Doppler Estimation of RADAR Signals using Complex Wavelets

This paper discusses the application of complex wavelet transform (CWT) which has significant advantages over real wavelet transform. CWT is a form of discrete wavelet transform, which generates complex coefficients by using a dual tree of wavelet filters to obtain their real and imaginary parts. In this paper we implement Selesnick’s idea of dual tree complex wavelet transform where it can be formulated for standard wavelet filters without special filter design. We examine the behaviour of 1 dimensional signal and implement the method for the analysis and synthesis of a signal. Analysis and synthesis of a signal is performed on a test signal to verify the CWT application on 1D signal. The same is implemented for the MST radar signal. In this paper, CWT with custom thresholding algorithm is proposed for the estimation of Doppler profiles. The proposed algorithm is self-consistent in estimating the Doppler of a MST RADAR signal, in contrast to existing methods, which estimates the Doppler manually and failed at higher altitudes. Keywords— Signal processing, MST radar, Doppler Estimation, Complex wavelets, custom thresholding. INTRODUCTION RADAR can be employed, in addition to the detection and characterization of hard targets, to probe the soft or distributed targets such as the Earth‟s atmosphere. Atmospheric radars, of interest to the current study, are known as clear air radars, and they operate typically in very high frequency (30–300 MHz) and ultrahigh-frequency (300 MHz– 3 GHz) bands. The turbulent fluctuations in the refractive index of the atmosphere serve as a target for these radars. The present algorithm used in atmospheric signal processing called “classical” processing can accurately estimate the Doppler frequencies of the backscattered signals up to a certain height. However, the technique fails at higher altitudes and even at lower altitudes when the data are corrupted with noise due to interference, clutter, etc. Bispectral-based estimation algorithm has been tried to eliminate noise [1]. However, this algorithm has the drawback of high computational cost. Multitaper spectral estimation algorithm has been applied for radar data [2]. This method has the advantage of reduced variance at the expense of broadened spectral peak. The fast Fourier transform (FFT) technique for power spectral estimation and “adaptive estimates technique” for estimating the moments of radar data has been proposed in [3]. Fig.1. Flow chart for ADP (EALG) This method considers a certain number of prominent peaks of the same range gate and tries to extract the best peak, which satisfies the criteria chosen for the adaptive method of estimation. The method, however, has failed to give consistent results. Hence, there is a need for development of better algorithms for efficient cleaning of spectrum. II. Existing Method The National Atmospheric Research Laboratory, Andhra Pradesh, India, has developed a package for processing the atmospheric data. They refer to it as the atmospheric data processor [4]. In this paper it is named as existing algorithm (EALG). The flowchart of EALG is given in Fig. 1. Coherent integration of the raw data (I and Q) collected by radar is performed. It improves the process gain by a factor of number of inter-pulse period. The presence of a quadrature component of the signal improves the signal-to-noise ratio (SNR). The normalization process will reduce the chance of data overflow due C. Madhu, V. Madhurima, K.Avinash kumar / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 2, Issue 5, SeptemberOctober 2012, pp.1927-1931 1928 | P a g e to any other succeeding operation. The data are windowed to reduce the leakage and picket fence effects. The spectrum of the signal is computed using FFT. The incoherent integration improves the detectability of the Doppler spectrum. The radar echoes may be corrupted by ground clutter, system bias, interference, etc. The data is to be cleaned from these problems before going for analysis. After performing power spectrum cleaning, one has to manually select a proper window size depending upon the wind shear [6], etc., from which the Doppler profile is estimated by using a maximum peak detection method [3]. Fig.2. Typical spectra of the east beam. (a) Before Spectral cleaning. (b) Doppler profile of east beam using the EALG. The EALG is able to detect the Doppler clearly up to 11 km as the noise level is very low. Above 11 km, noise is dominating, and, hence, the accuracy of the Doppler estimated using the EALG is doubtful as is discussed in the subsequent sections. To overcome the effect of noise at high altitudes, a wavelet-based denoising algorithm is applied to the radar data before computing its spectrum [5]. This paper gives better results compared to [4], but this method fails to extract the exact frequency components after denoising at higher altitudes. To overcome this effect we proposed a new method, where spectrum is estimated prior to denoising and then denoised using Complex Wavelet Transform (CWT) with the help of Custom thresholding method. It is named as proposed algorithm (PALG) in this letter. III. Complex Wavelet Transform (CWT) Complex wavelet transforms (CWT) uses complex-valued filtering (analytic filter) that decomposes the real/complex signals into real and imaginary parts in transform domain. The real and imaginary coefficients are used to compute amplitude and phase information, just the type of information needed to accurately describe the energy localization of oscillating functions (wavelet basis). The Fourier transform is based on complexvalued oscillating sinusoids cos ( ) sin( ) j t e t j t      The corresponding complex-valued scaling function and complex-valued wavelet is given as ( ) ( ) j ( ) c r i t t t       where ( ) r t  is real and even, ( ) i j t  is imaginary and odd. Gabor introduced the Hilbert transform into signal theory in [9], by defining a complex extension of a real signal ( ) f t as: ( ) ( ) ( ) x t f t j g t   where, ( ) g t is the Hilbert transform of ( ) f t and denoted as 1/2 { ( )} ( 1) H f t and j   . The signal ( ) g t is the 90 shifted version of ( ) f t as shown in figure (3.1 a).The real part ( ) f t and imaginary part ( ) g t of the analytic signal ( ) x t are also termed as the „Hardy Space‟ projections of original real signal ( ) f t in Hilbert space. Signal ( ) g t is orthogonal to ( ) f t . In the time domain, ( ) g t can be represented as [7] 1 ( ) 1 ( ) { ( )} ( )* f t g t H f t d f t t t     