Research ArticleA Generalized Oblique Projection Filter with Flexible Parameterfor Interference Suppression

Yi-ming Wang12 Xing-peng Mao1 Hong Hong1 Jie Zhang2 and Yu-mei Cui1

1 School of Electronics and Information Engineering Harbin Institute of Technology Harbin Heilongjiang 150001 China2The First Institute of Oceanography SOA Qing Dao Shandong 266061 China

Correspondence should be addressed to Xing-peng Mao mxphiteducn

Received 25 April 2014 Accepted 20 October 2014

Academic Editor Michelangelo Villano

Copyright copy 2015 Yi-ming Wang et al This 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

A generalized oblique projection (GOP) with an adjustable parameter defined as interference suppression cost (ISC) is proposedTherefore an optional optimized signal to interference-plus-noise ratio (SINR) and user controlled actions on the interferencefiltering are presented in this GOP framework Theoretical analysis and numerical simulation demonstrate that when the ISC isderived from minimum variance distortionless response (MVDR) algorithm the SINR performance of GOP filter is better thanboth MVDR and oblique projection (OP) filters Further an application of GOP filter in ionospheric clutter cancellation in a highfrequency surface wave radar (HFSWR) system is given The ISC is designed specifically to introduce an extra coherent loss tothe clutters and a satisfying clutter suppression result is achieved Besides the examples given more designs of GOP filter can beinspired by the flexibility of ISC As a generalized form of OP filter GOP filter expands the connotation of oblique projection basedtechnique and could be used in spatial filtering polarization filtering and other array signal processing applications

1 Introduction

As an effective subspace basedmethod oblique projection [1ndash3] is used to project measurements into a low-rank subspacealong a direction that is oblique to the subspace In factthis kind of method is an extension of the widely usedorthogonal projection and has been applied in radars [4ndash6] communications [7 8] navigations [9] image processing[10] and many other areas [11 12] The subspaces of theoblique projection processed can be either orthogonal ornonorthogonal which relaxed the orthogonal requirementbetween subspaces

The advantage of the oblique projection in retaining thetarget signals and mitigating the interference has been apromising technique and greatly extended its applicationsin array signals processing The oblique projection utilizesthe difference between the desired and unwanted signals toextract the target while suppressing interference As the arraywhich is formed by a group of sensors sited in a prede-termined pattern generates a featured directional steeringvector spatial information has been used in constructing

an oblique projection operator [13ndash16] Except for the spatialinformation polarization information is also explored inoblique projection to distinguish the target and interfer-ence [4 17] Conventional oblique projection based filteringtechniques focus on eliminating the interference completelywhich may imply a maximized signal to interference ratio(SIR)

One of the problems with the emphasis of maximizingSIR output is that the target signal may be distorted [18]The oblique projection can resolve it well whereas the otherproblem is that when the angle separation between subspacesis small the noise will be amplified which leads to a loss insignal to interference-plus-noise ratio (SINR) One way totackle this problem is to expand single processing domainto multiple domains When more domains are cooperatedthe angle separation can be improved A collaborative range-angle-polarization filter [19] which takes advantage of thedifferences between the signal and interferences in the jointdomains is constructed based on the vector sensitive array

However when the target and interference are quite closein multidomain the angle separation of subspaces is still

Hindawi Publishing CorporationInternational Journal of Antennas and PropagationVolume 2015 Article ID 320769 11 pageshttpdxdoiorg1011552015320769

2 International Journal of Antennas and Propagation

small To fundamentally solve the problem a generalizedoblique projection (GOP) filter is proposed based on thefurther research of the traditional oblique projection (OP)operator Theoretical analysis and simulation results demon-strate that the GOP filter has an improved SINR outputcapability Some of the unique properties of the GOP andthe flexibilities of interference suppression cost (ISC) by usingconventional adaptive signal processing technologies [20 21]or being designed according to a specific high frequencyradar application are also explored

The remaining sections of this paper are organized asfollows In Section 2 the linear model especially its explicitform in two scenarios of array spatial and polarizationfiltering is presented It is followed by a brief introductionof the OP filter and short analysis of its SINR performanceIn Section 3 the generalized form of GOP operator isderived Four fundamental properties with proofs are givenIn Section 4 the spatial GOP is derived and the SINRperformance of GOP OP and MVDR is evaluated followedby numerical simulations In Section 5 the GOP filter inpolarization domain is discussed and practical applicationin the ionospheric clutter cancellation problem of a highfrequency radar system is demonstrated Finally the lastsection concludes the present work in this paper

2 Array Received Signal Model andOblique Projection Filter

21 The Linear Model As the signals are characterized asa weighted sum of modes a linear algebraic frameworkis applied to vector-valued signals such as those obtainedfrom a sensor array [1] Assume there are full rank matricesA isin S119896times119898 and B isin H119896times119905 with their columns being linearlyindependent The subspaces spanned by them are hencedisjoint (unnecessarily orthogonal) which are composed of 119896

observations and 119898 or 119905 parameters Also when the additiveGaussian white noise n is considered the received linearsignal model can be described as

x = A120603 + B120599 + n (1)

where 120603 120599 represent mode weights for vectors A and Brespectively

The linear model presented here is based on the conceptof subspaces which are not required to be orthogonalIn practical scenarios spatial subspaces and polarizationsubspaces can be constructed

Scenario 1 Array Signal Model in Spatial Domain The signalsreceived by a uniform linear array (ULA) are a mixture ofdesired target echoes and interferences from various spatialdirections Under far field assumption the received signal ofthe 119873 element array can be described as

x (119905) = a12057911205931

sdot 119904 (119905) +

119872minus1

sum

119898=2

a120579119898120593119898

sdot 119894 (119905) + n (119905) (2)

where the spatial steering vector of 119898th signal is given by

a120579119898120593119898

= [1 119890minus1198952120587119889 sin 120579

119898sin120593119898119891119888

sdot sdot sdot 119890minus1198952120587(119873minus1)119889 sin 120579

119898sin120593119898119891119888

]

119879

(3)

with 120579 120593 denoting respective azimuth and pitch angles and 119889

being the distance between adjacent sensor elementsThe subspaces spanned by column vector a120579

11205931

aredefined as the target subspace with the description of ⟨a120579

11205931

⟩

and ⟨a12057921205932

sdot sdot sdot a120579119898120593119898

⟩ is defined as interference subspacecorrespondingly

Scenario 2 Array Signal Model in Polarization Domain Ina polarization sensor with biorthogonal polarized antennasthe target subspace and the interference subspace are spannedby their polarization vectors marked by Ps and Pi respec-tively The signals received can therefore be described as

x (119905) = Ps119904 (119905) + Pi119894 (119905) + n (119905) (4)

where Ps = [cos 120574119904 sin 120574119904119890119895120578119904]119879 Pi = [cos 120574119894 sin 120574119894119890

119895120578119894]119879 and

120574119904 120574119894 and 120578119904 120578119894 depict the respective amplitude relationshipand the phase difference between orthogonal electric fields ofthe target signal and interference

22 Oblique Projection Filter Consider two full-column-rank complex matrices A isin S119899times119898 and B isin H119899times119896 with 119898 + 119896 le

119899 then the columns ofA and B are both linearly independentand disjoint Let ⟨A⟩ and ⟨B⟩ denote the subspaces spannedby the columns of A and B respectively then the obliqueprojection operator EAB onto A along B is defined as

EAB = A (A119867PperpBA)

minus1

A119867PperpB (5)

where PperpB is

PperpB = I minus B (B119867B)

minus1

B119867 (6)

Then EAB has the following properties

E2AB = EAB

EABA = A

EABB = 0

(7)

Therefore we have the output of OP filter as

xOP (119905) = EABx (119905) = EAB (A119904 (119905) + B119894 (119905) + n (119905))

= A119904 (119905) + EABn (119905)

(8)

The scalar form of the OP filter output is

119904OP (119905) =

A119867

A2EABx (119905) = 119904 (119905) +

A119867

A2EABn (119905) (9)

International Journal of Antennas and Propagation 3

The OP operator recovers the desired signal and elim-inates interference completely Therefore the SINR of theoutput can be expressed as

SINR =

119875119904

119875119894 + 119875119899

=

119864

10038161003816100381610038161003816A119867EABA119904 (119905) A

10038161003816100381610038161003816

2

119864 1003816100381610038161003816A119867EABn (119905) A

1003816100381610038161003816

2

=

1205902

119904A2

1205902119899trace EABE119867AB

=

1205902

119904

1205902119899

A2 sin2120595

(10)

where 1205902

119904 1205902119899stand for the power of target and additive noise

respectively and the principle angle between A and B isdefined as

120595 = arccos(

10038171003817100381710038171003817A119867B1003817

1003817100381710038171003817

A B

) (11)

As observed from (8) a portion of noise is retainedmixedwith the target signal The noise power after filtering is givenby

119875119899 = 119864 1003817100381710038171003817EABn (119905)

1003817100381710038171003817

2 =

1

sin2 (120595)

1205902

119899 (12)

From (9) and (12) we can observe that the noise powerafter filtering is closely related to the principle angle Whensubspaces ⟨A⟩ and ⟨B⟩ get close which implies a smallprinciple angle the noise power will be amplified In thissituation although the interference is totally eliminated theenhanced noise power may result in a significant SINR lossThis is an inevitable problem of the OP filter

3 Generalized Oblique Projection Filter

The OP filter focuses on the suppression of interferenceand lacks of the control of the noise power To obtain aflexible control of the power of the noise and interferencesimultaneously a novel oblique projection is proposed whichis named GOP

31 Generalized Oblique Projection Operator Taking thenoise into consideration and introducing an ISC of 120577 theGOP operator can be derived by solving the following linearconstrained optimum problem as

min w119867w

st w119867A = 1

w119867B = 120577

(13)

where A and B are the vectors that span target subspace andinterference subspace

From the constraint equation in (13) we have

w119867B minus 120577w119867A = w119867 (B minus 120577A) = 0 (14)

which implicates B minus 120577A isin ⟨w⟩perp

Also we have

w119867A = w119867 (P(Bminus120577A)A + Pperp(Bminus120577A)A)

= w119867Pperp(Bminus120577A)A = 1

(15)

where the orthogonal projection operator ofBminus120577A is definedas

Pperp(Bminus120577A) = I minus (B minus 120577A)

sdot [(B minus 120577A)119867

sdot (B minus 120577A)]

minus1

(B minus 120577A)119867

(16)

Therefore the optimum problem in (13) can be trans-formed into the following

min w119867w

st w119867Pperp(Bminus120577A)A = 1

B minus 120577A isin ⟨w⟩perp

(17)

To solve this problem a cost function is constructed byLagrange multiplier method as

119865 (119908) = w119867w + 120582 (w119867Pperp(Bminus120577A)A minus 1) (18)

Taking derivative of (18) with respect to w the optimumweight is obtained as

w = minus

120582

2

Pperp(Bminus120577A)A (19)

Substitute 119908 into the constraint condition w119867Pperp(Bminus120577A)A =

1 we have

minus

120582

2

A119867Pperp(Bminus120577A)

119867Pperp(Bminus120577A)A = 1 (20)

Consider that Pperp(Bminus120577A)

119867= Pperp(Bminus120577A) and P

perp

(Bminus120577A)2

= Pperp(Bminus120577A)

the cost factor is

120582 = minus2 (A119867Pperp(Bminus120577A)A)

minus1

(21)

Substitute 120582 into (19) we have the explicit weight as

w = Pperp(Bminus120577A)A (A119867Pperp

(Bminus120577A)A)

minus1

= ((A119867Pperp(Bminus120577A)A)

minus1

A119867Pperp(Bminus120577A))

119867

= (

A119867

A2EAB120577)

119867

(22)

where the GOP operator is derived from (22) as

EAB120577 = A (A119867Pperp(Bminus120577A)A)

minus1

A119867Pperp(Bminus120577A) (23)

Compare (23) with (5) the expressions of GOP and OPshare the similar expression It will be shown that the GOPoperator presented is related to the OP operator and orthog-onal projection operator However GOP is the extended formof them and some special properties are generated by theGOP

4 International Journal of Antennas and Propagation

32 Properties of the GOP Four fundamental propertiesof the GOP are presented The idempotence of GOP andthe oblique projection abilities are given respectively inProperty 1The connections of OP and orthogonal projectionwith GOP are shown in Property 2 The enlargement of theprinciple angle by GOP compared to OP is discussed inProperty 3 which implies a reduction of the noise poweroutput Lastly in Property 4 the maximized SINR conditionin GOP is presented

Property 1 Consider

E2AB120577 = EAB120577

EAB120577A = A

EAB120577B = 120577A

(24)

Examine (24) the GOP operator has equivalent filteringeffect when the operator is multiplied It recovers the desiredsignal without amplitude and phase distortion whereas partof the interference is projected into the target subspace and isreserved by GOPThe target signal after GOP filtering can beexpressed as

119878GOP (119905) =

A119867

A2EAB120577x (119905)

= 119904 (119905) + 120577119894 (119905) +

A119867

A2EAB120577n (119905)

(25)

Proof Since Pperp(Bminus120577A) is a square matrix and A is a column

vector we have

E2AB120577 = A (A119867Pperp(Bminus120577A)A)

minus1

A119867Pperp(Bminus120577A)

sdot A (A119867Pperp(Bminus120577A)A)

minus1

A119867Pperp(Bminus120577A)

= A (A119867Pperp(Bminus120577A)A)

minus1

(A119867Pperp(Bminus120577A)A)

times (A119867Pperp(Bminus120577A)A)

minus1

A119867Pperp(Bminus120577A)

= A (A119867Pperp(Bminus120577A)A)

minus1

A119867Pperp(Bminus120577A) = EAB120577

EAB120577A = A (A119867Pperp(Bminus120577A)A)

minus1

(A119867Pperp(Bminus120577A)A) = A

(26)

Since B minus 120577A is a column vector from (16) we have

Pperp(Bminus120577A) (B minus 120577A) = 0

EAB120577 (B minus 120577A) = A (A119867Pperp(Bminus120577A)A)

minus1

A119867Pperp(Bminus120577A) (B minus 120577A)

= 0 997904rArr EAB120577B = 120577A

(27)

Property 2 The ISC 120577 can be real or complex and its absolutevalue |120577| isin [0 1] When 120577 = ⟨AB⟩AB GOP becomesan orthogonal operator and

EAB120577 = PA 120577 =⟨AB⟩

A B

(28)

When 120577 = 0 GOP degrades to an OP and shares the sameexpression in (5) and

EAB120577 = EAB 120577 = 0 (29)

Proof Suppose 120577 equals the inner product of A and B

⟨A (B minus 120577A)⟩ = A119867 (B minus 120577A)

= A119867B minus

A119867AA119867BA B

= 0

(30)

Therefore subspace ⟨A⟩ is orthogonal to subspace ⟨B minus

120577A⟩ and substitute (16) into (23) we have

EAB120577 = (EAB120577)119867

= A (A119867A)

minus1

A119867 = PA (31)

where PA represents the orthogonal projection of ASuppose 120577 is set to zero hence

EAB120577 = A (A119867Pperp(Bminus120577A)A)

minus1

A119867Pperp(Bminus120577A)

= A (A119867PperpBA)

minus1

A119867PperpB = EAB

(32)

Correspondingly the target signal recovered by GOP andOP is identical in this case

119878GOP (119905) = 119878OP (119905) 120577 = 0 (33)

Property 3 The principle angle of GOP is adjusted by 120577When 120577 isin (0 cos120595] the principle angle of GOP can beenlarged which is given by

1205951015840

gt 120595 120577 isin (0 cos120595] (34)

where 1205951015840 represents the principle angle of GOP and 120595

represents the principle angle of OP under the sameA and BWith a proper setting of the ISC the principle angle betweensubspaces can be enlarged

International Journal of Antennas and Propagation 5

Proof The square of the cosine of the new principle angle is

cos21205951015840 =(A119867B1015840)

119867

(A119867B1015840)1003817100381710038171003817A1198671003817

100381710038171003817

2 1003817100381710038171003817B1015840100381710038171003817

1003817

2

=

(B minus 120577A)119867AA119867 (B minus 120577A)

A119867A (B minus 120577A)119867

(B minus 120577A)

=

(B119867A119867ABA119867A) minus 120577 (A119867B + B119867A) + 1205772A119867A

B119867B minus 120577 (A119867B + B119867A) + 1205772A119867A

=

(cos120595 minus 120577)2

1205772

minus 2120577 cos120595 + 1

=

1

1 + (1 minus cos2120595) (cos120595 minus 120577)2

(35)

Since (35) is a monotonically declining function of 120577

under the condition of 120577 isin [0 cos120595] it is evident that

1205951015840

= 120595 120577 = 0 (36)

or 1205951015840

gt 120595 120577 isin (0 cos120595] (37)

Equation (37) demonstrates that when 120577 is set in therange of (0 cos120595] the principle angle of GOP is enlargedAccording to the expression of output noise power in (12)the noise power of GOP will be less than that of OP

1198751015840

119899lt 119875119899

(38)

Property 4 Suppose INR is known a priori a maximizedSINR which is the SINR upper bound of GOP can beobtained and the corresponding ICS is given as

120577opt =

cos120595

1 + 119873 sdot INR sin2120595 (39)

such that the maximum SINR is obtained as

SINRmax =

(SIR + 119873 sdot SNR sin2120595) 119873 sdot SNRSIR + 119873 sdot SNR

(40)

where 119873 represents the number of array elements

Proof The SINR output of the GOP filter can be expressed as

SINR =

119875119904

1198751015840

119894+ 1198751015840119899

=

119875119904

1205772119875119894 + 119875119899119873 sin21205951015840

= (

1205772

SIR+

1

119873 sin21205951015840SNR)

minus1

= (

1205772

SIR+

1 minus 2120577 cos120595 + 1205772

119873 sin2120595SNR)

minus1

(41)

To have the maximum value of SINR the first orderderivative of (41) with respect to 120577 is taken therefore theoptimum 120577opt that will give the maximum SINR in (40) isobtained as in (39)

4 GOP in Spatial Filtering

By using the spatial difference between the target and inter-ference spatial filtering is an effective method to reduce thepower of unwanted signals including output noise In theconstruction of spatial GOP filter the design of ISC param-eter is flexible It can be generated by using the conventionaladaptive spatial filtering methods such as minimum variancedistortionless response (MVDR) algorithm [20]

The constrained criterion of MVDR is described as

minw w119879Rw

st w119867A = 1

(42)

where A is the spatial vector for the target signal and R =

119864x(119905)x119867(119905) represents the covariance matrix of the receivedsignal

The weight of MVDR can be obtained as

wMVDR = Rminus1A (A119867Rminus1A)

minus1

(43)

Therefore the ISC obtained from wMVDR is expressed as

120577MVDR = w119867MVDRB = (Rminus1A (A119867Rminus1A)

minus1

)

119867

B (44)

It should be noted that the restoration of the targetis not related to 120577 which is the fundamental property ofGOP as given in (25) The interference suppression effect isdetermined by 120577 only As a result except for MVDR moreadaptive beamforming methods can be utilized However asthe information required by MVDR is usually easy to obtainit is more representative to derive 120577 from wMVDR In thefollowing part the SINR performance of theMVDR OP andGOP with 120577 given in (44) is analyzed and compared

41 SINRs Comparison of GOP and MVDR The SINR per-formance of the GOP and MVDR filter is evaluated TheSINRs for GOP and MVDR filter are given in (45) and (46)respectively as

SINRGOP =

119864 |wA119904 (119899)|2

119864 |wB119894 (119899)|2 + 119864 |wn(119899)|

2

=

119864 |wA|2 1205902

119904

119864 |wB|2 1205902

119894+ |w|2

1205902119899

(45)

where w = A119867EAB120577A2 Consider

SINRMVDR =

119864 1003816100381610038161003816wMVDRA119904 (119899)

1003816100381610038161003816

2

119864 1003816100381610038161003816wMVDRB119894 (119899)

1003816100381610038161003816

2 + 119864

1003816100381610038161003816wMVDRn(119899)

1003816100381610038161003816

2

=

119864 1003816100381610038161003816wMVDRA

1003816100381610038161003816

2 1205902

119904

119864 1003816100381610038161003816wMVDRB

1003816100381610038161003816

2 1205902

119894+

1003816100381610038161003816wMVDR

1003816100381610038161003816

21205902119899

(46)

6 International Journal of Antennas and Propagation

Observing (13) (42) (43) and (44) we get

w119867A = w119867MVDRA

w119867B = w119867MVDRB

(47)

Substitute (47) into (45) and (46) it can be observed thatthe difference of output SINRs is decided by the power ofnoise after filtering

Investigating the objective function in (13) we get wGOPwhich satisfies min(w119867GOPwGOP) hence |wGOP|

2le |wMVDR|

2This leads to

SINRGOP ge SINRMVDR (48)

Both of these filters attempt to reduce the interference andnoise while producing the distortionless response Howeverthe GOP filter has a better treatment to the noise andinterference which results in a higher SINR

42 SINRs Comparison of GOP and OP The SINR perfor-mance of the GOP and OP filter is evaluated The SINR forOP filter is written as

SINROP =

119864 1003816100381610038161003816wOPA119904 (119899)

1003816100381610038161003816

2

119864 1003816100381610038161003816wOPB119894 (119899)

1003816100381610038161003816

2 + 119864

1003816100381610038161003816wOPn(119899)

1003816100381610038161003816

2

=

1205902

119904

1205902119899

1003817100381710038171003817EAB

1003817100381710038171003817

2 A2

(49)

where wOP = A119867EABA2

Let the ratio between SINRs of GOP and OP filter be

119896 =

SINRGOPSINROP

=

1003817100381710038171003817EAB

1003817100381710038171003817

21205902

119899 A2

12057721205902

119894+

10038161003816100381610038161003816A119867EAB120577 A

210038161003816100381610038161003816

2

1205902119899

=

1

1198731205772INR sin2120595 +

1003817100381710038171003817B minus 120577A1003817

100381710038171003817

2119873

=

1

1198851205772

minus 2 cos120595120577 + 1

(50)

where 119885 = 1 + 119873 sin2120595INR A2

= 119873 and 119873 is the numberof the array elements

As the value of 119896 is determined by the principle angleINR the number of array elements and ISC simultaneouslyit is not easy to be analyzed without numerical evaluationsHowever we can make a reasonable assumption under twoextreme cases where spatial difference between the target andinterference approaches 90 degrees or 0 degrees

Case 1 (120595 rarr 90∘) The angular separation between target

and interference is nearly orthogonal which means thespatial difference ismaximized An aggressive action is taken

and the interference is expected to be eliminated completelyRewrite (50) as

1198961 =

1

119873 sin21205951205761 + 21205751 + 1 + 1205772 (51)

where 1205761 = 1205772INR and 1205751 = 120577 cos120595

To evaluate (51) numerically let 120595 = 898∘ and 120577 = 0 we

have sin2120595 asymp 1 1205772 = 0 and 1205751 = 0 Since the INR is boundedby a practical maximum of 60 dB we have 1205761 = 0 1198961 = 1 and

SINRGOP = SINROP (52)

Case 2 (120595 rarr 0∘) When the angular separation between

target and interference is very close the principle angle isnear zero For OP filter its SINR is not satisfying due tothe amplified noise power as given in (12) However theproposed GOP filter can be expected to be more conservativein rejecting the interference and shifting the focus in reducingthe noise power output That means when INR is low whichmeans noise power is comparably high the ISC is approach-ing one However if noise power is comparably much lowerthan interference resulting in a very high INR the ISC isapproaching zero to facilitate interference suppression Werewrite (50) as

1198962 =

1

1198731205762 + 1205752 + 1205772 (53)

where 1205762 = (120577 sin120595)2INR and 1205751 = 2120577 cos120595 + 1

To evaluate (53) numerically let 120595 = 001∘ and 120577 isin

[10minus5

1] we have sin2120595 = 0 hence 1205762 = 0 Therefore wehave 1205752 + 120577

2ge 1 1198962 ge 1 and

SINRGOP ge SINROP (54)

From the theoretical analysis of the two cases the SINRoutputs from both filters have an identical performance whenthe spatial difference between the target and interference islarge However GOP filter has a superior performance thanOP filter when the spatial difference is small

Moreover according to Property 4 of GOP there is anoptimized 120577opt in maximizing SINR output if the INR canbe obtained in advance By substituting (39) (50) can berewritten as

119896 =

1

119885 (120577opt minus cos120595119885)

2

+ 1 minus cos2120595119885

=

1

1 minus cos2120595119885

ge 1

(55)

where 120577opt = cos120595119885Therefore we have

SINRGOP ge SINROP (56)

43 Simulations Assume an ULA of 10 antenna elementswith half wavelength spacing between adjacent elements thecarrier frequency is 1198910 = 5MHz Under the conditions of

International Journal of Antennas and Propagation 7

0 10 20 30 40 50 60 70 80 90

0

10

20

30

SIN

R im

prov

emen

t (dB

)

84 85 86 87 88 89 90

1981985

1991995

202005

minus40

minus30

minus20

minus10

120595 (deg)

OptimumMVDR

OPGOP

Figure 1 SINR improvement versus 120595

20 25 30 35 40 45 50 55 6015

20

25

30

35

40

45

50

55

60

65

INR (dB)

SIN

R im

prov

emen

t (dB

)

MVDR (SIR = minus30dB)OP (SIR = minus30dB)GOP (SIR = minus30dB)MVDR (SIR = minus20dB)OP (SIR = minus20dB)

GOP (SIR = minus20dB)MVDR (SIR = minus10dB)OP (SIR = minus10dB)GOP (SIR = minus10dB)

Figure 2 SINR improvement versus INR for Case 1

SNR = 10 dB and SIR = minus10 dB the SINR improvementversus 120595 for MVDR OP GOP and GOP with optimum ISCis shown in Figure 1

From Figure 1 it can be observed that the principle angleshave great impacts on the SINR performance of the threespatial filters With the principle angle less than 10 degreesa sharper decrease appears in SINR for the OP filter thanboth GOP and MVDR filters However when the principleangle increases to nearly 90 degrees GOP and OP filtersperform slightly better than MVDR filter The GOP spatialfilter demonstrates a superior performance than OP and

20 25 30 35 40 45 50 55 60

0

5

10

15

INR (dB)

SIN

R im

prov

emen

t (dB

)

MVDR (SIR = minus30dB)OP (SIR = minus30dB)GOP (SIR = minus30dB)MVDR (SIR = minus20dB)OP (SIR = minus20dB)

GOP (SIR = minus20dB)MVDR (SIR = minus10dB)OP (SIR = minus10dB)GOP (SIR = minus10dB)

minus35

minus30

minus25

minus20

minus15

minus10

minus5

Figure 3 SINR improvement versus INR for Case 2

MVDR filters in the whole angle range further it coincideswith the maximized SINR derived in (40)

In the following the principle angle is fixed and theperformances of three filters under different INRs are inves-tigated The INRs span from 20 dB to 60 dB while the SIRsare of minus10 dB minus20 dB and minus30 dB respectively The principleangles are set to near 90 degrees and 0 degrees respectivelywhich correspond to the cases in Section 42

In Figures 2 and 3 the principle angles are set to 898degrees and 018 degrees respectively which correspond toCases 1 and 2 It is found that the ISC varies slightly aroundzero when the INRs change for Case 1 and ISC varies inrange of [27 times 10

minus5 1] for Case 2 As shown in Figure 2 the

SINR improvements of the GOP and OP increase linearlywith INRs however the MVDR shows an inferior SINRimprovement In Figure 3 the principle angle is small whichmeans that the spatial difference between the target andinterference reducesThe noise power amplifying effect of OPis significant resulting in a severe SINR performance lossIn contrast the GOP and MVDR filters have better SINRimprovements which exceed 30 dB at highest than OP filterIn general the GOP filter generates a superior performancethan both OP and MVDR filters The numerical simulationshave verified the theoretical analysis of the spatial filterspresented

5 GOP in Polarization Filtering of HF Radar

High frequency surface wave radar (HFSWR) [22] operatesin the short wave band which facilities the over-the-horizondetection over the sea surface However signals in this bandwill also get reflected by the ionosphere leading to a stronginterference to the target detection or sea state remote sens-ing In this section we explored the polarization information

8 International Journal of Antennas and Propagation

in the HFSWR and extended the application of the GOP filterin polarization filtering further a challenging ionosphericclutter mitigation problem in HFSWR is addressed

51 Generalized Oblique Projection Polarization Filter Asthe linear signal model presented in (4) a pair of thepolarization parameters represent the amplitude relationshipand the phase difference between the echoes received by theorthogonal dual-polarized radar sensor

Suppose the polarization parameters of the target andinterference are different then the target polarization sub-space ⟨Ps⟩ and interference polarization subspace ⟨Pi⟩ aredisjoint Note that the polarization subspace is independentof the specific radar signal waveforms The polarizationsubspace is constructed by the difference of the polarizationstate Therefore the target and interference subspaces in (23)can be given as

A = [

cos 120574119904

sin 120574119904119890119895120578119904] B = [

cos 120574119894

sin 120574119894119890119895120578119894] (57)

where 120574 and 120578 are the polarization pair with subscripts 119904 and119894 representing target and interference

There are two sets of the parameters that need to bedecided that is the echoes polarization set and the ISC Thepolarization angle is obtained as

120574 = 119905119892minus1

(

1003816100381610038161003816119909119881 (119905)

1003816100381610038161003816

1003816100381610038161003816119909119867 (119905)

1003816100381610038161003816

) (58)

and the polarization phase difference as

120578 = arg (119909119881 (119905)) minus arg (119909119867 (119905)) (59)

where 119909119881(119905) 119909119867(119905) represent the vertically and horizontallypolarized signal components and arg(sdot sdot sdot ) indicates phase ofthe signal

By the inflexibility of the polarized state in the temporaldomain and the frequency domain [18] these parameters canbe calculated using frequency transformed signal also TheISC is a free variable which can be designed according to thespecific application

However it can be proved that if the ISC is set to zerothis GOP polarization filter becomesOP polarization filter Inconstrained condition that is subspace ⟨Ps⟩ is orthogonal to⟨Pi⟩ the GOP polarization filter degrades into an orthogonalpolarization filter

52 Ionospheric Clutter Cancellation in HFSWR The char-acteristics of the ionosphere reflected echoes received byHFSWR are

(1) nonstationary(2) multiclutters(3) widely spread in range and Doppler bins

In addition to that there are ionospheric clutters return-ing from the sea surface whichmake their polarization statesclose to the target or the spatial difference between the

Time domain signal

Segmentations and FFT

Frequency domainpolarization estimations

Coherentintegration

Logic product

GOP filtering fortime segment 1

GOP filtering for

1st clutterGOP filtering fortime segment 1

GOP filtering for

Filtering output

time segment K time segment K

Jth clutter

middot middot middot

Figure 4 Ionospheric clutter mitigation process flow

clutters and target is not obvious Those characteristics leadto an unsolved clutter mitigation problem so far

As the radar arrays cannot effectively distinguish thetarget and interference spatially in this scenario the arraypolarization diversity and the coherent integration processare explored To handle those characteristics segmentationsof the time domain signals are introduced in an effort toapproach the real clutter parameters andmultipleGOPfilterswith flexible parameters 120577 are constructed The flowchart toillustrate the ionospheric clutter mitigation process is shownin Figure 4

In the dual-polarized HFSWR system the time domainsignal is range processed After proper signal segmentationsthe polarization states are estimated according to (58) and(59) with frequency transformed signal componentsThe sig-nals returned from the ship target over sea surface will retainvertically polarized state whereas the ionosphere reflectedclutters will be ellipse polarized with strong horizontallypolarized components The target and clutter polarizationsubspaces (A and B for GOP) are therefore obtained by thepolarization threshold A total number of 119870 segments of thetime divided data after filtering are connected and coherentintegration is performed However by the special designof GOP polarization filter an extra integration loss to theionospheric clutter will be brought in

By Property 1 of GOP the target polarization subspacesare retained while the ionospheric clutters are controlledby the free variable 120577 which is designed to introducerandom phase shift Therefore after GOP processing asignificant coherent integration loss will be introduced tothe ionospheric clutters when the time divided segmentsare reconnected and fast Fourier transformed However thetargetrsquos amplitude and phase are unchanged and its coherentintegration performance is not affected

The free variable of 120577(119899) is designed as

120577 (119899) = rnd (1205751 1205752 119899) 119890119895rnd(120573

11205732119899)

119899 isin [1 119870] (60)

where rnd(1205751 1205752 119899) represents random arrays from the uni-form distribution with amplitude range [1205751 1205752] and random

International Journal of Antennas and Propagation 9

20 40 60 80 100 1200

5

10

15

20

25

Segment numbers

Coh

eren

t int

egra

tion

loss

(dB)

120590120573 = 21205875

120590120573 = 1205872

120590120573 = 120587

120590120573 = 2120587

Figure 5 Coherent loss versus segment numbers under differentphase ranges

phase term 119890119895rnd(120573

11205732119899) with phase range [1205731 1205732] and 119899

denotes the sequence number of 120577 generatedIn deciding the parameters of 120577 the number of segmen-

tation and the phase ranges are of importance In Figure 5the segmentation number is chosen to be 64 and at that pointphase range of [0 2120587] is picked by simulation results of idealexponential signals The reasons are that more segmentationnumbers can only introduce at most 3 dB loss further whilemore segments indicate shorter time in coherent integrationand result in more estimation errors which may degradethe performance of the filter Therefore the parameters areobtained in consideration of the extra coherent loss andpotential estimation error

After logic product process [18] which reserves thesmallest points in Doppler spectrum from all the filteringresults the final output in each range bin is obtained as

Y (120596) =

119873

sum

119899=1

120575 (120596 minus 120596119899)

times

119869

min119895=1

(FFT[

119870

sum

119896=1

EAB120585119896119895x119896 (119899seg119896)])

(61)

where 119873 represents the length of FFT 120596119899 represents thefrequency at point 119899 119869 represents the total number of theclutters 119870 is the total number of segmentations EAB120585119896119895is the 119896th GOP in time domain for the suppression of 119895thclutter and x119896(119899seg119896) is the 119896th time segmented datawith 119899seg119896denoting the sampled points in the corresponding segment

In the HFSWR field experiment the vertically polarizedsignal was transmitted with a carrier frequency of 7Mhzby a half-wave dipole antenna The data was collected by adistant polarized high frequency linear array with 15-meterseparation between the vertically and horizontally polarizedelements The coherent integration time was 4 minutes

50 100 150 200 250

Doppler bins

Pow

er (d

B)

After filteringBefore filtering

Target

minus90

minus80

minus70

minus60

minus50

minus40

minus30

minus20

minus10

Figure 6 Doppler spectrum at range bin 79

Figure 6 gives theDoppler spectrumafter integration at rangebin 79 which is obtained from experimentally derived datawith red dashed line denoting spectrum before filtering andblue solid line denoting spectrum after process It can beobserved that there are several peaks well above minus30 dBbefore filtering which create an unfavorable ship detectionenvironment However the ship target at Doppler bin 183can be distinguished easily since the ionospheric clutters aresuppressed by about 10 dB in average whereas the targetsignal is undistorted

Besides ship detection the other focus can be drawn onthe sea state remote sensing A successful sea state inversionalgorithm depends on the correct and accurate extractionsof Bragg In Figure 7 the double first order Bragg peaks atDoppler bins (in between the vertically green dashed lines)are contaminated by the ionospheric clutters After GOPfiltering the contaminations of ionosphere are minimizedmoreover the SINR of the negative Bragg peaks was raisedaround 12 dB which facilitates its extraction algorithms

The Doppler spectrums from all the range bins arethen collected together forming a range-Doppler spectrumFigure 8(a) presents the original range-Doppler spectrumwhich is contaminated by the ionospheric clutters fromrange bins 73 to 96 whereas Figure 8(b) describes thespectrum after being processed by GOP filters Obviouslythe ionospheric clutters which widely spread in range andDoppler bins are suppressed effectively The average SINRimprovement is above 10 dB in this experiment

6 Conclusions

In this paper a novel GOP with adjustable ISC parameter hasbeen proposed It is proved to be an extension of OP andfour fundamental properties are presented with proofs Theconstruction of GOP filters is demonstrated with examplesof spatial and polarization filtering respectively In thefirst example with ISC derived from adaptive beamforming

10 International Journal of Antennas and Propagation

After filteringBefore filtering

50 100 150 200 250Doppler bins

Pow

er (d

B)

Positive BraggNegative Bragg

minus90

minus80

minus70

minus60

minus50

minus40

minus30

minus20

minus10

Figure 7 Doppler spectrum at range bin 89

20

40

60

80

100

120

140

160

50 100 150 200 250Doppler bins

Rang

e bin

s

(a) Original range-Doppler spectrum

20

40

60

80

100

120

140

160

50 100 150 200 250Doppler bins

Rang

e bin

s

(b) Range-Doppler spectrum after GOP filter

Figure 8 Range-Doppler spectrum of HFSWR

algorithm the SINR performance of GOP filter is shownto be better than MVDR and OP filters both theoreticallyand numerically A GOP polarization filter is constructedwith manually designed ISC in the second example An extracoherent loss is introduced to the ionospheric clutters bypurpose and a satisfying clutter suppression result inHFSWRis achieved Besides the examples givenmore designs of GOPfilter can be inspired by the flexibilities of ISC It can beconcluded that GOP filter is a promising filtering techniquefor interference suppression and capable of being used inspatial filtering polarization filtering and other array signalprocessing applications

Conflict of Interests

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

Acknowledgments

This project is sponsored by the National Marine TechnologyProgram for Public Welfare (no 200905029) National Nat-ural Science Foundation of China (no 61171180) and TeamResearch Foundation for Fundamental Research Program inFIO China (no GY0213T03)

References

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

[2] L Rebollo-Neira ldquoOblique matching pursuitrdquo IEEE SignalProcessing Letters vol 14 no 10 pp 703ndash706 2007

[3] GW Stewart ldquoOn the numerical analysis of oblique projectorsrdquoSIAM Journal on Matrix Analysis and Applications vol 32 no1 pp 309ndash348 2011

International Journal of Antennas and Propagation 11

[4] X-P Mao A-J Liu H-J Hou H Hong R Guo and W-BDeng ldquoOblique projection polarisation filtering for interferencesuppression in high-frequency surface wave radarrdquo IET RadarSonar and Navigation vol 6 no 2 pp 71ndash80 2012

[5] 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 (Chinese)

[6] Q-Y Zhang B Cao L Jin and N-T Zhang ldquoOblique pro-jection polarization filtering-based interference suppressionsfor radar sensor networksrdquo EURASIP Journal on WirelessCommunications and Networking vol 2010 Article ID 6051032010

[7] X Yu and L Tong ldquoJoint channel and symbol estimation byoblique projectionsrdquo IEEE Transactions on Signal Processingvol 49 no 12 pp 3074ndash3083 2001

[8] Q Zhang B Cao JWang and N Zhang ldquoPolarization filteringtechnique based on oblique projectionsrdquo Science China F vol53 no 5 pp 1056ndash1066 2010

[9] Y Cui K Liu and J Wang ldquoDirection-of-arrival estimationfor coherent GPS signals based on oblique projectionrdquo SignalProcessing vol 92 no 1 pp 294ndash299 2012

[10] Y Hu X Zhang F Zhu and H Lv ldquoImage recognition usingiterative oblique projectionrdquo Electronics Letters vol 41 no 20pp 1109ndash1110 2005

[11] G Hellbourg R Weber C Capdessus and A-J BoonstraldquoOblique projection beamforming for RFI mitigation in radioastronomyrdquo in Proceedings of the IEEE Statistical Signal Process-ing Workshop (SSP rsquo12) pp 93ndash96 IEEE August 2012

[12] P De ldquoNew methods for sensing bandlimited signals in cogni-tive radiordquo in Proceedings of the IEEE 65th Vehicular TechnologyConference (VTC 07-Spring) pp 1916ndash1920 Dublin IrelandApril 2007

[13] R Boyer ldquoOblique projection for source estimation in a com-petitive environment algorithm and statistical analysisrdquo SignalProcessing vol 89 no 12 pp 2547ndash2554 2009

[14] M L McCloud and L L Scharf ldquoA new subspace identificationalgorithm for high-resolution DOA estimationrdquo IEEE Transac-tions on Antennas and Propagation vol 50 no 10 pp 1382ndash1390 2002

[15] R Boyer andG Bouleux ldquoOblique projections for direction-of-arrival estimation with prior knowledgerdquo IEEE Transactions onSignal Processing vol 56 no 4 pp 1374ndash1387 2008

[16] H Hong X-P Mao C Hu R Guo W-B Deng and PJiang ldquoNarrow-band null phase-shift spatial filter based onoblique projectionrdquo in Proceedings of the IEEERadar Conference(RADAR rsquo13) pp 1ndash5 Ottawa Canada May 2013

[17] Z H Xu Y P Ni and L Jin ldquoResolution theory of polarizationsensitive array signalsrdquo in Proceedings of the CIE InternationalConference on Radar (ICR rsquo06) pp 1ndash4 IEEE Shanghai ChinaOctober 2006

[18] 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

[19] Y-M Wang X-P Mao J Zhang and H Hong ldquoA multi-domain collaborative filter based on polarization sensitivefrequency diverse arrayrdquo in Proceedings of the IEEE RadarConference pp 0507ndash0511 Cincinnati Ohio USA May 2014

[20] M Souden J Benesty and S Affes ldquoA study of the LCMVandMVDRnoise reduction filtersrdquo IEEE Transactions on SignalProcessing vol 58 no 9 pp 4925ndash4935 2010

[21] Y M Cui X P Mao and H Hong ldquoA novel adaptive filter forinterference suppressionrdquo in Proceedings of the IEEE Region 10Conference vol 31194 pp 1ndash5 IEEE 2013

[22] H C Chan ldquoCharacterization of ionospheric clutter in HFsurface wave radarrdquo Tech Rep 2003-114 Defence RampDCanadaOttawa Canada 2003

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RotatingMachinery

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Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

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Shock and Vibration

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Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

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Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

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Volume 2014

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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

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Navigation and Observation

International Journal of

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DistributedSensor Networks

International Journal of

2 International Journal of Antennas and Propagation

small To fundamentally solve the problem a generalizedoblique projection (GOP) filter is proposed based on thefurther research of the traditional oblique projection (OP)operator Theoretical analysis and simulation results demon-strate that the GOP filter has an improved SINR outputcapability Some of the unique properties of the GOP andthe flexibilities of interference suppression cost (ISC) by usingconventional adaptive signal processing technologies [20 21]or being designed according to a specific high frequencyradar application are also explored

The remaining sections of this paper are organized asfollows In Section 2 the linear model especially its explicitform in two scenarios of array spatial and polarizationfiltering is presented It is followed by a brief introductionof the OP filter and short analysis of its SINR performanceIn Section 3 the generalized form of GOP operator isderived Four fundamental properties with proofs are givenIn Section 4 the spatial GOP is derived and the SINRperformance of GOP OP and MVDR is evaluated followedby numerical simulations In Section 5 the GOP filter inpolarization domain is discussed and practical applicationin the ionospheric clutter cancellation problem of a highfrequency radar system is demonstrated Finally the lastsection concludes the present work in this paper

2 Array Received Signal Model andOblique Projection Filter

21 The Linear Model As the signals are characterized asa weighted sum of modes a linear algebraic frameworkis applied to vector-valued signals such as those obtainedfrom a sensor array [1] Assume there are full rank matricesA isin S119896times119898 and B isin H119896times119905 with their columns being linearlyindependent The subspaces spanned by them are hencedisjoint (unnecessarily orthogonal) which are composed of 119896

observations and 119898 or 119905 parameters Also when the additiveGaussian white noise n is considered the received linearsignal model can be described as

x = A120603 + B120599 + n (1)

where 120603 120599 represent mode weights for vectors A and Brespectively

The linear model presented here is based on the conceptof subspaces which are not required to be orthogonalIn practical scenarios spatial subspaces and polarizationsubspaces can be constructed

Scenario 1 Array Signal Model in Spatial Domain The signalsreceived by a uniform linear array (ULA) are a mixture ofdesired target echoes and interferences from various spatialdirections Under far field assumption the received signal ofthe 119873 element array can be described as

x (119905) = a12057911205931

sdot 119904 (119905) +

119872minus1

sum

119898=2

a120579119898120593119898

sdot 119894 (119905) + n (119905) (2)

where the spatial steering vector of 119898th signal is given by

a120579119898120593119898

= [1 119890minus1198952120587119889 sin 120579

119898sin120593119898119891119888

sdot sdot sdot 119890minus1198952120587(119873minus1)119889 sin 120579

119898sin120593119898119891119888

]

119879

(3)

with 120579 120593 denoting respective azimuth and pitch angles and 119889

being the distance between adjacent sensor elementsThe subspaces spanned by column vector a120579

11205931

aredefined as the target subspace with the description of ⟨a120579

11205931

⟩

and ⟨a12057921205932

sdot sdot sdot a120579119898120593119898

⟩ is defined as interference subspacecorrespondingly

Scenario 2 Array Signal Model in Polarization Domain Ina polarization sensor with biorthogonal polarized antennasthe target subspace and the interference subspace are spannedby their polarization vectors marked by Ps and Pi respec-tively The signals received can therefore be described as

x (119905) = Ps119904 (119905) + Pi119894 (119905) + n (119905) (4)

where Ps = [cos 120574119904 sin 120574119904119890119895120578119904]119879 Pi = [cos 120574119894 sin 120574119894119890

119895120578119894]119879 and

120574119904 120574119894 and 120578119904 120578119894 depict the respective amplitude relationshipand the phase difference between orthogonal electric fields ofthe target signal and interference

22 Oblique Projection Filter Consider two full-column-rank complex matrices A isin S119899times119898 and B isin H119899times119896 with 119898 + 119896 le

119899 then the columns ofA and B are both linearly independentand disjoint Let ⟨A⟩ and ⟨B⟩ denote the subspaces spannedby the columns of A and B respectively then the obliqueprojection operator EAB onto A along B is defined as

EAB = A (A119867PperpBA)

minus1

A119867PperpB (5)

where PperpB is

PperpB = I minus B (B119867B)

minus1

B119867 (6)

Then EAB has the following properties

E2AB = EAB

EABA = A

EABB = 0

(7)

Therefore we have the output of OP filter as

xOP (119905) = EABx (119905) = EAB (A119904 (119905) + B119894 (119905) + n (119905))

= A119904 (119905) + EABn (119905)

(8)

The scalar form of the OP filter output is

119904OP (119905) =

A119867

A2EABx (119905) = 119904 (119905) +

A119867

A2EABn (119905) (9)

International Journal of Antennas and Propagation 3

The OP operator recovers the desired signal and elim-inates interference completely Therefore the SINR of theoutput can be expressed as

SINR =

119875119904

119875119894 + 119875119899

=

119864

10038161003816100381610038161003816A119867EABA119904 (119905) A

10038161003816100381610038161003816

2

119864 1003816100381610038161003816A119867EABn (119905) A

1003816100381610038161003816

2

=

1205902

119904A2

1205902119899trace EABE119867AB

=

1205902

119904

1205902119899

A2 sin2120595

(10)

where 1205902

119904 1205902119899stand for the power of target and additive noise

respectively and the principle angle between A and B isdefined as

120595 = arccos(

10038171003817100381710038171003817A119867B1003817

1003817100381710038171003817

A B

) (11)

As observed from (8) a portion of noise is retainedmixedwith the target signal The noise power after filtering is givenby

119875119899 = 119864 1003817100381710038171003817EABn (119905)

1003817100381710038171003817

2 =

1

sin2 (120595)

1205902

119899 (12)

From (9) and (12) we can observe that the noise powerafter filtering is closely related to the principle angle Whensubspaces ⟨A⟩ and ⟨B⟩ get close which implies a smallprinciple angle the noise power will be amplified In thissituation although the interference is totally eliminated theenhanced noise power may result in a significant SINR lossThis is an inevitable problem of the OP filter

3 Generalized Oblique Projection Filter

The OP filter focuses on the suppression of interferenceand lacks of the control of the noise power To obtain aflexible control of the power of the noise and interferencesimultaneously a novel oblique projection is proposed whichis named GOP

31 Generalized Oblique Projection Operator Taking thenoise into consideration and introducing an ISC of 120577 theGOP operator can be derived by solving the following linearconstrained optimum problem as

min w119867w

st w119867A = 1

w119867B = 120577

(13)

where A and B are the vectors that span target subspace andinterference subspace

From the constraint equation in (13) we have

w119867B minus 120577w119867A = w119867 (B minus 120577A) = 0 (14)

which implicates B minus 120577A isin ⟨w⟩perp

Also we have

w119867A = w119867 (P(Bminus120577A)A + Pperp(Bminus120577A)A)

= w119867Pperp(Bminus120577A)A = 1

(15)

where the orthogonal projection operator ofBminus120577A is definedas

Pperp(Bminus120577A) = I minus (B minus 120577A)

sdot [(B minus 120577A)119867

sdot (B minus 120577A)]

minus1

(B minus 120577A)119867

(16)

Therefore the optimum problem in (13) can be trans-formed into the following

min w119867w

st w119867Pperp(Bminus120577A)A = 1

B minus 120577A isin ⟨w⟩perp

(17)

To solve this problem a cost function is constructed byLagrange multiplier method as

119865 (119908) = w119867w + 120582 (w119867Pperp(Bminus120577A)A minus 1) (18)

Taking derivative of (18) with respect to w the optimumweight is obtained as

w = minus

120582

2

Pperp(Bminus120577A)A (19)

Substitute 119908 into the constraint condition w119867Pperp(Bminus120577A)A =

1 we have

minus

120582

2

A119867Pperp(Bminus120577A)

119867Pperp(Bminus120577A)A = 1 (20)

Consider that Pperp(Bminus120577A)

119867= Pperp(Bminus120577A) and P

perp

(Bminus120577A)2

= Pperp(Bminus120577A)

the cost factor is

120582 = minus2 (A119867Pperp(Bminus120577A)A)

minus1

(21)

Substitute 120582 into (19) we have the explicit weight as

w = Pperp(Bminus120577A)A (A119867Pperp

(Bminus120577A)A)

minus1

= ((A119867Pperp(Bminus120577A)A)

minus1

A119867Pperp(Bminus120577A))

119867

= (

A119867

A2EAB120577)

119867

(22)

where the GOP operator is derived from (22) as

EAB120577 = A (A119867Pperp(Bminus120577A)A)

minus1

A119867Pperp(Bminus120577A) (23)

Compare (23) with (5) the expressions of GOP and OPshare the similar expression It will be shown that the GOPoperator presented is related to the OP operator and orthog-onal projection operator However GOP is the extended formof them and some special properties are generated by theGOP

4 International Journal of Antennas and Propagation

32 Properties of the GOP Four fundamental propertiesof the GOP are presented The idempotence of GOP andthe oblique projection abilities are given respectively inProperty 1The connections of OP and orthogonal projectionwith GOP are shown in Property 2 The enlargement of theprinciple angle by GOP compared to OP is discussed inProperty 3 which implies a reduction of the noise poweroutput Lastly in Property 4 the maximized SINR conditionin GOP is presented

Property 1 Consider

E2AB120577 = EAB120577

EAB120577A = A

EAB120577B = 120577A

(24)

Examine (24) the GOP operator has equivalent filteringeffect when the operator is multiplied It recovers the desiredsignal without amplitude and phase distortion whereas partof the interference is projected into the target subspace and isreserved by GOPThe target signal after GOP filtering can beexpressed as

119878GOP (119905) =

A119867

A2EAB120577x (119905)

= 119904 (119905) + 120577119894 (119905) +

A119867

A2EAB120577n (119905)

(25)

Proof Since Pperp(Bminus120577A) is a square matrix and A is a column

vector we have

E2AB120577 = A (A119867Pperp(Bminus120577A)A)

minus1

A119867Pperp(Bminus120577A)

sdot A (A119867Pperp(Bminus120577A)A)

minus1

A119867Pperp(Bminus120577A)

= A (A119867Pperp(Bminus120577A)A)

minus1

(A119867Pperp(Bminus120577A)A)

times (A119867Pperp(Bminus120577A)A)

minus1

A119867Pperp(Bminus120577A)

= A (A119867Pperp(Bminus120577A)A)

minus1

A119867Pperp(Bminus120577A) = EAB120577

EAB120577A = A (A119867Pperp(Bminus120577A)A)

minus1

(A119867Pperp(Bminus120577A)A) = A

(26)

Since B minus 120577A is a column vector from (16) we have

Pperp(Bminus120577A) (B minus 120577A) = 0

EAB120577 (B minus 120577A) = A (A119867Pperp(Bminus120577A)A)

minus1

A119867Pperp(Bminus120577A) (B minus 120577A)

= 0 997904rArr EAB120577B = 120577A

(27)

Property 2 The ISC 120577 can be real or complex and its absolutevalue |120577| isin [0 1] When 120577 = ⟨AB⟩AB GOP becomesan orthogonal operator and

EAB120577 = PA 120577 =⟨AB⟩

A B

(28)

When 120577 = 0 GOP degrades to an OP and shares the sameexpression in (5) and

EAB120577 = EAB 120577 = 0 (29)

Proof Suppose 120577 equals the inner product of A and B

⟨A (B minus 120577A)⟩ = A119867 (B minus 120577A)

= A119867B minus

A119867AA119867BA B

= 0

(30)

Therefore subspace ⟨A⟩ is orthogonal to subspace ⟨B minus

120577A⟩ and substitute (16) into (23) we have

EAB120577 = (EAB120577)119867

= A (A119867A)

minus1

A119867 = PA (31)

where PA represents the orthogonal projection of ASuppose 120577 is set to zero hence

EAB120577 = A (A119867Pperp(Bminus120577A)A)

minus1

A119867Pperp(Bminus120577A)

= A (A119867PperpBA)

minus1

A119867PperpB = EAB

(32)

Correspondingly the target signal recovered by GOP andOP is identical in this case

119878GOP (119905) = 119878OP (119905) 120577 = 0 (33)

Property 3 The principle angle of GOP is adjusted by 120577When 120577 isin (0 cos120595] the principle angle of GOP can beenlarged which is given by

1205951015840

gt 120595 120577 isin (0 cos120595] (34)

where 1205951015840 represents the principle angle of GOP and 120595

represents the principle angle of OP under the sameA and BWith a proper setting of the ISC the principle angle betweensubspaces can be enlarged

International Journal of Antennas and Propagation 5

Proof The square of the cosine of the new principle angle is

cos21205951015840 =(A119867B1015840)

119867

(A119867B1015840)1003817100381710038171003817A1198671003817

100381710038171003817

2 1003817100381710038171003817B1015840100381710038171003817

1003817

2

=

(B minus 120577A)119867AA119867 (B minus 120577A)

A119867A (B minus 120577A)119867

(B minus 120577A)

=

(B119867A119867ABA119867A) minus 120577 (A119867B + B119867A) + 1205772A119867A

B119867B minus 120577 (A119867B + B119867A) + 1205772A119867A

=

(cos120595 minus 120577)2

1205772

minus 2120577 cos120595 + 1

=

1

1 + (1 minus cos2120595) (cos120595 minus 120577)2

(35)

Since (35) is a monotonically declining function of 120577

under the condition of 120577 isin [0 cos120595] it is evident that

1205951015840

= 120595 120577 = 0 (36)

or 1205951015840

gt 120595 120577 isin (0 cos120595] (37)

Equation (37) demonstrates that when 120577 is set in therange of (0 cos120595] the principle angle of GOP is enlargedAccording to the expression of output noise power in (12)the noise power of GOP will be less than that of OP

1198751015840

119899lt 119875119899

(38)

Property 4 Suppose INR is known a priori a maximizedSINR which is the SINR upper bound of GOP can beobtained and the corresponding ICS is given as

120577opt =

cos120595

1 + 119873 sdot INR sin2120595 (39)

such that the maximum SINR is obtained as

SINRmax =

(SIR + 119873 sdot SNR sin2120595) 119873 sdot SNRSIR + 119873 sdot SNR

(40)

where 119873 represents the number of array elements

Proof The SINR output of the GOP filter can be expressed as

SINR =

119875119904

1198751015840

119894+ 1198751015840119899

=

119875119904

1205772119875119894 + 119875119899119873 sin21205951015840

= (

1205772

SIR+

1

119873 sin21205951015840SNR)

minus1

= (

1205772

SIR+

1 minus 2120577 cos120595 + 1205772

119873 sin2120595SNR)

minus1

(41)

To have the maximum value of SINR the first orderderivative of (41) with respect to 120577 is taken therefore theoptimum 120577opt that will give the maximum SINR in (40) isobtained as in (39)

4 GOP in Spatial Filtering

By using the spatial difference between the target and inter-ference spatial filtering is an effective method to reduce thepower of unwanted signals including output noise In theconstruction of spatial GOP filter the design of ISC param-eter is flexible It can be generated by using the conventionaladaptive spatial filtering methods such as minimum variancedistortionless response (MVDR) algorithm [20]

The constrained criterion of MVDR is described as

minw w119879Rw

st w119867A = 1

(42)

where A is the spatial vector for the target signal and R =

119864x(119905)x119867(119905) represents the covariance matrix of the receivedsignal

The weight of MVDR can be obtained as

wMVDR = Rminus1A (A119867Rminus1A)

minus1

(43)

Therefore the ISC obtained from wMVDR is expressed as

120577MVDR = w119867MVDRB = (Rminus1A (A119867Rminus1A)

minus1

)

119867

B (44)

It should be noted that the restoration of the targetis not related to 120577 which is the fundamental property ofGOP as given in (25) The interference suppression effect isdetermined by 120577 only As a result except for MVDR moreadaptive beamforming methods can be utilized However asthe information required by MVDR is usually easy to obtainit is more representative to derive 120577 from wMVDR In thefollowing part the SINR performance of theMVDR OP andGOP with 120577 given in (44) is analyzed and compared

41 SINRs Comparison of GOP and MVDR The SINR per-formance of the GOP and MVDR filter is evaluated TheSINRs for GOP and MVDR filter are given in (45) and (46)respectively as

SINRGOP =

119864 |wA119904 (119899)|2

119864 |wB119894 (119899)|2 + 119864 |wn(119899)|

2

=

119864 |wA|2 1205902

119904

119864 |wB|2 1205902

119894+ |w|2

1205902119899

(45)

where w = A119867EAB120577A2 Consider

SINRMVDR =

119864 1003816100381610038161003816wMVDRA119904 (119899)

1003816100381610038161003816

2

119864 1003816100381610038161003816wMVDRB119894 (119899)

1003816100381610038161003816

2 + 119864

1003816100381610038161003816wMVDRn(119899)

1003816100381610038161003816

2

=

119864 1003816100381610038161003816wMVDRA

1003816100381610038161003816

2 1205902

119904

119864 1003816100381610038161003816wMVDRB

1003816100381610038161003816

2 1205902

119894+

1003816100381610038161003816wMVDR

1003816100381610038161003816

21205902119899

(46)

6 International Journal of Antennas and Propagation

Observing (13) (42) (43) and (44) we get

w119867A = w119867MVDRA

w119867B = w119867MVDRB

(47)

Substitute (47) into (45) and (46) it can be observed thatthe difference of output SINRs is decided by the power ofnoise after filtering

Investigating the objective function in (13) we get wGOPwhich satisfies min(w119867GOPwGOP) hence |wGOP|

2le |wMVDR|

2This leads to

SINRGOP ge SINRMVDR (48)

Both of these filters attempt to reduce the interference andnoise while producing the distortionless response Howeverthe GOP filter has a better treatment to the noise andinterference which results in a higher SINR

42 SINRs Comparison of GOP and OP The SINR perfor-mance of the GOP and OP filter is evaluated The SINR forOP filter is written as

SINROP =

119864 1003816100381610038161003816wOPA119904 (119899)

1003816100381610038161003816

2

119864 1003816100381610038161003816wOPB119894 (119899)

1003816100381610038161003816

2 + 119864

1003816100381610038161003816wOPn(119899)

1003816100381610038161003816

2

=

1205902

119904

1205902119899

1003817100381710038171003817EAB

1003817100381710038171003817

2 A2

(49)

where wOP = A119867EABA2

Let the ratio between SINRs of GOP and OP filter be

119896 =

SINRGOPSINROP

=

1003817100381710038171003817EAB

1003817100381710038171003817

21205902

119899 A2

12057721205902

119894+

10038161003816100381610038161003816A119867EAB120577 A

210038161003816100381610038161003816

2

1205902119899

=

1

1198731205772INR sin2120595 +

1003817100381710038171003817B minus 120577A1003817

100381710038171003817

2119873

=

1

1198851205772

minus 2 cos120595120577 + 1

(50)

where 119885 = 1 + 119873 sin2120595INR A2

= 119873 and 119873 is the numberof the array elements

As the value of 119896 is determined by the principle angleINR the number of array elements and ISC simultaneouslyit is not easy to be analyzed without numerical evaluationsHowever we can make a reasonable assumption under twoextreme cases where spatial difference between the target andinterference approaches 90 degrees or 0 degrees

Case 1 (120595 rarr 90∘) The angular separation between target

and interference is nearly orthogonal which means thespatial difference ismaximized An aggressive action is taken

and the interference is expected to be eliminated completelyRewrite (50) as

1198961 =

1

119873 sin21205951205761 + 21205751 + 1 + 1205772 (51)

where 1205761 = 1205772INR and 1205751 = 120577 cos120595

To evaluate (51) numerically let 120595 = 898∘ and 120577 = 0 we

have sin2120595 asymp 1 1205772 = 0 and 1205751 = 0 Since the INR is boundedby a practical maximum of 60 dB we have 1205761 = 0 1198961 = 1 and

SINRGOP = SINROP (52)

Case 2 (120595 rarr 0∘) When the angular separation between

target and interference is very close the principle angle isnear zero For OP filter its SINR is not satisfying due tothe amplified noise power as given in (12) However theproposed GOP filter can be expected to be more conservativein rejecting the interference and shifting the focus in reducingthe noise power output That means when INR is low whichmeans noise power is comparably high the ISC is approach-ing one However if noise power is comparably much lowerthan interference resulting in a very high INR the ISC isapproaching zero to facilitate interference suppression Werewrite (50) as

1198962 =

1

1198731205762 + 1205752 + 1205772 (53)

where 1205762 = (120577 sin120595)2INR and 1205751 = 2120577 cos120595 + 1

To evaluate (53) numerically let 120595 = 001∘ and 120577 isin

[10minus5

1] we have sin2120595 = 0 hence 1205762 = 0 Therefore wehave 1205752 + 120577

2ge 1 1198962 ge 1 and

SINRGOP ge SINROP (54)

From the theoretical analysis of the two cases the SINRoutputs from both filters have an identical performance whenthe spatial difference between the target and interference islarge However GOP filter has a superior performance thanOP filter when the spatial difference is small

Moreover according to Property 4 of GOP there is anoptimized 120577opt in maximizing SINR output if the INR canbe obtained in advance By substituting (39) (50) can berewritten as

119896 =

1

119885 (120577opt minus cos120595119885)

2

+ 1 minus cos2120595119885

=

1

1 minus cos2120595119885

ge 1

(55)

where 120577opt = cos120595119885Therefore we have

SINRGOP ge SINROP (56)

43 Simulations Assume an ULA of 10 antenna elementswith half wavelength spacing between adjacent elements thecarrier frequency is 1198910 = 5MHz Under the conditions of

International Journal of Antennas and Propagation 7

0 10 20 30 40 50 60 70 80 90

0

10

20

30

SIN

R im

prov

emen

t (dB

)

84 85 86 87 88 89 90

1981985

1991995

202005

minus40

minus30

minus20

minus10

120595 (deg)

OptimumMVDR

OPGOP

Figure 1 SINR improvement versus 120595

20 25 30 35 40 45 50 55 6015

20

25

30

35

40

45

50

55

60

65

INR (dB)

SIN

R im

prov

emen

t (dB

)

MVDR (SIR = minus30dB)OP (SIR = minus30dB)GOP (SIR = minus30dB)MVDR (SIR = minus20dB)OP (SIR = minus20dB)

GOP (SIR = minus20dB)MVDR (SIR = minus10dB)OP (SIR = minus10dB)GOP (SIR = minus10dB)

Figure 2 SINR improvement versus INR for Case 1

SNR = 10 dB and SIR = minus10 dB the SINR improvementversus 120595 for MVDR OP GOP and GOP with optimum ISCis shown in Figure 1

From Figure 1 it can be observed that the principle angleshave great impacts on the SINR performance of the threespatial filters With the principle angle less than 10 degreesa sharper decrease appears in SINR for the OP filter thanboth GOP and MVDR filters However when the principleangle increases to nearly 90 degrees GOP and OP filtersperform slightly better than MVDR filter The GOP spatialfilter demonstrates a superior performance than OP and

20 25 30 35 40 45 50 55 60

0

5

10

15

INR (dB)

SIN

R im

prov

emen

t (dB

)

MVDR (SIR = minus30dB)OP (SIR = minus30dB)GOP (SIR = minus30dB)MVDR (SIR = minus20dB)OP (SIR = minus20dB)

GOP (SIR = minus20dB)MVDR (SIR = minus10dB)OP (SIR = minus10dB)GOP (SIR = minus10dB)

minus35

minus30

minus25

minus20

minus15

minus10

minus5

Figure 3 SINR improvement versus INR for Case 2

MVDR filters in the whole angle range further it coincideswith the maximized SINR derived in (40)

In the following the principle angle is fixed and theperformances of three filters under different INRs are inves-tigated The INRs span from 20 dB to 60 dB while the SIRsare of minus10 dB minus20 dB and minus30 dB respectively The principleangles are set to near 90 degrees and 0 degrees respectivelywhich correspond to the cases in Section 42

In Figures 2 and 3 the principle angles are set to 898degrees and 018 degrees respectively which correspond toCases 1 and 2 It is found that the ISC varies slightly aroundzero when the INRs change for Case 1 and ISC varies inrange of [27 times 10

minus5 1] for Case 2 As shown in Figure 2 the

SINR improvements of the GOP and OP increase linearlywith INRs however the MVDR shows an inferior SINRimprovement In Figure 3 the principle angle is small whichmeans that the spatial difference between the target andinterference reducesThe noise power amplifying effect of OPis significant resulting in a severe SINR performance lossIn contrast the GOP and MVDR filters have better SINRimprovements which exceed 30 dB at highest than OP filterIn general the GOP filter generates a superior performancethan both OP and MVDR filters The numerical simulationshave verified the theoretical analysis of the spatial filterspresented

5 GOP in Polarization Filtering of HF Radar

High frequency surface wave radar (HFSWR) [22] operatesin the short wave band which facilities the over-the-horizondetection over the sea surface However signals in this bandwill also get reflected by the ionosphere leading to a stronginterference to the target detection or sea state remote sens-ing In this section we explored the polarization information

8 International Journal of Antennas and Propagation

in the HFSWR and extended the application of the GOP filterin polarization filtering further a challenging ionosphericclutter mitigation problem in HFSWR is addressed

51 Generalized Oblique Projection Polarization Filter Asthe linear signal model presented in (4) a pair of thepolarization parameters represent the amplitude relationshipand the phase difference between the echoes received by theorthogonal dual-polarized radar sensor

Suppose the polarization parameters of the target andinterference are different then the target polarization sub-space ⟨Ps⟩ and interference polarization subspace ⟨Pi⟩ aredisjoint Note that the polarization subspace is independentof the specific radar signal waveforms The polarizationsubspace is constructed by the difference of the polarizationstate Therefore the target and interference subspaces in (23)can be given as

A = [

cos 120574119904

sin 120574119904119890119895120578119904] B = [

cos 120574119894

sin 120574119894119890119895120578119894] (57)

where 120574 and 120578 are the polarization pair with subscripts 119904 and119894 representing target and interference

There are two sets of the parameters that need to bedecided that is the echoes polarization set and the ISC Thepolarization angle is obtained as

120574 = 119905119892minus1

(

1003816100381610038161003816119909119881 (119905)

1003816100381610038161003816

1003816100381610038161003816119909119867 (119905)

1003816100381610038161003816

) (58)

and the polarization phase difference as

120578 = arg (119909119881 (119905)) minus arg (119909119867 (119905)) (59)

where 119909119881(119905) 119909119867(119905) represent the vertically and horizontallypolarized signal components and arg(sdot sdot sdot ) indicates phase ofthe signal

By the inflexibility of the polarized state in the temporaldomain and the frequency domain [18] these parameters canbe calculated using frequency transformed signal also TheISC is a free variable which can be designed according to thespecific application

However it can be proved that if the ISC is set to zerothis GOP polarization filter becomesOP polarization filter Inconstrained condition that is subspace ⟨Ps⟩ is orthogonal to⟨Pi⟩ the GOP polarization filter degrades into an orthogonalpolarization filter

52 Ionospheric Clutter Cancellation in HFSWR The char-acteristics of the ionosphere reflected echoes received byHFSWR are

(1) nonstationary(2) multiclutters(3) widely spread in range and Doppler bins

In addition to that there are ionospheric clutters return-ing from the sea surface whichmake their polarization statesclose to the target or the spatial difference between the

Time domain signal

Segmentations and FFT

Frequency domainpolarization estimations

Coherentintegration

Logic product

GOP filtering fortime segment 1

GOP filtering for

1st clutterGOP filtering fortime segment 1

GOP filtering for

Filtering output

time segment K time segment K

Jth clutter

middot middot middot

Figure 4 Ionospheric clutter mitigation process flow

clutters and target is not obvious Those characteristics leadto an unsolved clutter mitigation problem so far

As the radar arrays cannot effectively distinguish thetarget and interference spatially in this scenario the arraypolarization diversity and the coherent integration processare explored To handle those characteristics segmentationsof the time domain signals are introduced in an effort toapproach the real clutter parameters andmultipleGOPfilterswith flexible parameters 120577 are constructed The flowchart toillustrate the ionospheric clutter mitigation process is shownin Figure 4

In the dual-polarized HFSWR system the time domainsignal is range processed After proper signal segmentationsthe polarization states are estimated according to (58) and(59) with frequency transformed signal componentsThe sig-nals returned from the ship target over sea surface will retainvertically polarized state whereas the ionosphere reflectedclutters will be ellipse polarized with strong horizontallypolarized components The target and clutter polarizationsubspaces (A and B for GOP) are therefore obtained by thepolarization threshold A total number of 119870 segments of thetime divided data after filtering are connected and coherentintegration is performed However by the special designof GOP polarization filter an extra integration loss to theionospheric clutter will be brought in

By Property 1 of GOP the target polarization subspacesare retained while the ionospheric clutters are controlledby the free variable 120577 which is designed to introducerandom phase shift Therefore after GOP processing asignificant coherent integration loss will be introduced tothe ionospheric clutters when the time divided segmentsare reconnected and fast Fourier transformed However thetargetrsquos amplitude and phase are unchanged and its coherentintegration performance is not affected

The free variable of 120577(119899) is designed as

120577 (119899) = rnd (1205751 1205752 119899) 119890119895rnd(120573

11205732119899)

119899 isin [1 119870] (60)

where rnd(1205751 1205752 119899) represents random arrays from the uni-form distribution with amplitude range [1205751 1205752] and random

International Journal of Antennas and Propagation 9

20 40 60 80 100 1200

5

10

15

20

25

Segment numbers

Coh

eren

t int

egra

tion

loss

(dB)

120590120573 = 21205875

120590120573 = 1205872

120590120573 = 120587

120590120573 = 2120587

Figure 5 Coherent loss versus segment numbers under differentphase ranges

phase term 119890119895rnd(120573

11205732119899) with phase range [1205731 1205732] and 119899

denotes the sequence number of 120577 generatedIn deciding the parameters of 120577 the number of segmen-

tation and the phase ranges are of importance In Figure 5the segmentation number is chosen to be 64 and at that pointphase range of [0 2120587] is picked by simulation results of idealexponential signals The reasons are that more segmentationnumbers can only introduce at most 3 dB loss further whilemore segments indicate shorter time in coherent integrationand result in more estimation errors which may degradethe performance of the filter Therefore the parameters areobtained in consideration of the extra coherent loss andpotential estimation error

After logic product process [18] which reserves thesmallest points in Doppler spectrum from all the filteringresults the final output in each range bin is obtained as

Y (120596) =

119873

sum

119899=1

120575 (120596 minus 120596119899)

times

119869

min119895=1

(FFT[

119870

sum

119896=1

EAB120585119896119895x119896 (119899seg119896)])

(61)

where 119873 represents the length of FFT 120596119899 represents thefrequency at point 119899 119869 represents the total number of theclutters 119870 is the total number of segmentations EAB120585119896119895is the 119896th GOP in time domain for the suppression of 119895thclutter and x119896(119899seg119896) is the 119896th time segmented datawith 119899seg119896denoting the sampled points in the corresponding segment

In the HFSWR field experiment the vertically polarizedsignal was transmitted with a carrier frequency of 7Mhzby a half-wave dipole antenna The data was collected by adistant polarized high frequency linear array with 15-meterseparation between the vertically and horizontally polarizedelements The coherent integration time was 4 minutes

50 100 150 200 250

Doppler bins

Pow

er (d

B)

After filteringBefore filtering

Target

minus90

minus80

minus70

minus60

minus50

minus40

minus30

minus20

minus10

Figure 6 Doppler spectrum at range bin 79

Figure 6 gives theDoppler spectrumafter integration at rangebin 79 which is obtained from experimentally derived datawith red dashed line denoting spectrum before filtering andblue solid line denoting spectrum after process It can beobserved that there are several peaks well above minus30 dBbefore filtering which create an unfavorable ship detectionenvironment However the ship target at Doppler bin 183can be distinguished easily since the ionospheric clutters aresuppressed by about 10 dB in average whereas the targetsignal is undistorted

Besides ship detection the other focus can be drawn onthe sea state remote sensing A successful sea state inversionalgorithm depends on the correct and accurate extractionsof Bragg In Figure 7 the double first order Bragg peaks atDoppler bins (in between the vertically green dashed lines)are contaminated by the ionospheric clutters After GOPfiltering the contaminations of ionosphere are minimizedmoreover the SINR of the negative Bragg peaks was raisedaround 12 dB which facilitates its extraction algorithms

The Doppler spectrums from all the range bins arethen collected together forming a range-Doppler spectrumFigure 8(a) presents the original range-Doppler spectrumwhich is contaminated by the ionospheric clutters fromrange bins 73 to 96 whereas Figure 8(b) describes thespectrum after being processed by GOP filters Obviouslythe ionospheric clutters which widely spread in range andDoppler bins are suppressed effectively The average SINRimprovement is above 10 dB in this experiment

6 Conclusions

In this paper a novel GOP with adjustable ISC parameter hasbeen proposed It is proved to be an extension of OP andfour fundamental properties are presented with proofs Theconstruction of GOP filters is demonstrated with examplesof spatial and polarization filtering respectively In thefirst example with ISC derived from adaptive beamforming

10 International Journal of Antennas and Propagation

After filteringBefore filtering

50 100 150 200 250Doppler bins

Pow

er (d

B)

Positive BraggNegative Bragg

minus90

minus80

minus70

minus60

minus50

minus40

minus30

minus20

minus10

Figure 7 Doppler spectrum at range bin 89

20

40

60

80

100

120

140

160

50 100 150 200 250Doppler bins

Rang

e bin

s

(a) Original range-Doppler spectrum

20

40

60

80

100

120

140

160

50 100 150 200 250Doppler bins

Rang

e bin

s

(b) Range-Doppler spectrum after GOP filter

Figure 8 Range-Doppler spectrum of HFSWR

algorithm the SINR performance of GOP filter is shownto be better than MVDR and OP filters both theoreticallyand numerically A GOP polarization filter is constructedwith manually designed ISC in the second example An extracoherent loss is introduced to the ionospheric clutters bypurpose and a satisfying clutter suppression result inHFSWRis achieved Besides the examples givenmore designs of GOPfilter can be inspired by the flexibilities of ISC It can beconcluded that GOP filter is a promising filtering techniquefor interference suppression and capable of being used inspatial filtering polarization filtering and other array signalprocessing applications

Conflict of Interests

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

Acknowledgments

This project is sponsored by the National Marine TechnologyProgram for Public Welfare (no 200905029) National Nat-ural Science Foundation of China (no 61171180) and TeamResearch Foundation for Fundamental Research Program inFIO China (no GY0213T03)

References

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

[2] L Rebollo-Neira ldquoOblique matching pursuitrdquo IEEE SignalProcessing Letters vol 14 no 10 pp 703ndash706 2007

[3] GW Stewart ldquoOn the numerical analysis of oblique projectorsrdquoSIAM Journal on Matrix Analysis and Applications vol 32 no1 pp 309ndash348 2011

International Journal of Antennas and Propagation 11

[4] X-P Mao A-J Liu H-J Hou H Hong R Guo and W-BDeng ldquoOblique projection polarisation filtering for interferencesuppression in high-frequency surface wave radarrdquo IET RadarSonar and Navigation vol 6 no 2 pp 71ndash80 2012

[5] 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 (Chinese)

[6] Q-Y Zhang B Cao L Jin and N-T Zhang ldquoOblique pro-jection polarization filtering-based interference suppressionsfor radar sensor networksrdquo EURASIP Journal on WirelessCommunications and Networking vol 2010 Article ID 6051032010

[7] X Yu and L Tong ldquoJoint channel and symbol estimation byoblique projectionsrdquo IEEE Transactions on Signal Processingvol 49 no 12 pp 3074ndash3083 2001

[8] Q Zhang B Cao JWang and N Zhang ldquoPolarization filteringtechnique based on oblique projectionsrdquo Science China F vol53 no 5 pp 1056ndash1066 2010

[9] Y Cui K Liu and J Wang ldquoDirection-of-arrival estimationfor coherent GPS signals based on oblique projectionrdquo SignalProcessing vol 92 no 1 pp 294ndash299 2012

[10] Y Hu X Zhang F Zhu and H Lv ldquoImage recognition usingiterative oblique projectionrdquo Electronics Letters vol 41 no 20pp 1109ndash1110 2005

[11] G Hellbourg R Weber C Capdessus and A-J BoonstraldquoOblique projection beamforming for RFI mitigation in radioastronomyrdquo in Proceedings of the IEEE Statistical Signal Process-ing Workshop (SSP rsquo12) pp 93ndash96 IEEE August 2012

[12] P De ldquoNew methods for sensing bandlimited signals in cogni-tive radiordquo in Proceedings of the IEEE 65th Vehicular TechnologyConference (VTC 07-Spring) pp 1916ndash1920 Dublin IrelandApril 2007

[13] R Boyer ldquoOblique projection for source estimation in a com-petitive environment algorithm and statistical analysisrdquo SignalProcessing vol 89 no 12 pp 2547ndash2554 2009

[14] M L McCloud and L L Scharf ldquoA new subspace identificationalgorithm for high-resolution DOA estimationrdquo IEEE Transac-tions on Antennas and Propagation vol 50 no 10 pp 1382ndash1390 2002

[15] R Boyer andG Bouleux ldquoOblique projections for direction-of-arrival estimation with prior knowledgerdquo IEEE Transactions onSignal Processing vol 56 no 4 pp 1374ndash1387 2008

[16] H Hong X-P Mao C Hu R Guo W-B Deng and PJiang ldquoNarrow-band null phase-shift spatial filter based onoblique projectionrdquo in Proceedings of the IEEERadar Conference(RADAR rsquo13) pp 1ndash5 Ottawa Canada May 2013

[17] Z H Xu Y P Ni and L Jin ldquoResolution theory of polarizationsensitive array signalsrdquo in Proceedings of the CIE InternationalConference on Radar (ICR rsquo06) pp 1ndash4 IEEE Shanghai ChinaOctober 2006

[18] 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

[19] Y-M Wang X-P Mao J Zhang and H Hong ldquoA multi-domain collaborative filter based on polarization sensitivefrequency diverse arrayrdquo in Proceedings of the IEEE RadarConference pp 0507ndash0511 Cincinnati Ohio USA May 2014

[20] M Souden J Benesty and S Affes ldquoA study of the LCMVandMVDRnoise reduction filtersrdquo IEEE Transactions on SignalProcessing vol 58 no 9 pp 4925ndash4935 2010

[21] Y M Cui X P Mao and H Hong ldquoA novel adaptive filter forinterference suppressionrdquo in Proceedings of the IEEE Region 10Conference vol 31194 pp 1ndash5 IEEE 2013

[22] H C Chan ldquoCharacterization of ionospheric clutter in HFsurface wave radarrdquo Tech Rep 2003-114 Defence RampDCanadaOttawa Canada 2003

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Electrical and Computer Engineering

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Volume 2014

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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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Chemical EngineeringInternational Journal of Antennas and

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DistributedSensor Networks

International Journal of

International Journal of Antennas and Propagation 3

The OP operator recovers the desired signal and elim-inates interference completely Therefore the SINR of theoutput can be expressed as

SINR =

119875119904

119875119894 + 119875119899

=

119864

10038161003816100381610038161003816A119867EABA119904 (119905) A

10038161003816100381610038161003816

2

119864 1003816100381610038161003816A119867EABn (119905) A

1003816100381610038161003816

2

=

1205902

119904A2

1205902119899trace EABE119867AB

=

1205902

119904

1205902119899

A2 sin2120595

(10)

where 1205902

119904 1205902119899stand for the power of target and additive noise

respectively and the principle angle between A and B isdefined as

120595 = arccos(

10038171003817100381710038171003817A119867B1003817

1003817100381710038171003817

A B

) (11)

As observed from (8) a portion of noise is retainedmixedwith the target signal The noise power after filtering is givenby

119875119899 = 119864 1003817100381710038171003817EABn (119905)

1003817100381710038171003817

2 =

1

sin2 (120595)

1205902

119899 (12)

From (9) and (12) we can observe that the noise powerafter filtering is closely related to the principle angle Whensubspaces ⟨A⟩ and ⟨B⟩ get close which implies a smallprinciple angle the noise power will be amplified In thissituation although the interference is totally eliminated theenhanced noise power may result in a significant SINR lossThis is an inevitable problem of the OP filter

3 Generalized Oblique Projection Filter

The OP filter focuses on the suppression of interferenceand lacks of the control of the noise power To obtain aflexible control of the power of the noise and interferencesimultaneously a novel oblique projection is proposed whichis named GOP

31 Generalized Oblique Projection Operator Taking thenoise into consideration and introducing an ISC of 120577 theGOP operator can be derived by solving the following linearconstrained optimum problem as

min w119867w

st w119867A = 1

w119867B = 120577

(13)

where A and B are the vectors that span target subspace andinterference subspace

From the constraint equation in (13) we have

w119867B minus 120577w119867A = w119867 (B minus 120577A) = 0 (14)

which implicates B minus 120577A isin ⟨w⟩perp

Also we have

w119867A = w119867 (P(Bminus120577A)A + Pperp(Bminus120577A)A)

= w119867Pperp(Bminus120577A)A = 1

(15)

where the orthogonal projection operator ofBminus120577A is definedas

Pperp(Bminus120577A) = I minus (B minus 120577A)

sdot [(B minus 120577A)119867

sdot (B minus 120577A)]

minus1

(B minus 120577A)119867

(16)

Therefore the optimum problem in (13) can be trans-formed into the following

min w119867w

st w119867Pperp(Bminus120577A)A = 1

B minus 120577A isin ⟨w⟩perp

(17)

To solve this problem a cost function is constructed byLagrange multiplier method as

119865 (119908) = w119867w + 120582 (w119867Pperp(Bminus120577A)A minus 1) (18)

Taking derivative of (18) with respect to w the optimumweight is obtained as

w = minus

120582

2

Pperp(Bminus120577A)A (19)

Substitute 119908 into the constraint condition w119867Pperp(Bminus120577A)A =

1 we have

minus

120582

2

A119867Pperp(Bminus120577A)

119867Pperp(Bminus120577A)A = 1 (20)

Consider that Pperp(Bminus120577A)

119867= Pperp(Bminus120577A) and P

perp

(Bminus120577A)2

= Pperp(Bminus120577A)

the cost factor is

120582 = minus2 (A119867Pperp(Bminus120577A)A)

minus1

(21)

Substitute 120582 into (19) we have the explicit weight as

w = Pperp(Bminus120577A)A (A119867Pperp

(Bminus120577A)A)

minus1

= ((A119867Pperp(Bminus120577A)A)

minus1

A119867Pperp(Bminus120577A))

119867

= (

A119867

A2EAB120577)

119867

(22)

where the GOP operator is derived from (22) as

EAB120577 = A (A119867Pperp(Bminus120577A)A)

minus1

A119867Pperp(Bminus120577A) (23)

Compare (23) with (5) the expressions of GOP and OPshare the similar expression It will be shown that the GOPoperator presented is related to the OP operator and orthog-onal projection operator However GOP is the extended formof them and some special properties are generated by theGOP

4 International Journal of Antennas and Propagation

32 Properties of the GOP Four fundamental propertiesof the GOP are presented The idempotence of GOP andthe oblique projection abilities are given respectively inProperty 1The connections of OP and orthogonal projectionwith GOP are shown in Property 2 The enlargement of theprinciple angle by GOP compared to OP is discussed inProperty 3 which implies a reduction of the noise poweroutput Lastly in Property 4 the maximized SINR conditionin GOP is presented

Property 1 Consider

E2AB120577 = EAB120577

EAB120577A = A

EAB120577B = 120577A

(24)

Examine (24) the GOP operator has equivalent filteringeffect when the operator is multiplied It recovers the desiredsignal without amplitude and phase distortion whereas partof the interference is projected into the target subspace and isreserved by GOPThe target signal after GOP filtering can beexpressed as

119878GOP (119905) =

A119867

A2EAB120577x (119905)

= 119904 (119905) + 120577119894 (119905) +

A119867

A2EAB120577n (119905)

(25)

Proof Since Pperp(Bminus120577A) is a square matrix and A is a column

vector we have

E2AB120577 = A (A119867Pperp(Bminus120577A)A)

minus1

A119867Pperp(Bminus120577A)

sdot A (A119867Pperp(Bminus120577A)A)

minus1

A119867Pperp(Bminus120577A)

= A (A119867Pperp(Bminus120577A)A)

minus1

(A119867Pperp(Bminus120577A)A)

times (A119867Pperp(Bminus120577A)A)

minus1

A119867Pperp(Bminus120577A)

= A (A119867Pperp(Bminus120577A)A)

minus1

A119867Pperp(Bminus120577A) = EAB120577

EAB120577A = A (A119867Pperp(Bminus120577A)A)

minus1

(A119867Pperp(Bminus120577A)A) = A

(26)

Since B minus 120577A is a column vector from (16) we have

Pperp(Bminus120577A) (B minus 120577A) = 0

EAB120577 (B minus 120577A) = A (A119867Pperp(Bminus120577A)A)

minus1

A119867Pperp(Bminus120577A) (B minus 120577A)

= 0 997904rArr EAB120577B = 120577A

(27)

Property 2 The ISC 120577 can be real or complex and its absolutevalue |120577| isin [0 1] When 120577 = ⟨AB⟩AB GOP becomesan orthogonal operator and

EAB120577 = PA 120577 =⟨AB⟩

A B

(28)

When 120577 = 0 GOP degrades to an OP and shares the sameexpression in (5) and

EAB120577 = EAB 120577 = 0 (29)

Proof Suppose 120577 equals the inner product of A and B

⟨A (B minus 120577A)⟩ = A119867 (B minus 120577A)

= A119867B minus

A119867AA119867BA B

= 0

(30)

Therefore subspace ⟨A⟩ is orthogonal to subspace ⟨B minus

120577A⟩ and substitute (16) into (23) we have

EAB120577 = (EAB120577)119867

= A (A119867A)

minus1

A119867 = PA (31)

where PA represents the orthogonal projection of ASuppose 120577 is set to zero hence

EAB120577 = A (A119867Pperp(Bminus120577A)A)

minus1

A119867Pperp(Bminus120577A)

= A (A119867PperpBA)

minus1

A119867PperpB = EAB

(32)

Correspondingly the target signal recovered by GOP andOP is identical in this case

119878GOP (119905) = 119878OP (119905) 120577 = 0 (33)

Property 3 The principle angle of GOP is adjusted by 120577When 120577 isin (0 cos120595] the principle angle of GOP can beenlarged which is given by

1205951015840

gt 120595 120577 isin (0 cos120595] (34)

where 1205951015840 represents the principle angle of GOP and 120595

represents the principle angle of OP under the sameA and BWith a proper setting of the ISC the principle angle betweensubspaces can be enlarged

International Journal of Antennas and Propagation 5

Proof The square of the cosine of the new principle angle is

cos21205951015840 =(A119867B1015840)

119867

(A119867B1015840)1003817100381710038171003817A1198671003817

100381710038171003817

2 1003817100381710038171003817B1015840100381710038171003817

1003817

2

=

(B minus 120577A)119867AA119867 (B minus 120577A)

A119867A (B minus 120577A)119867

(B minus 120577A)

=

(B119867A119867ABA119867A) minus 120577 (A119867B + B119867A) + 1205772A119867A

B119867B minus 120577 (A119867B + B119867A) + 1205772A119867A

=

(cos120595 minus 120577)2

1205772

minus 2120577 cos120595 + 1

=

1

1 + (1 minus cos2120595) (cos120595 minus 120577)2

(35)

Since (35) is a monotonically declining function of 120577

under the condition of 120577 isin [0 cos120595] it is evident that

1205951015840

= 120595 120577 = 0 (36)

or 1205951015840

gt 120595 120577 isin (0 cos120595] (37)

Equation (37) demonstrates that when 120577 is set in therange of (0 cos120595] the principle angle of GOP is enlargedAccording to the expression of output noise power in (12)the noise power of GOP will be less than that of OP

1198751015840

119899lt 119875119899

(38)

Property 4 Suppose INR is known a priori a maximizedSINR which is the SINR upper bound of GOP can beobtained and the corresponding ICS is given as

120577opt =

cos120595

1 + 119873 sdot INR sin2120595 (39)

such that the maximum SINR is obtained as

SINRmax =

(SIR + 119873 sdot SNR sin2120595) 119873 sdot SNRSIR + 119873 sdot SNR

(40)

where 119873 represents the number of array elements

Proof The SINR output of the GOP filter can be expressed as

SINR =

119875119904

1198751015840

119894+ 1198751015840119899

=

119875119904

1205772119875119894 + 119875119899119873 sin21205951015840

= (

1205772

SIR+

1

119873 sin21205951015840SNR)

minus1

= (

1205772

SIR+

1 minus 2120577 cos120595 + 1205772

119873 sin2120595SNR)

minus1

(41)

To have the maximum value of SINR the first orderderivative of (41) with respect to 120577 is taken therefore theoptimum 120577opt that will give the maximum SINR in (40) isobtained as in (39)

4 GOP in Spatial Filtering

By using the spatial difference between the target and inter-ference spatial filtering is an effective method to reduce thepower of unwanted signals including output noise In theconstruction of spatial GOP filter the design of ISC param-eter is flexible It can be generated by using the conventionaladaptive spatial filtering methods such as minimum variancedistortionless response (MVDR) algorithm [20]

The constrained criterion of MVDR is described as

minw w119879Rw

st w119867A = 1

(42)

where A is the spatial vector for the target signal and R =

119864x(119905)x119867(119905) represents the covariance matrix of the receivedsignal

The weight of MVDR can be obtained as

wMVDR = Rminus1A (A119867Rminus1A)

minus1

(43)

Therefore the ISC obtained from wMVDR is expressed as

120577MVDR = w119867MVDRB = (Rminus1A (A119867Rminus1A)

minus1

)

119867

B (44)

It should be noted that the restoration of the targetis not related to 120577 which is the fundamental property ofGOP as given in (25) The interference suppression effect isdetermined by 120577 only As a result except for MVDR moreadaptive beamforming methods can be utilized However asthe information required by MVDR is usually easy to obtainit is more representative to derive 120577 from wMVDR In thefollowing part the SINR performance of theMVDR OP andGOP with 120577 given in (44) is analyzed and compared

41 SINRs Comparison of GOP and MVDR The SINR per-formance of the GOP and MVDR filter is evaluated TheSINRs for GOP and MVDR filter are given in (45) and (46)respectively as

SINRGOP =

119864 |wA119904 (119899)|2

119864 |wB119894 (119899)|2 + 119864 |wn(119899)|

2

=

119864 |wA|2 1205902

119904

119864 |wB|2 1205902

119894+ |w|2

1205902119899

(45)

where w = A119867EAB120577A2 Consider

SINRMVDR =

119864 1003816100381610038161003816wMVDRA119904 (119899)

1003816100381610038161003816

2

119864 1003816100381610038161003816wMVDRB119894 (119899)

1003816100381610038161003816

2 + 119864

1003816100381610038161003816wMVDRn(119899)

1003816100381610038161003816

2

=

119864 1003816100381610038161003816wMVDRA

1003816100381610038161003816

2 1205902

119904

119864 1003816100381610038161003816wMVDRB

1003816100381610038161003816

2 1205902

119894+

1003816100381610038161003816wMVDR

1003816100381610038161003816

21205902119899

(46)

6 International Journal of Antennas and Propagation

Observing (13) (42) (43) and (44) we get

w119867A = w119867MVDRA

w119867B = w119867MVDRB

(47)

Substitute (47) into (45) and (46) it can be observed thatthe difference of output SINRs is decided by the power ofnoise after filtering

Investigating the objective function in (13) we get wGOPwhich satisfies min(w119867GOPwGOP) hence |wGOP|

2le |wMVDR|

2This leads to

SINRGOP ge SINRMVDR (48)

Both of these filters attempt to reduce the interference andnoise while producing the distortionless response Howeverthe GOP filter has a better treatment to the noise andinterference which results in a higher SINR

42 SINRs Comparison of GOP and OP The SINR perfor-mance of the GOP and OP filter is evaluated The SINR forOP filter is written as

SINROP =

119864 1003816100381610038161003816wOPA119904 (119899)

1003816100381610038161003816

2

119864 1003816100381610038161003816wOPB119894 (119899)

1003816100381610038161003816

2 + 119864

1003816100381610038161003816wOPn(119899)

1003816100381610038161003816

2

=

1205902

119904

1205902119899

1003817100381710038171003817EAB

1003817100381710038171003817

2 A2

(49)

where wOP = A119867EABA2

Let the ratio between SINRs of GOP and OP filter be

119896 =

SINRGOPSINROP

=

1003817100381710038171003817EAB

1003817100381710038171003817

21205902

119899 A2

12057721205902

119894+

10038161003816100381610038161003816A119867EAB120577 A

210038161003816100381610038161003816

2

1205902119899

=

1

1198731205772INR sin2120595 +

1003817100381710038171003817B minus 120577A1003817

100381710038171003817

2119873

=

1

1198851205772

minus 2 cos120595120577 + 1

(50)

where 119885 = 1 + 119873 sin2120595INR A2

= 119873 and 119873 is the numberof the array elements

As the value of 119896 is determined by the principle angleINR the number of array elements and ISC simultaneouslyit is not easy to be analyzed without numerical evaluationsHowever we can make a reasonable assumption under twoextreme cases where spatial difference between the target andinterference approaches 90 degrees or 0 degrees

Case 1 (120595 rarr 90∘) The angular separation between target

and interference is nearly orthogonal which means thespatial difference ismaximized An aggressive action is taken

and the interference is expected to be eliminated completelyRewrite (50) as

1198961 =

1

119873 sin21205951205761 + 21205751 + 1 + 1205772 (51)

where 1205761 = 1205772INR and 1205751 = 120577 cos120595

To evaluate (51) numerically let 120595 = 898∘ and 120577 = 0 we

have sin2120595 asymp 1 1205772 = 0 and 1205751 = 0 Since the INR is boundedby a practical maximum of 60 dB we have 1205761 = 0 1198961 = 1 and

SINRGOP = SINROP (52)

Case 2 (120595 rarr 0∘) When the angular separation between

target and interference is very close the principle angle isnear zero For OP filter its SINR is not satisfying due tothe amplified noise power as given in (12) However theproposed GOP filter can be expected to be more conservativein rejecting the interference and shifting the focus in reducingthe noise power output That means when INR is low whichmeans noise power is comparably high the ISC is approach-ing one However if noise power is comparably much lowerthan interference resulting in a very high INR the ISC isapproaching zero to facilitate interference suppression Werewrite (50) as

1198962 =

1

1198731205762 + 1205752 + 1205772 (53)

where 1205762 = (120577 sin120595)2INR and 1205751 = 2120577 cos120595 + 1

To evaluate (53) numerically let 120595 = 001∘ and 120577 isin

[10minus5

1] we have sin2120595 = 0 hence 1205762 = 0 Therefore wehave 1205752 + 120577

2ge 1 1198962 ge 1 and

SINRGOP ge SINROP (54)

From the theoretical analysis of the two cases the SINRoutputs from both filters have an identical performance whenthe spatial difference between the target and interference islarge However GOP filter has a superior performance thanOP filter when the spatial difference is small

Moreover according to Property 4 of GOP there is anoptimized 120577opt in maximizing SINR output if the INR canbe obtained in advance By substituting (39) (50) can berewritten as

119896 =

1

119885 (120577opt minus cos120595119885)

2

+ 1 minus cos2120595119885

=

1

1 minus cos2120595119885

ge 1

(55)

where 120577opt = cos120595119885Therefore we have

SINRGOP ge SINROP (56)

43 Simulations Assume an ULA of 10 antenna elementswith half wavelength spacing between adjacent elements thecarrier frequency is 1198910 = 5MHz Under the conditions of

International Journal of Antennas and Propagation 7

0 10 20 30 40 50 60 70 80 90

0

10

20

30

SIN

R im

prov

emen

t (dB

)

84 85 86 87 88 89 90

1981985

1991995

202005

minus40

minus30

minus20

minus10

120595 (deg)

OptimumMVDR

OPGOP

Figure 1 SINR improvement versus 120595

20 25 30 35 40 45 50 55 6015

20

25

30

35

40

45

50

55

60

65

INR (dB)

SIN

R im

prov

emen

t (dB

)

MVDR (SIR = minus30dB)OP (SIR = minus30dB)GOP (SIR = minus30dB)MVDR (SIR = minus20dB)OP (SIR = minus20dB)

GOP (SIR = minus20dB)MVDR (SIR = minus10dB)OP (SIR = minus10dB)GOP (SIR = minus10dB)

Figure 2 SINR improvement versus INR for Case 1

SNR = 10 dB and SIR = minus10 dB the SINR improvementversus 120595 for MVDR OP GOP and GOP with optimum ISCis shown in Figure 1

From Figure 1 it can be observed that the principle angleshave great impacts on the SINR performance of the threespatial filters With the principle angle less than 10 degreesa sharper decrease appears in SINR for the OP filter thanboth GOP and MVDR filters However when the principleangle increases to nearly 90 degrees GOP and OP filtersperform slightly better than MVDR filter The GOP spatialfilter demonstrates a superior performance than OP and

20 25 30 35 40 45 50 55 60

0

5

10

15

INR (dB)

SIN

R im

prov

emen

t (dB

)

MVDR (SIR = minus30dB)OP (SIR = minus30dB)GOP (SIR = minus30dB)MVDR (SIR = minus20dB)OP (SIR = minus20dB)

GOP (SIR = minus20dB)MVDR (SIR = minus10dB)OP (SIR = minus10dB)GOP (SIR = minus10dB)

minus35

minus30

minus25

minus20

minus15

minus10

minus5

Figure 3 SINR improvement versus INR for Case 2

MVDR filters in the whole angle range further it coincideswith the maximized SINR derived in (40)

In the following the principle angle is fixed and theperformances of three filters under different INRs are inves-tigated The INRs span from 20 dB to 60 dB while the SIRsare of minus10 dB minus20 dB and minus30 dB respectively The principleangles are set to near 90 degrees and 0 degrees respectivelywhich correspond to the cases in Section 42

In Figures 2 and 3 the principle angles are set to 898degrees and 018 degrees respectively which correspond toCases 1 and 2 It is found that the ISC varies slightly aroundzero when the INRs change for Case 1 and ISC varies inrange of [27 times 10

minus5 1] for Case 2 As shown in Figure 2 the

SINR improvements of the GOP and OP increase linearlywith INRs however the MVDR shows an inferior SINRimprovement In Figure 3 the principle angle is small whichmeans that the spatial difference between the target andinterference reducesThe noise power amplifying effect of OPis significant resulting in a severe SINR performance lossIn contrast the GOP and MVDR filters have better SINRimprovements which exceed 30 dB at highest than OP filterIn general the GOP filter generates a superior performancethan both OP and MVDR filters The numerical simulationshave verified the theoretical analysis of the spatial filterspresented

5 GOP in Polarization Filtering of HF Radar

High frequency surface wave radar (HFSWR) [22] operatesin the short wave band which facilities the over-the-horizondetection over the sea surface However signals in this bandwill also get reflected by the ionosphere leading to a stronginterference to the target detection or sea state remote sens-ing In this section we explored the polarization information

8 International Journal of Antennas and Propagation

in the HFSWR and extended the application of the GOP filterin polarization filtering further a challenging ionosphericclutter mitigation problem in HFSWR is addressed

51 Generalized Oblique Projection Polarization Filter Asthe linear signal model presented in (4) a pair of thepolarization parameters represent the amplitude relationshipand the phase difference between the echoes received by theorthogonal dual-polarized radar sensor

Suppose the polarization parameters of the target andinterference are different then the target polarization sub-space ⟨Ps⟩ and interference polarization subspace ⟨Pi⟩ aredisjoint Note that the polarization subspace is independentof the specific radar signal waveforms The polarizationsubspace is constructed by the difference of the polarizationstate Therefore the target and interference subspaces in (23)can be given as

A = [

cos 120574119904

sin 120574119904119890119895120578119904] B = [

cos 120574119894

sin 120574119894119890119895120578119894] (57)

where 120574 and 120578 are the polarization pair with subscripts 119904 and119894 representing target and interference

There are two sets of the parameters that need to bedecided that is the echoes polarization set and the ISC Thepolarization angle is obtained as

120574 = 119905119892minus1

(

1003816100381610038161003816119909119881 (119905)

1003816100381610038161003816

1003816100381610038161003816119909119867 (119905)

1003816100381610038161003816

) (58)

and the polarization phase difference as

120578 = arg (119909119881 (119905)) minus arg (119909119867 (119905)) (59)

where 119909119881(119905) 119909119867(119905) represent the vertically and horizontallypolarized signal components and arg(sdot sdot sdot ) indicates phase ofthe signal

By the inflexibility of the polarized state in the temporaldomain and the frequency domain [18] these parameters canbe calculated using frequency transformed signal also TheISC is a free variable which can be designed according to thespecific application

However it can be proved that if the ISC is set to zerothis GOP polarization filter becomesOP polarization filter Inconstrained condition that is subspace ⟨Ps⟩ is orthogonal to⟨Pi⟩ the GOP polarization filter degrades into an orthogonalpolarization filter

52 Ionospheric Clutter Cancellation in HFSWR The char-acteristics of the ionosphere reflected echoes received byHFSWR are

(1) nonstationary(2) multiclutters(3) widely spread in range and Doppler bins

In addition to that there are ionospheric clutters return-ing from the sea surface whichmake their polarization statesclose to the target or the spatial difference between the

Time domain signal

Segmentations and FFT

Frequency domainpolarization estimations

Coherentintegration

Logic product

GOP filtering fortime segment 1

GOP filtering for

1st clutterGOP filtering fortime segment 1

GOP filtering for

Filtering output

time segment K time segment K

Jth clutter

middot middot middot

Figure 4 Ionospheric clutter mitigation process flow

clutters and target is not obvious Those characteristics leadto an unsolved clutter mitigation problem so far

As the radar arrays cannot effectively distinguish thetarget and interference spatially in this scenario the arraypolarization diversity and the coherent integration processare explored To handle those characteristics segmentationsof the time domain signals are introduced in an effort toapproach the real clutter parameters andmultipleGOPfilterswith flexible parameters 120577 are constructed The flowchart toillustrate the ionospheric clutter mitigation process is shownin Figure 4

In the dual-polarized HFSWR system the time domainsignal is range processed After proper signal segmentationsthe polarization states are estimated according to (58) and(59) with frequency transformed signal componentsThe sig-nals returned from the ship target over sea surface will retainvertically polarized state whereas the ionosphere reflectedclutters will be ellipse polarized with strong horizontallypolarized components The target and clutter polarizationsubspaces (A and B for GOP) are therefore obtained by thepolarization threshold A total number of 119870 segments of thetime divided data after filtering are connected and coherentintegration is performed However by the special designof GOP polarization filter an extra integration loss to theionospheric clutter will be brought in

By Property 1 of GOP the target polarization subspacesare retained while the ionospheric clutters are controlledby the free variable 120577 which is designed to introducerandom phase shift Therefore after GOP processing asignificant coherent integration loss will be introduced tothe ionospheric clutters when the time divided segmentsare reconnected and fast Fourier transformed However thetargetrsquos amplitude and phase are unchanged and its coherentintegration performance is not affected

The free variable of 120577(119899) is designed as

120577 (119899) = rnd (1205751 1205752 119899) 119890119895rnd(120573

11205732119899)

119899 isin [1 119870] (60)

where rnd(1205751 1205752 119899) represents random arrays from the uni-form distribution with amplitude range [1205751 1205752] and random

International Journal of Antennas and Propagation 9

20 40 60 80 100 1200

5

10

15

20

25

Segment numbers

Coh

eren

t int

egra

tion

loss

(dB)

120590120573 = 21205875

120590120573 = 1205872

120590120573 = 120587

120590120573 = 2120587

Figure 5 Coherent loss versus segment numbers under differentphase ranges

phase term 119890119895rnd(120573

11205732119899) with phase range [1205731 1205732] and 119899

denotes the sequence number of 120577 generatedIn deciding the parameters of 120577 the number of segmen-

tation and the phase ranges are of importance In Figure 5the segmentation number is chosen to be 64 and at that pointphase range of [0 2120587] is picked by simulation results of idealexponential signals The reasons are that more segmentationnumbers can only introduce at most 3 dB loss further whilemore segments indicate shorter time in coherent integrationand result in more estimation errors which may degradethe performance of the filter Therefore the parameters areobtained in consideration of the extra coherent loss andpotential estimation error

After logic product process [18] which reserves thesmallest points in Doppler spectrum from all the filteringresults the final output in each range bin is obtained as

Y (120596) =

119873

sum

119899=1

120575 (120596 minus 120596119899)

times

119869

min119895=1

(FFT[

119870

sum

119896=1

EAB120585119896119895x119896 (119899seg119896)])

(61)

where 119873 represents the length of FFT 120596119899 represents thefrequency at point 119899 119869 represents the total number of theclutters 119870 is the total number of segmentations EAB120585119896119895is the 119896th GOP in time domain for the suppression of 119895thclutter and x119896(119899seg119896) is the 119896th time segmented datawith 119899seg119896denoting the sampled points in the corresponding segment

In the HFSWR field experiment the vertically polarizedsignal was transmitted with a carrier frequency of 7Mhzby a half-wave dipole antenna The data was collected by adistant polarized high frequency linear array with 15-meterseparation between the vertically and horizontally polarizedelements The coherent integration time was 4 minutes

50 100 150 200 250

Doppler bins

Pow

er (d

B)

After filteringBefore filtering

Target

minus90

minus80

minus70

minus60

minus50

minus40

minus30

minus20

minus10

Figure 6 Doppler spectrum at range bin 79

Figure 6 gives theDoppler spectrumafter integration at rangebin 79 which is obtained from experimentally derived datawith red dashed line denoting spectrum before filtering andblue solid line denoting spectrum after process It can beobserved that there are several peaks well above minus30 dBbefore filtering which create an unfavorable ship detectionenvironment However the ship target at Doppler bin 183can be distinguished easily since the ionospheric clutters aresuppressed by about 10 dB in average whereas the targetsignal is undistorted

Besides ship detection the other focus can be drawn onthe sea state remote sensing A successful sea state inversionalgorithm depends on the correct and accurate extractionsof Bragg In Figure 7 the double first order Bragg peaks atDoppler bins (in between the vertically green dashed lines)are contaminated by the ionospheric clutters After GOPfiltering the contaminations of ionosphere are minimizedmoreover the SINR of the negative Bragg peaks was raisedaround 12 dB which facilitates its extraction algorithms

The Doppler spectrums from all the range bins arethen collected together forming a range-Doppler spectrumFigure 8(a) presents the original range-Doppler spectrumwhich is contaminated by the ionospheric clutters fromrange bins 73 to 96 whereas Figure 8(b) describes thespectrum after being processed by GOP filters Obviouslythe ionospheric clutters which widely spread in range andDoppler bins are suppressed effectively The average SINRimprovement is above 10 dB in this experiment

6 Conclusions

In this paper a novel GOP with adjustable ISC parameter hasbeen proposed It is proved to be an extension of OP andfour fundamental properties are presented with proofs Theconstruction of GOP filters is demonstrated with examplesof spatial and polarization filtering respectively In thefirst example with ISC derived from adaptive beamforming

10 International Journal of Antennas and Propagation

After filteringBefore filtering

50 100 150 200 250Doppler bins

Pow

er (d

B)

Positive BraggNegative Bragg

minus90

minus80

minus70

minus60

minus50

minus40

minus30

minus20

minus10

Figure 7 Doppler spectrum at range bin 89

20

40

60

80

100

120

140

160

50 100 150 200 250Doppler bins

Rang

e bin

s

(a) Original range-Doppler spectrum

20

40

60

80

100

120

140

160

50 100 150 200 250Doppler bins

Rang

e bin

s

(b) Range-Doppler spectrum after GOP filter

Figure 8 Range-Doppler spectrum of HFSWR

algorithm the SINR performance of GOP filter is shownto be better than MVDR and OP filters both theoreticallyand numerically A GOP polarization filter is constructedwith manually designed ISC in the second example An extracoherent loss is introduced to the ionospheric clutters bypurpose and a satisfying clutter suppression result inHFSWRis achieved Besides the examples givenmore designs of GOPfilter can be inspired by the flexibilities of ISC It can beconcluded that GOP filter is a promising filtering techniquefor interference suppression and capable of being used inspatial filtering polarization filtering and other array signalprocessing applications

Conflict of Interests

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

Acknowledgments

This project is sponsored by the National Marine TechnologyProgram for Public Welfare (no 200905029) National Nat-ural Science Foundation of China (no 61171180) and TeamResearch Foundation for Fundamental Research Program inFIO China (no GY0213T03)

References

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

[2] L Rebollo-Neira ldquoOblique matching pursuitrdquo IEEE SignalProcessing Letters vol 14 no 10 pp 703ndash706 2007

[3] GW Stewart ldquoOn the numerical analysis of oblique projectorsrdquoSIAM Journal on Matrix Analysis and Applications vol 32 no1 pp 309ndash348 2011

International Journal of Antennas and Propagation 11

[4] X-P Mao A-J Liu H-J Hou H Hong R Guo and W-BDeng ldquoOblique projection polarisation filtering for interferencesuppression in high-frequency surface wave radarrdquo IET RadarSonar and Navigation vol 6 no 2 pp 71ndash80 2012

[5] 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 (Chinese)

[6] Q-Y Zhang B Cao L Jin and N-T Zhang ldquoOblique pro-jection polarization filtering-based interference suppressionsfor radar sensor networksrdquo EURASIP Journal on WirelessCommunications and Networking vol 2010 Article ID 6051032010

[7] X Yu and L Tong ldquoJoint channel and symbol estimation byoblique projectionsrdquo IEEE Transactions on Signal Processingvol 49 no 12 pp 3074ndash3083 2001

[8] Q Zhang B Cao JWang and N Zhang ldquoPolarization filteringtechnique based on oblique projectionsrdquo Science China F vol53 no 5 pp 1056ndash1066 2010

[9] Y Cui K Liu and J Wang ldquoDirection-of-arrival estimationfor coherent GPS signals based on oblique projectionrdquo SignalProcessing vol 92 no 1 pp 294ndash299 2012

[10] Y Hu X Zhang F Zhu and H Lv ldquoImage recognition usingiterative oblique projectionrdquo Electronics Letters vol 41 no 20pp 1109ndash1110 2005

[11] G Hellbourg R Weber C Capdessus and A-J BoonstraldquoOblique projection beamforming for RFI mitigation in radioastronomyrdquo in Proceedings of the IEEE Statistical Signal Process-ing Workshop (SSP rsquo12) pp 93ndash96 IEEE August 2012

[12] P De ldquoNew methods for sensing bandlimited signals in cogni-tive radiordquo in Proceedings of the IEEE 65th Vehicular TechnologyConference (VTC 07-Spring) pp 1916ndash1920 Dublin IrelandApril 2007

[13] R Boyer ldquoOblique projection for source estimation in a com-petitive environment algorithm and statistical analysisrdquo SignalProcessing vol 89 no 12 pp 2547ndash2554 2009

[14] M L McCloud and L L Scharf ldquoA new subspace identificationalgorithm for high-resolution DOA estimationrdquo IEEE Transac-tions on Antennas and Propagation vol 50 no 10 pp 1382ndash1390 2002

[15] R Boyer andG Bouleux ldquoOblique projections for direction-of-arrival estimation with prior knowledgerdquo IEEE Transactions onSignal Processing vol 56 no 4 pp 1374ndash1387 2008

[16] H Hong X-P Mao C Hu R Guo W-B Deng and PJiang ldquoNarrow-band null phase-shift spatial filter based onoblique projectionrdquo in Proceedings of the IEEERadar Conference(RADAR rsquo13) pp 1ndash5 Ottawa Canada May 2013

[17] Z H Xu Y P Ni and L Jin ldquoResolution theory of polarizationsensitive array signalsrdquo in Proceedings of the CIE InternationalConference on Radar (ICR rsquo06) pp 1ndash4 IEEE Shanghai ChinaOctober 2006

[18] 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

[19] Y-M Wang X-P Mao J Zhang and H Hong ldquoA multi-domain collaborative filter based on polarization sensitivefrequency diverse arrayrdquo in Proceedings of the IEEE RadarConference pp 0507ndash0511 Cincinnati Ohio USA May 2014

[20] M Souden J Benesty and S Affes ldquoA study of the LCMVandMVDRnoise reduction filtersrdquo IEEE Transactions on SignalProcessing vol 58 no 9 pp 4925ndash4935 2010

[21] Y M Cui X P Mao and H Hong ldquoA novel adaptive filter forinterference suppressionrdquo in Proceedings of the IEEE Region 10Conference vol 31194 pp 1ndash5 IEEE 2013

[22] H C Chan ldquoCharacterization of ionospheric clutter in HFsurface wave radarrdquo Tech Rep 2003-114 Defence RampDCanadaOttawa Canada 2003

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VLSI Design

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DistributedSensor Networks

International Journal of

4 International Journal of Antennas and Propagation

32 Properties of the GOP Four fundamental propertiesof the GOP are presented The idempotence of GOP andthe oblique projection abilities are given respectively inProperty 1The connections of OP and orthogonal projectionwith GOP are shown in Property 2 The enlargement of theprinciple angle by GOP compared to OP is discussed inProperty 3 which implies a reduction of the noise poweroutput Lastly in Property 4 the maximized SINR conditionin GOP is presented

Property 1 Consider

E2AB120577 = EAB120577

EAB120577A = A

EAB120577B = 120577A

(24)

Examine (24) the GOP operator has equivalent filteringeffect when the operator is multiplied It recovers the desiredsignal without amplitude and phase distortion whereas partof the interference is projected into the target subspace and isreserved by GOPThe target signal after GOP filtering can beexpressed as

119878GOP (119905) =

A119867

A2EAB120577x (119905)

= 119904 (119905) + 120577119894 (119905) +

A119867

A2EAB120577n (119905)

(25)

Proof Since Pperp(Bminus120577A) is a square matrix and A is a column

vector we have

E2AB120577 = A (A119867Pperp(Bminus120577A)A)

minus1

A119867Pperp(Bminus120577A)

sdot A (A119867Pperp(Bminus120577A)A)

minus1

A119867Pperp(Bminus120577A)

= A (A119867Pperp(Bminus120577A)A)

minus1

(A119867Pperp(Bminus120577A)A)

times (A119867Pperp(Bminus120577A)A)

minus1

A119867Pperp(Bminus120577A)

= A (A119867Pperp(Bminus120577A)A)

minus1

A119867Pperp(Bminus120577A) = EAB120577

EAB120577A = A (A119867Pperp(Bminus120577A)A)

minus1

(A119867Pperp(Bminus120577A)A) = A

(26)

Since B minus 120577A is a column vector from (16) we have

Pperp(Bminus120577A) (B minus 120577A) = 0

EAB120577 (B minus 120577A) = A (A119867Pperp(Bminus120577A)A)

minus1

A119867Pperp(Bminus120577A) (B minus 120577A)

= 0 997904rArr EAB120577B = 120577A

(27)

Property 2 The ISC 120577 can be real or complex and its absolutevalue |120577| isin [0 1] When 120577 = ⟨AB⟩AB GOP becomesan orthogonal operator and

EAB120577 = PA 120577 =⟨AB⟩

A B

(28)

When 120577 = 0 GOP degrades to an OP and shares the sameexpression in (5) and

EAB120577 = EAB 120577 = 0 (29)

Proof Suppose 120577 equals the inner product of A and B

⟨A (B minus 120577A)⟩ = A119867 (B minus 120577A)

= A119867B minus

A119867AA119867BA B

= 0

(30)

Therefore subspace ⟨A⟩ is orthogonal to subspace ⟨B minus

120577A⟩ and substitute (16) into (23) we have

EAB120577 = (EAB120577)119867

= A (A119867A)

minus1

A119867 = PA (31)

where PA represents the orthogonal projection of ASuppose 120577 is set to zero hence

EAB120577 = A (A119867Pperp(Bminus120577A)A)

minus1

A119867Pperp(Bminus120577A)

= A (A119867PperpBA)

minus1

A119867PperpB = EAB

(32)

Correspondingly the target signal recovered by GOP andOP is identical in this case

119878GOP (119905) = 119878OP (119905) 120577 = 0 (33)

Property 3 The principle angle of GOP is adjusted by 120577When 120577 isin (0 cos120595] the principle angle of GOP can beenlarged which is given by

1205951015840

gt 120595 120577 isin (0 cos120595] (34)

where 1205951015840 represents the principle angle of GOP and 120595

represents the principle angle of OP under the sameA and BWith a proper setting of the ISC the principle angle betweensubspaces can be enlarged

International Journal of Antennas and Propagation 5

Proof The square of the cosine of the new principle angle is

cos21205951015840 =(A119867B1015840)

119867

(A119867B1015840)1003817100381710038171003817A1198671003817

100381710038171003817

2 1003817100381710038171003817B1015840100381710038171003817

1003817

2

=

(B minus 120577A)119867AA119867 (B minus 120577A)

A119867A (B minus 120577A)119867

(B minus 120577A)

=

(B119867A119867ABA119867A) minus 120577 (A119867B + B119867A) + 1205772A119867A

B119867B minus 120577 (A119867B + B119867A) + 1205772A119867A

=

(cos120595 minus 120577)2

1205772

minus 2120577 cos120595 + 1

=

1

1 + (1 minus cos2120595) (cos120595 minus 120577)2

(35)

Since (35) is a monotonically declining function of 120577

under the condition of 120577 isin [0 cos120595] it is evident that

1205951015840

= 120595 120577 = 0 (36)

or 1205951015840

gt 120595 120577 isin (0 cos120595] (37)

Equation (37) demonstrates that when 120577 is set in therange of (0 cos120595] the principle angle of GOP is enlargedAccording to the expression of output noise power in (12)the noise power of GOP will be less than that of OP

1198751015840

119899lt 119875119899

(38)

Property 4 Suppose INR is known a priori a maximizedSINR which is the SINR upper bound of GOP can beobtained and the corresponding ICS is given as

120577opt =

cos120595

1 + 119873 sdot INR sin2120595 (39)

such that the maximum SINR is obtained as

SINRmax =

(SIR + 119873 sdot SNR sin2120595) 119873 sdot SNRSIR + 119873 sdot SNR

(40)

where 119873 represents the number of array elements

Proof The SINR output of the GOP filter can be expressed as

SINR =

119875119904

1198751015840

119894+ 1198751015840119899

=

119875119904

1205772119875119894 + 119875119899119873 sin21205951015840

= (

1205772

SIR+

1

119873 sin21205951015840SNR)

minus1

= (

1205772

SIR+

1 minus 2120577 cos120595 + 1205772

119873 sin2120595SNR)

minus1

(41)

To have the maximum value of SINR the first orderderivative of (41) with respect to 120577 is taken therefore theoptimum 120577opt that will give the maximum SINR in (40) isobtained as in (39)

4 GOP in Spatial Filtering

By using the spatial difference between the target and inter-ference spatial filtering is an effective method to reduce thepower of unwanted signals including output noise In theconstruction of spatial GOP filter the design of ISC param-eter is flexible It can be generated by using the conventionaladaptive spatial filtering methods such as minimum variancedistortionless response (MVDR) algorithm [20]

The constrained criterion of MVDR is described as

minw w119879Rw

st w119867A = 1

(42)

where A is the spatial vector for the target signal and R =

119864x(119905)x119867(119905) represents the covariance matrix of the receivedsignal

The weight of MVDR can be obtained as

wMVDR = Rminus1A (A119867Rminus1A)

minus1

(43)

Therefore the ISC obtained from wMVDR is expressed as

120577MVDR = w119867MVDRB = (Rminus1A (A119867Rminus1A)

minus1

)

119867

B (44)

It should be noted that the restoration of the targetis not related to 120577 which is the fundamental property ofGOP as given in (25) The interference suppression effect isdetermined by 120577 only As a result except for MVDR moreadaptive beamforming methods can be utilized However asthe information required by MVDR is usually easy to obtainit is more representative to derive 120577 from wMVDR In thefollowing part the SINR performance of theMVDR OP andGOP with 120577 given in (44) is analyzed and compared

41 SINRs Comparison of GOP and MVDR The SINR per-formance of the GOP and MVDR filter is evaluated TheSINRs for GOP and MVDR filter are given in (45) and (46)respectively as

SINRGOP =

119864 |wA119904 (119899)|2

119864 |wB119894 (119899)|2 + 119864 |wn(119899)|

2

=

119864 |wA|2 1205902

119904

119864 |wB|2 1205902

119894+ |w|2

1205902119899

(45)

where w = A119867EAB120577A2 Consider

SINRMVDR =

119864 1003816100381610038161003816wMVDRA119904 (119899)

1003816100381610038161003816

2

119864 1003816100381610038161003816wMVDRB119894 (119899)

1003816100381610038161003816

2 + 119864

1003816100381610038161003816wMVDRn(119899)

1003816100381610038161003816

2

=

119864 1003816100381610038161003816wMVDRA

1003816100381610038161003816

2 1205902

119904

119864 1003816100381610038161003816wMVDRB

1003816100381610038161003816

2 1205902

119894+

1003816100381610038161003816wMVDR

1003816100381610038161003816

21205902119899

(46)

6 International Journal of Antennas and Propagation

Observing (13) (42) (43) and (44) we get

w119867A = w119867MVDRA

w119867B = w119867MVDRB

(47)

Substitute (47) into (45) and (46) it can be observed thatthe difference of output SINRs is decided by the power ofnoise after filtering

Investigating the objective function in (13) we get wGOPwhich satisfies min(w119867GOPwGOP) hence |wGOP|

2le |wMVDR|

2This leads to

SINRGOP ge SINRMVDR (48)

Both of these filters attempt to reduce the interference andnoise while producing the distortionless response Howeverthe GOP filter has a better treatment to the noise andinterference which results in a higher SINR

42 SINRs Comparison of GOP and OP The SINR perfor-mance of the GOP and OP filter is evaluated The SINR forOP filter is written as

SINROP =

119864 1003816100381610038161003816wOPA119904 (119899)

1003816100381610038161003816

2

119864 1003816100381610038161003816wOPB119894 (119899)

1003816100381610038161003816

2 + 119864

1003816100381610038161003816wOPn(119899)

1003816100381610038161003816

2

=

1205902

119904

1205902119899

1003817100381710038171003817EAB

1003817100381710038171003817

2 A2

(49)

where wOP = A119867EABA2

Let the ratio between SINRs of GOP and OP filter be

119896 =

SINRGOPSINROP

=

1003817100381710038171003817EAB

1003817100381710038171003817

21205902

119899 A2

12057721205902

119894+

10038161003816100381610038161003816A119867EAB120577 A

210038161003816100381610038161003816

2

1205902119899

=

1

1198731205772INR sin2120595 +

1003817100381710038171003817B minus 120577A1003817

100381710038171003817

2119873

=

1

1198851205772

minus 2 cos120595120577 + 1

(50)

where 119885 = 1 + 119873 sin2120595INR A2

= 119873 and 119873 is the numberof the array elements

As the value of 119896 is determined by the principle angleINR the number of array elements and ISC simultaneouslyit is not easy to be analyzed without numerical evaluationsHowever we can make a reasonable assumption under twoextreme cases where spatial difference between the target andinterference approaches 90 degrees or 0 degrees

Case 1 (120595 rarr 90∘) The angular separation between target

and interference is nearly orthogonal which means thespatial difference ismaximized An aggressive action is taken

and the interference is expected to be eliminated completelyRewrite (50) as

1198961 =

1

119873 sin21205951205761 + 21205751 + 1 + 1205772 (51)

where 1205761 = 1205772INR and 1205751 = 120577 cos120595

To evaluate (51) numerically let 120595 = 898∘ and 120577 = 0 we

have sin2120595 asymp 1 1205772 = 0 and 1205751 = 0 Since the INR is boundedby a practical maximum of 60 dB we have 1205761 = 0 1198961 = 1 and

SINRGOP = SINROP (52)

Case 2 (120595 rarr 0∘) When the angular separation between

target and interference is very close the principle angle isnear zero For OP filter its SINR is not satisfying due tothe amplified noise power as given in (12) However theproposed GOP filter can be expected to be more conservativein rejecting the interference and shifting the focus in reducingthe noise power output That means when INR is low whichmeans noise power is comparably high the ISC is approach-ing one However if noise power is comparably much lowerthan interference resulting in a very high INR the ISC isapproaching zero to facilitate interference suppression Werewrite (50) as

1198962 =

1

1198731205762 + 1205752 + 1205772 (53)

where 1205762 = (120577 sin120595)2INR and 1205751 = 2120577 cos120595 + 1

To evaluate (53) numerically let 120595 = 001∘ and 120577 isin

[10minus5

1] we have sin2120595 = 0 hence 1205762 = 0 Therefore wehave 1205752 + 120577

2ge 1 1198962 ge 1 and

SINRGOP ge SINROP (54)

From the theoretical analysis of the two cases the SINRoutputs from both filters have an identical performance whenthe spatial difference between the target and interference islarge However GOP filter has a superior performance thanOP filter when the spatial difference is small

Moreover according to Property 4 of GOP there is anoptimized 120577opt in maximizing SINR output if the INR canbe obtained in advance By substituting (39) (50) can berewritten as

119896 =

1

119885 (120577opt minus cos120595119885)

2

+ 1 minus cos2120595119885

=

1

1 minus cos2120595119885

ge 1

(55)

where 120577opt = cos120595119885Therefore we have

SINRGOP ge SINROP (56)

43 Simulations Assume an ULA of 10 antenna elementswith half wavelength spacing between adjacent elements thecarrier frequency is 1198910 = 5MHz Under the conditions of

International Journal of Antennas and Propagation 7

0 10 20 30 40 50 60 70 80 90

0

10

20

30

SIN

R im

prov

emen

t (dB

)

84 85 86 87 88 89 90

1981985

1991995

202005

minus40

minus30

minus20

minus10

120595 (deg)

OptimumMVDR

OPGOP

Figure 1 SINR improvement versus 120595

20 25 30 35 40 45 50 55 6015

20

25

30

35

40

45

50

55

60

65

INR (dB)

SIN

R im

prov

emen

t (dB

)

MVDR (SIR = minus30dB)OP (SIR = minus30dB)GOP (SIR = minus30dB)MVDR (SIR = minus20dB)OP (SIR = minus20dB)

GOP (SIR = minus20dB)MVDR (SIR = minus10dB)OP (SIR = minus10dB)GOP (SIR = minus10dB)

Figure 2 SINR improvement versus INR for Case 1

SNR = 10 dB and SIR = minus10 dB the SINR improvementversus 120595 for MVDR OP GOP and GOP with optimum ISCis shown in Figure 1

From Figure 1 it can be observed that the principle angleshave great impacts on the SINR performance of the threespatial filters With the principle angle less than 10 degreesa sharper decrease appears in SINR for the OP filter thanboth GOP and MVDR filters However when the principleangle increases to nearly 90 degrees GOP and OP filtersperform slightly better than MVDR filter The GOP spatialfilter demonstrates a superior performance than OP and

20 25 30 35 40 45 50 55 60

0

5

10

15

INR (dB)

SIN

R im

prov

emen

t (dB

)

MVDR (SIR = minus30dB)OP (SIR = minus30dB)GOP (SIR = minus30dB)MVDR (SIR = minus20dB)OP (SIR = minus20dB)

GOP (SIR = minus20dB)MVDR (SIR = minus10dB)OP (SIR = minus10dB)GOP (SIR = minus10dB)

minus35

minus30

minus25

minus20

minus15

minus10

minus5

Figure 3 SINR improvement versus INR for Case 2

MVDR filters in the whole angle range further it coincideswith the maximized SINR derived in (40)

In the following the principle angle is fixed and theperformances of three filters under different INRs are inves-tigated The INRs span from 20 dB to 60 dB while the SIRsare of minus10 dB minus20 dB and minus30 dB respectively The principleangles are set to near 90 degrees and 0 degrees respectivelywhich correspond to the cases in Section 42

In Figures 2 and 3 the principle angles are set to 898degrees and 018 degrees respectively which correspond toCases 1 and 2 It is found that the ISC varies slightly aroundzero when the INRs change for Case 1 and ISC varies inrange of [27 times 10

minus5 1] for Case 2 As shown in Figure 2 the

SINR improvements of the GOP and OP increase linearlywith INRs however the MVDR shows an inferior SINRimprovement In Figure 3 the principle angle is small whichmeans that the spatial difference between the target andinterference reducesThe noise power amplifying effect of OPis significant resulting in a severe SINR performance lossIn contrast the GOP and MVDR filters have better SINRimprovements which exceed 30 dB at highest than OP filterIn general the GOP filter generates a superior performancethan both OP and MVDR filters The numerical simulationshave verified the theoretical analysis of the spatial filterspresented

5 GOP in Polarization Filtering of HF Radar

High frequency surface wave radar (HFSWR) [22] operatesin the short wave band which facilities the over-the-horizondetection over the sea surface However signals in this bandwill also get reflected by the ionosphere leading to a stronginterference to the target detection or sea state remote sens-ing In this section we explored the polarization information

8 International Journal of Antennas and Propagation

in the HFSWR and extended the application of the GOP filterin polarization filtering further a challenging ionosphericclutter mitigation problem in HFSWR is addressed

51 Generalized Oblique Projection Polarization Filter Asthe linear signal model presented in (4) a pair of thepolarization parameters represent the amplitude relationshipand the phase difference between the echoes received by theorthogonal dual-polarized radar sensor

Suppose the polarization parameters of the target andinterference are different then the target polarization sub-space ⟨Ps⟩ and interference polarization subspace ⟨Pi⟩ aredisjoint Note that the polarization subspace is independentof the specific radar signal waveforms The polarizationsubspace is constructed by the difference of the polarizationstate Therefore the target and interference subspaces in (23)can be given as

A = [

cos 120574119904

sin 120574119904119890119895120578119904] B = [

cos 120574119894

sin 120574119894119890119895120578119894] (57)

where 120574 and 120578 are the polarization pair with subscripts 119904 and119894 representing target and interference

There are two sets of the parameters that need to bedecided that is the echoes polarization set and the ISC Thepolarization angle is obtained as

120574 = 119905119892minus1

(

1003816100381610038161003816119909119881 (119905)

1003816100381610038161003816

1003816100381610038161003816119909119867 (119905)

1003816100381610038161003816

) (58)

and the polarization phase difference as

120578 = arg (119909119881 (119905)) minus arg (119909119867 (119905)) (59)

where 119909119881(119905) 119909119867(119905) represent the vertically and horizontallypolarized signal components and arg(sdot sdot sdot ) indicates phase ofthe signal

By the inflexibility of the polarized state in the temporaldomain and the frequency domain [18] these parameters canbe calculated using frequency transformed signal also TheISC is a free variable which can be designed according to thespecific application

However it can be proved that if the ISC is set to zerothis GOP polarization filter becomesOP polarization filter Inconstrained condition that is subspace ⟨Ps⟩ is orthogonal to⟨Pi⟩ the GOP polarization filter degrades into an orthogonalpolarization filter

52 Ionospheric Clutter Cancellation in HFSWR The char-acteristics of the ionosphere reflected echoes received byHFSWR are

(1) nonstationary(2) multiclutters(3) widely spread in range and Doppler bins

In addition to that there are ionospheric clutters return-ing from the sea surface whichmake their polarization statesclose to the target or the spatial difference between the

Time domain signal

Segmentations and FFT

Frequency domainpolarization estimations

Coherentintegration

Logic product

GOP filtering fortime segment 1

GOP filtering for

1st clutterGOP filtering fortime segment 1

GOP filtering for

Filtering output

time segment K time segment K

Jth clutter

middot middot middot

Figure 4 Ionospheric clutter mitigation process flow

clutters and target is not obvious Those characteristics leadto an unsolved clutter mitigation problem so far

As the radar arrays cannot effectively distinguish thetarget and interference spatially in this scenario the arraypolarization diversity and the coherent integration processare explored To handle those characteristics segmentationsof the time domain signals are introduced in an effort toapproach the real clutter parameters andmultipleGOPfilterswith flexible parameters 120577 are constructed The flowchart toillustrate the ionospheric clutter mitigation process is shownin Figure 4

In the dual-polarized HFSWR system the time domainsignal is range processed After proper signal segmentationsthe polarization states are estimated according to (58) and(59) with frequency transformed signal componentsThe sig-nals returned from the ship target over sea surface will retainvertically polarized state whereas the ionosphere reflectedclutters will be ellipse polarized with strong horizontallypolarized components The target and clutter polarizationsubspaces (A and B for GOP) are therefore obtained by thepolarization threshold A total number of 119870 segments of thetime divided data after filtering are connected and coherentintegration is performed However by the special designof GOP polarization filter an extra integration loss to theionospheric clutter will be brought in

By Property 1 of GOP the target polarization subspacesare retained while the ionospheric clutters are controlledby the free variable 120577 which is designed to introducerandom phase shift Therefore after GOP processing asignificant coherent integration loss will be introduced tothe ionospheric clutters when the time divided segmentsare reconnected and fast Fourier transformed However thetargetrsquos amplitude and phase are unchanged and its coherentintegration performance is not affected

The free variable of 120577(119899) is designed as

120577 (119899) = rnd (1205751 1205752 119899) 119890119895rnd(120573

11205732119899)

119899 isin [1 119870] (60)

where rnd(1205751 1205752 119899) represents random arrays from the uni-form distribution with amplitude range [1205751 1205752] and random

International Journal of Antennas and Propagation 9

20 40 60 80 100 1200

5

10

15

20

25

Segment numbers

Coh

eren

t int

egra

tion

loss

(dB)

120590120573 = 21205875

120590120573 = 1205872

120590120573 = 120587

120590120573 = 2120587

Figure 5 Coherent loss versus segment numbers under differentphase ranges

phase term 119890119895rnd(120573

11205732119899) with phase range [1205731 1205732] and 119899

denotes the sequence number of 120577 generatedIn deciding the parameters of 120577 the number of segmen-

tation and the phase ranges are of importance In Figure 5the segmentation number is chosen to be 64 and at that pointphase range of [0 2120587] is picked by simulation results of idealexponential signals The reasons are that more segmentationnumbers can only introduce at most 3 dB loss further whilemore segments indicate shorter time in coherent integrationand result in more estimation errors which may degradethe performance of the filter Therefore the parameters areobtained in consideration of the extra coherent loss andpotential estimation error

After logic product process [18] which reserves thesmallest points in Doppler spectrum from all the filteringresults the final output in each range bin is obtained as

Y (120596) =

119873

sum

119899=1

120575 (120596 minus 120596119899)

times

119869

min119895=1

(FFT[

119870

sum

119896=1

EAB120585119896119895x119896 (119899seg119896)])

(61)

where 119873 represents the length of FFT 120596119899 represents thefrequency at point 119899 119869 represents the total number of theclutters 119870 is the total number of segmentations EAB120585119896119895is the 119896th GOP in time domain for the suppression of 119895thclutter and x119896(119899seg119896) is the 119896th time segmented datawith 119899seg119896denoting the sampled points in the corresponding segment

In the HFSWR field experiment the vertically polarizedsignal was transmitted with a carrier frequency of 7Mhzby a half-wave dipole antenna The data was collected by adistant polarized high frequency linear array with 15-meterseparation between the vertically and horizontally polarizedelements The coherent integration time was 4 minutes

50 100 150 200 250

Doppler bins

Pow

er (d

B)

After filteringBefore filtering

Target

minus90

minus80

minus70

minus60

minus50

minus40

minus30

minus20

minus10

Figure 6 Doppler spectrum at range bin 79

Figure 6 gives theDoppler spectrumafter integration at rangebin 79 which is obtained from experimentally derived datawith red dashed line denoting spectrum before filtering andblue solid line denoting spectrum after process It can beobserved that there are several peaks well above minus30 dBbefore filtering which create an unfavorable ship detectionenvironment However the ship target at Doppler bin 183can be distinguished easily since the ionospheric clutters aresuppressed by about 10 dB in average whereas the targetsignal is undistorted

Besides ship detection the other focus can be drawn onthe sea state remote sensing A successful sea state inversionalgorithm depends on the correct and accurate extractionsof Bragg In Figure 7 the double first order Bragg peaks atDoppler bins (in between the vertically green dashed lines)are contaminated by the ionospheric clutters After GOPfiltering the contaminations of ionosphere are minimizedmoreover the SINR of the negative Bragg peaks was raisedaround 12 dB which facilitates its extraction algorithms

The Doppler spectrums from all the range bins arethen collected together forming a range-Doppler spectrumFigure 8(a) presents the original range-Doppler spectrumwhich is contaminated by the ionospheric clutters fromrange bins 73 to 96 whereas Figure 8(b) describes thespectrum after being processed by GOP filters Obviouslythe ionospheric clutters which widely spread in range andDoppler bins are suppressed effectively The average SINRimprovement is above 10 dB in this experiment

6 Conclusions

In this paper a novel GOP with adjustable ISC parameter hasbeen proposed It is proved to be an extension of OP andfour fundamental properties are presented with proofs Theconstruction of GOP filters is demonstrated with examplesof spatial and polarization filtering respectively In thefirst example with ISC derived from adaptive beamforming

10 International Journal of Antennas and Propagation

After filteringBefore filtering

50 100 150 200 250Doppler bins

Pow

er (d

B)

Positive BraggNegative Bragg

minus90

minus80

minus70

minus60

minus50

minus40

minus30

minus20

minus10

Figure 7 Doppler spectrum at range bin 89

20

40

60

80

100

120

140

160

50 100 150 200 250Doppler bins

Rang

e bin

s

(a) Original range-Doppler spectrum

20

40

60

80

100

120

140

160

50 100 150 200 250Doppler bins

Rang

e bin

s

(b) Range-Doppler spectrum after GOP filter

Figure 8 Range-Doppler spectrum of HFSWR

algorithm the SINR performance of GOP filter is shownto be better than MVDR and OP filters both theoreticallyand numerically A GOP polarization filter is constructedwith manually designed ISC in the second example An extracoherent loss is introduced to the ionospheric clutters bypurpose and a satisfying clutter suppression result inHFSWRis achieved Besides the examples givenmore designs of GOPfilter can be inspired by the flexibilities of ISC It can beconcluded that GOP filter is a promising filtering techniquefor interference suppression and capable of being used inspatial filtering polarization filtering and other array signalprocessing applications

Conflict of Interests

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

Acknowledgments

This project is sponsored by the National Marine TechnologyProgram for Public Welfare (no 200905029) National Nat-ural Science Foundation of China (no 61171180) and TeamResearch Foundation for Fundamental Research Program inFIO China (no GY0213T03)

References

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

[2] L Rebollo-Neira ldquoOblique matching pursuitrdquo IEEE SignalProcessing Letters vol 14 no 10 pp 703ndash706 2007

[3] GW Stewart ldquoOn the numerical analysis of oblique projectorsrdquoSIAM Journal on Matrix Analysis and Applications vol 32 no1 pp 309ndash348 2011

International Journal of Antennas and Propagation 11

[4] X-P Mao A-J Liu H-J Hou H Hong R Guo and W-BDeng ldquoOblique projection polarisation filtering for interferencesuppression in high-frequency surface wave radarrdquo IET RadarSonar and Navigation vol 6 no 2 pp 71ndash80 2012

[5] 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 (Chinese)

[6] Q-Y Zhang B Cao L Jin and N-T Zhang ldquoOblique pro-jection polarization filtering-based interference suppressionsfor radar sensor networksrdquo EURASIP Journal on WirelessCommunications and Networking vol 2010 Article ID 6051032010

[7] X Yu and L Tong ldquoJoint channel and symbol estimation byoblique projectionsrdquo IEEE Transactions on Signal Processingvol 49 no 12 pp 3074ndash3083 2001

[8] Q Zhang B Cao JWang and N Zhang ldquoPolarization filteringtechnique based on oblique projectionsrdquo Science China F vol53 no 5 pp 1056ndash1066 2010

[9] Y Cui K Liu and J Wang ldquoDirection-of-arrival estimationfor coherent GPS signals based on oblique projectionrdquo SignalProcessing vol 92 no 1 pp 294ndash299 2012

[10] Y Hu X Zhang F Zhu and H Lv ldquoImage recognition usingiterative oblique projectionrdquo Electronics Letters vol 41 no 20pp 1109ndash1110 2005

[11] G Hellbourg R Weber C Capdessus and A-J BoonstraldquoOblique projection beamforming for RFI mitigation in radioastronomyrdquo in Proceedings of the IEEE Statistical Signal Process-ing Workshop (SSP rsquo12) pp 93ndash96 IEEE August 2012

[12] P De ldquoNew methods for sensing bandlimited signals in cogni-tive radiordquo in Proceedings of the IEEE 65th Vehicular TechnologyConference (VTC 07-Spring) pp 1916ndash1920 Dublin IrelandApril 2007

[13] R Boyer ldquoOblique projection for source estimation in a com-petitive environment algorithm and statistical analysisrdquo SignalProcessing vol 89 no 12 pp 2547ndash2554 2009

[14] M L McCloud and L L Scharf ldquoA new subspace identificationalgorithm for high-resolution DOA estimationrdquo IEEE Transac-tions on Antennas and Propagation vol 50 no 10 pp 1382ndash1390 2002

[15] R Boyer andG Bouleux ldquoOblique projections for direction-of-arrival estimation with prior knowledgerdquo IEEE Transactions onSignal Processing vol 56 no 4 pp 1374ndash1387 2008

[16] H Hong X-P Mao C Hu R Guo W-B Deng and PJiang ldquoNarrow-band null phase-shift spatial filter based onoblique projectionrdquo in Proceedings of the IEEERadar Conference(RADAR rsquo13) pp 1ndash5 Ottawa Canada May 2013

[17] Z H Xu Y P Ni and L Jin ldquoResolution theory of polarizationsensitive array signalsrdquo in Proceedings of the CIE InternationalConference on Radar (ICR rsquo06) pp 1ndash4 IEEE Shanghai ChinaOctober 2006

[18] 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

[19] Y-M Wang X-P Mao J Zhang and H Hong ldquoA multi-domain collaborative filter based on polarization sensitivefrequency diverse arrayrdquo in Proceedings of the IEEE RadarConference pp 0507ndash0511 Cincinnati Ohio USA May 2014

[20] M Souden J Benesty and S Affes ldquoA study of the LCMVandMVDRnoise reduction filtersrdquo IEEE Transactions on SignalProcessing vol 58 no 9 pp 4925ndash4935 2010

[21] Y M Cui X P Mao and H Hong ldquoA novel adaptive filter forinterference suppressionrdquo in Proceedings of the IEEE Region 10Conference vol 31194 pp 1ndash5 IEEE 2013

[22] H C Chan ldquoCharacterization of ionospheric clutter in HFsurface wave radarrdquo Tech Rep 2003-114 Defence RampDCanadaOttawa Canada 2003

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Submit your manuscripts athttpwwwhindawicom

VLSI Design

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Shock and Vibration

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Electrical and Computer Engineering

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Volume 2014

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Chemical EngineeringInternational Journal of Antennas and

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Navigation and Observation

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DistributedSensor Networks

International Journal of

International Journal of Antennas and Propagation 5

Proof The square of the cosine of the new principle angle is

cos21205951015840 =(A119867B1015840)

119867

(A119867B1015840)1003817100381710038171003817A1198671003817

100381710038171003817

2 1003817100381710038171003817B1015840100381710038171003817

1003817

2

=

(B minus 120577A)119867AA119867 (B minus 120577A)

A119867A (B minus 120577A)119867

(B minus 120577A)

=

(B119867A119867ABA119867A) minus 120577 (A119867B + B119867A) + 1205772A119867A

B119867B minus 120577 (A119867B + B119867A) + 1205772A119867A

=

(cos120595 minus 120577)2

1205772

minus 2120577 cos120595 + 1

=

1

1 + (1 minus cos2120595) (cos120595 minus 120577)2

(35)

Since (35) is a monotonically declining function of 120577

under the condition of 120577 isin [0 cos120595] it is evident that

1205951015840

= 120595 120577 = 0 (36)

or 1205951015840

gt 120595 120577 isin (0 cos120595] (37)

Equation (37) demonstrates that when 120577 is set in therange of (0 cos120595] the principle angle of GOP is enlargedAccording to the expression of output noise power in (12)the noise power of GOP will be less than that of OP

1198751015840

119899lt 119875119899

(38)

Property 4 Suppose INR is known a priori a maximizedSINR which is the SINR upper bound of GOP can beobtained and the corresponding ICS is given as

120577opt =

cos120595

1 + 119873 sdot INR sin2120595 (39)

such that the maximum SINR is obtained as

SINRmax =

(SIR + 119873 sdot SNR sin2120595) 119873 sdot SNRSIR + 119873 sdot SNR

(40)

where 119873 represents the number of array elements

Proof The SINR output of the GOP filter can be expressed as

SINR =

119875119904

1198751015840

119894+ 1198751015840119899

=

119875119904

1205772119875119894 + 119875119899119873 sin21205951015840

= (

1205772

SIR+

1

119873 sin21205951015840SNR)

minus1

= (

1205772

SIR+

1 minus 2120577 cos120595 + 1205772

119873 sin2120595SNR)

minus1

(41)

To have the maximum value of SINR the first orderderivative of (41) with respect to 120577 is taken therefore theoptimum 120577opt that will give the maximum SINR in (40) isobtained as in (39)

4 GOP in Spatial Filtering

By using the spatial difference between the target and inter-ference spatial filtering is an effective method to reduce thepower of unwanted signals including output noise In theconstruction of spatial GOP filter the design of ISC param-eter is flexible It can be generated by using the conventionaladaptive spatial filtering methods such as minimum variancedistortionless response (MVDR) algorithm [20]

The constrained criterion of MVDR is described as

minw w119879Rw

st w119867A = 1

(42)

where A is the spatial vector for the target signal and R =

119864x(119905)x119867(119905) represents the covariance matrix of the receivedsignal

The weight of MVDR can be obtained as

wMVDR = Rminus1A (A119867Rminus1A)

minus1

(43)

Therefore the ISC obtained from wMVDR is expressed as

120577MVDR = w119867MVDRB = (Rminus1A (A119867Rminus1A)

minus1

)

119867

B (44)

It should be noted that the restoration of the targetis not related to 120577 which is the fundamental property ofGOP as given in (25) The interference suppression effect isdetermined by 120577 only As a result except for MVDR moreadaptive beamforming methods can be utilized However asthe information required by MVDR is usually easy to obtainit is more representative to derive 120577 from wMVDR In thefollowing part the SINR performance of theMVDR OP andGOP with 120577 given in (44) is analyzed and compared

41 SINRs Comparison of GOP and MVDR The SINR per-formance of the GOP and MVDR filter is evaluated TheSINRs for GOP and MVDR filter are given in (45) and (46)respectively as

SINRGOP =

119864 |wA119904 (119899)|2

119864 |wB119894 (119899)|2 + 119864 |wn(119899)|

2

=

119864 |wA|2 1205902

119904

119864 |wB|2 1205902

119894+ |w|2

1205902119899

(45)

where w = A119867EAB120577A2 Consider

SINRMVDR =

119864 1003816100381610038161003816wMVDRA119904 (119899)

1003816100381610038161003816

2

119864 1003816100381610038161003816wMVDRB119894 (119899)

1003816100381610038161003816

2 + 119864

1003816100381610038161003816wMVDRn(119899)

1003816100381610038161003816

2

=

119864 1003816100381610038161003816wMVDRA

1003816100381610038161003816

2 1205902

119904

119864 1003816100381610038161003816wMVDRB

1003816100381610038161003816

2 1205902

119894+

1003816100381610038161003816wMVDR

1003816100381610038161003816

21205902119899

(46)

6 International Journal of Antennas and Propagation

Observing (13) (42) (43) and (44) we get

w119867A = w119867MVDRA

w119867B = w119867MVDRB

(47)

Substitute (47) into (45) and (46) it can be observed thatthe difference of output SINRs is decided by the power ofnoise after filtering

Investigating the objective function in (13) we get wGOPwhich satisfies min(w119867GOPwGOP) hence |wGOP|

2le |wMVDR|

2This leads to

SINRGOP ge SINRMVDR (48)

Both of these filters attempt to reduce the interference andnoise while producing the distortionless response Howeverthe GOP filter has a better treatment to the noise andinterference which results in a higher SINR

42 SINRs Comparison of GOP and OP The SINR perfor-mance of the GOP and OP filter is evaluated The SINR forOP filter is written as

SINROP =

119864 1003816100381610038161003816wOPA119904 (119899)

1003816100381610038161003816

2

119864 1003816100381610038161003816wOPB119894 (119899)

1003816100381610038161003816

2 + 119864

1003816100381610038161003816wOPn(119899)

1003816100381610038161003816

2

=

1205902

119904

1205902119899

1003817100381710038171003817EAB

1003817100381710038171003817

2 A2

(49)

where wOP = A119867EABA2

Let the ratio between SINRs of GOP and OP filter be

119896 =

SINRGOPSINROP

=

1003817100381710038171003817EAB

1003817100381710038171003817

21205902

119899 A2

12057721205902

119894+

10038161003816100381610038161003816A119867EAB120577 A

210038161003816100381610038161003816

2

1205902119899

=

1

1198731205772INR sin2120595 +

1003817100381710038171003817B minus 120577A1003817

100381710038171003817

2119873

=

1

1198851205772

minus 2 cos120595120577 + 1

(50)

where 119885 = 1 + 119873 sin2120595INR A2

= 119873 and 119873 is the numberof the array elements

As the value of 119896 is determined by the principle angleINR the number of array elements and ISC simultaneouslyit is not easy to be analyzed without numerical evaluationsHowever we can make a reasonable assumption under twoextreme cases where spatial difference between the target andinterference approaches 90 degrees or 0 degrees

Case 1 (120595 rarr 90∘) The angular separation between target

and interference is nearly orthogonal which means thespatial difference ismaximized An aggressive action is taken

and the interference is expected to be eliminated completelyRewrite (50) as

1198961 =

1

119873 sin21205951205761 + 21205751 + 1 + 1205772 (51)

where 1205761 = 1205772INR and 1205751 = 120577 cos120595

To evaluate (51) numerically let 120595 = 898∘ and 120577 = 0 we

have sin2120595 asymp 1 1205772 = 0 and 1205751 = 0 Since the INR is boundedby a practical maximum of 60 dB we have 1205761 = 0 1198961 = 1 and

SINRGOP = SINROP (52)

Case 2 (120595 rarr 0∘) When the angular separation between

target and interference is very close the principle angle isnear zero For OP filter its SINR is not satisfying due tothe amplified noise power as given in (12) However theproposed GOP filter can be expected to be more conservativein rejecting the interference and shifting the focus in reducingthe noise power output That means when INR is low whichmeans noise power is comparably high the ISC is approach-ing one However if noise power is comparably much lowerthan interference resulting in a very high INR the ISC isapproaching zero to facilitate interference suppression Werewrite (50) as

1198962 =

1

1198731205762 + 1205752 + 1205772 (53)

where 1205762 = (120577 sin120595)2INR and 1205751 = 2120577 cos120595 + 1

To evaluate (53) numerically let 120595 = 001∘ and 120577 isin

[10minus5

1] we have sin2120595 = 0 hence 1205762 = 0 Therefore wehave 1205752 + 120577

2ge 1 1198962 ge 1 and

SINRGOP ge SINROP (54)

From the theoretical analysis of the two cases the SINRoutputs from both filters have an identical performance whenthe spatial difference between the target and interference islarge However GOP filter has a superior performance thanOP filter when the spatial difference is small

Moreover according to Property 4 of GOP there is anoptimized 120577opt in maximizing SINR output if the INR canbe obtained in advance By substituting (39) (50) can berewritten as

119896 =

1

119885 (120577opt minus cos120595119885)

2

+ 1 minus cos2120595119885

=

1

1 minus cos2120595119885

ge 1

(55)

where 120577opt = cos120595119885Therefore we have

SINRGOP ge SINROP (56)

43 Simulations Assume an ULA of 10 antenna elementswith half wavelength spacing between adjacent elements thecarrier frequency is 1198910 = 5MHz Under the conditions of

International Journal of Antennas and Propagation 7

0 10 20 30 40 50 60 70 80 90

0

10

20

30

SIN

R im

prov

emen

t (dB

)

84 85 86 87 88 89 90

1981985

1991995

202005

minus40

minus30

minus20

minus10

120595 (deg)

OptimumMVDR

OPGOP

Figure 1 SINR improvement versus 120595

20 25 30 35 40 45 50 55 6015

20

25

30

35

40

45

50

55

60

65

INR (dB)

SIN

R im

prov

emen

t (dB

)

MVDR (SIR = minus30dB)OP (SIR = minus30dB)GOP (SIR = minus30dB)MVDR (SIR = minus20dB)OP (SIR = minus20dB)

GOP (SIR = minus20dB)MVDR (SIR = minus10dB)OP (SIR = minus10dB)GOP (SIR = minus10dB)

Figure 2 SINR improvement versus INR for Case 1

SNR = 10 dB and SIR = minus10 dB the SINR improvementversus 120595 for MVDR OP GOP and GOP with optimum ISCis shown in Figure 1

From Figure 1 it can be observed that the principle angleshave great impacts on the SINR performance of the threespatial filters With the principle angle less than 10 degreesa sharper decrease appears in SINR for the OP filter thanboth GOP and MVDR filters However when the principleangle increases to nearly 90 degrees GOP and OP filtersperform slightly better than MVDR filter The GOP spatialfilter demonstrates a superior performance than OP and

20 25 30 35 40 45 50 55 60

0

5

10

15

INR (dB)

SIN

R im

prov

emen

t (dB

)

MVDR (SIR = minus30dB)OP (SIR = minus30dB)GOP (SIR = minus30dB)MVDR (SIR = minus20dB)OP (SIR = minus20dB)

GOP (SIR = minus20dB)MVDR (SIR = minus10dB)OP (SIR = minus10dB)GOP (SIR = minus10dB)

minus35

minus30

minus25

minus20

minus15

minus10

minus5

Figure 3 SINR improvement versus INR for Case 2

MVDR filters in the whole angle range further it coincideswith the maximized SINR derived in (40)

In the following the principle angle is fixed and theperformances of three filters under different INRs are inves-tigated The INRs span from 20 dB to 60 dB while the SIRsare of minus10 dB minus20 dB and minus30 dB respectively The principleangles are set to near 90 degrees and 0 degrees respectivelywhich correspond to the cases in Section 42

In Figures 2 and 3 the principle angles are set to 898degrees and 018 degrees respectively which correspond toCases 1 and 2 It is found that the ISC varies slightly aroundzero when the INRs change for Case 1 and ISC varies inrange of [27 times 10

minus5 1] for Case 2 As shown in Figure 2 the

SINR improvements of the GOP and OP increase linearlywith INRs however the MVDR shows an inferior SINRimprovement In Figure 3 the principle angle is small whichmeans that the spatial difference between the target andinterference reducesThe noise power amplifying effect of OPis significant resulting in a severe SINR performance lossIn contrast the GOP and MVDR filters have better SINRimprovements which exceed 30 dB at highest than OP filterIn general the GOP filter generates a superior performancethan both OP and MVDR filters The numerical simulationshave verified the theoretical analysis of the spatial filterspresented

5 GOP in Polarization Filtering of HF Radar

High frequency surface wave radar (HFSWR) [22] operatesin the short wave band which facilities the over-the-horizondetection over the sea surface However signals in this bandwill also get reflected by the ionosphere leading to a stronginterference to the target detection or sea state remote sens-ing In this section we explored the polarization information

8 International Journal of Antennas and Propagation

in the HFSWR and extended the application of the GOP filterin polarization filtering further a challenging ionosphericclutter mitigation problem in HFSWR is addressed

51 Generalized Oblique Projection Polarization Filter Asthe linear signal model presented in (4) a pair of thepolarization parameters represent the amplitude relationshipand the phase difference between the echoes received by theorthogonal dual-polarized radar sensor

Suppose the polarization parameters of the target andinterference are different then the target polarization sub-space ⟨Ps⟩ and interference polarization subspace ⟨Pi⟩ aredisjoint Note that the polarization subspace is independentof the specific radar signal waveforms The polarizationsubspace is constructed by the difference of the polarizationstate Therefore the target and interference subspaces in (23)can be given as

A = [

cos 120574119904

sin 120574119904119890119895120578119904] B = [

cos 120574119894

sin 120574119894119890119895120578119894] (57)

where 120574 and 120578 are the polarization pair with subscripts 119904 and119894 representing target and interference

There are two sets of the parameters that need to bedecided that is the echoes polarization set and the ISC Thepolarization angle is obtained as

120574 = 119905119892minus1

(

1003816100381610038161003816119909119881 (119905)

1003816100381610038161003816

1003816100381610038161003816119909119867 (119905)

1003816100381610038161003816

) (58)

and the polarization phase difference as

120578 = arg (119909119881 (119905)) minus arg (119909119867 (119905)) (59)

where 119909119881(119905) 119909119867(119905) represent the vertically and horizontallypolarized signal components and arg(sdot sdot sdot ) indicates phase ofthe signal

By the inflexibility of the polarized state in the temporaldomain and the frequency domain [18] these parameters canbe calculated using frequency transformed signal also TheISC is a free variable which can be designed according to thespecific application

However it can be proved that if the ISC is set to zerothis GOP polarization filter becomesOP polarization filter Inconstrained condition that is subspace ⟨Ps⟩ is orthogonal to⟨Pi⟩ the GOP polarization filter degrades into an orthogonalpolarization filter

52 Ionospheric Clutter Cancellation in HFSWR The char-acteristics of the ionosphere reflected echoes received byHFSWR are

(1) nonstationary(2) multiclutters(3) widely spread in range and Doppler bins

In addition to that there are ionospheric clutters return-ing from the sea surface whichmake their polarization statesclose to the target or the spatial difference between the

Time domain signal

Segmentations and FFT

Frequency domainpolarization estimations

Coherentintegration

Logic product

GOP filtering fortime segment 1

GOP filtering for

1st clutterGOP filtering fortime segment 1

GOP filtering for

Filtering output

time segment K time segment K

Jth clutter

middot middot middot

Figure 4 Ionospheric clutter mitigation process flow

clutters and target is not obvious Those characteristics leadto an unsolved clutter mitigation problem so far

As the radar arrays cannot effectively distinguish thetarget and interference spatially in this scenario the arraypolarization diversity and the coherent integration processare explored To handle those characteristics segmentationsof the time domain signals are introduced in an effort toapproach the real clutter parameters andmultipleGOPfilterswith flexible parameters 120577 are constructed The flowchart toillustrate the ionospheric clutter mitigation process is shownin Figure 4

In the dual-polarized HFSWR system the time domainsignal is range processed After proper signal segmentationsthe polarization states are estimated according to (58) and(59) with frequency transformed signal componentsThe sig-nals returned from the ship target over sea surface will retainvertically polarized state whereas the ionosphere reflectedclutters will be ellipse polarized with strong horizontallypolarized components The target and clutter polarizationsubspaces (A and B for GOP) are therefore obtained by thepolarization threshold A total number of 119870 segments of thetime divided data after filtering are connected and coherentintegration is performed However by the special designof GOP polarization filter an extra integration loss to theionospheric clutter will be brought in

By Property 1 of GOP the target polarization subspacesare retained while the ionospheric clutters are controlledby the free variable 120577 which is designed to introducerandom phase shift Therefore after GOP processing asignificant coherent integration loss will be introduced tothe ionospheric clutters when the time divided segmentsare reconnected and fast Fourier transformed However thetargetrsquos amplitude and phase are unchanged and its coherentintegration performance is not affected

The free variable of 120577(119899) is designed as

120577 (119899) = rnd (1205751 1205752 119899) 119890119895rnd(120573

11205732119899)

119899 isin [1 119870] (60)

where rnd(1205751 1205752 119899) represents random arrays from the uni-form distribution with amplitude range [1205751 1205752] and random

International Journal of Antennas and Propagation 9

20 40 60 80 100 1200

5

10

15

20

25

Segment numbers

Coh

eren

t int

egra

tion

loss

(dB)

120590120573 = 21205875

120590120573 = 1205872

120590120573 = 120587

120590120573 = 2120587

Figure 5 Coherent loss versus segment numbers under differentphase ranges

phase term 119890119895rnd(120573

11205732119899) with phase range [1205731 1205732] and 119899

denotes the sequence number of 120577 generatedIn deciding the parameters of 120577 the number of segmen-

tation and the phase ranges are of importance In Figure 5the segmentation number is chosen to be 64 and at that pointphase range of [0 2120587] is picked by simulation results of idealexponential signals The reasons are that more segmentationnumbers can only introduce at most 3 dB loss further whilemore segments indicate shorter time in coherent integrationand result in more estimation errors which may degradethe performance of the filter Therefore the parameters areobtained in consideration of the extra coherent loss andpotential estimation error

After logic product process [18] which reserves thesmallest points in Doppler spectrum from all the filteringresults the final output in each range bin is obtained as

Y (120596) =

119873

sum

119899=1

120575 (120596 minus 120596119899)

times

119869

min119895=1

(FFT[

119870

sum

119896=1

EAB120585119896119895x119896 (119899seg119896)])

(61)

where 119873 represents the length of FFT 120596119899 represents thefrequency at point 119899 119869 represents the total number of theclutters 119870 is the total number of segmentations EAB120585119896119895is the 119896th GOP in time domain for the suppression of 119895thclutter and x119896(119899seg119896) is the 119896th time segmented datawith 119899seg119896denoting the sampled points in the corresponding segment

In the HFSWR field experiment the vertically polarizedsignal was transmitted with a carrier frequency of 7Mhzby a half-wave dipole antenna The data was collected by adistant polarized high frequency linear array with 15-meterseparation between the vertically and horizontally polarizedelements The coherent integration time was 4 minutes

50 100 150 200 250

Doppler bins

Pow

er (d

B)

After filteringBefore filtering

Target

minus90

minus80

minus70

minus60

minus50

minus40

minus30

minus20

minus10

Figure 6 Doppler spectrum at range bin 79

Figure 6 gives theDoppler spectrumafter integration at rangebin 79 which is obtained from experimentally derived datawith red dashed line denoting spectrum before filtering andblue solid line denoting spectrum after process It can beobserved that there are several peaks well above minus30 dBbefore filtering which create an unfavorable ship detectionenvironment However the ship target at Doppler bin 183can be distinguished easily since the ionospheric clutters aresuppressed by about 10 dB in average whereas the targetsignal is undistorted

Besides ship detection the other focus can be drawn onthe sea state remote sensing A successful sea state inversionalgorithm depends on the correct and accurate extractionsof Bragg In Figure 7 the double first order Bragg peaks atDoppler bins (in between the vertically green dashed lines)are contaminated by the ionospheric clutters After GOPfiltering the contaminations of ionosphere are minimizedmoreover the SINR of the negative Bragg peaks was raisedaround 12 dB which facilitates its extraction algorithms

The Doppler spectrums from all the range bins arethen collected together forming a range-Doppler spectrumFigure 8(a) presents the original range-Doppler spectrumwhich is contaminated by the ionospheric clutters fromrange bins 73 to 96 whereas Figure 8(b) describes thespectrum after being processed by GOP filters Obviouslythe ionospheric clutters which widely spread in range andDoppler bins are suppressed effectively The average SINRimprovement is above 10 dB in this experiment

6 Conclusions

In this paper a novel GOP with adjustable ISC parameter hasbeen proposed It is proved to be an extension of OP andfour fundamental properties are presented with proofs Theconstruction of GOP filters is demonstrated with examplesof spatial and polarization filtering respectively In thefirst example with ISC derived from adaptive beamforming

10 International Journal of Antennas and Propagation

After filteringBefore filtering

50 100 150 200 250Doppler bins

Pow

er (d

B)

Positive BraggNegative Bragg

minus90

minus80

minus70

minus60

minus50

minus40

minus30

minus20

minus10

Figure 7 Doppler spectrum at range bin 89

20

40

60

80

100

120

140

160

50 100 150 200 250Doppler bins

Rang

e bin

s

(a) Original range-Doppler spectrum

20

40

60

80

100

120

140

160

50 100 150 200 250Doppler bins

Rang

e bin

s

(b) Range-Doppler spectrum after GOP filter

Figure 8 Range-Doppler spectrum of HFSWR

algorithm the SINR performance of GOP filter is shownto be better than MVDR and OP filters both theoreticallyand numerically A GOP polarization filter is constructedwith manually designed ISC in the second example An extracoherent loss is introduced to the ionospheric clutters bypurpose and a satisfying clutter suppression result inHFSWRis achieved Besides the examples givenmore designs of GOPfilter can be inspired by the flexibilities of ISC It can beconcluded that GOP filter is a promising filtering techniquefor interference suppression and capable of being used inspatial filtering polarization filtering and other array signalprocessing applications

Conflict of Interests

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

Acknowledgments

This project is sponsored by the National Marine TechnologyProgram for Public Welfare (no 200905029) National Nat-ural Science Foundation of China (no 61171180) and TeamResearch Foundation for Fundamental Research Program inFIO China (no GY0213T03)

References

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

[2] L Rebollo-Neira ldquoOblique matching pursuitrdquo IEEE SignalProcessing Letters vol 14 no 10 pp 703ndash706 2007

[3] GW Stewart ldquoOn the numerical analysis of oblique projectorsrdquoSIAM Journal on Matrix Analysis and Applications vol 32 no1 pp 309ndash348 2011

International Journal of Antennas and Propagation 11

[4] X-P Mao A-J Liu H-J Hou H Hong R Guo and W-BDeng ldquoOblique projection polarisation filtering for interferencesuppression in high-frequency surface wave radarrdquo IET RadarSonar and Navigation vol 6 no 2 pp 71ndash80 2012

[5] 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 (Chinese)

[6] Q-Y Zhang B Cao L Jin and N-T Zhang ldquoOblique pro-jection polarization filtering-based interference suppressionsfor radar sensor networksrdquo EURASIP Journal on WirelessCommunications and Networking vol 2010 Article ID 6051032010

[7] X Yu and L Tong ldquoJoint channel and symbol estimation byoblique projectionsrdquo IEEE Transactions on Signal Processingvol 49 no 12 pp 3074ndash3083 2001

[8] Q Zhang B Cao JWang and N Zhang ldquoPolarization filteringtechnique based on oblique projectionsrdquo Science China F vol53 no 5 pp 1056ndash1066 2010

[9] Y Cui K Liu and J Wang ldquoDirection-of-arrival estimationfor coherent GPS signals based on oblique projectionrdquo SignalProcessing vol 92 no 1 pp 294ndash299 2012

[10] Y Hu X Zhang F Zhu and H Lv ldquoImage recognition usingiterative oblique projectionrdquo Electronics Letters vol 41 no 20pp 1109ndash1110 2005

[11] G Hellbourg R Weber C Capdessus and A-J BoonstraldquoOblique projection beamforming for RFI mitigation in radioastronomyrdquo in Proceedings of the IEEE Statistical Signal Process-ing Workshop (SSP rsquo12) pp 93ndash96 IEEE August 2012

[12] P De ldquoNew methods for sensing bandlimited signals in cogni-tive radiordquo in Proceedings of the IEEE 65th Vehicular TechnologyConference (VTC 07-Spring) pp 1916ndash1920 Dublin IrelandApril 2007

[13] R Boyer ldquoOblique projection for source estimation in a com-petitive environment algorithm and statistical analysisrdquo SignalProcessing vol 89 no 12 pp 2547ndash2554 2009

[14] M L McCloud and L L Scharf ldquoA new subspace identificationalgorithm for high-resolution DOA estimationrdquo IEEE Transac-tions on Antennas and Propagation vol 50 no 10 pp 1382ndash1390 2002

[15] R Boyer andG Bouleux ldquoOblique projections for direction-of-arrival estimation with prior knowledgerdquo IEEE Transactions onSignal Processing vol 56 no 4 pp 1374ndash1387 2008

[16] H Hong X-P Mao C Hu R Guo W-B Deng and PJiang ldquoNarrow-band null phase-shift spatial filter based onoblique projectionrdquo in Proceedings of the IEEERadar Conference(RADAR rsquo13) pp 1ndash5 Ottawa Canada May 2013

[17] Z H Xu Y P Ni and L Jin ldquoResolution theory of polarizationsensitive array signalsrdquo in Proceedings of the CIE InternationalConference on Radar (ICR rsquo06) pp 1ndash4 IEEE Shanghai ChinaOctober 2006

[18] 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

[19] Y-M Wang X-P Mao J Zhang and H Hong ldquoA multi-domain collaborative filter based on polarization sensitivefrequency diverse arrayrdquo in Proceedings of the IEEE RadarConference pp 0507ndash0511 Cincinnati Ohio USA May 2014

[20] M Souden J Benesty and S Affes ldquoA study of the LCMVandMVDRnoise reduction filtersrdquo IEEE Transactions on SignalProcessing vol 58 no 9 pp 4925ndash4935 2010

[21] Y M Cui X P Mao and H Hong ldquoA novel adaptive filter forinterference suppressionrdquo in Proceedings of the IEEE Region 10Conference vol 31194 pp 1ndash5 IEEE 2013

[22] H C Chan ldquoCharacterization of ionospheric clutter in HFsurface wave radarrdquo Tech Rep 2003-114 Defence RampDCanadaOttawa Canada 2003

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VLSI Design

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Shock and Vibration

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Electrical and Computer Engineering

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Volume 2014

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DistributedSensor Networks

International Journal of

6 International Journal of Antennas and Propagation

Observing (13) (42) (43) and (44) we get

w119867A = w119867MVDRA

w119867B = w119867MVDRB

(47)

Substitute (47) into (45) and (46) it can be observed thatthe difference of output SINRs is decided by the power ofnoise after filtering

Investigating the objective function in (13) we get wGOPwhich satisfies min(w119867GOPwGOP) hence |wGOP|

2le |wMVDR|

2This leads to

SINRGOP ge SINRMVDR (48)

Both of these filters attempt to reduce the interference andnoise while producing the distortionless response Howeverthe GOP filter has a better treatment to the noise andinterference which results in a higher SINR

42 SINRs Comparison of GOP and OP The SINR perfor-mance of the GOP and OP filter is evaluated The SINR forOP filter is written as

SINROP =

119864 1003816100381610038161003816wOPA119904 (119899)

1003816100381610038161003816

2

119864 1003816100381610038161003816wOPB119894 (119899)

1003816100381610038161003816

2 + 119864

1003816100381610038161003816wOPn(119899)

1003816100381610038161003816

2

=

1205902

119904

1205902119899

1003817100381710038171003817EAB

1003817100381710038171003817

2 A2

(49)

where wOP = A119867EABA2

Let the ratio between SINRs of GOP and OP filter be

119896 =

SINRGOPSINROP

=

1003817100381710038171003817EAB

1003817100381710038171003817

21205902

119899 A2

12057721205902

119894+

10038161003816100381610038161003816A119867EAB120577 A

210038161003816100381610038161003816

2

1205902119899

=

1

1198731205772INR sin2120595 +

1003817100381710038171003817B minus 120577A1003817

100381710038171003817

2119873

=

1

1198851205772

minus 2 cos120595120577 + 1

(50)

where 119885 = 1 + 119873 sin2120595INR A2

= 119873 and 119873 is the numberof the array elements

As the value of 119896 is determined by the principle angleINR the number of array elements and ISC simultaneouslyit is not easy to be analyzed without numerical evaluationsHowever we can make a reasonable assumption under twoextreme cases where spatial difference between the target andinterference approaches 90 degrees or 0 degrees

Case 1 (120595 rarr 90∘) The angular separation between target

and interference is nearly orthogonal which means thespatial difference ismaximized An aggressive action is taken

and the interference is expected to be eliminated completelyRewrite (50) as

1198961 =

1

119873 sin21205951205761 + 21205751 + 1 + 1205772 (51)

where 1205761 = 1205772INR and 1205751 = 120577 cos120595

To evaluate (51) numerically let 120595 = 898∘ and 120577 = 0 we

have sin2120595 asymp 1 1205772 = 0 and 1205751 = 0 Since the INR is boundedby a practical maximum of 60 dB we have 1205761 = 0 1198961 = 1 and

SINRGOP = SINROP (52)

Case 2 (120595 rarr 0∘) When the angular separation between

target and interference is very close the principle angle isnear zero For OP filter its SINR is not satisfying due tothe amplified noise power as given in (12) However theproposed GOP filter can be expected to be more conservativein rejecting the interference and shifting the focus in reducingthe noise power output That means when INR is low whichmeans noise power is comparably high the ISC is approach-ing one However if noise power is comparably much lowerthan interference resulting in a very high INR the ISC isapproaching zero to facilitate interference suppression Werewrite (50) as

1198962 =

1

1198731205762 + 1205752 + 1205772 (53)

where 1205762 = (120577 sin120595)2INR and 1205751 = 2120577 cos120595 + 1

To evaluate (53) numerically let 120595 = 001∘ and 120577 isin

[10minus5

1] we have sin2120595 = 0 hence 1205762 = 0 Therefore wehave 1205752 + 120577

2ge 1 1198962 ge 1 and

SINRGOP ge SINROP (54)

From the theoretical analysis of the two cases the SINRoutputs from both filters have an identical performance whenthe spatial difference between the target and interference islarge However GOP filter has a superior performance thanOP filter when the spatial difference is small

Moreover according to Property 4 of GOP there is anoptimized 120577opt in maximizing SINR output if the INR canbe obtained in advance By substituting (39) (50) can berewritten as

119896 =

1

119885 (120577opt minus cos120595119885)

2

+ 1 minus cos2120595119885

=

1

1 minus cos2120595119885

ge 1

(55)

where 120577opt = cos120595119885Therefore we have

SINRGOP ge SINROP (56)

43 Simulations Assume an ULA of 10 antenna elementswith half wavelength spacing between adjacent elements thecarrier frequency is 1198910 = 5MHz Under the conditions of

International Journal of Antennas and Propagation 7

0 10 20 30 40 50 60 70 80 90

0

10

20

30

SIN

R im

prov

emen

t (dB

)

84 85 86 87 88 89 90

1981985

1991995

202005

minus40

minus30

minus20

minus10

120595 (deg)

OptimumMVDR

OPGOP

Figure 1 SINR improvement versus 120595

20 25 30 35 40 45 50 55 6015

20

25

30

35

40

45

50

55

60

65

INR (dB)

SIN

R im

prov

emen

t (dB

)

MVDR (SIR = minus30dB)OP (SIR = minus30dB)GOP (SIR = minus30dB)MVDR (SIR = minus20dB)OP (SIR = minus20dB)

GOP (SIR = minus20dB)MVDR (SIR = minus10dB)OP (SIR = minus10dB)GOP (SIR = minus10dB)

Figure 2 SINR improvement versus INR for Case 1

SNR = 10 dB and SIR = minus10 dB the SINR improvementversus 120595 for MVDR OP GOP and GOP with optimum ISCis shown in Figure 1

From Figure 1 it can be observed that the principle angleshave great impacts on the SINR performance of the threespatial filters With the principle angle less than 10 degreesa sharper decrease appears in SINR for the OP filter thanboth GOP and MVDR filters However when the principleangle increases to nearly 90 degrees GOP and OP filtersperform slightly better than MVDR filter The GOP spatialfilter demonstrates a superior performance than OP and

20 25 30 35 40 45 50 55 60

0

5

10

15

INR (dB)

SIN

R im

prov

emen

t (dB

)

MVDR (SIR = minus30dB)OP (SIR = minus30dB)GOP (SIR = minus30dB)MVDR (SIR = minus20dB)OP (SIR = minus20dB)

GOP (SIR = minus20dB)MVDR (SIR = minus10dB)OP (SIR = minus10dB)GOP (SIR = minus10dB)

minus35

minus30

minus25

minus20

minus15

minus10

minus5

Figure 3 SINR improvement versus INR for Case 2

MVDR filters in the whole angle range further it coincideswith the maximized SINR derived in (40)

In the following the principle angle is fixed and theperformances of three filters under different INRs are inves-tigated The INRs span from 20 dB to 60 dB while the SIRsare of minus10 dB minus20 dB and minus30 dB respectively The principleangles are set to near 90 degrees and 0 degrees respectivelywhich correspond to the cases in Section 42

In Figures 2 and 3 the principle angles are set to 898degrees and 018 degrees respectively which correspond toCases 1 and 2 It is found that the ISC varies slightly aroundzero when the INRs change for Case 1 and ISC varies inrange of [27 times 10

minus5 1] for Case 2 As shown in Figure 2 the

SINR improvements of the GOP and OP increase linearlywith INRs however the MVDR shows an inferior SINRimprovement In Figure 3 the principle angle is small whichmeans that the spatial difference between the target andinterference reducesThe noise power amplifying effect of OPis significant resulting in a severe SINR performance lossIn contrast the GOP and MVDR filters have better SINRimprovements which exceed 30 dB at highest than OP filterIn general the GOP filter generates a superior performancethan both OP and MVDR filters The numerical simulationshave verified the theoretical analysis of the spatial filterspresented

5 GOP in Polarization Filtering of HF Radar

High frequency surface wave radar (HFSWR) [22] operatesin the short wave band which facilities the over-the-horizondetection over the sea surface However signals in this bandwill also get reflected by the ionosphere leading to a stronginterference to the target detection or sea state remote sens-ing In this section we explored the polarization information

8 International Journal of Antennas and Propagation

in the HFSWR and extended the application of the GOP filterin polarization filtering further a challenging ionosphericclutter mitigation problem in HFSWR is addressed

51 Generalized Oblique Projection Polarization Filter Asthe linear signal model presented in (4) a pair of thepolarization parameters represent the amplitude relationshipand the phase difference between the echoes received by theorthogonal dual-polarized radar sensor

Suppose the polarization parameters of the target andinterference are different then the target polarization sub-space ⟨Ps⟩ and interference polarization subspace ⟨Pi⟩ aredisjoint Note that the polarization subspace is independentof the specific radar signal waveforms The polarizationsubspace is constructed by the difference of the polarizationstate Therefore the target and interference subspaces in (23)can be given as

A = [

cos 120574119904

sin 120574119904119890119895120578119904] B = [

cos 120574119894

sin 120574119894119890119895120578119894] (57)

where 120574 and 120578 are the polarization pair with subscripts 119904 and119894 representing target and interference

There are two sets of the parameters that need to bedecided that is the echoes polarization set and the ISC Thepolarization angle is obtained as

120574 = 119905119892minus1

(

1003816100381610038161003816119909119881 (119905)

1003816100381610038161003816

1003816100381610038161003816119909119867 (119905)

1003816100381610038161003816

) (58)

and the polarization phase difference as

120578 = arg (119909119881 (119905)) minus arg (119909119867 (119905)) (59)

where 119909119881(119905) 119909119867(119905) represent the vertically and horizontallypolarized signal components and arg(sdot sdot sdot ) indicates phase ofthe signal

By the inflexibility of the polarized state in the temporaldomain and the frequency domain [18] these parameters canbe calculated using frequency transformed signal also TheISC is a free variable which can be designed according to thespecific application

However it can be proved that if the ISC is set to zerothis GOP polarization filter becomesOP polarization filter Inconstrained condition that is subspace ⟨Ps⟩ is orthogonal to⟨Pi⟩ the GOP polarization filter degrades into an orthogonalpolarization filter

52 Ionospheric Clutter Cancellation in HFSWR The char-acteristics of the ionosphere reflected echoes received byHFSWR are

(1) nonstationary(2) multiclutters(3) widely spread in range and Doppler bins

In addition to that there are ionospheric clutters return-ing from the sea surface whichmake their polarization statesclose to the target or the spatial difference between the

Time domain signal

Segmentations and FFT

Frequency domainpolarization estimations

Coherentintegration

Logic product

GOP filtering fortime segment 1

GOP filtering for

1st clutterGOP filtering fortime segment 1

GOP filtering for

Filtering output

time segment K time segment K

Jth clutter

middot middot middot

Figure 4 Ionospheric clutter mitigation process flow

clutters and target is not obvious Those characteristics leadto an unsolved clutter mitigation problem so far

As the radar arrays cannot effectively distinguish thetarget and interference spatially in this scenario the arraypolarization diversity and the coherent integration processare explored To handle those characteristics segmentationsof the time domain signals are introduced in an effort toapproach the real clutter parameters andmultipleGOPfilterswith flexible parameters 120577 are constructed The flowchart toillustrate the ionospheric clutter mitigation process is shownin Figure 4

In the dual-polarized HFSWR system the time domainsignal is range processed After proper signal segmentationsthe polarization states are estimated according to (58) and(59) with frequency transformed signal componentsThe sig-nals returned from the ship target over sea surface will retainvertically polarized state whereas the ionosphere reflectedclutters will be ellipse polarized with strong horizontallypolarized components The target and clutter polarizationsubspaces (A and B for GOP) are therefore obtained by thepolarization threshold A total number of 119870 segments of thetime divided data after filtering are connected and coherentintegration is performed However by the special designof GOP polarization filter an extra integration loss to theionospheric clutter will be brought in

By Property 1 of GOP the target polarization subspacesare retained while the ionospheric clutters are controlledby the free variable 120577 which is designed to introducerandom phase shift Therefore after GOP processing asignificant coherent integration loss will be introduced tothe ionospheric clutters when the time divided segmentsare reconnected and fast Fourier transformed However thetargetrsquos amplitude and phase are unchanged and its coherentintegration performance is not affected

The free variable of 120577(119899) is designed as

120577 (119899) = rnd (1205751 1205752 119899) 119890119895rnd(120573

11205732119899)

119899 isin [1 119870] (60)

where rnd(1205751 1205752 119899) represents random arrays from the uni-form distribution with amplitude range [1205751 1205752] and random

International Journal of Antennas and Propagation 9

20 40 60 80 100 1200

5

10

15

20

25

Segment numbers

Coh

eren

t int

egra

tion

loss

(dB)

120590120573 = 21205875

120590120573 = 1205872

120590120573 = 120587

120590120573 = 2120587

Figure 5 Coherent loss versus segment numbers under differentphase ranges

phase term 119890119895rnd(120573

11205732119899) with phase range [1205731 1205732] and 119899

denotes the sequence number of 120577 generatedIn deciding the parameters of 120577 the number of segmen-

tation and the phase ranges are of importance In Figure 5the segmentation number is chosen to be 64 and at that pointphase range of [0 2120587] is picked by simulation results of idealexponential signals The reasons are that more segmentationnumbers can only introduce at most 3 dB loss further whilemore segments indicate shorter time in coherent integrationand result in more estimation errors which may degradethe performance of the filter Therefore the parameters areobtained in consideration of the extra coherent loss andpotential estimation error

After logic product process [18] which reserves thesmallest points in Doppler spectrum from all the filteringresults the final output in each range bin is obtained as

Y (120596) =

119873

sum

119899=1

120575 (120596 minus 120596119899)

times

119869

min119895=1

(FFT[

119870

sum

119896=1

EAB120585119896119895x119896 (119899seg119896)])

(61)

where 119873 represents the length of FFT 120596119899 represents thefrequency at point 119899 119869 represents the total number of theclutters 119870 is the total number of segmentations EAB120585119896119895is the 119896th GOP in time domain for the suppression of 119895thclutter and x119896(119899seg119896) is the 119896th time segmented datawith 119899seg119896denoting the sampled points in the corresponding segment

In the HFSWR field experiment the vertically polarizedsignal was transmitted with a carrier frequency of 7Mhzby a half-wave dipole antenna The data was collected by adistant polarized high frequency linear array with 15-meterseparation between the vertically and horizontally polarizedelements The coherent integration time was 4 minutes

50 100 150 200 250

Doppler bins

Pow

er (d

B)

After filteringBefore filtering

Target

minus90

minus80

minus70

minus60

minus50

minus40

minus30

minus20

minus10

Figure 6 Doppler spectrum at range bin 79

Figure 6 gives theDoppler spectrumafter integration at rangebin 79 which is obtained from experimentally derived datawith red dashed line denoting spectrum before filtering andblue solid line denoting spectrum after process It can beobserved that there are several peaks well above minus30 dBbefore filtering which create an unfavorable ship detectionenvironment However the ship target at Doppler bin 183can be distinguished easily since the ionospheric clutters aresuppressed by about 10 dB in average whereas the targetsignal is undistorted

Besides ship detection the other focus can be drawn onthe sea state remote sensing A successful sea state inversionalgorithm depends on the correct and accurate extractionsof Bragg In Figure 7 the double first order Bragg peaks atDoppler bins (in between the vertically green dashed lines)are contaminated by the ionospheric clutters After GOPfiltering the contaminations of ionosphere are minimizedmoreover the SINR of the negative Bragg peaks was raisedaround 12 dB which facilitates its extraction algorithms

The Doppler spectrums from all the range bins arethen collected together forming a range-Doppler spectrumFigure 8(a) presents the original range-Doppler spectrumwhich is contaminated by the ionospheric clutters fromrange bins 73 to 96 whereas Figure 8(b) describes thespectrum after being processed by GOP filters Obviouslythe ionospheric clutters which widely spread in range andDoppler bins are suppressed effectively The average SINRimprovement is above 10 dB in this experiment

6 Conclusions

In this paper a novel GOP with adjustable ISC parameter hasbeen proposed It is proved to be an extension of OP andfour fundamental properties are presented with proofs Theconstruction of GOP filters is demonstrated with examplesof spatial and polarization filtering respectively In thefirst example with ISC derived from adaptive beamforming

10 International Journal of Antennas and Propagation

After filteringBefore filtering

50 100 150 200 250Doppler bins

Pow

er (d

B)

Positive BraggNegative Bragg

minus90

minus80

minus70

minus60

minus50

minus40

minus30

minus20

minus10

Figure 7 Doppler spectrum at range bin 89

20

40

60

80

100

120

140

160

50 100 150 200 250Doppler bins

Rang

e bin

s

(a) Original range-Doppler spectrum

20

40

60

80

100

120

140

160

50 100 150 200 250Doppler bins

Rang

e bin

s

(b) Range-Doppler spectrum after GOP filter

Figure 8 Range-Doppler spectrum of HFSWR

algorithm the SINR performance of GOP filter is shownto be better than MVDR and OP filters both theoreticallyand numerically A GOP polarization filter is constructedwith manually designed ISC in the second example An extracoherent loss is introduced to the ionospheric clutters bypurpose and a satisfying clutter suppression result inHFSWRis achieved Besides the examples givenmore designs of GOPfilter can be inspired by the flexibilities of ISC It can beconcluded that GOP filter is a promising filtering techniquefor interference suppression and capable of being used inspatial filtering polarization filtering and other array signalprocessing applications

Conflict of Interests

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

Acknowledgments

This project is sponsored by the National Marine TechnologyProgram for Public Welfare (no 200905029) National Nat-ural Science Foundation of China (no 61171180) and TeamResearch Foundation for Fundamental Research Program inFIO China (no GY0213T03)

References

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

[2] L Rebollo-Neira ldquoOblique matching pursuitrdquo IEEE SignalProcessing Letters vol 14 no 10 pp 703ndash706 2007

[3] GW Stewart ldquoOn the numerical analysis of oblique projectorsrdquoSIAM Journal on Matrix Analysis and Applications vol 32 no1 pp 309ndash348 2011

International Journal of Antennas and Propagation 11

[4] X-P Mao A-J Liu H-J Hou H Hong R Guo and W-BDeng ldquoOblique projection polarisation filtering for interferencesuppression in high-frequency surface wave radarrdquo IET RadarSonar and Navigation vol 6 no 2 pp 71ndash80 2012

[5] 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 (Chinese)

[6] Q-Y Zhang B Cao L Jin and N-T Zhang ldquoOblique pro-jection polarization filtering-based interference suppressionsfor radar sensor networksrdquo EURASIP Journal on WirelessCommunications and Networking vol 2010 Article ID 6051032010

[7] X Yu and L Tong ldquoJoint channel and symbol estimation byoblique projectionsrdquo IEEE Transactions on Signal Processingvol 49 no 12 pp 3074ndash3083 2001

[8] Q Zhang B Cao JWang and N Zhang ldquoPolarization filteringtechnique based on oblique projectionsrdquo Science China F vol53 no 5 pp 1056ndash1066 2010

[9] Y Cui K Liu and J Wang ldquoDirection-of-arrival estimationfor coherent GPS signals based on oblique projectionrdquo SignalProcessing vol 92 no 1 pp 294ndash299 2012

[10] Y Hu X Zhang F Zhu and H Lv ldquoImage recognition usingiterative oblique projectionrdquo Electronics Letters vol 41 no 20pp 1109ndash1110 2005

[11] G Hellbourg R Weber C Capdessus and A-J BoonstraldquoOblique projection beamforming for RFI mitigation in radioastronomyrdquo in Proceedings of the IEEE Statistical Signal Process-ing Workshop (SSP rsquo12) pp 93ndash96 IEEE August 2012

[12] P De ldquoNew methods for sensing bandlimited signals in cogni-tive radiordquo in Proceedings of the IEEE 65th Vehicular TechnologyConference (VTC 07-Spring) pp 1916ndash1920 Dublin IrelandApril 2007

[13] R Boyer ldquoOblique projection for source estimation in a com-petitive environment algorithm and statistical analysisrdquo SignalProcessing vol 89 no 12 pp 2547ndash2554 2009

[14] M L McCloud and L L Scharf ldquoA new subspace identificationalgorithm for high-resolution DOA estimationrdquo IEEE Transac-tions on Antennas and Propagation vol 50 no 10 pp 1382ndash1390 2002

[15] R Boyer andG Bouleux ldquoOblique projections for direction-of-arrival estimation with prior knowledgerdquo IEEE Transactions onSignal Processing vol 56 no 4 pp 1374ndash1387 2008

[16] H Hong X-P Mao C Hu R Guo W-B Deng and PJiang ldquoNarrow-band null phase-shift spatial filter based onoblique projectionrdquo in Proceedings of the IEEERadar Conference(RADAR rsquo13) pp 1ndash5 Ottawa Canada May 2013

[17] Z H Xu Y P Ni and L Jin ldquoResolution theory of polarizationsensitive array signalsrdquo in Proceedings of the CIE InternationalConference on Radar (ICR rsquo06) pp 1ndash4 IEEE Shanghai ChinaOctober 2006

[18] 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

[19] Y-M Wang X-P Mao J Zhang and H Hong ldquoA multi-domain collaborative filter based on polarization sensitivefrequency diverse arrayrdquo in Proceedings of the IEEE RadarConference pp 0507ndash0511 Cincinnati Ohio USA May 2014

[20] M Souden J Benesty and S Affes ldquoA study of the LCMVandMVDRnoise reduction filtersrdquo IEEE Transactions on SignalProcessing vol 58 no 9 pp 4925ndash4935 2010

[21] Y M Cui X P Mao and H Hong ldquoA novel adaptive filter forinterference suppressionrdquo in Proceedings of the IEEE Region 10Conference vol 31194 pp 1ndash5 IEEE 2013

[22] H C Chan ldquoCharacterization of ionospheric clutter in HFsurface wave radarrdquo Tech Rep 2003-114 Defence RampDCanadaOttawa Canada 2003

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

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Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

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DistributedSensor Networks

International Journal of

International Journal of Antennas and Propagation 7

0 10 20 30 40 50 60 70 80 90

0

10

20

30

SIN

R im

prov

emen

t (dB

)

84 85 86 87 88 89 90

1981985

1991995

202005

minus40

minus30

minus20

minus10

120595 (deg)

OptimumMVDR

OPGOP

Figure 1 SINR improvement versus 120595

20 25 30 35 40 45 50 55 6015

20

25

30

35

40

45

50

55

60

65

INR (dB)

SIN

R im

prov

emen

t (dB

)

MVDR (SIR = minus30dB)OP (SIR = minus30dB)GOP (SIR = minus30dB)MVDR (SIR = minus20dB)OP (SIR = minus20dB)

GOP (SIR = minus20dB)MVDR (SIR = minus10dB)OP (SIR = minus10dB)GOP (SIR = minus10dB)

Figure 2 SINR improvement versus INR for Case 1

SNR = 10 dB and SIR = minus10 dB the SINR improvementversus 120595 for MVDR OP GOP and GOP with optimum ISCis shown in Figure 1

From Figure 1 it can be observed that the principle angleshave great impacts on the SINR performance of the threespatial filters With the principle angle less than 10 degreesa sharper decrease appears in SINR for the OP filter thanboth GOP and MVDR filters However when the principleangle increases to nearly 90 degrees GOP and OP filtersperform slightly better than MVDR filter The GOP spatialfilter demonstrates a superior performance than OP and

20 25 30 35 40 45 50 55 60

0

5

10

15

INR (dB)

SIN

R im

prov

emen

t (dB

)

MVDR (SIR = minus30dB)OP (SIR = minus30dB)GOP (SIR = minus30dB)MVDR (SIR = minus20dB)OP (SIR = minus20dB)

GOP (SIR = minus20dB)MVDR (SIR = minus10dB)OP (SIR = minus10dB)GOP (SIR = minus10dB)

minus35

minus30

minus25

minus20

minus15

minus10

minus5

Figure 3 SINR improvement versus INR for Case 2

MVDR filters in the whole angle range further it coincideswith the maximized SINR derived in (40)

In the following the principle angle is fixed and theperformances of three filters under different INRs are inves-tigated The INRs span from 20 dB to 60 dB while the SIRsare of minus10 dB minus20 dB and minus30 dB respectively The principleangles are set to near 90 degrees and 0 degrees respectivelywhich correspond to the cases in Section 42

In Figures 2 and 3 the principle angles are set to 898degrees and 018 degrees respectively which correspond toCases 1 and 2 It is found that the ISC varies slightly aroundzero when the INRs change for Case 1 and ISC varies inrange of [27 times 10

minus5 1] for Case 2 As shown in Figure 2 the

SINR improvements of the GOP and OP increase linearlywith INRs however the MVDR shows an inferior SINRimprovement In Figure 3 the principle angle is small whichmeans that the spatial difference between the target andinterference reducesThe noise power amplifying effect of OPis significant resulting in a severe SINR performance lossIn contrast the GOP and MVDR filters have better SINRimprovements which exceed 30 dB at highest than OP filterIn general the GOP filter generates a superior performancethan both OP and MVDR filters The numerical simulationshave verified the theoretical analysis of the spatial filterspresented

5 GOP in Polarization Filtering of HF Radar

High frequency surface wave radar (HFSWR) [22] operatesin the short wave band which facilities the over-the-horizondetection over the sea surface However signals in this bandwill also get reflected by the ionosphere leading to a stronginterference to the target detection or sea state remote sens-ing In this section we explored the polarization information

8 International Journal of Antennas and Propagation

in the HFSWR and extended the application of the GOP filterin polarization filtering further a challenging ionosphericclutter mitigation problem in HFSWR is addressed

51 Generalized Oblique Projection Polarization Filter Asthe linear signal model presented in (4) a pair of thepolarization parameters represent the amplitude relationshipand the phase difference between the echoes received by theorthogonal dual-polarized radar sensor

Suppose the polarization parameters of the target andinterference are different then the target polarization sub-space ⟨Ps⟩ and interference polarization subspace ⟨Pi⟩ aredisjoint Note that the polarization subspace is independentof the specific radar signal waveforms The polarizationsubspace is constructed by the difference of the polarizationstate Therefore the target and interference subspaces in (23)can be given as

A = [

cos 120574119904

sin 120574119904119890119895120578119904] B = [

cos 120574119894

sin 120574119894119890119895120578119894] (57)

where 120574 and 120578 are the polarization pair with subscripts 119904 and119894 representing target and interference

There are two sets of the parameters that need to bedecided that is the echoes polarization set and the ISC Thepolarization angle is obtained as

120574 = 119905119892minus1

(

1003816100381610038161003816119909119881 (119905)

1003816100381610038161003816

1003816100381610038161003816119909119867 (119905)

1003816100381610038161003816

) (58)

and the polarization phase difference as

120578 = arg (119909119881 (119905)) minus arg (119909119867 (119905)) (59)

where 119909119881(119905) 119909119867(119905) represent the vertically and horizontallypolarized signal components and arg(sdot sdot sdot ) indicates phase ofthe signal

By the inflexibility of the polarized state in the temporaldomain and the frequency domain [18] these parameters canbe calculated using frequency transformed signal also TheISC is a free variable which can be designed according to thespecific application

However it can be proved that if the ISC is set to zerothis GOP polarization filter becomesOP polarization filter Inconstrained condition that is subspace ⟨Ps⟩ is orthogonal to⟨Pi⟩ the GOP polarization filter degrades into an orthogonalpolarization filter

52 Ionospheric Clutter Cancellation in HFSWR The char-acteristics of the ionosphere reflected echoes received byHFSWR are

(1) nonstationary(2) multiclutters(3) widely spread in range and Doppler bins

In addition to that there are ionospheric clutters return-ing from the sea surface whichmake their polarization statesclose to the target or the spatial difference between the

Time domain signal

Segmentations and FFT

Frequency domainpolarization estimations

Coherentintegration

Logic product

GOP filtering fortime segment 1

GOP filtering for

1st clutterGOP filtering fortime segment 1

GOP filtering for

Filtering output

time segment K time segment K

Jth clutter

middot middot middot

Figure 4 Ionospheric clutter mitigation process flow

clutters and target is not obvious Those characteristics leadto an unsolved clutter mitigation problem so far

As the radar arrays cannot effectively distinguish thetarget and interference spatially in this scenario the arraypolarization diversity and the coherent integration processare explored To handle those characteristics segmentationsof the time domain signals are introduced in an effort toapproach the real clutter parameters andmultipleGOPfilterswith flexible parameters 120577 are constructed The flowchart toillustrate the ionospheric clutter mitigation process is shownin Figure 4

In the dual-polarized HFSWR system the time domainsignal is range processed After proper signal segmentationsthe polarization states are estimated according to (58) and(59) with frequency transformed signal componentsThe sig-nals returned from the ship target over sea surface will retainvertically polarized state whereas the ionosphere reflectedclutters will be ellipse polarized with strong horizontallypolarized components The target and clutter polarizationsubspaces (A and B for GOP) are therefore obtained by thepolarization threshold A total number of 119870 segments of thetime divided data after filtering are connected and coherentintegration is performed However by the special designof GOP polarization filter an extra integration loss to theionospheric clutter will be brought in

By Property 1 of GOP the target polarization subspacesare retained while the ionospheric clutters are controlledby the free variable 120577 which is designed to introducerandom phase shift Therefore after GOP processing asignificant coherent integration loss will be introduced tothe ionospheric clutters when the time divided segmentsare reconnected and fast Fourier transformed However thetargetrsquos amplitude and phase are unchanged and its coherentintegration performance is not affected

The free variable of 120577(119899) is designed as

120577 (119899) = rnd (1205751 1205752 119899) 119890119895rnd(120573

11205732119899)

119899 isin [1 119870] (60)

where rnd(1205751 1205752 119899) represents random arrays from the uni-form distribution with amplitude range [1205751 1205752] and random

International Journal of Antennas and Propagation 9

20 40 60 80 100 1200

5

10

15

20

25

Segment numbers

Coh

eren

t int

egra

tion

loss

(dB)

120590120573 = 21205875

120590120573 = 1205872

120590120573 = 120587

120590120573 = 2120587

Figure 5 Coherent loss versus segment numbers under differentphase ranges

phase term 119890119895rnd(120573

11205732119899) with phase range [1205731 1205732] and 119899

denotes the sequence number of 120577 generatedIn deciding the parameters of 120577 the number of segmen-

tation and the phase ranges are of importance In Figure 5the segmentation number is chosen to be 64 and at that pointphase range of [0 2120587] is picked by simulation results of idealexponential signals The reasons are that more segmentationnumbers can only introduce at most 3 dB loss further whilemore segments indicate shorter time in coherent integrationand result in more estimation errors which may degradethe performance of the filter Therefore the parameters areobtained in consideration of the extra coherent loss andpotential estimation error

After logic product process [18] which reserves thesmallest points in Doppler spectrum from all the filteringresults the final output in each range bin is obtained as

Y (120596) =

119873

sum

119899=1

120575 (120596 minus 120596119899)

times

119869

min119895=1

(FFT[

119870

sum

119896=1

EAB120585119896119895x119896 (119899seg119896)])

(61)

where 119873 represents the length of FFT 120596119899 represents thefrequency at point 119899 119869 represents the total number of theclutters 119870 is the total number of segmentations EAB120585119896119895is the 119896th GOP in time domain for the suppression of 119895thclutter and x119896(119899seg119896) is the 119896th time segmented datawith 119899seg119896denoting the sampled points in the corresponding segment

In the HFSWR field experiment the vertically polarizedsignal was transmitted with a carrier frequency of 7Mhzby a half-wave dipole antenna The data was collected by adistant polarized high frequency linear array with 15-meterseparation between the vertically and horizontally polarizedelements The coherent integration time was 4 minutes

50 100 150 200 250

Doppler bins

Pow

er (d

B)

After filteringBefore filtering

Target

minus90

minus80

minus70

minus60

minus50

minus40

minus30

minus20

minus10

Figure 6 Doppler spectrum at range bin 79

Figure 6 gives theDoppler spectrumafter integration at rangebin 79 which is obtained from experimentally derived datawith red dashed line denoting spectrum before filtering andblue solid line denoting spectrum after process It can beobserved that there are several peaks well above minus30 dBbefore filtering which create an unfavorable ship detectionenvironment However the ship target at Doppler bin 183can be distinguished easily since the ionospheric clutters aresuppressed by about 10 dB in average whereas the targetsignal is undistorted

Besides ship detection the other focus can be drawn onthe sea state remote sensing A successful sea state inversionalgorithm depends on the correct and accurate extractionsof Bragg In Figure 7 the double first order Bragg peaks atDoppler bins (in between the vertically green dashed lines)are contaminated by the ionospheric clutters After GOPfiltering the contaminations of ionosphere are minimizedmoreover the SINR of the negative Bragg peaks was raisedaround 12 dB which facilitates its extraction algorithms

The Doppler spectrums from all the range bins arethen collected together forming a range-Doppler spectrumFigure 8(a) presents the original range-Doppler spectrumwhich is contaminated by the ionospheric clutters fromrange bins 73 to 96 whereas Figure 8(b) describes thespectrum after being processed by GOP filters Obviouslythe ionospheric clutters which widely spread in range andDoppler bins are suppressed effectively The average SINRimprovement is above 10 dB in this experiment

6 Conclusions

In this paper a novel GOP with adjustable ISC parameter hasbeen proposed It is proved to be an extension of OP andfour fundamental properties are presented with proofs Theconstruction of GOP filters is demonstrated with examplesof spatial and polarization filtering respectively In thefirst example with ISC derived from adaptive beamforming

10 International Journal of Antennas and Propagation

After filteringBefore filtering

50 100 150 200 250Doppler bins

Pow

er (d

B)

Positive BraggNegative Bragg

minus90

minus80

minus70

minus60

minus50

minus40

minus30

minus20

minus10

Figure 7 Doppler spectrum at range bin 89

20

40

60

80

100

120

140

160

50 100 150 200 250Doppler bins

Rang

e bin

s

(a) Original range-Doppler spectrum

20

40

60

80

100

120

140

160

50 100 150 200 250Doppler bins

Rang

e bin

s

(b) Range-Doppler spectrum after GOP filter

Figure 8 Range-Doppler spectrum of HFSWR

algorithm the SINR performance of GOP filter is shownto be better than MVDR and OP filters both theoreticallyand numerically A GOP polarization filter is constructedwith manually designed ISC in the second example An extracoherent loss is introduced to the ionospheric clutters bypurpose and a satisfying clutter suppression result inHFSWRis achieved Besides the examples givenmore designs of GOPfilter can be inspired by the flexibilities of ISC It can beconcluded that GOP filter is a promising filtering techniquefor interference suppression and capable of being used inspatial filtering polarization filtering and other array signalprocessing applications

Conflict of Interests

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

Acknowledgments

This project is sponsored by the National Marine TechnologyProgram for Public Welfare (no 200905029) National Nat-ural Science Foundation of China (no 61171180) and TeamResearch Foundation for Fundamental Research Program inFIO China (no GY0213T03)

References

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

[2] L Rebollo-Neira ldquoOblique matching pursuitrdquo IEEE SignalProcessing Letters vol 14 no 10 pp 703ndash706 2007

[3] GW Stewart ldquoOn the numerical analysis of oblique projectorsrdquoSIAM Journal on Matrix Analysis and Applications vol 32 no1 pp 309ndash348 2011

International Journal of Antennas and Propagation 11

[4] X-P Mao A-J Liu H-J Hou H Hong R Guo and W-BDeng ldquoOblique projection polarisation filtering for interferencesuppression in high-frequency surface wave radarrdquo IET RadarSonar and Navigation vol 6 no 2 pp 71ndash80 2012

[5] 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 (Chinese)

[6] Q-Y Zhang B Cao L Jin and N-T Zhang ldquoOblique pro-jection polarization filtering-based interference suppressionsfor radar sensor networksrdquo EURASIP Journal on WirelessCommunications and Networking vol 2010 Article ID 6051032010

[7] X Yu and L Tong ldquoJoint channel and symbol estimation byoblique projectionsrdquo IEEE Transactions on Signal Processingvol 49 no 12 pp 3074ndash3083 2001

[8] Q Zhang B Cao JWang and N Zhang ldquoPolarization filteringtechnique based on oblique projectionsrdquo Science China F vol53 no 5 pp 1056ndash1066 2010

[9] Y Cui K Liu and J Wang ldquoDirection-of-arrival estimationfor coherent GPS signals based on oblique projectionrdquo SignalProcessing vol 92 no 1 pp 294ndash299 2012

[10] Y Hu X Zhang F Zhu and H Lv ldquoImage recognition usingiterative oblique projectionrdquo Electronics Letters vol 41 no 20pp 1109ndash1110 2005

[11] G Hellbourg R Weber C Capdessus and A-J BoonstraldquoOblique projection beamforming for RFI mitigation in radioastronomyrdquo in Proceedings of the IEEE Statistical Signal Process-ing Workshop (SSP rsquo12) pp 93ndash96 IEEE August 2012

[12] P De ldquoNew methods for sensing bandlimited signals in cogni-tive radiordquo in Proceedings of the IEEE 65th Vehicular TechnologyConference (VTC 07-Spring) pp 1916ndash1920 Dublin IrelandApril 2007

[13] R Boyer ldquoOblique projection for source estimation in a com-petitive environment algorithm and statistical analysisrdquo SignalProcessing vol 89 no 12 pp 2547ndash2554 2009

[14] M L McCloud and L L Scharf ldquoA new subspace identificationalgorithm for high-resolution DOA estimationrdquo IEEE Transac-tions on Antennas and Propagation vol 50 no 10 pp 1382ndash1390 2002

[15] R Boyer andG Bouleux ldquoOblique projections for direction-of-arrival estimation with prior knowledgerdquo IEEE Transactions onSignal Processing vol 56 no 4 pp 1374ndash1387 2008

[16] H Hong X-P Mao C Hu R Guo W-B Deng and PJiang ldquoNarrow-band null phase-shift spatial filter based onoblique projectionrdquo in Proceedings of the IEEERadar Conference(RADAR rsquo13) pp 1ndash5 Ottawa Canada May 2013

[17] Z H Xu Y P Ni and L Jin ldquoResolution theory of polarizationsensitive array signalsrdquo in Proceedings of the CIE InternationalConference on Radar (ICR rsquo06) pp 1ndash4 IEEE Shanghai ChinaOctober 2006

[18] 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

[19] Y-M Wang X-P Mao J Zhang and H Hong ldquoA multi-domain collaborative filter based on polarization sensitivefrequency diverse arrayrdquo in Proceedings of the IEEE RadarConference pp 0507ndash0511 Cincinnati Ohio USA May 2014

[20] M Souden J Benesty and S Affes ldquoA study of the LCMVandMVDRnoise reduction filtersrdquo IEEE Transactions on SignalProcessing vol 58 no 9 pp 4925ndash4935 2010

[21] Y M Cui X P Mao and H Hong ldquoA novel adaptive filter forinterference suppressionrdquo in Proceedings of the IEEE Region 10Conference vol 31194 pp 1ndash5 IEEE 2013

[22] H C Chan ldquoCharacterization of ionospheric clutter in HFsurface wave radarrdquo Tech Rep 2003-114 Defence RampDCanadaOttawa Canada 2003

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

8 International Journal of Antennas and Propagation

in the HFSWR and extended the application of the GOP filterin polarization filtering further a challenging ionosphericclutter mitigation problem in HFSWR is addressed

51 Generalized Oblique Projection Polarization Filter Asthe linear signal model presented in (4) a pair of thepolarization parameters represent the amplitude relationshipand the phase difference between the echoes received by theorthogonal dual-polarized radar sensor

Suppose the polarization parameters of the target andinterference are different then the target polarization sub-space ⟨Ps⟩ and interference polarization subspace ⟨Pi⟩ aredisjoint Note that the polarization subspace is independentof the specific radar signal waveforms The polarizationsubspace is constructed by the difference of the polarizationstate Therefore the target and interference subspaces in (23)can be given as

A = [

cos 120574119904

sin 120574119904119890119895120578119904] B = [

cos 120574119894

sin 120574119894119890119895120578119894] (57)

where 120574 and 120578 are the polarization pair with subscripts 119904 and119894 representing target and interference

There are two sets of the parameters that need to bedecided that is the echoes polarization set and the ISC Thepolarization angle is obtained as

120574 = 119905119892minus1

(

1003816100381610038161003816119909119881 (119905)

1003816100381610038161003816

1003816100381610038161003816119909119867 (119905)

1003816100381610038161003816

) (58)

and the polarization phase difference as

120578 = arg (119909119881 (119905)) minus arg (119909119867 (119905)) (59)

where 119909119881(119905) 119909119867(119905) represent the vertically and horizontallypolarized signal components and arg(sdot sdot sdot ) indicates phase ofthe signal

By the inflexibility of the polarized state in the temporaldomain and the frequency domain [18] these parameters canbe calculated using frequency transformed signal also TheISC is a free variable which can be designed according to thespecific application

However it can be proved that if the ISC is set to zerothis GOP polarization filter becomesOP polarization filter Inconstrained condition that is subspace ⟨Ps⟩ is orthogonal to⟨Pi⟩ the GOP polarization filter degrades into an orthogonalpolarization filter

52 Ionospheric Clutter Cancellation in HFSWR The char-acteristics of the ionosphere reflected echoes received byHFSWR are

(1) nonstationary(2) multiclutters(3) widely spread in range and Doppler bins

In addition to that there are ionospheric clutters return-ing from the sea surface whichmake their polarization statesclose to the target or the spatial difference between the

Time domain signal

Segmentations and FFT

Frequency domainpolarization estimations

Coherentintegration

Logic product

GOP filtering fortime segment 1

GOP filtering for

1st clutterGOP filtering fortime segment 1

GOP filtering for

Filtering output

time segment K time segment K

Jth clutter

middot middot middot

Figure 4 Ionospheric clutter mitigation process flow

clutters and target is not obvious Those characteristics leadto an unsolved clutter mitigation problem so far

As the radar arrays cannot effectively distinguish thetarget and interference spatially in this scenario the arraypolarization diversity and the coherent integration processare explored To handle those characteristics segmentationsof the time domain signals are introduced in an effort toapproach the real clutter parameters andmultipleGOPfilterswith flexible parameters 120577 are constructed The flowchart toillustrate the ionospheric clutter mitigation process is shownin Figure 4

In the dual-polarized HFSWR system the time domainsignal is range processed After proper signal segmentationsthe polarization states are estimated according to (58) and(59) with frequency transformed signal componentsThe sig-nals returned from the ship target over sea surface will retainvertically polarized state whereas the ionosphere reflectedclutters will be ellipse polarized with strong horizontallypolarized components The target and clutter polarizationsubspaces (A and B for GOP) are therefore obtained by thepolarization threshold A total number of 119870 segments of thetime divided data after filtering are connected and coherentintegration is performed However by the special designof GOP polarization filter an extra integration loss to theionospheric clutter will be brought in

By Property 1 of GOP the target polarization subspacesare retained while the ionospheric clutters are controlledby the free variable 120577 which is designed to introducerandom phase shift Therefore after GOP processing asignificant coherent integration loss will be introduced tothe ionospheric clutters when the time divided segmentsare reconnected and fast Fourier transformed However thetargetrsquos amplitude and phase are unchanged and its coherentintegration performance is not affected

The free variable of 120577(119899) is designed as

120577 (119899) = rnd (1205751 1205752 119899) 119890119895rnd(120573

11205732119899)

119899 isin [1 119870] (60)

where rnd(1205751 1205752 119899) represents random arrays from the uni-form distribution with amplitude range [1205751 1205752] and random

International Journal of Antennas and Propagation 9

20 40 60 80 100 1200

5

10

15

20

25

Segment numbers

Coh

eren

t int

egra

tion

loss

(dB)

120590120573 = 21205875

120590120573 = 1205872

120590120573 = 120587

120590120573 = 2120587

Figure 5 Coherent loss versus segment numbers under differentphase ranges

phase term 119890119895rnd(120573

11205732119899) with phase range [1205731 1205732] and 119899

denotes the sequence number of 120577 generatedIn deciding the parameters of 120577 the number of segmen-

tation and the phase ranges are of importance In Figure 5the segmentation number is chosen to be 64 and at that pointphase range of [0 2120587] is picked by simulation results of idealexponential signals The reasons are that more segmentationnumbers can only introduce at most 3 dB loss further whilemore segments indicate shorter time in coherent integrationand result in more estimation errors which may degradethe performance of the filter Therefore the parameters areobtained in consideration of the extra coherent loss andpotential estimation error

After logic product process [18] which reserves thesmallest points in Doppler spectrum from all the filteringresults the final output in each range bin is obtained as

Y (120596) =

119873

sum

119899=1

120575 (120596 minus 120596119899)

times

119869

min119895=1

(FFT[

119870

sum

119896=1

EAB120585119896119895x119896 (119899seg119896)])

(61)

where 119873 represents the length of FFT 120596119899 represents thefrequency at point 119899 119869 represents the total number of theclutters 119870 is the total number of segmentations EAB120585119896119895is the 119896th GOP in time domain for the suppression of 119895thclutter and x119896(119899seg119896) is the 119896th time segmented datawith 119899seg119896denoting the sampled points in the corresponding segment

In the HFSWR field experiment the vertically polarizedsignal was transmitted with a carrier frequency of 7Mhzby a half-wave dipole antenna The data was collected by adistant polarized high frequency linear array with 15-meterseparation between the vertically and horizontally polarizedelements The coherent integration time was 4 minutes

50 100 150 200 250

Doppler bins

Pow

er (d

B)

After filteringBefore filtering

Target

minus90

minus80

minus70

minus60

minus50

minus40

minus30

minus20

minus10

Figure 6 Doppler spectrum at range bin 79

Figure 6 gives theDoppler spectrumafter integration at rangebin 79 which is obtained from experimentally derived datawith red dashed line denoting spectrum before filtering andblue solid line denoting spectrum after process It can beobserved that there are several peaks well above minus30 dBbefore filtering which create an unfavorable ship detectionenvironment However the ship target at Doppler bin 183can be distinguished easily since the ionospheric clutters aresuppressed by about 10 dB in average whereas the targetsignal is undistorted

Besides ship detection the other focus can be drawn onthe sea state remote sensing A successful sea state inversionalgorithm depends on the correct and accurate extractionsof Bragg In Figure 7 the double first order Bragg peaks atDoppler bins (in between the vertically green dashed lines)are contaminated by the ionospheric clutters After GOPfiltering the contaminations of ionosphere are minimizedmoreover the SINR of the negative Bragg peaks was raisedaround 12 dB which facilitates its extraction algorithms

The Doppler spectrums from all the range bins arethen collected together forming a range-Doppler spectrumFigure 8(a) presents the original range-Doppler spectrumwhich is contaminated by the ionospheric clutters fromrange bins 73 to 96 whereas Figure 8(b) describes thespectrum after being processed by GOP filters Obviouslythe ionospheric clutters which widely spread in range andDoppler bins are suppressed effectively The average SINRimprovement is above 10 dB in this experiment

6 Conclusions

In this paper a novel GOP with adjustable ISC parameter hasbeen proposed It is proved to be an extension of OP andfour fundamental properties are presented with proofs Theconstruction of GOP filters is demonstrated with examplesof spatial and polarization filtering respectively In thefirst example with ISC derived from adaptive beamforming

10 International Journal of Antennas and Propagation

After filteringBefore filtering

50 100 150 200 250Doppler bins

Pow

er (d

B)

Positive BraggNegative Bragg

minus90

minus80

minus70

minus60

minus50

minus40

minus30

minus20

minus10

Figure 7 Doppler spectrum at range bin 89

20

40

60

80

100

120

140

160

50 100 150 200 250Doppler bins

Rang

e bin

s

(a) Original range-Doppler spectrum

20

40

60

80

100

120

140

160

50 100 150 200 250Doppler bins

Rang

e bin

s

(b) Range-Doppler spectrum after GOP filter

Figure 8 Range-Doppler spectrum of HFSWR

algorithm the SINR performance of GOP filter is shownto be better than MVDR and OP filters both theoreticallyand numerically A GOP polarization filter is constructedwith manually designed ISC in the second example An extracoherent loss is introduced to the ionospheric clutters bypurpose and a satisfying clutter suppression result inHFSWRis achieved Besides the examples givenmore designs of GOPfilter can be inspired by the flexibilities of ISC It can beconcluded that GOP filter is a promising filtering techniquefor interference suppression and capable of being used inspatial filtering polarization filtering and other array signalprocessing applications

Conflict of Interests

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

Acknowledgments

This project is sponsored by the National Marine TechnologyProgram for Public Welfare (no 200905029) National Nat-ural Science Foundation of China (no 61171180) and TeamResearch Foundation for Fundamental Research Program inFIO China (no GY0213T03)

References

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

[2] L Rebollo-Neira ldquoOblique matching pursuitrdquo IEEE SignalProcessing Letters vol 14 no 10 pp 703ndash706 2007

[3] GW Stewart ldquoOn the numerical analysis of oblique projectorsrdquoSIAM Journal on Matrix Analysis and Applications vol 32 no1 pp 309ndash348 2011

International Journal of Antennas and Propagation 11

[4] X-P Mao A-J Liu H-J Hou H Hong R Guo and W-BDeng ldquoOblique projection polarisation filtering for interferencesuppression in high-frequency surface wave radarrdquo IET RadarSonar and Navigation vol 6 no 2 pp 71ndash80 2012

[5] 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 (Chinese)

[6] Q-Y Zhang B Cao L Jin and N-T Zhang ldquoOblique pro-jection polarization filtering-based interference suppressionsfor radar sensor networksrdquo EURASIP Journal on WirelessCommunications and Networking vol 2010 Article ID 6051032010

[7] X Yu and L Tong ldquoJoint channel and symbol estimation byoblique projectionsrdquo IEEE Transactions on Signal Processingvol 49 no 12 pp 3074ndash3083 2001

[8] Q Zhang B Cao JWang and N Zhang ldquoPolarization filteringtechnique based on oblique projectionsrdquo Science China F vol53 no 5 pp 1056ndash1066 2010

[9] Y Cui K Liu and J Wang ldquoDirection-of-arrival estimationfor coherent GPS signals based on oblique projectionrdquo SignalProcessing vol 92 no 1 pp 294ndash299 2012

[10] Y Hu X Zhang F Zhu and H Lv ldquoImage recognition usingiterative oblique projectionrdquo Electronics Letters vol 41 no 20pp 1109ndash1110 2005

[11] G Hellbourg R Weber C Capdessus and A-J BoonstraldquoOblique projection beamforming for RFI mitigation in radioastronomyrdquo in Proceedings of the IEEE Statistical Signal Process-ing Workshop (SSP rsquo12) pp 93ndash96 IEEE August 2012

[12] P De ldquoNew methods for sensing bandlimited signals in cogni-tive radiordquo in Proceedings of the IEEE 65th Vehicular TechnologyConference (VTC 07-Spring) pp 1916ndash1920 Dublin IrelandApril 2007

[13] R Boyer ldquoOblique projection for source estimation in a com-petitive environment algorithm and statistical analysisrdquo SignalProcessing vol 89 no 12 pp 2547ndash2554 2009

[14] M L McCloud and L L Scharf ldquoA new subspace identificationalgorithm for high-resolution DOA estimationrdquo IEEE Transac-tions on Antennas and Propagation vol 50 no 10 pp 1382ndash1390 2002

[15] R Boyer andG Bouleux ldquoOblique projections for direction-of-arrival estimation with prior knowledgerdquo IEEE Transactions onSignal Processing vol 56 no 4 pp 1374ndash1387 2008

[16] H Hong X-P Mao C Hu R Guo W-B Deng and PJiang ldquoNarrow-band null phase-shift spatial filter based onoblique projectionrdquo in Proceedings of the IEEERadar Conference(RADAR rsquo13) pp 1ndash5 Ottawa Canada May 2013

[17] Z H Xu Y P Ni and L Jin ldquoResolution theory of polarizationsensitive array signalsrdquo in Proceedings of the CIE InternationalConference on Radar (ICR rsquo06) pp 1ndash4 IEEE Shanghai ChinaOctober 2006

[18] 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

[19] Y-M Wang X-P Mao J Zhang and H Hong ldquoA multi-domain collaborative filter based on polarization sensitivefrequency diverse arrayrdquo in Proceedings of the IEEE RadarConference pp 0507ndash0511 Cincinnati Ohio USA May 2014

[20] M Souden J Benesty and S Affes ldquoA study of the LCMVandMVDRnoise reduction filtersrdquo IEEE Transactions on SignalProcessing vol 58 no 9 pp 4925ndash4935 2010

[21] Y M Cui X P Mao and H Hong ldquoA novel adaptive filter forinterference suppressionrdquo in Proceedings of the IEEE Region 10Conference vol 31194 pp 1ndash5 IEEE 2013

[22] H C Chan ldquoCharacterization of ionospheric clutter in HFsurface wave radarrdquo Tech Rep 2003-114 Defence RampDCanadaOttawa Canada 2003

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

International Journal of Antennas and Propagation 9

20 40 60 80 100 1200

5

10

15

20

25

Segment numbers

Coh

eren

t int

egra

tion

loss

(dB)

120590120573 = 21205875

120590120573 = 1205872

120590120573 = 120587

120590120573 = 2120587

Figure 5 Coherent loss versus segment numbers under differentphase ranges

phase term 119890119895rnd(120573

11205732119899) with phase range [1205731 1205732] and 119899

denotes the sequence number of 120577 generatedIn deciding the parameters of 120577 the number of segmen-

tation and the phase ranges are of importance In Figure 5the segmentation number is chosen to be 64 and at that pointphase range of [0 2120587] is picked by simulation results of idealexponential signals The reasons are that more segmentationnumbers can only introduce at most 3 dB loss further whilemore segments indicate shorter time in coherent integrationand result in more estimation errors which may degradethe performance of the filter Therefore the parameters areobtained in consideration of the extra coherent loss andpotential estimation error

After logic product process [18] which reserves thesmallest points in Doppler spectrum from all the filteringresults the final output in each range bin is obtained as

Y (120596) =

119873

sum

119899=1

120575 (120596 minus 120596119899)

times

119869

min119895=1

(FFT[

119870

sum

119896=1

EAB120585119896119895x119896 (119899seg119896)])

(61)

where 119873 represents the length of FFT 120596119899 represents thefrequency at point 119899 119869 represents the total number of theclutters 119870 is the total number of segmentations EAB120585119896119895is the 119896th GOP in time domain for the suppression of 119895thclutter and x119896(119899seg119896) is the 119896th time segmented datawith 119899seg119896denoting the sampled points in the corresponding segment

In the HFSWR field experiment the vertically polarizedsignal was transmitted with a carrier frequency of 7Mhzby a half-wave dipole antenna The data was collected by adistant polarized high frequency linear array with 15-meterseparation between the vertically and horizontally polarizedelements The coherent integration time was 4 minutes

50 100 150 200 250

Doppler bins

Pow

er (d

B)

After filteringBefore filtering

Target

minus90

minus80

minus70

minus60

minus50

minus40

minus30

minus20

minus10

Figure 6 Doppler spectrum at range bin 79

Figure 6 gives theDoppler spectrumafter integration at rangebin 79 which is obtained from experimentally derived datawith red dashed line denoting spectrum before filtering andblue solid line denoting spectrum after process It can beobserved that there are several peaks well above minus30 dBbefore filtering which create an unfavorable ship detectionenvironment However the ship target at Doppler bin 183can be distinguished easily since the ionospheric clutters aresuppressed by about 10 dB in average whereas the targetsignal is undistorted

Besides ship detection the other focus can be drawn onthe sea state remote sensing A successful sea state inversionalgorithm depends on the correct and accurate extractionsof Bragg In Figure 7 the double first order Bragg peaks atDoppler bins (in between the vertically green dashed lines)are contaminated by the ionospheric clutters After GOPfiltering the contaminations of ionosphere are minimizedmoreover the SINR of the negative Bragg peaks was raisedaround 12 dB which facilitates its extraction algorithms

The Doppler spectrums from all the range bins arethen collected together forming a range-Doppler spectrumFigure 8(a) presents the original range-Doppler spectrumwhich is contaminated by the ionospheric clutters fromrange bins 73 to 96 whereas Figure 8(b) describes thespectrum after being processed by GOP filters Obviouslythe ionospheric clutters which widely spread in range andDoppler bins are suppressed effectively The average SINRimprovement is above 10 dB in this experiment

6 Conclusions

In this paper a novel GOP with adjustable ISC parameter hasbeen proposed It is proved to be an extension of OP andfour fundamental properties are presented with proofs Theconstruction of GOP filters is demonstrated with examplesof spatial and polarization filtering respectively In thefirst example with ISC derived from adaptive beamforming

10 International Journal of Antennas and Propagation

After filteringBefore filtering

50 100 150 200 250Doppler bins

Pow

er (d

B)

Positive BraggNegative Bragg

minus90

minus80

minus70

minus60

minus50

minus40

minus30

minus20

minus10

Figure 7 Doppler spectrum at range bin 89

20

40

60

80

100

120

140

160

50 100 150 200 250Doppler bins

Rang

e bin

s

(a) Original range-Doppler spectrum

20

40

60

80

100

120

140

160

50 100 150 200 250Doppler bins

Rang

e bin

s

(b) Range-Doppler spectrum after GOP filter

Figure 8 Range-Doppler spectrum of HFSWR

algorithm the SINR performance of GOP filter is shownto be better than MVDR and OP filters both theoreticallyand numerically A GOP polarization filter is constructedwith manually designed ISC in the second example An extracoherent loss is introduced to the ionospheric clutters bypurpose and a satisfying clutter suppression result inHFSWRis achieved Besides the examples givenmore designs of GOPfilter can be inspired by the flexibilities of ISC It can beconcluded that GOP filter is a promising filtering techniquefor interference suppression and capable of being used inspatial filtering polarization filtering and other array signalprocessing applications

Conflict of Interests

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

Acknowledgments

This project is sponsored by the National Marine TechnologyProgram for Public Welfare (no 200905029) National Nat-ural Science Foundation of China (no 61171180) and TeamResearch Foundation for Fundamental Research Program inFIO China (no GY0213T03)

References

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

[2] L Rebollo-Neira ldquoOblique matching pursuitrdquo IEEE SignalProcessing Letters vol 14 no 10 pp 703ndash706 2007

[3] GW Stewart ldquoOn the numerical analysis of oblique projectorsrdquoSIAM Journal on Matrix Analysis and Applications vol 32 no1 pp 309ndash348 2011

International Journal of Antennas and Propagation 11

[4] X-P Mao A-J Liu H-J Hou H Hong R Guo and W-BDeng ldquoOblique projection polarisation filtering for interferencesuppression in high-frequency surface wave radarrdquo IET RadarSonar and Navigation vol 6 no 2 pp 71ndash80 2012

[5] 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 (Chinese)

[6] Q-Y Zhang B Cao L Jin and N-T Zhang ldquoOblique pro-jection polarization filtering-based interference suppressionsfor radar sensor networksrdquo EURASIP Journal on WirelessCommunications and Networking vol 2010 Article ID 6051032010

[7] X Yu and L Tong ldquoJoint channel and symbol estimation byoblique projectionsrdquo IEEE Transactions on Signal Processingvol 49 no 12 pp 3074ndash3083 2001

[8] Q Zhang B Cao JWang and N Zhang ldquoPolarization filteringtechnique based on oblique projectionsrdquo Science China F vol53 no 5 pp 1056ndash1066 2010

[9] Y Cui K Liu and J Wang ldquoDirection-of-arrival estimationfor coherent GPS signals based on oblique projectionrdquo SignalProcessing vol 92 no 1 pp 294ndash299 2012

[10] Y Hu X Zhang F Zhu and H Lv ldquoImage recognition usingiterative oblique projectionrdquo Electronics Letters vol 41 no 20pp 1109ndash1110 2005

[11] G Hellbourg R Weber C Capdessus and A-J BoonstraldquoOblique projection beamforming for RFI mitigation in radioastronomyrdquo in Proceedings of the IEEE Statistical Signal Process-ing Workshop (SSP rsquo12) pp 93ndash96 IEEE August 2012

[12] P De ldquoNew methods for sensing bandlimited signals in cogni-tive radiordquo in Proceedings of the IEEE 65th Vehicular TechnologyConference (VTC 07-Spring) pp 1916ndash1920 Dublin IrelandApril 2007

[13] R Boyer ldquoOblique projection for source estimation in a com-petitive environment algorithm and statistical analysisrdquo SignalProcessing vol 89 no 12 pp 2547ndash2554 2009

[14] M L McCloud and L L Scharf ldquoA new subspace identificationalgorithm for high-resolution DOA estimationrdquo IEEE Transac-tions on Antennas and Propagation vol 50 no 10 pp 1382ndash1390 2002

[15] R Boyer andG Bouleux ldquoOblique projections for direction-of-arrival estimation with prior knowledgerdquo IEEE Transactions onSignal Processing vol 56 no 4 pp 1374ndash1387 2008

[16] H Hong X-P Mao C Hu R Guo W-B Deng and PJiang ldquoNarrow-band null phase-shift spatial filter based onoblique projectionrdquo in Proceedings of the IEEERadar Conference(RADAR rsquo13) pp 1ndash5 Ottawa Canada May 2013

[17] Z H Xu Y P Ni and L Jin ldquoResolution theory of polarizationsensitive array signalsrdquo in Proceedings of the CIE InternationalConference on Radar (ICR rsquo06) pp 1ndash4 IEEE Shanghai ChinaOctober 2006

[18] 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

[19] Y-M Wang X-P Mao J Zhang and H Hong ldquoA multi-domain collaborative filter based on polarization sensitivefrequency diverse arrayrdquo in Proceedings of the IEEE RadarConference pp 0507ndash0511 Cincinnati Ohio USA May 2014

[20] M Souden J Benesty and S Affes ldquoA study of the LCMVandMVDRnoise reduction filtersrdquo IEEE Transactions on SignalProcessing vol 58 no 9 pp 4925ndash4935 2010

[21] Y M Cui X P Mao and H Hong ldquoA novel adaptive filter forinterference suppressionrdquo in Proceedings of the IEEE Region 10Conference vol 31194 pp 1ndash5 IEEE 2013

[22] H C Chan ldquoCharacterization of ionospheric clutter in HFsurface wave radarrdquo Tech Rep 2003-114 Defence RampDCanadaOttawa Canada 2003

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

10 International Journal of Antennas and Propagation

After filteringBefore filtering

50 100 150 200 250Doppler bins

Pow

er (d

B)

Positive BraggNegative Bragg

minus90

minus80

minus70

minus60

minus50

minus40

minus30

minus20

minus10

Figure 7 Doppler spectrum at range bin 89

20

40

60

80

100

120

140

160

50 100 150 200 250Doppler bins

Rang

e bin

s

(a) Original range-Doppler spectrum

20

40

60

80

100

120

140

160

50 100 150 200 250Doppler bins

Rang

e bin

s

(b) Range-Doppler spectrum after GOP filter

Figure 8 Range-Doppler spectrum of HFSWR

algorithm the SINR performance of GOP filter is shownto be better than MVDR and OP filters both theoreticallyand numerically A GOP polarization filter is constructedwith manually designed ISC in the second example An extracoherent loss is introduced to the ionospheric clutters bypurpose and a satisfying clutter suppression result inHFSWRis achieved Besides the examples givenmore designs of GOPfilter can be inspired by the flexibilities of ISC It can beconcluded that GOP filter is a promising filtering techniquefor interference suppression and capable of being used inspatial filtering polarization filtering and other array signalprocessing applications

Conflict of Interests

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

Acknowledgments

This project is sponsored by the National Marine TechnologyProgram for Public Welfare (no 200905029) National Nat-ural Science Foundation of China (no 61171180) and TeamResearch Foundation for Fundamental Research Program inFIO China (no GY0213T03)

References

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

[2] L Rebollo-Neira ldquoOblique matching pursuitrdquo IEEE SignalProcessing Letters vol 14 no 10 pp 703ndash706 2007

[3] GW Stewart ldquoOn the numerical analysis of oblique projectorsrdquoSIAM Journal on Matrix Analysis and Applications vol 32 no1 pp 309ndash348 2011

International Journal of Antennas and Propagation 11

[4] X-P Mao A-J Liu H-J Hou H Hong R Guo and W-BDeng ldquoOblique projection polarisation filtering for interferencesuppression in high-frequency surface wave radarrdquo IET RadarSonar and Navigation vol 6 no 2 pp 71ndash80 2012

[5] 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 (Chinese)

[6] Q-Y Zhang B Cao L Jin and N-T Zhang ldquoOblique pro-jection polarization filtering-based interference suppressionsfor radar sensor networksrdquo EURASIP Journal on WirelessCommunications and Networking vol 2010 Article ID 6051032010

[7] X Yu and L Tong ldquoJoint channel and symbol estimation byoblique projectionsrdquo IEEE Transactions on Signal Processingvol 49 no 12 pp 3074ndash3083 2001

[8] Q Zhang B Cao JWang and N Zhang ldquoPolarization filteringtechnique based on oblique projectionsrdquo Science China F vol53 no 5 pp 1056ndash1066 2010

[9] Y Cui K Liu and J Wang ldquoDirection-of-arrival estimationfor coherent GPS signals based on oblique projectionrdquo SignalProcessing vol 92 no 1 pp 294ndash299 2012

[10] Y Hu X Zhang F Zhu and H Lv ldquoImage recognition usingiterative oblique projectionrdquo Electronics Letters vol 41 no 20pp 1109ndash1110 2005

[11] G Hellbourg R Weber C Capdessus and A-J BoonstraldquoOblique projection beamforming for RFI mitigation in radioastronomyrdquo in Proceedings of the IEEE Statistical Signal Process-ing Workshop (SSP rsquo12) pp 93ndash96 IEEE August 2012

[12] P De ldquoNew methods for sensing bandlimited signals in cogni-tive radiordquo in Proceedings of the IEEE 65th Vehicular TechnologyConference (VTC 07-Spring) pp 1916ndash1920 Dublin IrelandApril 2007

[13] R Boyer ldquoOblique projection for source estimation in a com-petitive environment algorithm and statistical analysisrdquo SignalProcessing vol 89 no 12 pp 2547ndash2554 2009

[14] M L McCloud and L L Scharf ldquoA new subspace identificationalgorithm for high-resolution DOA estimationrdquo IEEE Transac-tions on Antennas and Propagation vol 50 no 10 pp 1382ndash1390 2002

[15] R Boyer andG Bouleux ldquoOblique projections for direction-of-arrival estimation with prior knowledgerdquo IEEE Transactions onSignal Processing vol 56 no 4 pp 1374ndash1387 2008

[16] H Hong X-P Mao C Hu R Guo W-B Deng and PJiang ldquoNarrow-band null phase-shift spatial filter based onoblique projectionrdquo in Proceedings of the IEEERadar Conference(RADAR rsquo13) pp 1ndash5 Ottawa Canada May 2013

[17] Z H Xu Y P Ni and L Jin ldquoResolution theory of polarizationsensitive array signalsrdquo in Proceedings of the CIE InternationalConference on Radar (ICR rsquo06) pp 1ndash4 IEEE Shanghai ChinaOctober 2006

[18] 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

[19] Y-M Wang X-P Mao J Zhang and H Hong ldquoA multi-domain collaborative filter based on polarization sensitivefrequency diverse arrayrdquo in Proceedings of the IEEE RadarConference pp 0507ndash0511 Cincinnati Ohio USA May 2014

[20] M Souden J Benesty and S Affes ldquoA study of the LCMVandMVDRnoise reduction filtersrdquo IEEE Transactions on SignalProcessing vol 58 no 9 pp 4925ndash4935 2010

[21] Y M Cui X P Mao and H Hong ldquoA novel adaptive filter forinterference suppressionrdquo in Proceedings of the IEEE Region 10Conference vol 31194 pp 1ndash5 IEEE 2013

[22] H C Chan ldquoCharacterization of ionospheric clutter in HFsurface wave radarrdquo Tech Rep 2003-114 Defence RampDCanadaOttawa Canada 2003

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

International Journal of Antennas and Propagation 11

[4] X-P Mao A-J Liu H-J Hou H Hong R Guo and W-BDeng ldquoOblique projection polarisation filtering for interferencesuppression in high-frequency surface wave radarrdquo IET RadarSonar and Navigation vol 6 no 2 pp 71ndash80 2012

[5] 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 (Chinese)

[6] Q-Y Zhang B Cao L Jin and N-T Zhang ldquoOblique pro-jection polarization filtering-based interference suppressionsfor radar sensor networksrdquo EURASIP Journal on WirelessCommunications and Networking vol 2010 Article ID 6051032010

[7] X Yu and L Tong ldquoJoint channel and symbol estimation byoblique projectionsrdquo IEEE Transactions on Signal Processingvol 49 no 12 pp 3074ndash3083 2001

[8] Q Zhang B Cao JWang and N Zhang ldquoPolarization filteringtechnique based on oblique projectionsrdquo Science China F vol53 no 5 pp 1056ndash1066 2010

[9] Y Cui K Liu and J Wang ldquoDirection-of-arrival estimationfor coherent GPS signals based on oblique projectionrdquo SignalProcessing vol 92 no 1 pp 294ndash299 2012

[10] Y Hu X Zhang F Zhu and H Lv ldquoImage recognition usingiterative oblique projectionrdquo Electronics Letters vol 41 no 20pp 1109ndash1110 2005

[11] G Hellbourg R Weber C Capdessus and A-J BoonstraldquoOblique projection beamforming for RFI mitigation in radioastronomyrdquo in Proceedings of the IEEE Statistical Signal Process-ing Workshop (SSP rsquo12) pp 93ndash96 IEEE August 2012

[12] P De ldquoNew methods for sensing bandlimited signals in cogni-tive radiordquo in Proceedings of the IEEE 65th Vehicular TechnologyConference (VTC 07-Spring) pp 1916ndash1920 Dublin IrelandApril 2007

[13] R Boyer ldquoOblique projection for source estimation in a com-petitive environment algorithm and statistical analysisrdquo SignalProcessing vol 89 no 12 pp 2547ndash2554 2009

[14] M L McCloud and L L Scharf ldquoA new subspace identificationalgorithm for high-resolution DOA estimationrdquo IEEE Transac-tions on Antennas and Propagation vol 50 no 10 pp 1382ndash1390 2002

[15] R Boyer andG Bouleux ldquoOblique projections for direction-of-arrival estimation with prior knowledgerdquo IEEE Transactions onSignal Processing vol 56 no 4 pp 1374ndash1387 2008

[16] H Hong X-P Mao C Hu R Guo W-B Deng and PJiang ldquoNarrow-band null phase-shift spatial filter based onoblique projectionrdquo in Proceedings of the IEEERadar Conference(RADAR rsquo13) pp 1ndash5 Ottawa Canada May 2013

[17] Z H Xu Y P Ni and L Jin ldquoResolution theory of polarizationsensitive array signalsrdquo in Proceedings of the CIE InternationalConference on Radar (ICR rsquo06) pp 1ndash4 IEEE Shanghai ChinaOctober 2006

[18] 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

[19] Y-M Wang X-P Mao J Zhang and H Hong ldquoA multi-domain collaborative filter based on polarization sensitivefrequency diverse arrayrdquo in Proceedings of the IEEE RadarConference pp 0507ndash0511 Cincinnati Ohio USA May 2014

[20] M Souden J Benesty and S Affes ldquoA study of the LCMVandMVDRnoise reduction filtersrdquo IEEE Transactions on SignalProcessing vol 58 no 9 pp 4925ndash4935 2010

[21] Y M Cui X P Mao and H Hong ldquoA novel adaptive filter forinterference suppressionrdquo in Proceedings of the IEEE Region 10Conference vol 31194 pp 1ndash5 IEEE 2013

[22] H C Chan ldquoCharacterization of ionospheric clutter in HFsurface wave radarrdquo Tech Rep 2003-114 Defence RampDCanadaOttawa Canada 2003

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of