NLFM Interference Suppressing Based on Time-Varying AR Modeling and Adaptive IIR Notch Filter

Transcription

1 Chinese Journal of Electronics Vol.0, No.4, Oct. 011 NLFM Interference Suppressing Based on Time-Varying AR Modeling and Adaptive IIR Notch Filter FENG Jining 1, YANG Xiaobo, DIAO Zhejun 1, GONG Wenfei 3 and WU Siliang 4 (1.The Electronic Engineering Department, Hebei Normal University, Shijiazhuang , China) (.Shijiazhuang Professional Technology Institute, Shijiazhuang , China) (3.School of Electronics and Information Engineering, Beijing Jiaotong University, Beijing , China) (4.School of Information Electronics, Beijing Institute of Technology, Beijing , China) Abstract Uing TVAR (Time varying AR) model and adaptive notch filter is a new method for the nonstationary jammer suppression in DSSS (Direct sequence spread spectrum). The performance of TVAR model for IF (Instantaneous frequency) estimation will be affected by some factors such as basis functions. Focusing on this problem, the optimal basis function of TVAR model for the IF estimation of the NLFM signal is obtained in this paper. Besides the depth and width of notching, the phase properties of notch filter affect the SINR of correlation output to the narrow band jammer suppression in DSSS, in response to the problem the closed solution of correlation output SINR improvement has been derived when a single frequency jammer passes through direct IIR notch filter, and its performance has been compared with those of five coefficient FIR filters. Later, a novel method for NLFM jammer suppression based on Fourier basis TVAR model and direct IIR notch filter is proposed. The simulation results show the effectiveness of the proposed method. Key words Direct sequence spread spectrum (DSSS) receiver, Time varing AR (TVAR) model, IIR adaptive notch filter, Anti-Jamming. I. Introduction The Direct sequence spread spectrum (DSSS) system is sensitive to non-stationary jammer. The problem about non-stationary jammer suppression, especially FM jammer suppression in DSSS communications has been attracting many researchers, many jammer suppression techniques are reported [1 7], and most of the techniques employ Instantaneous frequency (IF) estimation and Time-frequency analysis (TFA). The method of Cohen class non-parameter timefrequency distribution is used to estimate IF [1,4 7], the disadvantages of this method are large computation burden and slow convergence. Another method for IF estimation is Short time Fourier transform (STFT) [8], but the accuracy of IF estimation by using STFT is poor, especially for fast changing non-stationary jammer. High-resolution IF estimation can be got by Time-varying AR (TVAR) model [,3,9,10], and the TVAR model coefficients can be estimated by Recursive least square(rls), then the convergence increases and the computation complexity decreases [10]. Shan proposed the FM jammer suppression in DSSS by using TVAR model and five coefficients FIR notch filters, and the time basis function of TVAR model is also used [10]. In addition to IF estimation, to the nonstationary interference suppression the other key techniques is filter design. The five coefficient FIR filters was used in Refs.[1] and [10], for the linear phase properties, and the performance of five coefficient FIR filters was studied in Ref.[1]. For IF estimation, besides the time basis function, there are Fourier basis function and Lagrange basis function TVAR model. For NLFM (No-linear frequency modulation) jammer suppression, the best basis function of TVAR model is selected through simulation in this paper. The direct IIR notch filter is used widely in engineering, besides the depth and width of notching, the phase properties of notch filter affect the SINR of correlation output to the narrow band jammer suppression, then the closed solution to output SINR improvement of correlation is derived after a narrow band jammer passes through direct IIR notch filter, and its narrow band jammer suppression performance is compared with five coefficients FIR filters. Based on the above analysis, a new FM interference suppression technique in DSSS based on Fourier basis function TVAR model and direct IIR notch filters is proposed in this paper. The paper is organised as follows. In Section II, the TVAR model of non-stationary jammer and the IF estimation based TVAR model are introduced. The performance of different TVAR model based basis function is compared in Section III. The closed solution to output SINR improvement of correla- Manuscript Received Sept. 010; Accepted Jan This work is supported by the Natural Science Foundation of Hebei Province (No.F ), Natural Science Foundation of Hebei Province (No.F ), National Natural Science Foundation of China (No ).

2 NLFM Interference Suppressing Based on Time-Varying AR Modeling and Adaptive IIR Notch Filter 677 tion, after a narrow band jammer passes through direct IIR notch filter, is derived, and the narrow band jammer suppression performance is compared with five coefficients FIR filters in Section IV. The performance of the proposed method is simulated in Section V. In Section VI, the conclusion is given. II. The IF Estimation of Non-stationary Jammer Based TVAR Model The TVAR modelling of non-stationary sequence x(n) with order p is [10] : p x(n) = a i(n)x(n i) + e(n) (1) i=1 in which e(n) is stationary white noise with zero mean and variance σ, and {a i(n), i = 1,,, p} are TVAR coefficients. The TVAR coefficients are modelled as linear combinations of a set of basis time function {u k (n), k = 1,,, q}: a i(n) = q a ik u k (n) () in which {u k (n), k = 1,,, q} are any basis functions, q is the order of basis, and a ik are polynomial functions of time n. The basis function used in Ref.[10] is: {u k (n) = n k } q (3) The basis function is the power of time, and it can be called time basis. Besides the time basis function, the Fourier basis function and Lagrange basis function are generally used [11]. Combining Eqs.(1) and () yields the prediction equation: p ( q ) x(n) = a ik u k (n) x(n i) + e(n) (4) i=1 The estimation of a ik aims to minimize the total squared prediction error: J(n) = ( p q x(n) + a ik u k (n)x(n i)) (5) n i=1 Minimizing the above error related to each coefficient leads to the equations: p q a ik c kl (i, j) = c 0l (0, j), 0 j p, 1 l q (6) i=1 where c kl (i, j) = n u k (n)u l (n)x(n i)x(n j), 0 k, l q If basis vector is expressed as [a 10,, a 1q,, a p1,, a pq] = θ, θ can be computed by using RLS [11], then we can construct the TVAR coefficients a i(n) with Eq.(), by rooting the polynomial which is formed by TVAR linear prediction filter 1 + p i=1 ai(n)z i at each instant n, we can get the timevarying poles: z i(n), i = 1,,, p. The instantaneous angles of certain poles proved estimation of the IF f(n): f(n) = ang[zi(n)] π where f s is sampling rate. f s, z i(n) 1 (7) III. The Performance Analysis of Basis The precision of IF estimation is determined by the order of TVAR, basis function, and the order of basis. For the FM jammer suppression in DSSS, Shan has given the principle on how to select the order of TVAR modelling [10] : for a signal consisting of M FM components in white noise with moderate Signal-to-noise ratio (SNR) or higher, a TVAR signal model can be used, with order p = M for complex exponential FM components and p = M for real signals. There are still two problems: one is selecting the basis function, and the other is selecting the order of TVAR. The optimal basis function of TVAR model for the Instantaneous frequency (IF) estimation of the NLFM signal was obtained by comparing IF estimation precise and anti-noise performance of several types basis functions, including time basis function, Fourier basis function, and Lagrange basis function through simulation. The NLFM signal used is: J(t) = P J cos(π(f 0t + f t 3 )) (8) where P J is the power of signal, f 0 = 45MHz is the central frequency of NLFM, and f = 800GHz/ms. The sampling rate is 1kHz, and the order of TVAR is. Fig.1 shows the timefrequency spectrum of the time basis function TVAR model respectively, with INR=0dB. The dimensions of basis function are all 3. Fig. 1. IF time-frequency spectrum based time basis. Stereogram; (b) Time-frequency plan Fig. shows the average IF estimation error (normalized to sampling rate) for different SNR (from 0 to 60dB), and dimension (from 1 to 0). The number of simulation is 100. Based on the simulation result, the following conclusions were obtained: (1) Time basis function: the IF estimation error increases because of the over fitting when the dimension of basis is larger than 10. The time basis function is constant when the dimension is 1, then the IF estimation error increases. IF estimation error increases significantly when SNR is below 0dB, it shows that the anti-noise ability is poor; () Lagrange basis function: over fitting does not occur, when the dimension is below 0. Lagrange basis function is constant when the dimension is 1, then the IF estimation error increases. IF estimation error increases significantly when SNR is below 10dB, it shows that the anti-noise ability is better than time basis function; (3) Fourier basis function: the IF estimation error increases because of the over fitting, when the dimension of basis is larger than 10. For IF estimation error increases significantly when SNR is below 10dB, this shows that the anti-noise ability of it is better than time basis function. the IF estimation precision of it is better than that of others when the dimension is lower. (a)

3 678 Chinese Journal of Electronics 011 Fig.. Average IF estimation error (normalized to sampling rate). (a) Time basis; (b) Fourier basis; (c) Lagrange basis Such conclusion can be drawn that the Fourier basis function is superior to others for NLFM signal IF estimation. IV. Adaptive Filter Design and Performance Analysis The direct IIR notch filter is used widely in engineering. The transfer function of IIR notch filter is: H(z) = (z ejω 0 )(z e jω 0 ) (z αe jω 0 )(z αe jω 0) = 1 + βz 1 + z 1 + αβz 1 + α z (9) β determines the notch frequency, let ω 0 is notch frequency, then ω 0 = arc cos( β) (10) α is structure factor of notch filter, and α < 1. Besides the depth and width of notching, the phase properties of notch filter affect the SINR of correlation output to the narrow band jammer suppression. It is necessary to derive the closed solution to output SINR improvement of correlation after the single frequency jammer passes through direct IIR notch filter. The correlation output SINR is derived as following. The DSSS signal is: r(n) = P sb(n)c(n) + j(n) + v(n) (11) where P s is the power of signal; b(n) is sign, b(n) {+1, 1}; c(n) {+1, 1} is PN code; j(n) is jammer; v(n) white noise process with zero mean and variance σ. c(n), j(n) and v(n) are independent to each other. The output of notch filter y(n) can be expressed as: y(n) = h(k)r(n k) (1) where {h(n), n = 0, 1,, } is impulse response of notch filter. The SINR of output of correlate after jammer be moved is [1] SINR 0(ζ) =LP sh (0)/ 1 1 =P s k=1 + 1 π h (k) + σ n h (k) S j(ω) H(ω) dω (13) where L is spreading gain, σ n is the power of noise, S j(ω) is the spectrum of jammer. Substituted Eq.(10) into Eq.(9), then: H(z) = According to initial value theorem, then: 1 cos(ω)z 1 + z 1 α cos(ω)z 1 + α z (14) 1 cos(ω)z 1 + z h(0) = lim H(z) = lim z z 1 α cos(ω)z 1 + α z = 1 (15) According to Parseval s Relation: h (k) = 1 H(z)H(z 1 )z 1 dz (16) πj c Substituting the transform function Eq.(14) into Eq.(16), according to Residue theorem, we have: h (k) = 1 α + 1 α ( + (α ) 1) (α + 1) α (α + 1) 1 α cos ω 0 + α 4 (17) According to Eq.(17), the jammer frequency have a certain power disturbances to the frequency of the notch filter impulse response, but disturbances is very small when α is close to 1, if disturbances is neglected, then h (k) = 1 H(z)H(z 1 )z 1 dz πj c = 1 (1 α) α α (1 + α) = 3α 1 α (1 + α) According to Eqs.(15), (17) and (18), then SINR 0(ζ) = LP sα (1 + α)/ In the ideal condition: =[α(3 α α ) 1]P s + (3α 1)α n 1 π + 1 π From Eq.(19), we have: (18) S j(ω) H(ω) dω (19) S j(ω) H(ω) dω = 0 (0) LP sα (1 + α) SINR 0(ζ) = [α(3 α α ) 1]P s + (3α 1)σn (1)

4 NLFM Interference Suppressing Based on Time-Varying AR Modeling and Adaptive IIR Notch Filter 679 If there is no notch filtering, the SINR is: LP s SINR no(ζ) = ρ j(0) + σn We define the SINR improvement factor: γ = SINR0(ζ) SINR no(ζ) = [ρ j(0) + σ n]α (1 + α) [α(3 α α ) 1]P s + (3α 1)σ n () (3) The numerator and denominator are divided by the power of DSSS signal, then γ = [SIR 1 + SNR 1 ]α (1 + α) [α(3 α α ) 1] + (3α 1)SNR 1 (4) Eq.(4) shows that γ is determined by SIR, SNR, and α. The SINR improvement factor of correlation output of five coefficient FIR notch filter is [1] : To evaluate the performance of the method proposed in this paper, we compare it with the methods using time basis TVAR and five coefficients FIR filter [10], and using STFFT and five coefficients FIR filter [8]. We consider a single-user code-on-pulse DSSS communication system with BPSK modulation and spreading gain is L = 103 chips per bit. To focus on the effect of jammer cancellation on correlation output SINR: SNR = 0dB NLFM jammer. The interference signal is same to Section III. The used TVAR model is a second-order autoregressive model (p = ), with the time-varying coefficient represented as a Fourier basis (q = 3), α of direct IIR notch filter is 0.9. Fig.4 shows the simulation result that frequency spectrum of the signal before and after the jammer passes through direct IIR notch filter with JNR = 0dB, the NLFM jammer is suppressed significantly. γ = [1 + cos (ω 0)] (σn + ρ j(0))/ 3 ( 3 = L + 3 cos (ω 0) 16 ) L cos (ω 0) P s + ( cos (ω 0) + [1 + cos (ω 0)] )σ n (5) where P s is the power of DSSS signal, L is spreading gain, ρ j autocorrelation function of jammer, ω 0 is normalized frequency, σn is the power of noise. The first part of denominator of Eq.(5) can be defined as general system s noise. When ω 0 = 0 and processing gain L, the system s noise of FIR approaches to 17P s/4. From Eq.(3), when α 1, the system s noise of IIR approaches 0. We can see that distortion of IIR notch filter is far less than that of FIR notch. Based on comparing Eqs.(3) and (5) we got the conclusion that the correlation output SINR improvement factor of the five coefficients FIR notch filter to the single frequency jammer suppression is determined by the SNR, SIR, angular frequency and spreading gain. However, the SINR improvement factor of correlation output of the direct IIR notch filter determined only by α. Fig. 4. Frequency spectrum of input and output of IIR notch filter The Fig.5 shows the correlation output SINR for different method. In this case, it is observed from figure that the performance of TVAR method of this paper is better than that of the method of Ref.[10], and significantly outperforms the method based STFFT of Ref.[8]. V. NLFM Jammer Suppression Based on the above analysis, a new jammer suppression method using Fourier basis function TVAR model and direct IIR notch filters was proposed in this paper. Fig.3 shows the basic principles of jammer suppression using TVAR model and IIR notch filter. Fig. 5. The correlation output SINR for different method VI. Conclusion Fig. 3. Basic principles of jammer suppression using TVAR model and IIR notch filter where r(n) is the DSSS signal (expressed as Eq.(11)), y(n) is the output of notch filter, ς is the correlation output. The simulation result shows that the Fourier basis function of TVAR model is superior to the time basis function and the Lagrange basis function for NLFM signal IF estimation, then for NLFM jammer suppression, the best basis functions of TVAR model is selected in this paper. The closed solution of output SINR improvement of correlation is derived after a

5 680 Chinese Journal of Electronics 011 narrow band jammer passes through direct IIR notch filter, and its narrow band jammer suppression performance is compared with five coefficients FIR filters, the result shows the performance of IIR notch filter is superior to the five coefficients FIR filters. Based on the above, a new FM interference suppression technique in DSSS based on Fourier basis function TVAR model and direct IIR notch filters is proposed in this paper. The performance of the method of this paper is superior to that of the method using STFFT and IIR filters, and time basis TVAR model and five coefficients FIR filters. References [1] G.M. Amin, Interference mitigation in spread spectrum communication systems using time-frequency distributions, IEEE Transactions on Signal Processing, Vol.45, No.1, pp , [] S. Barbarossa and Anna Scaglione, Adaptive time-varying cancellation of wideband jammers in spread-spectrum communications based on timefrequency distributions, IEEE Transactions on Signal Processing, Vol.47, No.4, pp , [3] L. Liu, H. Ge, Subspace projection and time-varying AR modeling for anti-jamming DS-CDMA communications, IEEE 14th Conference on Annual Wirelss and Optical Communications, USA, pp , Apr [4] M.G. Amin and A.R. Lindsey, Time-frequency receiver for nonstationary interference excision in spread spectrum communication systems, AFRL-IF -RS-TR Final Technical Report, April 000. [5] C. Wang and M.G. Amin, Time-frequency distribution spectral polynomials for instantaneous frequency estimation, IEEE Transactions on Signal Processing, Vol.76, No., pp.11 17, [6] S.R. Lach, M.G. Amin and A.R. Lindsey, Broadband nonstationary interference excision for spectrum communications using time-frequency synthesis, Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing, Seattle, Vol.6, pp , May [7] S.R. Lach and M.G. Amin, Multiple component interference excisionin spread spectrum communication using wigner distribution synthesis technique, Proceedings of IEEE Sanroff Symposium on Advances in Wired and Wireless Communications, pp , March [8] M. Chen, Narrowband interference notch suppression of spread spectrum communication systems, Ph.D. Dissertation, Southwest Jiaotong University, 006. [9] P. Shan and A.A. Beex, High-resolution instantaneous frequency estimation based on time- varying AR modeling, Proceeding of the IEEE-SP International Symposium on Time- Frequency and Time-Scale Analysis, Pittsburgh, USA, pp , Oct [10] P. Shan and A.A. Beex, FM interference suppression in spread spectrum communication using time-varying autoregressive model based instaneous frequency estimation, IEEE International Conference on Acoustics, Speech and Signal Processing, New York, pp , March [11] H.Y. Wang, T.S. Qiu and Z. Chen, Non-stationary Random Signal Analysis and Processing (second edition), Beijing, National Defense Industry Press, Chapter 1, Section 3, 008. [1] C.H. Zhang, J. Zhu and S.L. Wang, The design of IIR filters for time-varying interference suppression in DSSS communications systems, Signal Process, Vol.3, No.4, pp , 007. FENG Jining was born in Jizhou, Hebei Province, China, in He received the Ph.D. degree from Beijing Institute of Technology. He is currently an associate professor of Hebei Normal University, M.S. instructor. His research interests cover the field of navigation signal processing and intelligent detection technique. ( fjn003@163.com) YANG Xiaobo was born in Funing, Hebei Province, China, in She received the M.S. degree from Yanshan University. She is currently a lecturer of Shijiazhuang Professional Technology Institute,Shijiazhuang, China. Her research interests cover the field of digital image processing and intelligent detection technique. ( fengjn003@163.com) DIAO Zhejun was born in Xinji, Hebei Province, China, in He received the B.E. degree from Nanjing Institute of Technology. He is currently a professor of Hebei Normal University, M.S. instructor. His research interests cover the field of digital signal processing and intelligent detection technique. ( diaozhj@hebtu.edu.cn) GONG Wenfei was born in Bozhou, Hebei Province, China, in He received the Ph.D. degree from Beijing Institute of Technology. He is currently a postdoctor in Beijing Jiaotong University. His present research interests include satellite navigation signal processing and anti-jamming technology. ( ise matlab@163.com) WU Siliang was born in Jixi, Hebei Province, China, in He received the Ph.D. degree from Harbin Institute of Technology. He is currently a professor of Beijing Institute of Technology, Ph.D. supervisor. He is a senior member of Chinese Institute of Electronics. His research interests cover the field of modern signal processing theory and application, radar system theory and technology, electronic systems simulation and signal simulation. ( siliangw@bit.edu.cn)