A Wigner Ville Distribution based method for detection of Gaussian contaminated sinusoidal signal in frequency domain

Detection and frequency estimation of sinusoidal signals from a finite number of noisy discrete-time measurements have applications in several fields, e.g., in sonar and Radar for moving target detection. In, Pulsed Doppler radar, a bunch of Coherent Pulse Interval (CPI) is processed to detect and estimate the frequency of sinusoidal signal corresponding to the speed of target. With the advent of Fast Fourier Transform (FFT) algorithm, the Periodogram and its variants such as Bartlett's procedure and Welch method, have been extensively in use for spectral analysis. In this paper a Wigner Ville Distribution (WVD) based new method is proposed for the detection and estimation of noisy sinusoidal signals in frequency domain. The Cross terms produced due to the bilinear nature of WVD are eliminated. The proposed method outperforms the Periodogram and its variants (Bartlett and Bartlett-based method proposed by reference [2]) for offbin frequencies. The performance is found to be comparable in case of in-bin frequencies. Due to Low-sidelobes reported by WVD, no additional window operation is used, consequently the proposed method outperforms the windowed version of Periodogram and its variants for all 'in' and 'off' bin frequencies. Also, frequency resolution remains intact. However, the issue of increased computation of proposed method can be tackled by using high speed devices and many proposed real time WVD implementation algorithms. Performances of the proposed WVD based method and the other mentioned methods are evaluated through computer simulations by generating Receiver Operating Characteristics (ROCs) via Monte Carlo trials.