Radar signal detection using wavelet thresholding

Transcription

1 Radar signal detection using wavelet thresholding H.Saidi 1, M. Modarres-Hashemi, S. Sadri, M.R.Ahavan 1, H.Mirmohammad sadeghi 1 1: Information & Communication Technology Institute, Isfahan University of Technology, Iran : Electrical&Computer Eng. Department, Isfahan University of Technology, Iran Tel.: , Fax: E_mail:saidi@icti.ir Abstract The purpose of the research is to study the effect of wavelet-based denoising (WBD) technique in radar signal processing. In this paper, Bloc thresholding is used for WBD and its performance is compared with general by simulation and experimental results. The comparisons which are based upon ROC and visual inspection of the resulting signals are accomplished for different Doppler frequencies and SNRs. The results show the better performance for WBD in the presence of targets with small Doppler frequency. I. Introduction With progress of the radar systems, some methods for signal processing and detection in radars have been developed. The radar target detection in the presence of interference is a crucial problem in radar signal processing. In recent years, wavelet transforms (WTs) has been introduced into signal processing by Mallat[1]. WT not only retains the characteristic of Fourier transform (FT) but also has fine local feature of short-time Fourier transform (STFT) and has become important analysis tool in applied mathematics, signal processing and other fields of science [1]. The application of wavelet analysis in radar systems has become an active research area []. In [] radar pulse edges have been detected by WT. In the wideband radars, delay and scale variation have been computed by WT [3, 4]. Finally in the ad-hoc detection of radar targets, WBD has been employed [5-1]. Obviously, one of the most important applications of WT in radar signal processing is WBD. In this paper, radar signal processing using WBD is described. In Sec.II, target echo and interference are modeled. Then a brief introduction of WT and its application to denoising are presented in Sec.III. In sec.iv, radar signal processing using WT is introduced and simulation and experimental results are depicted. Finally, the analysis of the results and a conclusion for whole paper will be made. II. Radar Signal Modeling Generally speaing, radar signal consists of target return and interference. If s is considered as the th complex sample of N dimensional target signal vector S in the constant PRF radar system, it can be written as [11, 1]: φ Ω s = A. e. e =,1,..., N 1 (1) where A and φ are the amplitude and the phase of the signal sample, respectively, and Ω is the Doppler frequency of the target normalized to PRF. In the coherent case, φ is an identical uniform random variable in [,π ] for all samples. A is modeled according to Swerling models [11, 1]. Interference is unwanted signal at the receiver. It usually contains the clutter and white Gaussian thermal noise. The critical interference in radar systems is the clutter. Determination of performance of the radar systems in clutter generally requires the representation of the clutter as a random process. A clutter model assumption is implicit in the design or analysis of the radar system. The simplest model is the Gaussian model. This type of clutter is usually associated with weather clutter, chaff, sea

2 clutter observed with low-resolution radar (pulsewith f.5µ s ) or with a high-resolution radar at high grazing angles ( φ f 5 ) and land clutter observed from high-grazing angles over undeveloped terrain. This means that the clutter envelope-detected amplitude probability density function follows a Rayleigh distribution with σ parameter: x x f ( x) =.exp( ) () σ σ The power spectral density is also approximated by a Gaussian-shaped function [13]: 1 ( f f) S( f ) =.exp( ) (3) πσ f σ f where σ f, f are standard deviation and central frequency of power spectral density, consecutively. since radar system is assumed ground surveillance radar, land echoes are dominant clutter [1].Therefore, the simulated clutter is assumed to be a correlative random signal with Rayleigh amplitude, uniform phase and Gaussian spectrum with zero mean frequency [13, 14]. III. Wavelet Transform WTs employ orthonormal basis functions with finite support (local in time), unlie FTs whose orthonormal basis functions are sinusoids (infinite extent in time). WTs span the signal space via frequency scales which are logarithmically evenly spaced (constant Q ). Thus, WTs represent signals in term of multiple resolutions. FTs span the signal space in linearly evenly spaced frequencies. Because of the localization property, WTs can provide nearly distortionless reconstruction of signals even in presence of sharp transitions [1]. The discrete wavelet transform (DWT) is a WT that enables a signal x(t) to be represented in term of scaling function φ (t) and shifted and dilated version of wavelet function ψ (t). Each function has an orthogonal basis as [1]: φ ψ ( t) ( t). φ(. ψ ( t ) t ) Where denotes scale or resolution index, and denotes translation location index. Thus, larger corresponds to a coarser scale. In order to obtain the wavelet coefficients for each basis in L ( R ), we tae an inner product given by [1]: v =< x( t), φ ( t) >= x( t). φ ( t) dt (5) w =< x( t), ψ ( t) >= x( t). ψ ( t) dt where v,, w,, x(t) denote scaling coefficient, wavelet coefficient, and input signal to the DWT respectively. Implementation of DWT is done by multiresolution analysis (MRA) using quadrature mirror filters [1]. One of the most important applications of the WT is noise elimination. Denoising is based on the principle of shrining wavelet coefficients toward zero to remove noise proposed by Donoho and Johnstone[15,16]. The WBD is obtained by the following 3 steps: transforming data into wavelet domain, shrining the empirical wavelet coefficients towards zero and transforming the shrun coefficient bac to the data domain. There are many denoising algorithms such as Universal, Minimax, Bloc thresholding [16]. Due to the fact that WBD is not dependent on the signal parameters, it is beneficial. It is very important to be (4)

3 mentioned that although aforementioned algorithms are derived for white Gaussian noise, all of them can remove other interferences adequately [17]. IV. Radar Signal analysis using WT WT of radar signal fully describes the signal. The most noticeable character of radar signal denosing is that it not only can suppress most of clutter, but also it doesn t lead to the reconstructed signal s obvious distortion [5]. This is ust what is wanted in radar signal processing. In this section, some radar signal processing using WBD are introduced. Wavelet base selection is the first step in wavelet decomposition. Whereas symmetric filters decrease distortion, near-symmetric Daubechies family such as Coiflet family is selected. Selection of denoising algorithm is the second step in wavelet thresholding. Bloc thresholding is a useful denoising method that simultaneous decisions are made to retain or to discard all the coefficients within a bloc [15]. Within each bloc (B), the coefficients are estimated via James-Stein-type shrinage rule [15]: λ.. σ ˆ L d = (1 ) d +. S where λ = 4. 55, = L =, σ, n are variance and length of input signal. The clutter suppression is the most important problem to which radar designer is faced. The simple solution is clutter reection using general. One of the important problems in using general is reection of targets with small radial velocity. In this section, a new method using WBD is proposed by which the reection probability of such targets is decreased. With respect to the fact that WBD is not dependent on the target Doppler frequency, this method is remarable which is verified by simulation results. Simulation has been carried out in different SNR, CNR and f Doppler. For example, In CNR=15dB, SNR=dB, clutter bandwidth=5hz with zero mean frequency and PRF=3Hz, signal vector with nonfluctuating target [18] is processed by two-pulse delay line canceller filter ([1-1]) and also by Bloc thresholding with four decomposition levels. After each of them, an energy detector is employed (Fig.1) and their ROC (receiver operating characteristic) is derived. ROC has been depicted S B d, Logn f d for f d =,,. As shown in Fig., for 5, WBD has better performance. Also, in Fig.3, PRF PRF 3 probability of detection versus SNR in CNR=1 db and f Doppler = Hz has been depicted which shows better performance for WBD in comparison with. In the rest, aforementioned technique has been employed to process real coastal L-band radar data In Fig.4 that x-axis and y-axis represent sample number of range and angle successively. As shown in Fig.5, reects the clutter and also the targets which have small radial velocity. But Fig.6 shows the best visual representation of scan obtained from proposed technique. Radar signal processing can be performed on the range cells [5, 1, 19]. Due to the fact that Bloc thresholding method reacts more rapidly to sudden frequency changes in the signal [15], it can be used to radar signal pulse processing [9]. In the future, we will propose some preliminary wors such as WT-CFAR processor. IV. Conclusion The main obective of this paper was to demonstrate application of WT in radar signal processing. The Bloc thresholding as WBD was employed for clutter reection in the detection processing. Given the signal characteristics as outlined above, WBD appears to provide more benefit in detection of targets with small radial velocity than general. Also, visual representation of sea returns verified our claim. In addition, due to easy implementation of this method, it is completely practical. (6)

4 References [1] Mallat,S., " A wavelet tour of signal processing", Academic Press, San Diego,CA,1998. [] Elsehely, E., Sobhy, M.I., "Detection of radar target pulse in the presence of noise and amming signal using the multiscale wavelet transform", IEEE International Symposium on Circuits and System,Vol.3,pp ,1999. [3] Peng,Y.N.,Tian,L.S.,Zhang,X.P, "Wavelet detectors for wide-band radar signals", CIE International Conference of Radar, pp.89-9, [4] Jiang,X., Zhang,J., "Wide-band signal detection based on time-scale domain two-dimentional correlation", MTS/IEEE Conference and Exhibition,Vol.3, pp , 1. [5] Liu R., Liu X., Suo, J., Wang, X., " The radar clutter processor with wavelet floating threshold ",Proceeding of CIE International Conference on Radar,pp.11-15,1. [6] Noel,S.,Szu,H., " Wavelets and neural networs for radar ",Russian Academy for Nonlinear Sciences,pp ,1998. [7] Lehmann, V., Tesche,G., " Wavelet based methods for improved wined profiler signal processing ", European Geophysical Society,pp ,1. [8] Guohuo,W., Siliang,Wu., " Denoising radar signals using complex wavelet,international symposium on signal processing ", Volume1, pp , 3. [9] saidi,h., Radar target detection using time-frequency transform", Master thesis, isfahan university of technology, 3. [1] Lampropoulos,G.A., Gigli,G., Damani,A. Rey,M., A new adaptive coherent CFAR wavelet detector, SPIE proceeding,vol.3491,pp ,1998. [11] taban,m.r., " Radar signal detection in pseudo-gaussian ", PhD thesis, isfahan university of technology,1998. [1] Solni,M.I., " Introduction to radar system ", New Yor ; McGraw-Hill,198. [13] scheleher D.C., " MTI and Pulsed Doppler Radar ", Artech House, [14] sheihi,a., zamani,a., simulation of base band ground surveillance radar signal ", ICEE, tabriz university, 3. [15] Burrus,C.S., Gopinath,R.G., " Introduction to wavelets and wavelet transforms ", New Yor,Prentice Hall,1998. [16] Vidanovic,B., " Statistical modeling of wavelets ", Johns Wiley&Sons Inc.,1999. [17] Borda,M.,Isar,D., " Whitening with wavelets ", Proceeding of IEEE Int.conf, ECCTD 97, August, [18] Xing,S., "The application of wavelet pacet to signal analysis of battle reconnaissance radar ", IEEE conf. on radar, pp , 1. [19] Steinbrunner,L., Scrapino,F., An analysis of wavelet-based denoising techniques as applied to a radar signal pulse, SPIE proceeding,vol.381,pp.7-83,1999.

5 1 bloc thresholding I Q Clutter suppression WBD/ Clutter suppression WBD/ ( ) ( ) + pd WBD (fd/prf=1/3) WBD (fd/prf=3/3) WBD (fd/prf=5/3) pd Figure1: Clutter suppression wavelet-based denoising pfa Figure: P d versus P fa real data SNR (db) Figure 3: P d versus SNR :[1-1] Figure4: real data WBD Figure 5: output of Figure 6: output of WBD