Adaptive Double Notch Filter for Interference Suppression in the GPS Receiver

Transcription

1 ICCAS5 June -5, KINTEX, Gyeonggi-Do, Korea Adaptive Double Notch Filter or Intererence Suppression in the GPS Receiver Eu-Geun Han, Geon-Woo Lee, Chansik Park, Dong-Ho Shin, Sung-Soo Lee and Sang Jeong Lee Departent o Electronics Engineering, Chungna National University, Daejeon, Korea (Tel : ; E-ail: yghanc@cslab.cnu.ac.kr) School o Electrical and Coputer Engineering, Chungbuk National University, Cheongju, Korea (Tel : ; E-ail: chansp@cbucc.chungbuk.ac.kr) Agency or Deence Developent (Tel : ; E-ail: snoopy@add.re.kr) Departent o Electrical and Coputer Engineering, Chungna National University, Daejeon, Korea (Tel : ; E-ail: eesjl@cslab.cnu.ac.kr) Abstract: In this paper, an eicient schee o the adaptive notch ilter is presented or rejecting the narrow bandwidth intererences(nbi) in GPS receiver. Designed is the lattice IIR double notch ilter or ore eicient suppression o the NBI with less coputational coplexity. The algorith is o recursive prediction error or and uses a special constrained odel o IIR with a inial nuber o paraeters. This paper chooses seven dierent jaing scenarios including one with jaing or evaluating the proposed ilter algorith. The siulation results to the jaing scenarios show that the proposed algorith adjusts the double notch ilter eectively or the given JSR, and provides better SNR than the conventional algoriths. Finally, it is shown that the advantages o the proposed ilter algorith can range as high as JSR 79dB in tie doain processing. Also, the ADNF(adaptive double notch ilter) guarantees that ore than SNR db o GPS receiver can be always aintained. In conclusion, there is enough evidence to believe that the proposed algorith will peror quite well or reoving intererence signals. Keywords: GPS, Intererence Suppression, Estiation, Anti-Jaing, EW, ECCM. INTRODUCTION The GPS navigation satellite syste is designed to serve both ilitary and coercial needs. Because o its EW(Electronic Warare) applications, the ability to tolerate signiicant aounts to intererence and jaing was an iportant consideration in the design o the signal structure. Obviously, any radio-navigation syste can be disrupted by an intererence o suiciently high power, and the GPS is no exception. So the DSSS(direct sequence spread spectru) technique in the GPS eploys the PRN(pseudo rando noise) to spread the spectru o data sequence over a uch wider bandwidth than required. But when the intererence is too strong to be suppressed by the given processing gain o the spread spectru syste, the GPS receiver no longer operates properly. More speciically, it has been shown that NBI(Narrow Bandwidth Intererence) suppression capability o the GPS receiver can be urther enhanced by eploying adaptive ilters prior to dispreading[,. In this paper, an eicient ilter algorith is presented or adaptive notch iltering in GPS receiver. Precisely this paper eploys the lattice IIR double notch ilter or ore eicient suppression o the narrow bandwidth intererence with less coputational coplexity. The algorith is o recursive prediction error(rpe) or and uses a special constrained odel o ininite ipulse response(iir) with a inial nuber o paraeters. This paper is organized as ollows. Section designs the optial IIR notch ilter. In Section 3, the lattice requency estiation algorith is derived. In Section 4, the proposed intererence suppression syste is presented. The adaptive double notch ilter is also illustrated in detail. Siulation results are provided in Section 5 and inally conclusions are given in Section 6.. OPTIMAL LATTICE NOTCH FILTER DESIGN In this section, the optial lattice IIR notch ilter is designed or using ADNF. The transer unction o the second order direct or IIR notch ilter can be expressed as Eq.(). The IIR ilter with getting sae position pole-zero is designed or that the optial notch ilter reoves requency actorω in soe signals. As the narrowband signals approach sinusoidal signals, the zeros and poles approach the unit circle. In the liit, the poles and zeros are on the unit circle at the sae locations. However, or stability, the poles have to be kept away ro the unit circle[3, 4. ( e H ( z) ( e jw jw jw α )( α ) () z z + a z + α a z jw )( e z e + z + α z In Eq.(), α is the pole-zero contraction actor that adjusts the width o the notch, and a cos( w ) deterines the notch requency. The value o α closer to iplies the narrower notch. The requency response and pole-zero plot is described as Fig. by α. But it is shown that the lattice or notch ilter provides better convergence properties, and ore accurate requency estiate copared to the direct or ipleentations[6. H + a z + z ) z ( z) + a ( + α ) z + α z In Eq.(), it is shown that the IIR notch ilter o lattice type yields the unbiased requency estiate regardless o the pole-zero contraction actor and the noise variance, whereas ()

2 ICCAS5 the direct or o Eq.() yields the biased estiate. However, both Eq.() and Eq.() are ore or less direct ipleentations o the rational ractional transer unction. With increasing ilter order the direct realization o the transer unction becoes ore and ore critical with respect to noise perorance, stability and coeicient sensitivity. To avoid these probles, the transition to state-space structures which require a higher ipleentation coplexity but oer ore lexibility with respect to the control o the naed drawbacks. In this paper, because the ladder ilters exhibit excellent properties with respect to coeicient sensitivity, which renders the very appropriate to act as a odel or estiation ipleentations. As stated previously, there can be any ipleentation schees o realizing the transer unction in Eq.(). But we ipleent the transer unction by cascading all-pole and all-zero lattice ilters as shown in Fig.()[3. Magnitude Response(dB) o Filter H(z) June -5, KINTEX, Gyeonggi-Do, Korea 3. ADAPTIVE LATTICE ESTIMATOR DESIGN For the derivation o the adaptive algorith in this section, consider the requency estiator consists o stages connected in cascade as in Fig.4. For presentation o ALE in Fig., these relations are reproduced here in the expanded or. ( ( + kb ( n ) (4) b ( b ( n ) + k ( In Eq.(4),,, 3,..., M and M is the inal order o the predictor. Speciically, the relection coeicient k is chosen so as to iniize the su o the ean-squared values o the orward and backward prediction errors. Let the cost unction J denote this su at the put o stage o the lattice predictor. 5 J + ( b ( (5) Magnitude (db) -5 - Substituting Eq.(4) in Eq.(5), we get the cost unction Eq.(6). { ( + b ( n ) } J as J [ + k (6) + k ( b ( n ) + k b ( n ) ( Noralized Frequency(Xpi rad/sple) Fig. The requency response o optial IIR notch ilter Through transor ethod o lattice structure o discovered by Gray and Markel, the lattice structure is showed using two-ultiplier lattice and reversion o the two-ultiplier lattice as Fig.(). Eq.(3) is derived ro the optial IIR notch ilter o lattice structure[7. + k z + k z H (3) ( z) + k ( + a ) z + a z In general, the relection coeicient k is coplex valued, as shown by k α + jβ (7) Thereore, dierentiating the cost unction J with respect to both the real and iaginary parts o k, we get the coplex-valued gradient. J J α J + j β Putting this gradient to zero, we ind that the optiu value o the relection coeicient, or which the cost unction J is iniu, equals Eq.(9) (8) k b ( n ) ( (,,..., ) (9) ( + b ( n ), o M It derives Eq.(9) ro Eq.(8) or the relection coeicient. Its use oer two interesting properties. The relection coeicient k, o satisies the condition o Eq.() as a iniu-phase design or the ALE. k, o or all () Fig. The structure o the lattice IIR notch ilter The ean-square values o the orward and backward prediction errors at the put o stage are related to those at its own input as ollows.

3 ICCAS5 ( ), n k o ( () b ( k, o b ( n ) As described Eq.(9), k, o involves the use o enseble averaging. Assuing that the input u ( is ergodic, we ay substitute tie averages or the expectation in the doinator and denoinator o this equation. We thus get the relection coeicient o stage in the AL7, 8. b () () + b () (3) +... k () () + b () + (3) + b () +... s () s () + s () s () + s () s (3) + s () s (3) +... s () + s () + s (3) +... The adaptive algorith or the estiation o input requency is suarized as ollows: N( λ N( n ) + ( λ) s( n ) D( λ D( n ) + ( λ) s ( n ) N( k( D( k(, k(,, ( k ( ( k γ k ( n ) + ( γ ) k.6 k ( > k ( < Adaptive Frequency Predictor Perorance [ s( + s( n ) (3) June -5, KINTEX, Gyeonggi-Do, Korea related in the or o k cos π ja, the requency estiate at tie n is given by ( arccos k( (4) ja π It is shown that the IIR notch ilter o lattice type yields the unbiased requency estiate regardless o the pole-zero contraction actor and the noise variance, whereas the direct or yields the biased estiate. In Fig.6, it is presented the designed adaptive estiator perorance. It can estiate the intererence requency within saples and reove the intererence signal within.9s. 4. ADAPTIVE DOUBLE NOTCH FILTER DESIGN In previous section, the pole-zero position is placed on unit circle because ALE is to reove intererence copletely. But the ininite notch depth o the IIR ilter reoves the inoration signal as well as the intererence thereby causing data distortion. Hence, the sel-noise that causes data distortion also needs to be reoved by adjusting the optial reverse notch ilter. The ALE has been used to estiate intererence center requency and to transitted estiated requency paraeters as Fig. 5. The proposed algorith ilter section consists o the optial notch ilter and reverse notch ilter. The optial reverse IIR notch ilter can be expressed as Eq.(5). H τ + τ z (5) ( z) + k, inv, inv ( + k ) z + k z.4. Magnitude Response(dB) o Filter H(z) estiation value saples Fig. 3 The adaptive estiator perorance When the input to the ALE is a sinusoid corrupted by intererence, the RLS(Recursive Least Square) algorith in inds and tracks the requency and consequently enhances the sine wave. In Eq.(6), k ( is the estiate o the coeicient k at tie n. k ( is the interediate value beore soothing, and s ( is the put o all-pole section. The initial values, D () and N () should be suiciently sall to get better transient properties. Also, λ is the orgetting actor, and γ is the soothing actor. The coeicient is clipped in the range o [-,, as shown in Eq(6). Because the noralized notch requency ja and k are Magnitude (db) Magnitude (db) Noralized Frequency(Xpi rad/sple) Magnitude Response(dB) o Filter H(z) tau.3 tau. tau. tau Noralized Frequency(Xpi rad/sple) Fig. 4 The requency response o the optial notch ilter

4 ICCAS5, inv In Eq.(5), k and k, inv with respect to the notch depth and width have gotten the sae values to each other or exact intererence estiation. Also, it is iportant that to decide τ and τ paraeter values or exact estiation o the intererence signal power. In Fig.(4), the closer k, inv is to unity, the narrower the notch ilter response (inside the notch requency) will ake the bias saller. So the paraeter τ is respected to notch ilter response level. Thereore, it should adjust the two paraeters with consideration or intererence power and bandwidth. In this section, the adaptive double notch ilter(adnf) is designed using the optial notch and reverse notch or suppress intererence in the GPS receiver as Fig. 5. The RF/IF stage has ed received GPS signal which is quantized with bit into the ADNF. And the ALE o ADNF stage can estiate intererence requency using paraeters o lattice notch ilters. Estiated requency can be looked up by the optial reverse notch ilter which should estiate intererence signal. The put o optial notch ilter and reverse notch ilter is transitted to the input o correlator. The proposed ilter algorith can be presented through atheatical echanis. The received signal in the su o signal, noise and intererence has gotten the siple odeling as Eq.(6). June -5, KINTEX, Gyeonggi-Do, Korea where w is the center requency o the intererence, and ϕ is the rando phase uniorly distributed over ( π Then the put signal o the ADNF is given by,π ). y( H ( z) v( p ( + j ( w ( (8) + where p (, j ( and w ( are the put coponents o the data, intererence, and Gaussian noise, respectively. H (z) is the transer unction o the ADNF. H ( z) H ( z) H ( z) (9) notch + Inverse In Eq.(9), H notch ( z) and ( z) H Inverse are the coponents o the ADNF transer unction, the transer unction o the optial notch ilter and the transer unction o the optial reverse notch ilter, respectively. Let s try to deine their put into the coponents o ADNF. y ( ynotch( + yinverse( H notch( z) v( + H Inverse( z) v( p ( + j ( + w ( j ( N. N. N. I. () The put o the notch and the inverse notch is deined by y notch ( and y Inverse (. p N. (, jn. ( and w N. ( are PN code, intererence and Gaussian noise at the optial notch put. j I. ( is the estiated intererence signal in the optial reverse notch ilter. ( j ( j ( j N. I. () When the optial reverse notch ilter perorance is axiized, it is deined as Eq.(). It is necessary that j ( is reoved as uch as possible and the pure PN code is aintained under regular condition. In order to help the ALE and reverse notch ilter to estiate intererence signal exactly, the adequate paraeters can be used. The perorance requireent o the optial reverse notch ilter is presented through the SNR o ADNF. Fig. 5 The GPS receiver structure using the adaptive double notch ilter v ( d( + j( + w( (6) where d ( is the data signal ultiplied by the PN code, j ( is a single tone intererence represented by a sine wave with rando phase, and w ( is the white Gaussian noise. I the data signal has noralized agnitude o or - and the PN code is long enough, d ( can be considered as a sequence p ( which is either or - with equal probability. Speciically, the input signal can be rewritten as v ( + Acos( wn + ϕ ) + w( (7) SNR p ( () ( y( ) Since it is obvious that E [ p ( in our odel, ( y( ) can be obtained by deriving E [ y( and E [ y ( with respect to the ipulse response o the ADNF. I we assue that p (, j ( and w ( are independent ro one another, p (, j ( and w ( can also be seen to be independent. Hence, it ollows that E [ y ( h k j w k (3)

5 ICCAS5 where h k is the ipulse response o the ADNF, and w σ j and σ are variances o j ( and w (, respectively. By the independence, E [ y( is also given by [ y p ( + + h E ( (4) Fro Eq.(), Eq(3) and Eq(4), the put SNR is described as SNR k h k j w h + (5) June -5, KINTEX, Gyeonggi-Do, Korea proposed ilter algorith at JSR 74dB. The higher value o JSR, the ore clear the ADNF perorance as the increasing rate o SNR and anti-jaing o the receiver. Table Seven Dierent Jaing Scenarios (Including one with jaing) Jaing Property Scenarios No Jaing Coherent CW (CCW) Frequency Hopping CW ᆞ White noise center requency : MHz ᆞ Center requency : MHz ᆞ Tie deviation : s ᆞ Frequency deviation : khz The put SNR o ADNF is presented to have kept the derived SNR axiizing. ( j ( j ( ) σ j ( (6) j notch inverse Thereore, the put SNR varies ro the put variance o intererence, σ j. Finally, the axiu put SNR is guaranteed by the estiation perorance o intererence in the proposed ilter algorith, ADNF. Swept CW (SCW) Aplitude Modulation (AM) Frequency Modulation (FM) ᆞ Center requency : MHz ᆞ Frequency deviation : ±5 khz ᆞ Center requency : MHz ᆞ Modulation requency : khz ᆞ Modulation depth : 5. % ᆞ Center requency : MHz ᆞ Modulation requency : khz ᆞ Frequency deviation : ±5 khz 5. SIMULATION RESULTS In this section, coputer siulation is perored to show the ADNF perorance using seven dierent jaing scenarios as Table. Each narrow-band jaing is deined as any unwanted signal occupying less than the entire ±.3MHz bandwidth o C/A code. Generally, the iniu value o db JSR was chosen because C/A acquisition at 4dB JSR is a coon ilitary requireent. The axiu value 8dB was chosen because no GPS receivers can track at 8dB JSR against a wideband jaer with eploying beasteering, nulling, or soe other ulti-eleent antenna technique in the ost odern weapon systes. There is siply not enough processing gain available[5. Fig. 6 shows the eect o narrowband intererence in the GPS receiver. When GPS receiver is tracking signal, it gradually increases the power o signal generator until ailing to track the signal. The perorance o GPS receiver are sensitive to likely In-Band intererences. In other words, In-Band intererence is ore inluential in the GPS receiver perorance than Out-Band intererence which is easily reoved by band-pass ilter. Using the proposed ilter algorith, ADNF, Fig. 7 shows the coparison o SNR or seven dierent jaing scenarios as JSR changes. It can perceive the JSR perorance o GPS receiver through generating jaing signal stage by stage. In Fig. 7, the ADNF guarantees that iniu JSR perorance o the receiver is ore than JSR 7dB in CCW, PM, Swept CW and Frequency Hopping CW jaing scenario. The receiver which has the ADNF get loss o lock ore than JSR 55dB in AM jaing scenario and to ail code tracking ore than JSR 49dB in FM jaing scenario. Fig. 8 shows that increasing rate o SNR is presented by seven dierent jaing scenarios. It presents dierence o SNR between the processing gain and the ADNF. It is evident that perorance with the ADNF enabled has alost increasing rate o SNR 5dB than the receiver with the Phase Modulation (PM) SNR [db. ᆞ Center requency : MHz ᆞ Phase repetition : 75 ns ᆞ Phase width : 75 ns Fig. 6 J/S versus Intererence Frequency at loss o lock JSR [db CW FHCW SCW AM FM PM Fig. 7 SNR versus JSR or each scenario Fig. 9 shows the coparison o beore the ADNF enabled and ater the ADNF enabled or each scenario. The receiver beore the ADNF enabled gets an average JSR 5dB

6 ICCAS5 perorance. However, the proposed ilter algorith guarantees that axiu JSR 79dB is presented with iproved intererence suppression. In CCW, Swept CW, PM and FHCW jaing scenario, the proposed ilter algorith guarantees high perorance o the GPS receiver, given the GPS receivers can not track at JSR 8dB against a jaer with eploying soe ulti-eleent antenna techniques. It also let receiver perorance ake the ore than JSR 4dB in AM, FM jaing scenario. In this result, i the GPS receiver itsel has anti-jaing perorance ore than beore, anti-jaing o the ADNF perorance has been iproved. SNR Increasing [db JSR [db JSR [db CCW FHCW SCW AM FM PM Fig. 8 ADNF perorance Increasing rate o SNR CCW FHCW Swept CW AM FM PM Filter OFF Filter ON Fig. 9 Coparison o ADNF perorance according to Jaing JSR [db CCW FHCW Swept CW AM FM PM JSR Increasing Fig. ADNF perorance Increasing rate o JSR One o EA(Electronic Attack) issions has to operate EA application during 3~8sec and be not sae position ore than 5 inutes or destroying and detecting the target by DF(Direction Finder). Because o this reason, FHCW and Swept CW intererence signal is used priarily or EA issions. In Fig.9, the proposed ilter algorith has showed a strong anti-jaing perorance in FHCW and Swept CW. Fig. also shows that the ADNF has presented increasing rate o JSR 4dB or ore in FHCW and Swept CW jaing scenario. The proposed ilter algorith has kept the good June -5, KINTEX, Gyeonggi-Do, Korea perorance o receiver against ECM(Electronic Counter Measures). In CCW and PM, the ADNF has guaranteed the best perorance the receiver o the seven scenarios. Because it is vulnerable to CCW and PM in coercial GPS chipset receiver, the GPS receiver can iniize the eect o intererence signal using the proposed ilter algorith. 6. CONCLUSION In this paper, the adaptive double notch ilter has been proposed or the excision o narrow-band intererence in GPS receiver. The zeros o the notch ilter are adjusted to induce the notch on the requency o the intererence using the adaptive requency estiators. However, i the zeros are on the unit circle, the notch depth is ininite and the ilter reoves the inoration as well as the intererence. This causes data distortion and the perorance o the receiver is degraded below the level o the case that no excision is perored. Hence the optial reverse notch ilter is proposed to preserve data as well as intererence estiation. For this purpose, we have designed the ADNF which GPS receiver structure has been aligned with parallel between the notch and reverse notch. As an estiator o the requency, we eployed the IIR adaptive line enhancer. Using the ADNF, the anti-jaing o receiver has gotten average JSR 64dB and increasing rate o JSR 38.dB. The siulation results show that ADNF has iproved anti-jaing, reliability and eiciency o the receiver. REFERENCES [ Bradord W. Parkinson and Jaes J. Spilker Jr., Global Positioning Syste: Theory and Applications, Aerican Institute o Aeronautics and Astronautics Inc., 996 [ Elliott D. Kaplan, Understanding GPS principles and applications, Artech House Publishers, 996 [3 Dietrich Schlichtharle, Digital Filters basic and design, Springer, [4 Ba-Ngu Vo, Antonio Cantoni, Kok Lay Teo, Filter Design with Tie Doain Mask Constraints: Theory and Applications, Kluwer Acadeic Publishers, [5 Gregory D. Rash, GPS Jaing in A Laboratory Environent, Naval Air Warare Center Weapons Division(NAWCWPNS), 997 [6 D.V. Bhaskar Rao and S.Y. Kung, Adaptive Notch Filtering or the Retrieval o Sinusoids in Noise, IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-3, pp.79-8, Aug [7 Bernard Widrow, Sauel D. Stearns, Adaptive Signal Processing, Prentice-Hall Inc., 985. [8 Sion Haykin, Adaptive Filter Theory, Prentice-Hall Inc., 996. [9 Na-Ik Cho, Chong-Ho Choi, Sang-Uk Lee, Adaptive Line Enhanceent by Using an IIR Lattice Notch Filter, IEEE Trans. Acoust., Speech, Signal Processing, vol. 37. No. 4. April, 989. [ Moeness G. Ain, Intererence Mitigation in Spread Spectru Counication Systes Using Tie-Frequency Distributions, IEEE Trans. Acoust., Speech, Signal Processing, vol. 45 No.. January, 997. [ Moneness G Ain, Chenshu Wang, Alan R. Lindsey, Optiu Intererence Excision in Spread Spectru Counications Using Open-Loop Adaptive Filters, IEEE Trans. Acoust., Speech, Signal Processing, vol. 47, No. 7. July 999.