Performance analysis on applications of LV distribution.
Date of Issue2013
School of Electrical and Electronic Engineering
Time-frequency analysis is widely used in revealing the joint time-frequency characteristics of non-stationary signals which have been used in many fields, such as sonar, wireless communication, radar target recognition and imaging. Many methods have been developed for processing these signals, such as the short-time Fourier transform (STFT), Wigner-Ville distribution (WVD), local polynomial periodogram (LPP), polynomial Fourier transform (PFT), fractional Fourier transform (FrFT), etc. Each of these methods has inherent merits and shortcomings, which lead to limited applications. For example, bilinear transforms, e.g., the WVD, provide high energy concentration but suffer from cross-terms. Linear transforms including STFT and PFT are free of cross-terms but can not achieve good signal concentration. Many efforts have been devoted to find methods having both high concentration and negligible cross-terms, usually by using various time-frequency windows, or kernels. However, there always exists a trade-off between auto-terms and cross-terms in kernel based distributions, which often limits further improvement on signal concentration in the time-frequency domain. Recently, a new time-frequency analysis method named Lv distribution (LVD) was proposed for multi-component linear frequency modulated (LFM) signals. The LVD is able to provide high signal concentration with negligible cross-terms. Different from the FrFT which indirectly provides estimations of frequency and chirp rate by searching rotation angles, the LVD directly represents the LFM signals in the frequency-chirp rate domain mainly by using a scaling operation on the time and lag variables. In principle, the LVD is bilinear, but simultaneously has the property of linear transforms based on coherent integration. Therefore it is considered to have advantages of both bilinear and linear transforms. However, since the LVD is very new, there are many challenges remaining. This thesis focuses on various related issues of LVD, including performance analysis, signal reconstruction, extensions and applications, to provide thorough analysis and performance of the LVD. First, some important performances of LVD including frequency-chirp rate resolution, signal energy concentration, detection, representation errors and computational complexity are discussed theoretically and experimentally. An efficient method is supposed to have the following characteristics: high resolution to distinguish signals closely located in the transform domain; high energy concentration to achieve high signal detection probability; low representation errors to estimate parameters of the signal accurately and low computational complexity to save costs of time and resources. Based on theoretical analysis and experimental results, it is shown that the LVD achieves desirable performances on these issues. Furthermore, comparison with other methods, such as FrFT, shows that LVD is preferred for LFM signal processing. Second, since the LVD has such impressive merits over other approaches theoretically, we will verify these advantages with applications. Three applications based on the LVD are presented. The first one is to use LVD to estimate chirp rates for the time-frequency representation (TFR) based on LPP. The parameter estimation is a key step for LPP to achieve a high quality TFR. In previous work, the PFT has been employed to estimate the chirp rates, resulting poor performance in heavy noise environments, because of the low accuracy in the parameter estimation. We aim to improve the LPP by using LVD instead of PFT. In the second application, we propose short-time Lv transform (STLVT) for processing long signal sequence. The STLVT is designed by applying the inverse Lv distribution (ILVD) to process consecutive segments of a long data sequence, where the ILVD is a transform to represent the signal in the time-frequency domain. Furthermore, it can reveal non-linear frequency modulated signals while the LVD can not. For an application on the spectrum sensing for cognitive ratio, we propose a method to jointly use the STLVT and Hough transform. The third application is to employ the LVD to suppress LFM interference for spread spectrum communications. To effectively eliminate intentional multiple component interference in communication systems is challenging, this is mainly due to the difficulties in accurately estimating the parameters of interference components, particularly in low signal-to-noise ratio (SNR) environments. Based on two concepts of interference cancellation and phase cancellation plus filtering, we propose adaptive interference suppression methods by using the LVD to estimate parameters of the jammer. To measure the concentration degree of LVD, a high-order statistics named skewness is also used. Simulation results based on Monte Carlo experiments show the proposed methods suppressing the interference effectively. Third, we investigate the signal reconstruction from the LVD domain to the time domain, and propose two signal recovery methods, named the LVD based signal reconstruction (LSR) and the LSR with suppressed cross-terms (LSRC), where the latter is an improvement of the former. Both of them can accurately recover the signal with small errors. Based on LSR and LSRC, applications including signal decomposition, de-noising and re-sampling are presented and verified, showing that they can effectively remove the noise in negative SNR environments and re-sample the signal to an arbitrary new sampling frequency with trivial errors. Finally, we extend LVD to a more general case, proposing the two-dimensional (2D) LVD for high dimensional applications (e.g., image processing). The 2D LVD, which is extended from the 1D LVD to a 2D version, inherits the properties from the 1D LVD so that it has both advantages of bilinear and linear methods to achieve high concentration and trivial cross-terms. At last, an application of the new 2D technique on image watermarking by using 2D LFM signals is presented. Simulations show that the 2D LVD works well against various attacks. The LVD has been considered to be a better analysis method for LFM signals. However, it has some limitations. It is not proper to be used for signals with arbitrary order of polynomial phase since the LVD is particularly designed for signals with the 2nd order polynomial phase. The LVD could not provide high resolution of chirp rate for signals whose time duration is short due to the uncertainty principle.
DRNTU::Engineering::Electrical and electronic engineering::Electronic systems::Signal processing