Research On The Basic Theory And Methods Of The Parameters Estimation For QFM Signals Based On The Linear Canonical Transform

The quadratic frequency modulated (QFM) signal is one of non-stationary signals,which can be found in nature and engineering applications widely. The time-frequencyanalysis and parameter estimation of QFM signals with noise are its common difficultieswhich must be solved in the practical application. Therefore, it is important and valuable toresearch the detection and parameter estimation for QFM signal.The traditional parameter estimation algorithms of a QFM signal mainly base onreducing the order of the QFM signal from by high-order nonlinear transform, and then usethe existing time-frequency analysis tool or construct a new time-frequency transformationto estimate parameters. But the higher-order non-linear transform of this kind of algorithmswill generate high input signal-to–noise ratio (SNR) threshold and low output SNR, ortheir computational cost is large. The linear canonical transform (LCT) as a generalizationof Fourier transform and fractional Fourier transform has three free parameters, so it ismore flexible. And the LCT has fast computation algorithm, so it does not suffer fromcomputation burden. In order to enrich and develop the basic theory of the LCT and explorenew kinds of parameter estimation algorithms with high performance of QFM signals, thepaper construct new time-frequency analysis tools based on the LCT combining with theadvantages of the LCT in the signal processing field. We study their related theory anddiscuss their applications in parameter estimation of QFM signals. The main contributionsand innovative results are as follows:Major contributions and novelty of the dissertation are given as follows:1. In order to study the parameter estimation algorithm of QFM signals, thisdissertation investigate the related basic theory of LCT. Firstly, a new ambiguityfunction based on LCT (LCTAF) is proposed, and a deep and comprehensive study on itsimportant properties is also done. The relationship between the LCTAF and other time-frequency analysis tools is further examined and we found that many common time-frequency distributions can be expressed by the LCTAF. The LCTAFs of some commonsignals are given out. As for the ambiguity function of signals after LCT, its convolutionproperty, product property and relevance principle are also studied. Secondly, a new time-frequency annlysis tool named the Wignler-Ville disitribution based on the LCT (WDL) is defined and its some new important properties are discussed. The relationships between theWDL and other time-frequency analysis distributions are derived and the WDLs of someimportant signals are analyzed. Lastly, as for the two dimention LCT, some of its commonproperties are derived and we propose the convolution and product theory in the twodimention LCT domain. And the numerical calculation of the two dimention LCT isverified by an example. The establishment of the basic theory of the LCT not only enrichesthe theoretical system of the LCT but also lays the theoretical foundation for the researchon the parameter estimation of the QFM signals.2. A parameter estimation algorithm of QFM signals is proposed based on thegeneralized LCT (GLCT). In the definition of LCT, replacing the signal itself by a forth-order nonlinear transform of the signal we define the GLCT and use it to estimate the third-order phase coefficient of the QFM signal. To study the performance of the algorithm, wecompare the GLCT algorithm with other fourth-order nonlinear transform algorithm in theaspects of mean square error (MSE), the output signal-to-noise ratio (SNR) and thecomutational complexity. The results show that the MSE of GLCT algorithm has lowerSNR threshold. When the input SNR satisfies certain conditions, the output SNR of theGLCT algorithm is higher and it needs less sampling points when getting a certain count ofoutput SNR than other fourh-order nonlinear transforms. Because the GLCT algorithm justneeds one dimensional maximum search and the LCT has fast computional algorithm, theGLCT algorithm has low computional complexity and high operation efficiency.3. We propose a new parameter estimation algorithm of the QFM signal by usingthe ambiguity function based on the LCT (LCTAF). The LCTAF has good focusingcharacteristics for the QFM signal and using this focusing characteristic the second-orderphase coefficient and third-order phase coefficient of the QFM signal can be estimated.Other coefficients can be obtained by dechirp technology and Fourier transform. Theoryanalysis and simulation results show that the LCTAF algorithm has very low SNR threshold(-3dB) for it just has two-order nonlinear transform. Compared with the fourth-and sixth-order nonlinear transform, the estimation precision is greatly improved in when the SNR islow. By analyzing the relationship between input SNR and the output SNR, we find thatwhen the input SNR is more than-10dB, the output SNR of the LCTAF algorithm ishigher than that of the GLCT algorithm, the integrated generalized ambiguity function(IGAF) and the polynomial phase transform(PPT) algorithm. If the input SNR is more than 7dB, the output SNR will be nearly the same when the sampling numbers of LCTAF,GLCT, IGAF and PPT are chosen as1:2:4:9. This means that the GLCT algorithm needsfewest sampling points to get a certain size of output SNR among the three algorithms.Because the GLCT algorithm can estimate three parameters at one time, the error transferfrom high order phase confficient to the low order phase confficient is small. It is to saythat the estimation of the low order phase confficient is more accurate.