Zhang and Y T Liu ldquoStudy of the polarization filteringtechnique of HF ground wave radarrdquo Journal of Systems ofEngineering and Electronics vol 22 no 3 pp 55ndash57 2000

[9] R Tian and X Tian ldquoNovel polarization filter design forwideband radarrdquo Journal of Systems Engineering and Electronicsvol 23 no 4 pp 522ndash528 2012

[10] X-P Mao Y-T Liu W-B Deng C-J Yu and Z-L Ma ldquoNullphase-shift instantaneous polarization filterrdquo Acta ElectronicaSinica vol 32 no 9 pp 1495ndash1498 2004

[11] X-P Mao and Y-T Liu ldquoNull phase-shift polarization filteringfor high-frequency radarrdquo IEEE Transactions on Aerospace andElectronic Systems vol 43 no 4 pp 1397ndash1408 2007

[12] X-P Mao Y-T Liu and W-B Deng ldquoFrequency domainnull phase-shift multinotch polarization filterrdquo Acta ElectronicaSinica vol 36 no 3 pp 537ndash542 2008

[13] X-P Mao A-J Liu W-B Deng B Cao and Q-Y Zhang ldquoAnoblique projecting polarization filterrdquo Acta Electronica Sinicavol 38 no 9 pp 2003ndash2008 2010

[14] X-P Mao A-J Liu and H-J Hou ldquoOblique projection polar-isation filtering for interference suppression in high-frequencysurface wave radarrdquo IET Radar Sonar andNavigation vol 6 no2 pp 71ndash80 2012


[15] R T Behrens and L L Scharf ldquoSignal processing applicationsof oblique projection operatorsrdquo IEEE Transactions on SignalProcessing vol 42 no 6 pp 1413ndash1424 1994

[16] K Davies Ionospheric Radio pp 225ndash230 Peter PeregrinusLondon UK 1990

[17] M Xingpeng L Yongtan D Weibo Y Changjun and MZilong ldquoSky wave interference of high-frequency surface waveradarrdquo Electronics Letters vol 40 no 15 pp 968ndash969 2004

[18] S Leinwoll Shortwave Propagation John Lyder Publisher NewYork NY USA 1959

[19] A Roueff J Chanussot and J I Mars ldquoEstimation of polariza-tion parameters using time-frequency representations and itsapplication to waves separationrdquo Signal Processing vol 86 no12 pp 3714ndash3731 2006

[20] Y T Liu R Q Xu andN Zhang ldquoProgress in HFSWR researchat Harbin institute of technologyrdquo in Proceeding of the IEEERadar Conference pp 522ndash528 Adelaide Australia September2003

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is still an open issue as the ionosphere clutter is usuallynonstationary In this paper two types of clutter cancel-lation approaches are given to suppress the nonstationaryionosphere clutter The range-Doppler domain polarizationsuppression (RDDPS) is designed for weak ionosphere clutterand performed in the range-Doppler domain while therange-time domain polarization suppression (RTDPS) isdesigned for strong ionosphere clutter The procedure ofclutter polarization estimation and clutter suppression insegments for the RTDPS is emphasized in our research Andthe segmentation parameter optimization is also discussed indetail to obtain a balance between the clutter cancellation andthe target restoration The specific utilization of RDDPS orRTDPS depends on the type of the clutter at the correspond-ing range cell

The remainder of this paper is organized as follows InSection 2 the design of OPPF is introduced and the impacton the performance of the OPPF by the estimation error isanalyzed The nonstationary ionosphere clutter cancellationscheme is proposed in Section 3 whereas the applications ofRDDPS and RTDPS are discussed in detail in Section 4Thenthe experimental performance evaluation of the proposedscheme is given in Section 4 Finally the conclusions aredrawn in Section 5

2 Oblique Projection Polarization Filter

21 Received Signal Model Suppose the received wavefrontis a completely polarized wave and its polarization angleand polarization angle difference are 120574 and 120578 respectivelyIgnoring the absolute phase the incident signal E(119905) can bedescribed by Jones vector as in [10] as

E (119905) = [ 119878 (119905) cos 120574119878 (119905) sin 120574 exp (119895120578)]

= [cos 120574

sin 120574 exp (119895120578)] 119878 (119905) = a119878 (119905) (1)

where 119878(119905) cos 120574 is the horizontally polarized componentof E(119905) while 119878(119905) sin 120574 exp(119895120578) is the vertically polarizedcomponent of E(119905) Vector a is defined as the polarizationsteering vector of E(119905) and

a = [ cos 120574sin 120574119890119895120578] (2)

22 OPPF and Error Analysis Suppose the polarizationsteering vectors of the target and interference are a119878 and a119868respectively If the two steering vectors satisfy a119878 = a119868 acorresponding polarization oblique projection operator canbe constructed by [13]

H = a119878(aH119878 Pperpa119868a119878)minus1aH119878 Pperpa119868

(3)

where Pperpa119868 = E minus a119868(aH119868 a119868)minus1aH119868 and E represents the unit

matrixThe fundamental property of this polarization oblique

projection operator can be given as

Ha119878 = a119878 Ha119868 = 0 (4)

The scalar form of (4) can be given as

(Adagger119878H) a119878 = 1 (Adagger119878H) a119868 = 0 (5)

where Adagger119878 = (aH119878 a119878)minus1aH119878

Usually the received signal is a linear combination of thetarget E119878(119905) = a119878119878(119905) interference E119868(119905) = a119868119868(119905) and noisen(119905) According to (4) the output of the OPPF can be givenas

E119878 (119905) = H (E119878 (119905) + E119868 (119905) + n (119905))

= Ha119878119878 (119905) +Ha119868119868 (119905) +Hn (119905)

= E119878 (119905) +Hn (119905)

(6)

When scalar form is required the filtering process can berewritten as

119878 (119905) = Adagger119878H (E119878 (119905) + E119868 (119905) + n (119905))

= Adagger119878Ha119878119878 (119905) + Adagger119878Ha119868119868 (119905) + A

dagger119878Hn (119905)

(7)

According to (5) (7) can be simplified as

119878 (119905) = 119878 (119905) + Adagger119878Hn (119905) (8)

Equations (6) and (8) indicate that the interference canbe completely cancelled and the target is restored withoutdistortion when the polarization steering vectors of the targetand interference which are utilized to build the subspaces ofdesired ranges and null spaces are estimated accurately

If the estimation accuracy is uncertain in order toanalyze the performance loss of OPPF that was caused bythe estimation error the mean square error (MSE) of thetarget can be defined as MSE = E119878(119905) minus 119878(119905)2F where119878(119905) is the recovered signal of the target 119878(119905) and E(sdot) and sdot F denote themathematical expectation and the Frobeniusnorm Substituting (7) into MSE the general form of MSE ofthe target 119878(119905) can be given as

MSE = E 10038171003817100381710038171003817Adagger119878Ha119878119878 (119905) + A

dagger119878Ha119868119868 (119905) + A

dagger119878Hn (119905) minus 119878 (119905)10038171003817100381710038171003817

2

F

(9)

where H = a119878(aH119878 Pperpa119868 a119878)minus1aH119878 P

perpa119868 Adagger119878 = (a

H119878 a119878)minus1aH119878 a119878 and

a119868 are the real polarization steering vectors of the targetand the interference and a119878 and a119868 are the estimated valuesrespectively

Supposing the target signal interference and noise areuncorrelated (9) can be simplified as

MSE = |119909|21205902119904 +1003816100381610038161003816119910100381610038161003816100381621205902119894 + |119911|

21205902 (10)

where

119909 = Adagger119878Ha119878 minus 1 (11)

119910 = Adagger119878Ha119868 (12)

119911 = radic1

sin2120595 (13)

120595 = arccos (10038161003816100381610038161003816aH119878 a11986810038161003816100381610038161003816) (14)


And 1205902119878 1205902119868 and 120590





MSE = |119911|21205902 (15)


MSE = |119909|21205902119878 + |119911|21205902 (16)


a119878 = (120572 + 120573) a119878 + ]a119868 (17)

where

120572 =aH119878 a119878

(1003816100381610038161003816aH11987810038161003816100381610038161003816100381610038161003816a1198781003816100381610038161003816)

120573 =(1003816100381610038161003816a11986810038161003816100381610038162aH119878 d minus a

H119878 a119868a

H119868 d)

(1003816100381610038161003816a119878100381610038161003816100381621003816100381610038161003816a11986810038161003816100381610038162minus aH119878a119868aH119868 a119878)

] =(1003816100381610038161003816a11987810038161003816100381610038162aH119868 d minus a

H119868 a119878a

H119878 d)

(1003816100381610038161003816a119878100381610038161003816100381621003816100381610038161003816a11986810038161003816100381610038162minus aH119878a119868aH119868 a119878)

d = a119878 minus 120572a119878

(18)




MSE = 1003816100381610038161003816120572 + 120573 minus 1100381610038161003816100381621205902119878 + |119911|

21205902 (20)




a119868 = (1205721015840+ 1205731015840) a119868 + ]

1015840a119878 (21)

where

1205721015840=

aH119868 a119868(1003816100381610038161003816aH11986810038161003816100381610038161003816100381610038161003816a1198681003816100381610038161003816)

1205731015840=(1003816100381610038161003816a11987810038161003816100381610038162aH119868 d minus a

H119868 a119878a

H119878 d1015840)

(1003816100381610038161003816a119868100381610038161003816100381621003816100381610038161003816a11987810038161003816100381610038162minus aH119868 a119878aH119878 a119868)

]1015840 =(1003816100381610038161003816a11986810038161003816100381610038162aH119878 d minus a

H119878 a119868a

H119868 d1015840)

(1003816100381610038161003816a119868100381610038161003816100381621003816100381610038161003816a11987810038161003816100381610038162minus a119868a119878aH119878 a119868)

d1015840 = a119868 minus 1205721015840a119868

(22)


119910 = Adagger119878H (1205721015840+ 1205731015840) a119868 + A

dagger119878H]1015840a119878 = V1015840 (23)


MSE = 10038161003816100381610038161003816]101584010038161003816100381610038161003816

21205902119868 + |119911|

21205902

= 1205902119878 (

10038161003816100381610038161003816]101584010038161003816100381610038161003816

2

SIR+|119911|2

SNR)

(24)

where SIR = 12059021198781205902119868 and SNR = 1205902119878120590

















Rawdata

Signalestimation



filter selection


RTDPS RDDPSor



Pretreatment

Range cell = 1 end









119889 (119895 119903) = radic(119881 (119895 119903))2+ (119867 (119895 119903))

2

120574 (119895 119903) = arctan (abs (119881 (119895 119903))abs (119867 (119895 119903))

)


(25)






(26)


11

Ω

Rang

e cel

ls

Doppler cells

Lj

J

R














E (119895 120596) = E119878 (119895 120596) + E119868 (119895 120596)

= E119878 (119895 120596) +119876

sum

119902=1

E119868119902 (119895 120596)

= a119878119878 (119895 120596) +119876

sum

119902=1

a119868119902119868119902 (119895 120596)

(28)



perpa119868119897a119878)minus1aH119878 P



Y119897 (119895 120596) = H119897E (119895 120596)

= H119897(a119878119878 (119895 120596) + a119868119897119868119897 (119895 120596)

+

119897minus1

sum

119902=1

a119868119902119868119902 (119895 120596) +119876

sum

119902=119897+1

a119868119902119868119902 (119895 120596))

= E119878 (119895 120596) +H119897119876

sum

119902=1119902 =119897

E119868119902 (119895 120596)

(29)




YRDDPS (119895 120596) =119877

sum

119903=1

120575 (120596 minus 120596119903)119871

min119897=1(H119897E (119895 120596)) (30)











E119868 (119895 119899) =119875

sum

119901=1

E119868119901 (119895 119899) 119873 (119901 minus 1)

119875lt 119899 le

119873119901

119875 (31)



E119868 (119895 119899) =119875

sum

119901=1

(E119868 CP119901 (119895 119899) + E119868 UP119901 (119895 119899))

=

119875

sum

119901=1

(a119868119901119868119901 (119895 119899) + E119868 UP119901 (119895 119899))

119873 (119901 minus 1)

119875lt 119899 le

119873119901

119875

(32)



E119878 (119895 119899) =119875

sum

119901=1

E119878119901 (119895 119899) =119875

sum

119901=1

a119878119878119901 (119895 119899)

119873 (119901 minus 1)

119875lt 119899 le

119873119901

119875

(33)













Doppler processing







perpa119868119901a119878)





E119878 (119895 119899) =119875

sum

119901=1

H119901 (E119878119901 (119895 119899) + E119868119901 (119895 119899))

=

119875

sum

119901=1

H119901a119878119878119901 (119895 119899) +H119901a119868119901119868119901 (119895 119899)

+H119901E119868 UP119901 (119895 119899)

=

119875

sum

119901=1

a119878119878119901 (119895 119899) +H119901E119868 UP119901 (119895 119899)

= E119878 (119895 119899) +119875

sum

119901=1

H119901E119868 UP119901 (119895 119899)

(34)



Pretreatment


Single-notchRTDPS

for clutter 1

Single-notchRTDPS

for clutter 2

Single-notchRTDPS

for clutter M


Logic product








sum

119901=1

H119901E119868 UP119901 (119895 119899)]

(35)






YRTDPS multi (119895 120596)

=

Rsum

119903=1

120575 (120596 minus 120596119903)119872

min119898=1

(YRTDPS single119898 (119895 120596))(36)




a119868119901 (120574119868ℎ119901 120578119868ℎ119901) = [[

cos 120574119868ℎ119901sin 120574119868ℎ119901 exp (119895120578119868ℎ119901)

]

]

(37)

where119889119868ℎ119901 = max [119889119868119896119901] 119896 ℎ isin [1 119870] (38)



170 172 174 176 178 180 182 184 186 188 19010

15

20

25

30

35

40


Pola

rizat

ion

angl

e

p = 1p = 4p = 7

p = 17p = 35








20 40 60 80 100 1200

20

40

60

80

100

120

140

Section number

Pola

rizat

ion

angl

e dist

ribut

ion

varia

nce


50 100 150 200 250minus80

minus75

minus70

minus65

minus60

minus55

minus50

minus45

minus40

minus35

minus30

Doppler cells

Pow

er (d

B)

OriginalP = 25

P = 40P = 60








119875opt = 40 (39)





minus90

minus80

minus70

minus60

minus50

minus40

minus30

minus20

minus10

RDDPSRTDPS

Synthetic target

50 100 150 200 250Doppler cells

Original

Pow

er (d

B)


minus90

minus80

minus70

minus60

minus50

minus40

minus30

minus20

RDDPSRTDPS

Synthetic target

50 100 150 200 250Doppler cells

Original

Pow

er (d

B)



5 Conclusion



20

40

60

80

100

120

140

160

180

50 100 150 200 250Doppler cells

Rang

e cel

ls

(dB)

minus110

minus100

minus90

minus80

minus70

minus60

minus50

minus40

minus30

minus20

minus10

0

Synthetictargets

(a)

20

40

60

80

100

120

140

160

180

50 100 150 200 250Doppler cells

Rang

e cel

ls

(dB)

minus110

minus100

minus90

minus80

minus70

minus60

minus50

minus40

minus30

minus20

minus10

0

Synthetictargets

(b)





Acknowledgment


References
























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










And 1205902119878 1205902119868 and 120590





MSE = |119911|21205902 (15)


MSE = |119909|21205902119878 + |119911|21205902 (16)


a119878 = (120572 + 120573) a119878 + ]a119868 (17)

where

120572 =aH119878 a119878

(1003816100381610038161003816aH11987810038161003816100381610038161003816100381610038161003816a1198781003816100381610038161003816)

120573 =(1003816100381610038161003816a11986810038161003816100381610038162aH119878 d minus a

H119878 a119868a

H119868 d)

(1003816100381610038161003816a119878100381610038161003816100381621003816100381610038161003816a11986810038161003816100381610038162minus aH119878a119868aH119868 a119878)

] =(1003816100381610038161003816a11987810038161003816100381610038162aH119868 d minus a

H119868 a119878a

H119878 d)

(1003816100381610038161003816a119878100381610038161003816100381621003816100381610038161003816a11986810038161003816100381610038162minus aH119878a119868aH119868 a119878)

d = a119878 minus 120572a119878

(18)




MSE = 1003816100381610038161003816120572 + 120573 minus 1100381610038161003816100381621205902119878 + |119911|

21205902 (20)




a119868 = (1205721015840+ 1205731015840) a119868 + ]

1015840a119878 (21)

where

1205721015840=

aH119868 a119868(1003816100381610038161003816aH11986810038161003816100381610038161003816100381610038161003816a1198681003816100381610038161003816)

1205731015840=(1003816100381610038161003816a11987810038161003816100381610038162aH119868 d minus a

H119868 a119878a

H119878 d1015840)

(1003816100381610038161003816a119868100381610038161003816100381621003816100381610038161003816a11987810038161003816100381610038162minus aH119868 a119878aH119878 a119868)

]1015840 =(1003816100381610038161003816a11986810038161003816100381610038162aH119878 d minus a

H119878 a119868a

H119868 d1015840)

(1003816100381610038161003816a119868100381610038161003816100381621003816100381610038161003816a11987810038161003816100381610038162minus a119868a119878aH119878 a119868)

d1015840 = a119868 minus 1205721015840a119868

(22)


119910 = Adagger119878H (1205721015840+ 1205731015840) a119868 + A

dagger119878H]1015840a119878 = V1015840 (23)


MSE = 10038161003816100381610038161003816]101584010038161003816100381610038161003816

21205902119868 + |119911|

21205902

= 1205902119878 (

10038161003816100381610038161003816]101584010038161003816100381610038161003816

2

SIR+|119911|2

SNR)

(24)

where SIR = 12059021198781205902119868 and SNR = 1205902119878120590

















Rawdata

Signalestimation



filter selection


RTDPS RDDPSor



Pretreatment

Range cell = 1 end









119889 (119895 119903) = radic(119881 (119895 119903))2+ (119867 (119895 119903))

2

120574 (119895 119903) = arctan (abs (119881 (119895 119903))abs (119867 (119895 119903))

)


(25)






(26)


11

Ω

Rang

e cel

ls

Doppler cells

Lj

J

R














E (119895 120596) = E119878 (119895 120596) + E119868 (119895 120596)

= E119878 (119895 120596) +119876

sum

119902=1

E119868119902 (119895 120596)

= a119878119878 (119895 120596) +119876

sum

119902=1

a119868119902119868119902 (119895 120596)

(28)



perpa119868119897a119878)minus1aH119878 P



Y119897 (119895 120596) = H119897E (119895 120596)

= H119897(a119878119878 (119895 120596) + a119868119897119868119897 (119895 120596)

+

119897minus1

sum

119902=1

a119868119902119868119902 (119895 120596) +119876

sum

119902=119897+1

a119868119902119868119902 (119895 120596))

= E119878 (119895 120596) +H119897119876

sum

119902=1119902 =119897

E119868119902 (119895 120596)

(29)




YRDDPS (119895 120596) =119877

sum

119903=1

120575 (120596 minus 120596119903)119871

min119897=1(H119897E (119895 120596)) (30)











E119868 (119895 119899) =119875

sum

119901=1

E119868119901 (119895 119899) 119873 (119901 minus 1)

119875lt 119899 le

119873119901

119875 (31)



E119868 (119895 119899) =119875

sum

119901=1

(E119868 CP119901 (119895 119899) + E119868 UP119901 (119895 119899))

=

119875

sum

119901=1

(a119868119901119868119901 (119895 119899) + E119868 UP119901 (119895 119899))

119873 (119901 minus 1)

119875lt 119899 le

119873119901

119875

(32)



E119878 (119895 119899) =119875

sum

119901=1

E119878119901 (119895 119899) =119875

sum

119901=1

a119878119878119901 (119895 119899)

119873 (119901 minus 1)

119875lt 119899 le

119873119901

119875

(33)













Doppler processing







perpa119868119901a119878)





E119878 (119895 119899) =119875

sum

119901=1

H119901 (E119878119901 (119895 119899) + E119868119901 (119895 119899))

=

119875

sum

119901=1

H119901a119878119878119901 (119895 119899) +H119901a119868119901119868119901 (119895 119899)

+H119901E119868 UP119901 (119895 119899)

=

119875

sum

119901=1

a119878119878119901 (119895 119899) +H119901E119868 UP119901 (119895 119899)

= E119878 (119895 119899) +119875

sum

119901=1

H119901E119868 UP119901 (119895 119899)

(34)



Pretreatment


Single-notchRTDPS

for clutter 1

Single-notchRTDPS

for clutter 2

Single-notchRTDPS

for clutter M


Logic product








sum

119901=1

H119901E119868 UP119901 (119895 119899)]

(35)






YRTDPS multi (119895 120596)

=

Rsum

119903=1

120575 (120596 minus 120596119903)119872

min119898=1

(YRTDPS single119898 (119895 120596))(36)




a119868119901 (120574119868ℎ119901 120578119868ℎ119901) = [[

cos 120574119868ℎ119901sin 120574119868ℎ119901 exp (119895120578119868ℎ119901)

]

]

(37)

where119889119868ℎ119901 = max [119889119868119896119901] 119896 ℎ isin [1 119870] (38)



170 172 174 176 178 180 182 184 186 188 19010

15

20

25

30

35

40


Pola

rizat

ion

angl

e

p = 1p = 4p = 7

p = 17p = 35








20 40 60 80 100 1200

20

40

60

80

100

120

140

Section number

Pola

rizat

ion

angl

e dist

ribut

ion

varia

nce


50 100 150 200 250minus80

minus75

minus70

minus65

minus60

minus55

minus50

minus45

minus40

minus35

minus30

Doppler cells

Pow

er (d

B)

OriginalP = 25

P = 40P = 60








119875opt = 40 (39)





minus90

minus80

minus70

minus60

minus50

minus40

minus30

minus20

minus10

RDDPSRTDPS

Synthetic target

50 100 150 200 250Doppler cells

Original

Pow

er (d

B)


minus90

minus80

minus70

minus60

minus50

minus40

minus30

minus20

RDDPSRTDPS

Synthetic target

50 100 150 200 250Doppler cells

Original

Pow

er (d

B)



5 Conclusion



20

40

60

80

100

120

140

160

180

50 100 150 200 250Doppler cells

Rang

e cel

ls

(dB)

minus110

minus100

minus90

minus80

minus70

minus60

minus50

minus40

minus30

minus20

minus10

0

Synthetictargets

(a)

20

40

60

80

100

120

140

160

180

50 100 150 200 250Doppler cells

Rang

e cel

ls

(dB)

minus110

minus100

minus90

minus80

minus70

minus60

minus50

minus40

minus30

minus20

minus10

0

Synthetictargets

(b)





Acknowledgment


References
























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation



















Rawdata

Signalestimation



filter selection


RTDPS RDDPSor



Pretreatment

Range cell = 1 end









119889 (119895 119903) = radic(119881 (119895 119903))2+ (119867 (119895 119903))

2

120574 (119895 119903) = arctan (abs (119881 (119895 119903))abs (119867 (119895 119903))

)


(25)






(26)


11

Ω

Rang

e cel

ls

Doppler cells

Lj

J

R














E (119895 120596) = E119878 (119895 120596) + E119868 (119895 120596)

= E119878 (119895 120596) +119876

sum

119902=1

E119868119902 (119895 120596)

= a119878119878 (119895 120596) +119876

sum

119902=1

a119868119902119868119902 (119895 120596)

(28)



perpa119868119897a119878)minus1aH119878 P



Y119897 (119895 120596) = H119897E (119895 120596)

= H119897(a119878119878 (119895 120596) + a119868119897119868119897 (119895 120596)

+

119897minus1

sum

119902=1

a119868119902119868119902 (119895 120596) +119876

sum

119902=119897+1

a119868119902119868119902 (119895 120596))

= E119878 (119895 120596) +H119897119876

sum

119902=1119902 =119897

E119868119902 (119895 120596)

(29)




YRDDPS (119895 120596) =119877

sum

119903=1

120575 (120596 minus 120596119903)119871

min119897=1(H119897E (119895 120596)) (30)











E119868 (119895 119899) =119875

sum

119901=1

E119868119901 (119895 119899) 119873 (119901 minus 1)

119875lt 119899 le

119873119901

119875 (31)



E119868 (119895 119899) =119875

sum

119901=1

(E119868 CP119901 (119895 119899) + E119868 UP119901 (119895 119899))

=

119875

sum

119901=1

(a119868119901119868119901 (119895 119899) + E119868 UP119901 (119895 119899))

119873 (119901 minus 1)

119875lt 119899 le

119873119901

119875

(32)



E119878 (119895 119899) =119875

sum

119901=1

E119878119901 (119895 119899) =119875

sum

119901=1

a119878119878119901 (119895 119899)

119873 (119901 minus 1)

119875lt 119899 le

119873119901

119875

(33)













Doppler processing







perpa119868119901a119878)





E119878 (119895 119899) =119875

sum

119901=1

H119901 (E119878119901 (119895 119899) + E119868119901 (119895 119899))

=

119875

sum

119901=1

H119901a119878119878119901 (119895 119899) +H119901a119868119901119868119901 (119895 119899)

+H119901E119868 UP119901 (119895 119899)

=

119875

sum

119901=1

a119878119878119901 (119895 119899) +H119901E119868 UP119901 (119895 119899)

= E119878 (119895 119899) +119875

sum

119901=1

H119901E119868 UP119901 (119895 119899)

(34)



Pretreatment


Single-notchRTDPS

for clutter 1

Single-notchRTDPS

for clutter 2

Single-notchRTDPS

for clutter M


Logic product








sum

119901=1

H119901E119868 UP119901 (119895 119899)]

(35)






YRTDPS multi (119895 120596)

=

Rsum

119903=1

120575 (120596 minus 120596119903)119872

min119898=1

(YRTDPS single119898 (119895 120596))(36)




a119868119901 (120574119868ℎ119901 120578119868ℎ119901) = [[

cos 120574119868ℎ119901sin 120574119868ℎ119901 exp (119895120578119868ℎ119901)

]

]

(37)

where119889119868ℎ119901 = max [119889119868119896119901] 119896 ℎ isin [1 119870] (38)



170 172 174 176 178 180 182 184 186 188 19010

15

20

25

30

35

40


Pola

rizat

ion

angl

e

p = 1p = 4p = 7

p = 17p = 35








20 40 60 80 100 1200

20

40

60

80

100

120

140

Section number

Pola

rizat

ion

angl

e dist

ribut

ion

varia

nce


50 100 150 200 250minus80

minus75

minus70

minus65

minus60

minus55

minus50

minus45

minus40

minus35

minus30

Doppler cells

Pow

er (d

B)

OriginalP = 25

P = 40P = 60








119875opt = 40 (39)





minus90

minus80

minus70

minus60

minus50

minus40

minus30

minus20

minus10

RDDPSRTDPS

Synthetic target

50 100 150 200 250Doppler cells

Original

Pow

er (d

B)


minus90

minus80

minus70

minus60

minus50

minus40

minus30

minus20

RDDPSRTDPS

Synthetic target

50 100 150 200 250Doppler cells

Original

Pow

er (d

B)



5 Conclusion



20

40

60

80

100

120

140

160

180

50 100 150 200 250Doppler cells

Rang

e cel

ls

(dB)

minus110

minus100

minus90

minus80

minus70

minus60

minus50

minus40

minus30

minus20

minus10

0

Synthetictargets

(a)

20

40

60

80

100

120

140

160

180

50 100 150 200 250Doppler cells

Rang

e cel

ls

(dB)

minus110

minus100

minus90

minus80

minus70

minus60

minus50

minus40

minus30

minus20

minus10

0

Synthetictargets

(b)





Acknowledgment


References
























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











119889 (119895 119903) = radic(119881 (119895 119903))2+ (119867 (119895 119903))

2

120574 (119895 119903) = arctan (abs (119881 (119895 119903))abs (119867 (119895 119903))

)


(25)






(26)


11

Ω

Rang

e cel

ls

Doppler cells

Lj

J

R














E (119895 120596) = E119878 (119895 120596) + E119868 (119895 120596)

= E119878 (119895 120596) +119876

sum

119902=1

E119868119902 (119895 120596)

= a119878119878 (119895 120596) +119876

sum

119902=1

a119868119902119868119902 (119895 120596)

(28)



perpa119868119897a119878)minus1aH119878 P



Y119897 (119895 120596) = H119897E (119895 120596)

= H119897(a119878119878 (119895 120596) + a119868119897119868119897 (119895 120596)

+

119897minus1

sum

119902=1

a119868119902119868119902 (119895 120596) +119876

sum

119902=119897+1

a119868119902119868119902 (119895 120596))

= E119878 (119895 120596) +H119897119876

sum

119902=1119902 =119897

E119868119902 (119895 120596)

(29)




YRDDPS (119895 120596) =119877

sum

119903=1

120575 (120596 minus 120596119903)119871

min119897=1(H119897E (119895 120596)) (30)











E119868 (119895 119899) =119875

sum

119901=1

E119868119901 (119895 119899) 119873 (119901 minus 1)

119875lt 119899 le

119873119901

119875 (31)



E119868 (119895 119899) =119875

sum

119901=1

(E119868 CP119901 (119895 119899) + E119868 UP119901 (119895 119899))

=

119875

sum

119901=1

(a119868119901119868119901 (119895 119899) + E119868 UP119901 (119895 119899))

119873 (119901 minus 1)

119875lt 119899 le

119873119901

119875

(32)



E119878 (119895 119899) =119875

sum

119901=1

E119878119901 (119895 119899) =119875

sum

119901=1

a119878119878119901 (119895 119899)

119873 (119901 minus 1)

119875lt 119899 le

119873119901

119875

(33)













Doppler processing







perpa119868119901a119878)





E119878 (119895 119899) =119875

sum

119901=1

H119901 (E119878119901 (119895 119899) + E119868119901 (119895 119899))

=

119875

sum

119901=1

H119901a119878119878119901 (119895 119899) +H119901a119868119901119868119901 (119895 119899)

+H119901E119868 UP119901 (119895 119899)

=

119875

sum

119901=1

a119878119878119901 (119895 119899) +H119901E119868 UP119901 (119895 119899)

= E119878 (119895 119899) +119875

sum

119901=1

H119901E119868 UP119901 (119895 119899)

(34)



Pretreatment


Single-notchRTDPS

for clutter 1

Single-notchRTDPS

for clutter 2

Single-notchRTDPS

for clutter M


Logic product








sum

119901=1

H119901E119868 UP119901 (119895 119899)]

(35)






YRTDPS multi (119895 120596)

=

Rsum

119903=1

120575 (120596 minus 120596119903)119872

min119898=1

(YRTDPS single119898 (119895 120596))(36)




a119868119901 (120574119868ℎ119901 120578119868ℎ119901) = [[

cos 120574119868ℎ119901sin 120574119868ℎ119901 exp (119895120578119868ℎ119901)

]

]

(37)

where119889119868ℎ119901 = max [119889119868119896119901] 119896 ℎ isin [1 119870] (38)



170 172 174 176 178 180 182 184 186 188 19010

15

20

25

30

35

40


Pola

rizat

ion

angl

e

p = 1p = 4p = 7

p = 17p = 35








20 40 60 80 100 1200

20

40

60

80

100

120

140

Section number

Pola

rizat

ion

angl

e dist

ribut

ion

varia

nce


50 100 150 200 250minus80

minus75

minus70

minus65

minus60

minus55

minus50

minus45

minus40

minus35

minus30

Doppler cells

Pow

er (d

B)

OriginalP = 25

P = 40P = 60








119875opt = 40 (39)





minus90

minus80

minus70

minus60

minus50

minus40

minus30

minus20

minus10

RDDPSRTDPS

Synthetic target

50 100 150 200 250Doppler cells

Original

Pow

er (d

B)


minus90

minus80

minus70

minus60

minus50

minus40

minus30

minus20

RDDPSRTDPS

Synthetic target

50 100 150 200 250Doppler cells

Original

Pow

er (d

B)



5 Conclusion



20

40

60

80

100

120

140

160

180

50 100 150 200 250Doppler cells

Rang

e cel

ls

(dB)

minus110

minus100

minus90

minus80

minus70

minus60

minus50

minus40

minus30

minus20

minus10

0

Synthetictargets

(a)

20

40

60

80

100

120

140

160

180

50 100 150 200 250Doppler cells

Rang

e cel

ls

(dB)

minus110

minus100

minus90

minus80

minus70

minus60

minus50

minus40

minus30

minus20

minus10

0

Synthetictargets

(b)





Acknowledgment


References
























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











E (119895 120596) = E119878 (119895 120596) + E119868 (119895 120596)

= E119878 (119895 120596) +119876

sum

119902=1

E119868119902 (119895 120596)

= a119878119878 (119895 120596) +119876

sum

119902=1

a119868119902119868119902 (119895 120596)

(28)



perpa119868119897a119878)minus1aH119878 P



Y119897 (119895 120596) = H119897E (119895 120596)

= H119897(a119878119878 (119895 120596) + a119868119897119868119897 (119895 120596)

+

119897minus1

sum

119902=1

a119868119902119868119902 (119895 120596) +119876

sum

119902=119897+1

a119868119902119868119902 (119895 120596))

= E119878 (119895 120596) +H119897119876

sum

119902=1119902 =119897

E119868119902 (119895 120596)

(29)




YRDDPS (119895 120596) =119877

sum

119903=1

120575 (120596 minus 120596119903)119871

min119897=1(H119897E (119895 120596)) (30)











E119868 (119895 119899) =119875

sum

119901=1

E119868119901 (119895 119899) 119873 (119901 minus 1)

119875lt 119899 le

119873119901

119875 (31)



E119868 (119895 119899) =119875

sum

119901=1

(E119868 CP119901 (119895 119899) + E119868 UP119901 (119895 119899))

=

119875

sum

119901=1

(a119868119901119868119901 (119895 119899) + E119868 UP119901 (119895 119899))

119873 (119901 minus 1)

119875lt 119899 le

119873119901

119875

(32)



E119878 (119895 119899) =119875

sum

119901=1

E119878119901 (119895 119899) =119875

sum

119901=1

a119878119878119901 (119895 119899)

119873 (119901 minus 1)

119875lt 119899 le

119873119901

119875

(33)













Doppler processing







perpa119868119901a119878)





E119878 (119895 119899) =119875

sum

119901=1

H119901 (E119878119901 (119895 119899) + E119868119901 (119895 119899))

=

119875

sum

119901=1

H119901a119878119878119901 (119895 119899) +H119901a119868119901119868119901 (119895 119899)

+H119901E119868 UP119901 (119895 119899)

=

119875

sum

119901=1

a119878119878119901 (119895 119899) +H119901E119868 UP119901 (119895 119899)

= E119878 (119895 119899) +119875

sum

119901=1

H119901E119868 UP119901 (119895 119899)

(34)



Pretreatment


Single-notchRTDPS

for clutter 1

Single-notchRTDPS

for clutter 2

Single-notchRTDPS

for clutter M


Logic product








sum

119901=1

H119901E119868 UP119901 (119895 119899)]

(35)






YRTDPS multi (119895 120596)

=

Rsum

119903=1

120575 (120596 minus 120596119903)119872

min119898=1

(YRTDPS single119898 (119895 120596))(36)




a119868119901 (120574119868ℎ119901 120578119868ℎ119901) = [[

cos 120574119868ℎ119901sin 120574119868ℎ119901 exp (119895120578119868ℎ119901)

]

]

(37)

where119889119868ℎ119901 = max [119889119868119896119901] 119896 ℎ isin [1 119870] (38)



170 172 174 176 178 180 182 184 186 188 19010

15

20

25

30

35

40


Pola

rizat

ion

angl

e

p = 1p = 4p = 7

p = 17p = 35








20 40 60 80 100 1200

20

40

60

80

100

120

140

Section number

Pola

rizat

ion

angl

e dist

ribut

ion

varia

nce


50 100 150 200 250minus80

minus75

minus70

minus65

minus60

minus55

minus50

minus45

minus40

minus35

minus30

Doppler cells

Pow

er (d

B)

OriginalP = 25

P = 40P = 60








119875opt = 40 (39)





minus90

minus80

minus70

minus60

minus50

minus40

minus30

minus20

minus10

RDDPSRTDPS

Synthetic target

50 100 150 200 250Doppler cells

Original

Pow

er (d

B)


minus90

minus80

minus70

minus60

minus50

minus40

minus30

minus20

RDDPSRTDPS

Synthetic target

50 100 150 200 250Doppler cells

Original

Pow

er (d

B)



5 Conclusion



20

40

60

80

100

120

140

160

180

50 100 150 200 250Doppler cells

Rang

e cel

ls

(dB)

minus110

minus100

minus90

minus80

minus70

minus60

minus50

minus40

minus30

minus20

minus10

0

Synthetictargets

(a)

20

40

60

80

100

120

140

160

180

50 100 150 200 250Doppler cells

Rang

e cel

ls

(dB)

minus110

minus100

minus90

minus80

minus70

minus60

minus50

minus40

minus30

minus20

minus10

0

Synthetictargets

(b)





Acknowledgment


References
























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation














E119868 (119895 119899) =119875

sum

119901=1

E119868119901 (119895 119899) 119873 (119901 minus 1)

119875lt 119899 le

119873119901

119875 (31)



E119868 (119895 119899) =119875

sum

119901=1

(E119868 CP119901 (119895 119899) + E119868 UP119901 (119895 119899))

=

119875

sum

119901=1

(a119868119901119868119901 (119895 119899) + E119868 UP119901 (119895 119899))

119873 (119901 minus 1)

119875lt 119899 le

119873119901

119875

(32)



E119878 (119895 119899) =119875

sum

119901=1

E119878119901 (119895 119899) =119875

sum

119901=1

a119878119878119901 (119895 119899)

119873 (119901 minus 1)

119875lt 119899 le

119873119901

119875

(33)













Doppler processing







perpa119868119901a119878)





E119878 (119895 119899) =119875

sum

119901=1

H119901 (E119878119901 (119895 119899) + E119868119901 (119895 119899))

=

119875

sum

119901=1

H119901a119878119878119901 (119895 119899) +H119901a119868119901119868119901 (119895 119899)

+H119901E119868 UP119901 (119895 119899)

=

119875

sum

119901=1

a119878119878119901 (119895 119899) +H119901E119868 UP119901 (119895 119899)

= E119878 (119895 119899) +119875

sum

119901=1

H119901E119868 UP119901 (119895 119899)

(34)



Pretreatment


Single-notchRTDPS

for clutter 1

Single-notchRTDPS

for clutter 2

Single-notchRTDPS

for clutter M


Logic product








sum

119901=1

H119901E119868 UP119901 (119895 119899)]

(35)






YRTDPS multi (119895 120596)

=

Rsum

119903=1

120575 (120596 minus 120596119903)119872

min119898=1

(YRTDPS single119898 (119895 120596))(36)




a119868119901 (120574119868ℎ119901 120578119868ℎ119901) = [[

cos 120574119868ℎ119901sin 120574119868ℎ119901 exp (119895120578119868ℎ119901)

]

]

(37)

where119889119868ℎ119901 = max [119889119868119896119901] 119896 ℎ isin [1 119870] (38)



170 172 174 176 178 180 182 184 186 188 19010

15

20

25

30

35

40


Pola

rizat

ion

angl

e

p = 1p = 4p = 7

p = 17p = 35








20 40 60 80 100 1200

20

40

60

80

100

120

140

Section number

Pola

rizat

ion

angl

e dist

ribut

ion

varia

nce


50 100 150 200 250minus80

minus75

minus70

minus65

minus60

minus55

minus50

minus45

minus40

minus35

minus30

Doppler cells

Pow

er (d

B)

OriginalP = 25

P = 40P = 60








119875opt = 40 (39)





minus90

minus80

minus70

minus60

minus50

minus40

minus30

minus20

minus10

RDDPSRTDPS

Synthetic target

50 100 150 200 250Doppler cells

Original

Pow

er (d

B)


minus90

minus80

minus70

minus60

minus50

minus40

minus30

minus20

RDDPSRTDPS

Synthetic target

50 100 150 200 250Doppler cells

Original

Pow

er (d

B)



5 Conclusion



20

40

60

80

100

120

140

160

180

50 100 150 200 250Doppler cells

Rang

e cel

ls

(dB)

minus110

minus100

minus90

minus80

minus70

minus60

minus50

minus40

minus30

minus20

minus10

0

Synthetictargets

(a)

20

40

60

80

100

120

140

160

180

50 100 150 200 250Doppler cells

Rang

e cel

ls

(dB)

minus110

minus100

minus90

minus80

minus70

minus60

minus50

minus40

minus30

minus20

minus10

0

Synthetictargets

(b)





Acknowledgment


References
























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











Pretreatment


Single-notchRTDPS

for clutter 1

Single-notchRTDPS

for clutter 2

Single-notchRTDPS

for clutter M


Logic product








sum

119901=1

H119901E119868 UP119901 (119895 119899)]

(35)






YRTDPS multi (119895 120596)

=

Rsum

119903=1

120575 (120596 minus 120596119903)119872

min119898=1

(YRTDPS single119898 (119895 120596))(36)




a119868119901 (120574119868ℎ119901 120578119868ℎ119901) = [[

cos 120574119868ℎ119901sin 120574119868ℎ119901 exp (119895120578119868ℎ119901)

]

]

(37)

where119889119868ℎ119901 = max [119889119868119896119901] 119896 ℎ isin [1 119870] (38)



170 172 174 176 178 180 182 184 186 188 19010

15

20

25

30

35

40


Pola

rizat

ion

angl

e

p = 1p = 4p = 7

p = 17p = 35








20 40 60 80 100 1200

20

40

60

80

100

120

140

Section number

Pola

rizat

ion

angl

e dist

ribut

ion

varia

nce


50 100 150 200 250minus80

minus75

minus70

minus65

minus60

minus55

minus50

minus45

minus40

minus35

minus30

Doppler cells

Pow

er (d

B)

OriginalP = 25

P = 40P = 60








119875opt = 40 (39)





minus90

minus80

minus70

minus60

minus50

minus40

minus30

minus20

minus10

RDDPSRTDPS

Synthetic target

50 100 150 200 250Doppler cells

Original

Pow

er (d

B)


minus90

minus80

minus70

minus60

minus50

minus40

minus30

minus20

RDDPSRTDPS

Synthetic target

50 100 150 200 250Doppler cells

Original

Pow

er (d

B)



5 Conclusion



20

40

60

80

100

120

140

160

180

50 100 150 200 250Doppler cells

Rang

e cel

ls

(dB)

minus110

minus100

minus90

minus80

minus70

minus60

minus50

minus40

minus30

minus20

minus10

0

Synthetictargets

(a)

20

40

60

80

100

120

140

160

180

50 100 150 200 250Doppler cells

Rang

e cel

ls

(dB)

minus110

minus100

minus90

minus80

minus70

minus60

minus50

minus40

minus30

minus20

minus10

0

Synthetictargets

(b)





Acknowledgment


References
























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










170 172 174 176 178 180 182 184 186 188 19010

15

20

25

30

35

40


Pola

rizat

ion

angl

e

p = 1p = 4p = 7

p = 17p = 35








20 40 60 80 100 1200

20

40

60

80

100

120

140

Section number

Pola

rizat

ion

angl

e dist

ribut

ion

varia

nce


50 100 150 200 250minus80

minus75

minus70

minus65

minus60

minus55

minus50

minus45

minus40

minus35

minus30

Doppler cells

Pow

er (d

B)

OriginalP = 25

P = 40P = 60








119875opt = 40 (39)





minus90

minus80

minus70

minus60

minus50

minus40

minus30

minus20

minus10

RDDPSRTDPS

Synthetic target

50 100 150 200 250Doppler cells

Original

Pow

er (d

B)


minus90

minus80

minus70

minus60

minus50

minus40

minus30

minus20

RDDPSRTDPS

Synthetic target

50 100 150 200 250Doppler cells

Original

Pow

er (d

B)



5 Conclusion



20

40

60

80

100

120

140

160

180

50 100 150 200 250Doppler cells

Rang

e cel

ls

(dB)

minus110

minus100

minus90

minus80

minus70

minus60

minus50

minus40

minus30

minus20

minus10

0

Synthetictargets

(a)

20

40

60

80

100

120

140

160

180

50 100 150 200 250Doppler cells

Rang

e cel

ls

(dB)

minus110

minus100

minus90

minus80

minus70

minus60

minus50

minus40

minus30

minus20

minus10

0

Synthetictargets

(b)





Acknowledgment


References
























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












119875opt = 40 (39)





minus90

minus80

minus70

minus60

minus50

minus40

minus30

minus20

minus10

RDDPSRTDPS

Synthetic target

50 100 150 200 250Doppler cells

Original

Pow

er (d

B)


minus90

minus80

minus70

minus60

minus50

minus40

minus30

minus20

RDDPSRTDPS

Synthetic target

50 100 150 200 250Doppler cells

Original

Pow

er (d

B)



5 Conclusion



20

40

60

80

100

120

140

160

180

50 100 150 200 250Doppler cells

Rang

e cel

ls

(dB)

minus110

minus100

minus90

minus80

minus70

minus60

minus50

minus40

minus30

minus20

minus10

0

Synthetictargets

(a)

20

40

60

80

100

120

140

160

180

50 100 150 200 250Doppler cells

Rang

e cel

ls

(dB)

minus110

minus100

minus90

minus80

minus70

minus60

minus50

minus40

minus30

minus20

minus10

0

Synthetictargets

(b)





Acknowledgment


References
























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










20

40

60

80

100

120

140

160

180

50 100 150 200 250Doppler cells

Rang

e cel

ls

(dB)

minus110

minus100

minus90

minus80

minus70

minus60

minus50

minus40

minus30

minus20

minus10

0

Synthetictargets

(a)

20

40

60

80

100

120

140

160

180

50 100 150 200 250Doppler cells

Rang

e cel

ls

(dB)

minus110

minus100

minus90

minus80

minus70

minus60

minus50

minus40

minus30

minus20

minus10

0

Synthetictargets

(b)





Acknowledgment


References
























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation


















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









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