Research on employment of adaptive beamformer based on weight iterative algorithm in suppressing radio frequency interferences

Transcription

1 Research on eployent of adaptve beaforer based on weght teratve algorth n suppressng rado frequency nterferences JP.3 Ren-Zhou Gu Dept. of electronc nforaton Wuhan Unversty Wuhan, Chna rzgu@6.co Z-Je Yang Dept. of electronc nforaton Wuhan Unversty Wuhan, Chna ZJY437@6.co Abstract By coparng the dsadvantages and advantages of conventonal algorths of adaptve beaforer, we put forward an adaptve beaforer based on weght teratve algorth for suppressng rado frequency nterference (RFI, accordng to the dstrbutng propertes of RFI n dfferent range cell. We get the ntal weght vector of the adaptve beaforer by utlzng the algorth of nu varance dstortonless response (MVDR. The other weght vectors are coputed by the algorth of lnearly constraned nu varance (LCMV based on the last te weght vector. The covarance atrx of the two algorths,.e. MVDV and LCMV, are constructed wth the array snapshots n the far range cells whch have not useful radar echo. Thus the free degree of antenna array s ncreased. The feasblty of the adaptve beaforer s proved by utlzng t to process the actual radar data. Keywords LCMV, MVDR, RFI, adaptve beaforer I. INTRODUCTION gh frequency ground wave radar works usually wthn the frequency range of 3~30Mz n whch there are serous RFI. ow to suppress the RFI effcently and prove the detectve ablty of hgh frequency ground wave radar s an portant proble []. At present, we can suppress RFI n the three felds,.e. te feld, frequency feld and space feld. The paper dscusses the proble of suppressng RFI n space feld. As for an antenna array, all knds of dsturbances such as ntended dsturbance, the dsturbance of adacent devces and clutter dsturbance can enter fro the anlobe of antenna array, at the sae te, they can coe n fro the sdelobes of antenna array. The frst thng whch we should consder s to nze the nfluences of dsturbances whch coe n fro sdelobes. In the frequency range n whch hgh frequency ground wave radar works, there exst any RFIs, whch are partcularly serous at nght. The power of RFI s 70~80dB greater than that of useful radar echo. It s dffcult to desgn the antenna, whose sdelobe s lower than -30dB~-40dB, accordng to the conteporary technology. Even f useful sgnal coes n fro anlobe and RFI enters fro sdelobe, the power of RFI s 30~50dB or ore greater than the power of useful sgnal []. That akes t dffcult to detect useful radar sgnal correctly. If the drecton of RFI s stable, we can desgn a correspondng pattern of antenna array so that the great null of pattern can appear n the drecton of RFI. owever, the drecton of RFI s dfferent fro te to te. So we hope the null of pattern can change accordng to the drecton of RFI autoatcally. So we propose a specal ethod of adaptve beaforer for suppressng RFI. The adaptve beaforer can be constructed wth antenna array havng the ablty of sgnal processng, whch can provde ore free degree to desgner. The adaptve beaforer can allocate the hgh gan to the desred drecton and adust low null to the drecton of RFI for the purpose of suppressng or reducng RFI. So the detectve ablty of radar syste can be enhanced. II. TE SELECTING SUITABLE ALGORITM OF ADAPTIVE BEAMFORMER The conventonal algorths of adaptve beaforer are lsted as follows, ultple sdelobe canceller (MSC, use of reference sgnal, axzaton of sgnal to nose rato (MSNR, lnearly constraned nu varance beaforng (LCMV, nu varance dstortonless response (MVDR. Dfferent algorths have dfferent propertes.. MSC beaforer MSC s the earlest algorth of beaforer. A MSC beaforer ncludes a an antenna wth hgh gan and one or a few auxlary antennas. Its functon s to cancel the part of dsturbance n the an antenna by adustng the weghts of auxlary antennas. The desred sgnal, whch occupes part of the output power, can be weakened along wth the nzaton of the whole power by selectng sutable weghts of auxlary antennas. When the SNR s hgh, the useful sgnal s weakened serously snce t occupes greater part of the whole power. So MSC s a useful ethod when SNR s low, because the optzaton of weghts has lttle nfluence on useful sgnal.. Beaforer of usng reference sgnal If the reference sgnal s known, the weghts of beaforer, whch are deterned by the autocorrelaton atrx of nput sgnal and the crosscorrelaton atrx between the nput sgnal and reference sgnal, can be coputed by nzng the dfference between the output of lnear cobnaton and the reference sgnal. But t s dffcult to select reference sgnal..3 MSNR beaforer The weght of beaforer based on MSNR algorth s selected by ensurng the bggest SNR. We should know the

2 autocorrelaton atrxes of nose and sgnal before usng the MSNR algorth..4 LCMV beaforer The algorths whch s concerned wth above are not sutable for any applcatons. The useful sgnal can be weakened n the MSC algorth, because ts power can not be known n advance. The lack of knowledge about reference sgnal lts the utlzaton of beaforer of usng reference sgnal. It s dffcult to estate the autocorrelaton atrxes of nose and sgnal n the applcaton of MSNR beaforer. All the lts can be overcoe by usng LCMV algorth. We allow the useful sgnal go through wth a certan phase and gan, whle preventng the dsturbances whose drectons are dfferent fro that of useful sgnal fro cong n. By dong that and also by nzng the output power of the beaforer, we can acqure the weghts of LCMV beaforer. So usng LCMV beaforer has the advantage of suppressng the dsturbances cong fro the other drectons whle preservng the useful sgnal..5 MVDR beaforer When beaforer has consstent response n the drecton of useful sgnal, LCMV algorth becoes MVDR algorth. The detals of MVDR algorth can be descrbed as follows. Usng MVDR algorth to suppress dsturbances as greatly as possble, we do not have to know the drecton of dsturbance or powers of useful sgnal and whte nose, we need only the drecton of useful sgnal. The lt of MVDR algorth can be expressed by the forulas n P( W = n( W R W ( ( xx W a θ 0 = ( That s to say, we nze the output power of MVDR beaforeer, whle ensurng that the gan of the useful sgnal equals one n the drecton of useful sgnal. The lt of forulas and can ensure the useful sgnal goes through wthout any loss, so the output power of beaforer s the sae as the power of useful sgnal. The output of axu SNR can be realzed by nzng the power of output nose whle ensurng that the power of useful sgnal s constant. The optzaton weght vectors can be acqured by the forula 3 accordng to the lted forulas and. Rxx a( θ0 WMVDR = (3 a ( θ0 Rxx a( θ0 The ethod requres that the nuber of dsturbances s saller than M- (M s the nuber of eleent n antenna array, because antenna array wth M eleents possesses M- free degree and one free degree s used as the lt of useful sgnal drecton [3,4]. There are two probles whch need consderng n the actual applcaton. Frst proble s how to construct the covarance atrx of the algorths n adaptve beaforer. Second proble s how to ensure the consstent and contnuous ocean echo durng the coherent ntegraton te despte the changng weghts. The two probles are dscussed n the followng two sectons. III. TE CONSTRUCT COVARIANCE MATRI The covarance atrx n forula 3 s constructed conventonally wth unlted snapshots. But t s estated by usng lted snapshots ( expressed wth n actual applcaton. It can be t Λ K R = K = ( t ( t,where K s the nuber of snapshots. We consder that the dsturbance has the property of te-varyng. Whle we are estatng the covarance atrx, the nuber of snapshots can not be so bg as to exceed the correlatve te of dsturbance. Otherwse the detectve ablty of radar would be reduced. owever, f the nuber of snapshots s too sall, the tes of changng weghts wll becoe too great. It s dffcult to process rapdly because of the ncrease of coputaton. Consderng the two factors,.e. the propertes of RFI and coputng capacty of algorth, we dvde the coherent ntegraton te nto n sectons. Each secton whch lasts 3s has q scannng perods. It s obvous that the aorty of sgnals whch the radar receves are echoes of ocean waves whch are contnuous n wde angle range. That s to say, the echoes of ocean waves n a test range cell have any drectons [5]. So, the echoes of ocean waves whose drecton are dfferent fro the desred drecton of adaptve beaforer are also suppressed. The proble can be overcoe by usng the specal covarance atrx estaton, whch s accordng to the propertes of RFI such as great power, a certan drecton and wde exstng range [6]. RFI exsts all range cells, but the useful sgnal of ocean wave occupes a sall part of range cells. To solve the proble entoned above, we can utlze the snapshots of far range cells whch have not useful sgnal of ocean wave to estate covarance atrx. The processng detals are descrbed as follows. Supposedly, the nuber of far dstance cells whch have not useful echo sgnal s N and there are p tes of scannng data before a certan ref pont of te n the far dstance cell. We can construct the vector [ ( ( ] T, k = x k p +, L, x k, T expresses transpose, s the nuber of far dstance cells, =,, L, Nref, k s the current te. So, at the current te k, the covarance atrx of estaton the RFI s expressed by the forula N ref R = x k k N,, ref (3. = ere s the transpose of coplex conugate. IV. TE SOLVING TE PROBLEM OF CONSISTENT DETECTION CAUSED BY ANTENNA PATTERN CANGE The purposes of utlzng adaptve beaforer are to suppress RFIs whch have dfferent drectons fro that of desred sgnal and to avod nfluencng the correct detecton of useful echo sgnal. That s to say, the consstent detecton of ocean echo should be preserved n the process of weght change. W, W, L, W n are the weght vectors whch correspond to M te parts entoned above and R, R, L, Rn are the covarance atrx correspondngly. Forula 3 can be conventonally solved by utlzng the saple atrx nverson (SMI algorth [7]. W s acqured by usng R accordng to MVDR crteron. Then the th output of adaptve beaforer can be expressed by usng the weght vector W and the nput (4

3 sgnal of antenna array durng the th te-span. It can be descrbed by y( t = W ( t,where t = q(, L, q (6. There exsts a proble to be dscussed n the next secton. W s acqured by usng covarance atrx R accordng to MVDR crteron. The output of beaforer can be expressed by y( t = W ( t, where t = 0,, L, q. It s obvous that the consstent detecton can be preserved durng the frst tespan, because the weght vector W s unchanged durng the frst te-span. If the second weght vector W of beaforer can be coputed by the sae ethod, we can ensure the consstent detecton durng the second te-span for the sae reason that the weght vector W s unchanged durng the second te-span. The adaptve beaforer durng the q scannngs conssts of the two beaforers whose weght vector are W and Wrespectvely. If weght vector W s coputed separately and wthout any relaton wth W, the consstent detecton can not be preserved where the last part of the frst te-span eets the ntal part of the second te-span, because the pattern of antenna array changes nstantaneously wth the varety of weght vector. ow to preserve the consstent detecton s the crux of the atter. We can ake the pattern of antenna array ore stable by usng loaded SMI (LSMI algorth whose saple can be expressed by R + αi, where α ust be selected properly. The weght vector based on LSMI algorth can be coputed by the forula W = V θ R + αi V θ R + αi V θ (7 [ ( { } ( ] { } ( The pattern becoes ore stable as α ncreases, but ts ablty of suppressng RFI s weakened. The value of α s great enough to change the adaptve beaforer nto conventonal dgtal beaforng. So n the selecton of α s value we should consder the balance between the stablty of pattern and the ablty of suppressng RFI [8]. The paper proposes the weght teratve algorth to ensure consstent detecton. The ntal weght vector s acqured by usng the conventonal MVDR crteron, but the other weght vectors s derved fro the late weght vector by usng the conventonal LCMV crteron. The change of antenna pattern s orthogonal to the echo subspace of the late te-span. So the purposes of suppressng RFI and overcong the dscontnuty caused by nstantaneous change of antenna pattern can be acheved at sae te. The followng llustrates how to construct the sgnal subspace. The ocean echo sgnal whch the radar receves can be expressed wth the forula ( ( ( { } ~ π f f t t r t A e A e { ( f f t ( t } e ( s + b + φ π s b + φ = + + t ~ A A express the apltudes of the negatve and postve frst-order spectral peaks of ocean echo respectvely. f b s Bragg frequency. φ ( t expresses the nfluence caused by ocean current. e ( t expresses the nfluence caused by the (8 second-order scatter. The echo sgnals of ocean current drectons can be expressed wth π ( fs + fb t π ( fs fb t c( t = cg + ca ( t e + cr ( t e (9 ere cg expresses the secton of zero ertz Doppler frequency. The nfluences of advance Bragg wave coponents can be descrbed wth, where I ( a, V ( πφ ( t ( t = A e + β ( t c θ a = πφ ( t A e ( t a, (0 β express the nfluences of the frstorder and second-order scatter of the th ocean wave respectvely. The nfluences of recede Bragg wave coponents can be descrbed wth I ~ πφ ( t cr ( t = A e + β r, ( t V ( θ ( ~ = πφ ( t, where A e β r, t express the nfluences of the frstorder and second-order scatter of the th ocean wave respectvely. We beleve that the Doppler shft caused by ocean current s not changed durng the sall te-span. Assung that the Doppler shft caused by ocean currents at the new te-span s δ f, we can express the ocean echo wth the forula c t = A p t, t = Q M l, L, QM ( ( ( ( ( = c, c τ, c τ (3, [ g a r ] π ( f f t ( f f t ( [ ] T + b π b t =, e, e ere A ( ( p (4 f = f s + δf, τ = Q( M. So we can express the sgnal subspace of the th te-span as A. That s to say, the sgnal subspace durng the coherent ntegraton te s n constant change. ow to realze the adaptve beaforer based on the weght teratve algorth s descrbed n the followng secton. The frst weght vector W s coputed by usng the covarance atrx R accordng to MVDR crteron. The second weght vector W s fored by ltng the change of correspondng antenna pattern to preserve orthogonal to the sgnal subspace of the second te-span. What s dscussed can be expressed wth the forula ( W W A = 0 (5 That akes the weght vector W change fro the weght vector W, and the dfference Δ W, = W W has no nfluence on the ocean echo data of the second te-span c( t = A p( t. In other words, the results of processng the second te-span ocean echo wth the output of beaforer whose weght s W are the sae as the results of processng the second te-span wth the output of beaforer whose weght s W. So the consstent detecton of the two te-spans can be preserved wth the above ethod. When the second-order scatter s consdered n the treatent, we utlze W to operate n ntal 7 pluses n the second tespan to ake the coputaton sple. We defne the forula

4 ( t W ( t W = for t = q, L, q + 6 (6 to ake the second flter satsfy the constrants of 7 lnear equatons. Because of lts of the 7 equatons, the change of W s orthogonal to the sgnal antenna pattern caused by subspace. The dscontnuty can be overcoe durng the two te-spans. In a word, the second beaforer based on weght W can suppress the nonstatonary RFIs and preserve consstent W detecton. The process can be expressed wth the followng forulas. We get the frst weght W fro forulas7 and 8 drectly based on MVDR algorth. nw R W (7 W ( θ W V = (8 The second weght W can be acqured by the forula 9 based on LCMV algorth. nw RW W subect to C W = f (9 ere C = V θ, Q, L, Q 6, [ ( ( ( ], ( Q W,, ( Q + + [ W ] T f = L 6. So, the weght W can be coputed wth the forula [ C R C ] W = R C f (0 The other ocean echo data n the surplus te-spans can be treated wth the sae ethod. The th weght vector can be coputed wth [ C R C ] f W = R (. ere C = V θ, q, L, q + 6 C [ ( ( ( ( ( ], ( q( W,, ( q( W f + 6 [ ] T = L. The teratve processng s not over untl the date of whole coherent ntegraton te s used. V. APPLICATION At frst, we select the actual data fro the Rado Propagaton Lab n Wuhan Unversty to extract ocean dynac paraeters on the Zhuaan Island of Zheang provnce n Chna at 3:45 on Apr The radar paraeters are set as follows. Carryng frequency s 7.973Mz and range resoluton s.5k. Sweep perod s 0.653s and coherent ntegraton te s about 3 nutes. The nuber of range cell s 3. The nuber of eleents n antenna array arranged n one lne s 8 and the dstance between two neghborng eleents s d. Each te-span s 3s. The 8 channels are calbrated n the phase and apltude. The drecton whch rght faces the antenna array s 0 degree. The desred drecton s 0 degree. The antenna pattern of conventonal beaforer s shown n Fg.. The correspondng Doppler spectru n the range cell s shown n Fg.. The antenna pattern of conventonal beaforer s fxed and ts null s statonary durng the coherent ntegraton te. It can not suppress te-varyng RFI effectvely. The negatve frstorder peak can not be seen because of the exstence of tevaryng RFI. The weght vector n the adaptve beaforer changes autoatcally once every 3S durng the whole coherent ntegraton te accordng to te-varyng RFI. The nulls of antenna pattern are adusted to trace the RFI varety. There are two antenna patterns whch correspond to two weght vectors aong all the weght vectors n Fg.3 and Fg.4. Fg. antenna pattern of conventonal beaforer Fg. Doppler spectru whch corresponds to conventonal beaforer Fg.3 an antenna pattern of adaptve beaforer The deepest null n Fg. s at 6 degree, but the deepest null n Fg. s at 37degree. That s to say, when the drecton of strongest RFI s te-varyng, the adaptve beaforer can adust the poston of the deepest pattern null to suppress t. The Doppler spectru n the sae range cell whch corresponds to

5 adaptve beaforer s shown n Fg.5. The negatve frst-order peak can be seen clearly. [3] Van Veen, B.D., Buckley, K.M., Beaforng: a versatle approach to spatal flterng[j], ASSP Magazne, IEEE, Volue: 5, Issue:, Aprl 988, Pages: 4-4. [4] Thoas Dean Moore, B.S.E.E., M.S.E.E., Analytc study of space-te and space-frequency adaptve processng for rado frequency nterference suppresson[d]., thess of degree doctor n the Oho State Unversty, 00. [5] YANG Shao-ln, KE eng-yu, WU Sh-ca, et al. Sgnal Preprocessng for Bearng Deternaton of Ocean Surface Radal Current Mappng Based on MUSIC[J], Modern Radar, 00, 3(4: [6] Madden, J.M., The adaptve suppresson of nterference n F ground wave radar[j], IEE Int. Conf. Radar 87, London, UK, pp [7] Gershan, A.B., Nchel, U., Bohe, J.F., Adaptve beaforng algorths wth robustness aganst aer oton[j], Sgnal Processng, IEEE Transactons on, Volue: 45, Issue: 7, July 997 Pages: [8] B. B. Carlson, Covarance atrx estaton errors and dagonal loadng n adaptve arrays[j], IEEE Trans. Aerosp. Electron. Syst., Vol.4, pp , July 988. [9] SEN Fu-ng, adaptve sgnal processng(m, IAN Unversty Press, March, 003. Fg.4 another antenna pattern of adaptve beaforer Fg.5 Doppler spectru correspondng wth adaptve beaforer VI. CONCLUSION The paper proposed the ethod of specal adaptve beaforer for suppressng RFI n the space feld. The ethod can prove the detectve ablty of hgh frequency ground wave radar. The frst weght vector s acqured by usng MVDR algorth. The other weght vectors are coputed by usng LCMV. The change of weght vector whch depends on the late weght vector s realzed by teratve ethod. So the prevous weght vector can nfluence latter weght vector. It can ensure the consstent detecton whle suppressng RFI. The ethod can be utlzed n the other phase-controlled array radars. Because the nuber of eleents n our antenna array s 8, the axu nuber of RFIs whch can be effectvely suppressed s 6. That s to say, the nuber of eleents n antenna array lts the ablty of suppressng RFI n the way entoned n ths paper. When the nuber of RFIs exceeds the degree of freedo n antenna array, usng the ethod n ths paper to suppress RFI can not acheve perfect effect [9]. REFERENCES [] Madden, J.M., The adaptve suppresson of nterference n F ground wave radar[j], IEE Int. Conf. Radar 87, London, UK, pp [] L C Codara. Applcaton of Antenna Array to Moble Councaton, Part II: Beaforng and Drecton of Arrval consderaton[j]. Proceedngs of the IEEE, 997, 85(8: