A Novel Continuous Wave Interference Detectable Adaptive Notch Filter for GPS Receivers

Transcription

1 A Novel Continuous Wave Interference Detectable Adaptive Notch Filter for GPS Receivers Ying-Ren Chien 1, Yi-Cheng Huang 2, De-Nian Yang 3, and Hen-Wai Tsao 4 Research Center for Information Technology Innovation, Academia Sinica 1,3 Institute of Information Science, Academia Sinica 3 Graduate Institute of Communication Engineering, National Taiwan University 2,4 {curtis 1,dnyang 3 }@iis.sinica.edu.tw, kshscoolevan@gmail.com 2, tsaohw@cc.ee.ntu.edu.tw 4 Abstract In this paper, we propose an interference detectable adaptive notch filter (ANF) for GPS receivers. The proposed ANF can estimate the existence of continuous wave interference (CWI) and its power, by exploiting the statistic value within an adaptive second-order infinite impulse response (IIR) filter. Moreover, our ANF is modulized, which allows more modules can be included to deal with multiple CWIs. We also design an adaptation algorithm for each ANF module and prove that the ANF module can adaptively notch the strongest CWI at its input, and this merit enables us to notch the primary CWIs with a limited number of ANF modules. Simulation results show that the adaption of the ANF modules converges in four iterations, and the signal to interference plus noise ratio (SINR) improvements can reach 21 db. I. INTRODUCTION A Global Positioning System (GPS) receiver inherently has the anti-jamming ability due to its characteristics of spreading spectrum. However, the performance of GPS receivers will severely degrade as the jamming signals are higher than the system s anti-jamming ability. The existing results [1] indicated that one of the most insidious jamming sources is the continuous wave interference (CWI), which can easily overwhelm a GPS receiver s analog-to-digital converter (ADC) at the analog front-end part and paralyze the GPS. CWI rejection by adaptive filtering techniques has attracted great attention recently and can be classified into timedomain [2] [4] and frequency-domain approaches [5] [7]. Rusch and Poor [2] proposed an enhanced nonlinear method to suppress the interferences. However, this approach requires a nonlinear function tanh, which is more computational intensive. Moreover, the performance depends on the correctness of the feedback data. In [4], the authors utilized a notch filter to reduce spurs and combined a feedback filter to cancel intersymbol-interferences caused by the notch filter. However, the performance may degrade due to the decision errors. Ma et al. [3] proposed an adaptive all-passed based notch filter to reject the CWIs. However, hardware cost may increase because the information of the covariance matrix and its inverse are required during the adaptation process. In addition, Wang et al. [5] designed a partial coefficient updating algorithm to adaptively update N sets of interference rejection blocks in frequency domain. Capozza et al. [6] proposed an N-sigma excision algorithm to null CWIs in frequency domain. Balaei and Dempster [7] devised a statistically hypothesis testing to detect GPS interference in frequency domain. Zhang et al. [8] proposed a wavelet transform based approach to suppress the CWIs. However, the major concerns about the above transferred domain approaches are the hardware complexity, which comes from Fast Fourier transform (FFT), inverse FFT, or wavelet transform blocks in the hardware. Moreover, the windowing blocks are desired to avoid significant spectral leakage issues [6] and hence incurs higher cost. In this paper, therefore, we propose a low-complexity timedomain approach, called the adaptive notch filter (ANF) module, which is able to detect, estimate, and notch one single-tone CWI. The ANF module is composed of a simple second-order IIR filter with the lattice structure. We show that if the 3 db bandwidth of the IIR filter is less than about 30 KHz, the non-linear phase response of the IIR filter brings almost zero offset on both the acquisition and tracking loops. Therefore, the proposed ANF does not require complicated FFT blocks. Moreover, to adaptively adjust the notch frequency, we crosscorrelate the output and internal adaptive signals of the ANF module. The power of the notched CWI can be simultaneously estimated by using the internal adaptive information embedded within the ANF module as well. Furthermore, we devise a novel jamming signal detection algorithm without using frequency-domain information. When there is no jamming signal, the received signal will bypass the ANF module so that the degradation of signal-to-noise ratio (SNR) caused by the ANF can be avoided. The proposed scheme can deal with multi-tone CWIs by cascading the ANF module, and we prove that each stage can notch the strongest CWI appearing at its input. The rest of this paper is organized as follows. Section II describes the system model and two performance evaluation metrics. We propose the adaptation algorithm of the ANF module and the corresponding CWI detection and estimation algorithms in Section III. Section IV presents simulation results and shows how to determine the 3 db bandwidth of the ANF modules and the value of CWI detection threshold. The performance of multiple CWIs detection and rejection are demonstrated as well. Finally, we conclude this paper in Section V.

2 A. Received signal models II. SYSTEM MODELS Figure 1 shows a GPS anti-jamming system model. The received signal r(t) is composed of GPS signal s(t), additive white Gaussian noise (AWGN) w(t) with zero mean and two-sided power spectral density N o /2, and CWI j(t). The transmitted GPS signal is assumed to be s(t) = 2P s [B(t) C(t)] cos(2πf L1 t + θ), (1) where P s is the power of signals with coarse acquisition (C/A) code C(t) with chip rate R c = MHz, D(t) is the navigation data,, θ is the phase delay, and f L1 denotes the carrier frequency of L1 ( MHz). The jamming signals are assumed to be multi-tone CWIs and can be expressed as K j(t) = 2PJ,i cos(2πf J,i t + θ J,i ), (2) i=1 where K is the number of CW interferences and P J,i, f J,i, and θ J,i are the power, frequency, and phase delay of the i th jamming signal, respectively. Note that r(t) is bandpass filtered, amplified, and down converted to the intermediate frequency (IF) f IF of 4.092MHz. Details about the proposed ANF module are explained in Section III. B. Performance evaluation metrics After the received signals r[n] pass through the ANF module, the proposed scheme notches not only the CWI but also the GPS signal on the notch frequency. Therefore, the performance of acquisition and tracking loops in the digital signal processing (DSP) block will deteriorate. To evaluate the performance of the acquisition and tracking loops, we propose two metrics, called signal to interference plus noise ratio (SINR) and phase bias, as defined as follows. Let SINR Γ denote the power ratio of the main peak value to other off-peak values after the received signals are despreaded, η[k] Γ AVG n =k,k±1 {η[n]}, (3) where k = arg max n {η[n]} denotes the index of the peak of the correlation output, {η[n]} denotes the output of circular cross correlation between the input of acquisition block and the C/A code, and AVG { } denotes the average operation. Note that the higher Γ leads to the better quality of the despreaded signals. Moreover, we define Γ a and Γ d as the SINR value when the proposed ANF modules are activated and deactivated, respectively. Therefore, the SINR improvement gains from the ANF modules can be defined as ΔΓ Γ a Γ d. (4) The other metric, phase bias ΔΦ, quantifies the zerocrossing code phase bias (tracking bias) at the code loop discriminator caused by the ANF module. ΔΦ Φ a (χ =0) Φ d (χ =0), (5) Discriminator output χ (unit: chips) Fig. 2. r[n] r(t) ADC Adaptation Fig. 1. Proposed ANF module H N (z) x[n] y[n] MUX CWI Detection A GPS anti-jamming system model. DSP Block w/o ANF with ANF Phase error Φ (unit: chips) An example to illustrate the phase bias caused by the ANF module. where Φ a and Φ d are the chip errors when the proposed ANF modules are activated and deactivated, respectively; χ denotes the output of the code loop discriminator. As illustrated in Fig. 2, due to the non-linear phase responses associated with an IIR notch filter, the output of the code loop discriminator has a bias and therefore results in tracking biases. The phase error of 1/16 chips is equivalent to the tracking error about 18 meters. However, our proposed ANF module is able to reduce the phase errors to zero by controlling its 3 db bandwidth smaller than certain value which is determined in Section IV later. III. PROPOSED CWI DETECTABLE ANF In this section, we propose using a second-order adaptive IIR notch filter with lattice structure as the ANF module for each stage. This time-domain approach can avoid the costly transfer domain blocks. Moreover, the impact of non-linear phase of the ANF filter can be minimized by controlling its 3 db bandwidth less than a certain value, such that the maximum value of phase biases ΔΦ becomes acceptable. We leverage the statistical value of the state within the ANF to detect CWI and estimate its power. Furthermore, the proposed ANF module can be cascaded to notch out multiple CWIs, ΔΦ

3 un [ ] rt () yn [ ] D 1-1 D ADC rn 1[ ] 1 Stage-1 K Stage-K rn 2[ ] r [ n] K r 1[ n] K DSP Block x[ n] Fig. 4. The block diagram of an anti-jamming GPS receiver with multiple ANF modules. Fig. 3. The block diagram of the second-order ANF. and as shown in the appendix, we prove that each stage can notch the strongest CWI appearing at its input. The details are described as follows. A. ANF architecture Figure 3 shows the block diagram with the input signals u[n], output signals y[n], and adaptive signals x[n]. The IIR notch filter is stable if both the absolute value of α and β are smaller than 1. The Z-domain transfer function of the notch filter is characterized by H N (z) Y (z) U(z) = 1+α 1 2βz 1 + z β(1 + α)z 1, (6) + αz 2 where Y (z) and U(z) are the Z-transform representations for y[n] and u[n], respectively. The 3 db bandwidth B and notch frequency ω N are controlled by α and β, respectively, and can be expressed as [9] α = 1 tan(b/2) 1 + tan(b/2) (7) β =cos(ω N ) with ω N [0,π], (8) Note that the adaptation for the 3 db bandwidth and notch frequency are independent with each other. If the CWI appears in the passband of the GPS signal, the ANF will notch both CWI and GPS signals. We fix the parameter α and only adapt β in this work to avoid notch too much GPS signals. The intuition behind the adaptation algorithm is explained as follows. If the CWI has been notched, y[n] s[n] +w[n] and x[n] j[n] must hold. In this case, the cross-correlation between j[n] and s[n] +w[n] is negligible. Therefore, we can exploit the correlation between y[n] and x[n] to adapt β. The proposed adaptation algorithm can be expressed β[n +1]=β[n] λ[n] {y[n]x[n]}, β < 1, (9) where λ[n] is a time-varying step-size. To speed up the convergence rate, we choose the time-varying step-size as [10] λ[n] = μ φ[n] with φ[n] =ρφ[n 1] + (1 ρ)x 2 [n], (10) where μ is the constant step-size for adjusting the convergence rate, φ[n] is an instantaneous power estimation of x[n], and 0 <ρ 1 is the forgetting factor. B. Detection of CWI and power estimation It has been shown that the transfer function H B (z) from u[n] to x[n] has band-pass property, and the corresponding frequency response has the maximum amplitude at the notch frequency [9]. Therefore, the transfer function can be expressed as H B (z) X(z) U(z) = 1+α (1 β)z β(1 + α)z 1. (11) + αz 2 We leverage the above property to estimate the jamming power ˆP J [n] at the discrete time index n, which can be expressed as φ[n] ˆP J [n] = G H B (e jωn ) 2, (12) where G is the gain from the received antenna to the input of ANF and φ is defined in (10). Moreover, we exploit the variance of β to detect whether the CWI appears. From (9) and (12), we have var(β) μ2 σ 2 w φ μ 2 σ 2 w ˆP J G H B (e jωn ) 2, (13) where var ( ) denotes the variance operator, and σ 2 w denotes the power of AWNG noise. When the CWI exists and has been notched, the value of var(β) becomes very small. We need to pre-define a threshold parameter ν and then periodically calculate var(β). If ν>var(β) holds, there is no CWI, and the notch filter will be bypassed. Otherwise, CWI appears, and the notch filter will not be bypassed. C. Multistage extension Unlike the costly transferred domain approach, which can cancel multiple CWIs in the transferred domain, our ANF module can only notch one CWI. However, we offer a lowcost alternative to notch out multiple CWIs by cascading the ANF modules as shown in Fig. 4. The multistage configuration will notch the i th strongest CWI at the i th ANF module during the adaptation processing. We explain this property as follows. Without loss of generality, we assume r 1 [n] suffers from K CWIs with jamming power P J,i for i =1,...,K, and P J,i >P J,j holds for i<j. The input signal at Stage-1 is given by r 1 [n] =s[n]+w[n]+j[n] K w[n]+ 2PJ,i cos(2πf J,i n + θ J,i ). (14) i=1

4 Since each ANF module is designed for notching only one CWI, Stage-1 needs to optimize its notch frequency to minimize the objective function defined in (16). The objective function of the i th stage is defined as the expectation of square value of its output, i.e. E [ r 2 i+1 [n]]. Therefore, for Stage-i with E [ r 2 i+1[n] ] β i = arg min β i E [ r 2 i+1[n] ] (15) K 2PJ,k H N (e jω J,k ) 2 k=i + σ2 w 2π π H N (e jω ) 2 dω, (16) where ω J,k = 2πf J,k. Note that H π N (e jω ) 2 dω is a constant depending on the parameter α i and is independent with β i. The minimal value of E [ ri+1 2 [n]] occurs when the i th strongest CWI has been notched out at the i th stage. The details of the proof can be found in the appendix. IV. SIMULATION RESULTS In this section, we show the performance of the proposed anti-jamming GPS receiver with four ANF modules and three CWIs. We perform the CWI detection, estimation, and cancellation in time domain, rather than transferred domain [5] [7]. In addition, this paper emphasizes on the abilities of CWI detection and estimation of the proposed ANF module. Therefore, our simulation results do not compare with previous works. Simulation results show that our adaptation algorithm converges in four iterations, and the resulting notch frequency corresponds to the jamming frequency. These three CWIs are notched in the first three stages, and the last stage detects no CWI in only two iterations. The amount of SINR improvements defined in (4) is evaluated as well. The parameters in our simulation are described as follows. The bandpass filter in the analog front-end is a 6-th order Butterworth filter with the center frequency at MHz, the automatic gain controller is adjusted every 5 ms, the sample rate of the ADC is MHz, and the number of bits of the ADC is 5-bit. We consider that the values of C/N o are between 35 to 55 db-hz. The parameters used by the adaption for β are: μ = 2 6 and ρ = A. Determination of the values of α and threshold ν We evaluate the maximum ΔΦ,defined in (5), for different choices of α to keep the biases within an acceptable level. Fig. 5(a) shows the maximum phase biases for all possible β under different 3 db bandwidth. Therefore, we let the 3 db bandwidth of the ANF module smaller than about 31 KHz, which corresponds to α = Furthermore, we check the impact of the non-linear phase response of the ANF module on the carrier tracking loop in GPS receivers. The algorithms adopted in the carrier frequency-locked loop (FLL) and carrier phase discriminator are four phase frequency discrimination (atan2) and Costas discrimination, respectively [1]. Maximum phase bias (unit: chips) db bandwidth B (unit: KHz) (a) (b) (c) Fig. 5. Determination of the 3 db bandwidth of the ANF module. (a) Maximum phase bias (b) FLL frequency discriminator (c) Costas phase discriminator. Figure 5(b) shows that unless β is not changed from one integration period (10ms) to the next period, we have to choose a large α to avoid the biases at the output of the FLL discriminator. Similarly, as shown in Fig. 5(c), if we set α =0.99, the output carrier phase error is very close to the ideal case, i.e. the ANF module is bypassed. Therefore, in the sequel, we choose α = 0.99 without explicitly specification. Figure 6 shows the value of var(β) under different circumstances. To avoid the false alarm, we choose ν = In this case, the probability of the false alarm is about 2%

5 var(β) ν C/No=45 db Hz, JSR=17 db C/No=45 db Hz, JSR=25 db C/No=55 db Hz, no jamming Estimated jamming power ˆPJ,i Stage 1 Stage 2 Stage 3 Stage 4 PJ,1 ˆPJ,1 PJ,2 ˆPJ,2 ˆPJ,3 PJ,3 ˆPJ,4 [var(β 4 ) >νhas been detected] E [ r 2 i+1] (unit: db) Time (unit: 5 ms) Fig. 6. Determination of the threshold ν. β 1 = β 2 =0.384 Stage 1 Stage 2 Stage 3 β3 = β Fig. 7. The objective functions for Stage-1 to Stage-3. when C/N o is 45 db-hz and JSR is 17 db. However, the false alarm rate is zero when JSR is 25 db. B. The performance of CWIs detection and rejection We use four-stage ANF modules to reject three CWIs and assume that C/N o is 45 db. The jamming frequency is MHz, 4.192MHz, and MHz, respectively, and the corresponding JSR values are 30 db, 50 db, and 40 db. The objective functions for Stage-1 to Stage-3 are shown in Fig. 7 and the corresponding optimal value of β are β1 = 0.038, β2 =0.038, and β3 =0, respectively. Figure 8 shows the estimation of the three CWIs at each stage. The estimation error increases when the JSR becomes smaller, due to the higher variation of β. Note that Stage-4 ANF module detects that var(β 4 ) >ν and bypasses the ANF module after 15 ms. Figure 9 shows the learning curves of β at each stage. As expected, the convergence rate is proportional to the JSR. Therefore, Stage-1, Stage-2, and Stage-3 sequentially converge. All these three stages converges in 25 ms (4 iterations). The resulting average values of β for the first three stages β Time (unit: ms) Fig. 8. Jamming power ˆP Ji estimation. β β β Stage 1 Stage 2 Stage 3 Stage Time (unit: ms) Fig. 9. The learning curve of β i at each stage. are 0.038, 0.038, and , respectively. The results indicate that the converged values are very close to their optimal value βi. Stage-4 diverges since there is no CWI at this stage. C. The SINR improvements ΔΓ Consider the case when C/N o is 45 db and α =0.996, which corresponds to the 3 db bandwidth B of about 10 khz. The SINR improvements ΔΓ are db, db, and 9.41 db when the CWI with f J =4.902MHz and JSRs are 50 db, 40 db, and 30 db, respectively. V. CONCLUSIONS In this paper, we have presented CWI detection and estimation algorithms operating in the time domain, which need no transferred domain information and therefore reduce the hardware cost, and proposed the ANF modules to notch multiple CWIs. Our algorithms leveraged the variation of β and the embedded band-pass characteristic of the ANF module to detect and estimate the strongest CWI that has been conducted into the i th stage. The threshold of CWI detection, ν, is determined according to C/N o and the acceptable false alarm probability. In addition, we have examined the impact of the non-linearity associated with the phase responses of ANF module on the acquisition and tracking loops. Simulation β 4

6 results have shown that: 1) The non-linear phase response of the ANF module causes zero phase bias if the 3 db bandwidth of the ANF is smaller than about 30 KHz; 2) the estimation error of jamming power is decreasing when the JSR is increasing; 3) the convergence time and resulting variation of β for each ANF module are decreasing when the JSR is increasing; 4) the proposed ANF module will adaptively adjust its notch frequency to the jamming frequency of the strongest CWI appears at its input when multiple CWIs appear; 5) the resulting SINR improvement reaches 21 db when the JSR is 50 db. APPENDIX In the appendix, we prove that cos 1 (βi ) equals to the jamming frequency with the strongest jamming power at the i th stage. As shown in [9], (6) is equivalent to H N (z) = 1 [1 + V (z)] 2 = 1 {1+ sin θ 2 sin θ 1 (1 + sin θ 2 )z 1 + z 2 } 2 1 sin θ 1 (1 + sin θ 2 )z 1 +sinθ 2 z 2, (17) where V (z) is the transfer function of an all-pass filter with θ 1 < 0.5π and θ 2 < 0.5π. Note that V (e jω )=e jφ(ω), where φ(ω) is the phase response of the all-pass filter. By comparing (6) with (17), we have α =sinθ 2 and β =sinθ 1. When ω equals to the notch frequency ω N, H N (e jφ(ωn ) )= 0 must hold. Hence, by solving V (e jωn )=e jπ,wehave ω N = θ π, (18) Consider the case that there are K CWIs at the i th ANF module and P J,m = max P J,i,fori =1,...,K. To minimize the cost function of the i th ANF module shown in (16), this optimization problem is therefore equivalent to min 2PJ,m HN (e jωj,m ) 2 + σ2 w θ 2 2π Note that π π HN (e jω ) 2 dω. (19) H N (e jω ) 2 dω = 1 [1 + V (e jω )][1 + V (e jω )]dω 4 π =0.5[1 + V (z = 0)] =0.5(1 + sin θ 2 ) =0.5(1 + α i ). (20) Let the derivative of the cost function in (19) with respect to θ 2 equal to 0. After some manipulation, we have where D(z) =1 sin θ 1 (1 + sin θ 2 )z 1 +sinθ 2 z 2. Since θ 1 <π/2, wehavecos θ 1 > 0; zeroing the remaining terms of (21) leads to [ e j2ω J,m ] 2 D(e jωj,m ) =1. (22) D(e jωj,m ) This condition must hold if and only if V (e jωj,m )= ej2ωj,m D(e jωj,m ) D(e jωj,m ) = ±1. (23) Finally, we obtain that V (e jωj,m ) = 1 when ω J,m = θ 1 + π/2 is the solution. Comparing the result with (18), we prove that the cost function is minimized when the notch frequency ω N equals to jamming frequency ω J,m, i.e. cos 1 (βi )=ω J,m. ACKNOWLEDGMENT This work was supported in part by MediaTek Inc. and National Science Council, R.O.C., under Grant NSC E MY3 and NSC E REFERENCES [1] E. D. Kaplan, Understanding GPS: Principles and Applications, 2nd ed. Artect House, [2] L. A. Rusch and H. V. Poor, Narrowband interference suppression in CDMA spread spectrum communications, IEEE Trans. Commun., vol. 42, no. 2/3/4, pp , Feb./Mar./Apr [3] W.-J. Ma, W.-L. Mao, and F.-R. Chang, Design of adaptive allpass based notch filter for narrowband anti-jamming GPS system, in Proceedings of IEEE International Symposium on Intelligent Signal Processing and Communication Systems, Dec. 2005, pp [4] S. Gunturi and J. Balakrishnan, Mitigation of narrowband interference in differentially modulated communication systems, in Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Apr. 2009, pp [5] Z.-S. Wang, M. Lv, and B. Tang, Paper application of partial coefficient update LMS algorithm to suppress narrowband interference in DSSS system, in Proceedings of International Conference on Electronic Measurement & Instruments (ICEMI), Feb. 2009, pp [6] P. T. Capozza, B. J. Holland, T. M. Hopkinson, and R. L. Landrau, A single-chip narrow-band frequency-domain excisor for a Global Positioning System (GPS) receiver, IEEE J. Solid-State Circuits, vol. 35, no. 3, pp , Mar [7] A. T. Balaei and A. G. Dempster, A statistical inference technique for GPS interference dection, IEEE Trans. Aerosp. Electron. Syst., vol. 45, no. 5, pp , Oct [8] L. Zhang, S. Yuan, Y. Chen, and J. Yang, Narrowband interference suppression in DSSS system based on frequency shift wavelet packet transform, in Proceedings of International Conference on Communication Software and Networks (ICCSN), Oct. 2009, pp [9] P. A. Regalia, Adaptive IIR Filtering in Signal Processing and Control. Marcel Dekker, [10] A. Mvuma, S. Nishimura, and T. Hinamoto, Adaptive IIR notch filter with controlled bandwidth for narrow-band interference suppression in DS-CDMA system, in Proceedings of IEEE International Symposium on Circuits and Systems, vol. 4, May 2003, pp = V (ejωj,m ) + V (e jωj,m ) θ 2 θ 2 =cosθ 1 cos θ 2 { e jω J,m } (1 e j2ωj,m ) D 2 + e jωj,m (1 e j2ωj,m ) (e jωj,m ) D 2, (21) (e jωj,m )