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1976 JOURNAL OF COMPUTERS, VOL. 6, NO. 9, SEPTEMBER 2011 A New Method of Detecting Multi-component LFM Signals Based on Blind Signal Processing 1 Qiang Guo 1 Space Control and Inertial Technology Research Center,Harbin Institute of Technology, P.R. China Email: guoqiang292004@163.com 2 Yajun Li and 1 Changhong Wang 2 College of Information and Communication Engineering, Harbin Engineering University,P.R.China Email: liyajun1985happy@163.com Abstract—To effectively detect and recognize multicomponent Linear Frequency-Modulated (LFM) emitter signals, a multi-component LFM emitter signal analysis method based on the complex Independent Component Analysis(ICA) which was combined with the Fractional Fourier Transform(FRFT) was proposed. The idea which was adopted to this method was the time-domain separation and then time-frequency analysis, and in the low SNR cases, the problem which is generally plagued by noised of feature extraction of multi-component LFM signal based on FRFT is overcame. Compared to the traditional method of timefrequency analysis, the computer simulation results show that the proposed method for the multi-component LFM signals separation and feature extraction was better. Index Terms—multi-component LFM emitter signals, timefrequency analysis, feature extraction,ICA I. INTRODUCTION Radar emitter signal detection is a key problem which is demanded to be resolved in modern electronic reconnaissance system. With large new complex radar systems in practice, a large number of pulses overlap and form the multi-component emitter signals(MCES)[1]. MCES analysis is a prerequisite and primary task for detecting and identifying emitter signals. Multicomponent Linear Frequency Modulated (LFM) emitter signals is a non-stationary signal which is commonly used in active sonar, radar imaging, fuse of missile and so on. As a new time-frequency analysis tool, FRFT is a generalization of the Fourier transform (FT). It not only has a natural link in classical FT, but also provides some characteristics which FT do not have. So FRFT is specially suitable for processing LFM class (chirp-like) signal. At present, regardless of the traditional parameter estimation or detection methods of multi-component LFM signal, most of them are based on time-frequency analysis or all finds of FT method[2]. The parameter estimation methods mainly through two-dimensional Manuscript received January 2, 2011; revised February 1, 2011; accepted February 28, 2011. Qiang Guo, Yajun Li,Changhong Wang. © 2011 ACADEMY PUBLISHER doi:10.4304/jcp.6.9.1976-1982 object function, and combined with two-dimensional search to estimate, such as the maximum likelihood method, the time-frequency analysis methods, FRFT, match fourier transform(DCFT)[3,4] ,S-method and so on. But when the low SNR, together with the existence of weak signal, the traditional detection method is often difficult to effectively detect the MCES, even lead to misjudgment of signal and noise ,so the result of crossterm suppression is not good. Above-mentioned issue has been a relatively difficult problem. In this paper, a multicomponent LFM emitter signal analysis method based on complex FastICA which was combined with FRFT was proposed. Firstly, complex ICA algorithm was used as time-domain separation for multi-component LFM emitter signals with noise. Secondly, determine the signal and noise by the automatic identification method of second central moment of FRFT. Lastly, the noise was removed and the LFM signals were detected by FRFT. The effect of noise can be greatly reduced. Simultaneously, the cross-terms are effectively deduced with higher time-frequency resolution. It is a good method for the multi-component LFM signals. Simulation results verify the effectiveness of this new method. II. MODEL OF MULTI-COMPONENT LFM EMITTER SIGNALS In modern electronic reconnaissance system, receiver often intercepted to pulses which emitted by multiple sources at the same time. A stream of pulses was formed through these pulses interleaved together. As the pulse signals density increases, the pulse formed MCES x() t ,the signal model is expressed as follows. k −1 ∑ i= 0 i 2 j2 π ( fit+ ( µ it /2)) , −∆t/2 ≤ t ≤ ∆ t/2 x() t = Ae + n() t (1) Where Ai is the amplitude of each signal, fi is initial frequency and µ i is chirp rate. nG() t is White Gauss Noise with zero mean and variance 2 σ . III. MULTI-COMPONENT LFM EMITTER SIGNALS ANALYSIS
JOURNAL OF COMPUTERS, VOL. 6, NO. 9, SEPTEMBER 2011 1977 In this paper, the flowchart of proposed multicomponent LFM signals analysis method is shown in Fig.1. Firstly, complex FastICA algorithm is used as the pretreatment of detection of multi-component LFM emitter signals. The emitter signals and noise were separated by it. Secondly, discriminate LFM signal and noise based on the automatic identification method of second-order central moment of FRFT. Then detect the separated LFM signals through FRFT after removing the noise. Through the above steps, the impact of noise was effectively reduced and the cross terms were effectively restrained. Last, the LFM signal parameter estimation can be completed through the conversion formula [1,5]. Figure 1. Multi-component LFM emitter signals analysis with low SNR A. Pretreatment 1)Problem Description As the number of mixed-signal (decided by the number of channel) received by the radar signal receiver and do not necessarily match the number of radar emitter signals, and LFM signal is non-stationary signal, so the complex ICA of the blind signal processing techniques was used in multi-component LFM signals with low SNR to do timedomain separation pretreatment. At present, most of the FastICA algorithm is mainly concentrated in the real domain in blind separation of mixed signals[7], but in practice, many real signal model is represented by linear mixed model of complex signals. Blind separation algorithm for complex signals is summarized into the methods based on higher order statistics and the methods based on second order statistics. It is actually an optimization problem, namely, how to make the separated independent component to maximum approach the source signal. Here we will extend the real domain variable to the complex domain[8,9]. Taking into account the observed mixed-signal is instantaneous linear mixing of the each source signal, the standard ICA linear model with noise as follows [3] n xi() t = ∑ aijsj() t + ni() t ( i = 1,2, ⋅⋅⋅ , m) (2) j= 1 © 2011 ACADEMY PUBLISHER iii iii iii Expressed in matrix form, ie. X = A S+ n (3) where X = ( x1, x2,..., xm) is the vector of observed random variables, S = ( s1, s2,..., sn) is the vector of statistically independent latent variables called the independent components, and A is an unknown constant complex mixing matrix. The above model is identifiable under the following fundamental restrictions: ① At most one of the independent components s j may be Gaussian. ② The matrix A must be of full column rank. The number of observing signals m is more than the number of source signals n . ( m≥ n) ,here m=n. ③ The various components of the source signals si ( i = 1,..., m) and observed signals x i are zero-mean and unit variance. In addition, the noise itself can be regarded as a source of signal to use BSS, and thus make the algorithm have a wider scope and greater robustness. Can be proved that we can find a matrix W by linear transformation to do m mixed-signal X , making between the each component of new vector Y obtained by transformating the X as independent as possible in the case m≥ n , that is H Y = W X (4) where, Y is the separated vector signal, that is, the estimated value of source signal vector S . Complex FastICA algorithm is a fixed-point algorithm using the batch processing. Compare with the ordinary ICA algorithm its convergence speed is more quickly. In this paper, we adopt complex FastICA algorithm in the pre-processing, in order to separate the multi-component LFM signals of low SNR in time-domain. 2)Time-domain separation technique of multi-component LFM signals with low SNR based on complex FastICA Multi-component LFM time-domain separation technique of basic complex FastICA algorithm includes two steps: first, preprocess the chosen mixed-signal X which was composed of multi-component LFM signals and noise, that is, using whitening treatment. Whitening treatment can be used to remove the correlation between signals, which simplifies the process of follow-up to the extraction of independent component, second is the extraction of independent components, namely, the completion of the mixed signals separation. Complex FastICA algorithm flow chart is shown in Fig.2. Figure 2. Algorithm flow chart of complex FastICA Complex FastICA is a fast optimization iterative algorithm using the batch approach which has a large number of samples of data involved in computation in each iteration. According to the central limit theorem, linear sum of a number of independent random variables will tend to Gaussian distribution, so complex FastICA mainly achieve the purpose of separation by measuring
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