Decection And Parameter Estimation Of Polynomial Phase Signal

In many real-life or technological applications such as radar, wirelesscommunications, and seismology, the signal of interest is nonstationary, and the phasehas a continuous instantaneous feature. The polynomial phase signal (PPS) model is themost common model to deal with these nonstationary signals, and the detection orparameter estimation has become a hot issue in signal processing domain. The existingalgorithms are classified into two categories. The maximum likelihood method andthenonlinear instantaneous least squares method are belonging to the first category,which have the advantage of high estimation accuracy and can approximate theCramér–Rao lower bound under the low SNR condition. However, their computationalcomplexity will dramatically increase along with the increasing of the order of phase.The second category includes a variety of time-frequency analysis tools such ashigh-order ambiguity function, polynomial Wigner–Ville distribution, which have theadvantage of low computational complexity. Comparing with the first categoryalgorithm, they have a higher SNR threshold and the estimation performance issuboptimal since the estimation accuracy of the lower-order phase parameters isdependent on that of the higher-order phase parameters. Furthermore, the nonliearity ofthe time-frequency tools may lead to cross-term interferences when dealing with themulti-component case.Linear transforms such as fractional Fourier transform, wavelet transform can beused to estimate the PPS with2order of phase (linear modulated frequency signal,chirp), which can avoid the cross-term interferences for multi-component case. For thePPS with order more than2, the reduction in computational complexity need theincreasing in nonlinear procedures, and then the estimation performance will decreasewith the increasing of nonlinear procedures. As a result, there are no unified selectioncriteria for estimating PPS. The algorithms should be chosen based on the compromiseof performance requirements, environment with SNR and computainal complexity.In this paper, the current basic research theories of learning have been firstlyinvestigated, which are focusing to fractional Fourier transform and high-order ambiguity function. And the study works of detection and parameter estimation of PPSare as follows.1. Analyze the properties of fractional Fourier transform and linear canonicaltransform, and present the fractional derivative formulations obtained by generalizingthe derivative property. Use linear canonical transform to yield a simplified lineartransform that provides better estimation performance for LFM signals as comparedwith fractional Fourier transform.2. Investigate the frequency spectrums of LFM signals and cubic phase signalwithin a finite interval, and propose a method to estimate the highest phase coefficientby using FFT directly or indirectly, which can reduce the range of2-demensions peaksearch and computational complexity.3. Investigate the identifiability issue of high-order ambiguity function algorithmwhen dealing with multicomponent PPS having the same highest order phasecoefficients, and prove that all cross-terms with interference have strict symmetryproperties. Based on such symmetry, we propose a new high-order ambiguity functionbased algorithm for multiple component PPSs, which completely eliminates thecross-terms.4. Analyze the parameter separation algorithm of PPS that separates the phaseparameters into two sets by nonlinear procedures,and then each set has half of theparameters. For multi-component case, the algorithm can construct symmetrical peaksand easily eliminates the cross-terms interference by the symmetry. Furthermore, usingtwo linear transforms to deal with the two signals respectively, the phase coefficientscan be obtained by peak search. As compared with high-order ambiguity functionalgorithm, parameter separation algorithm increases the eatimation performance at lowSNR, while sacrifices some computational convenience.5. Investigate the Taylor expansion of PPS, and prpose a linear transform calledfrom polynomial to Hermite polynomial. Based on the transform, all the parameters ofPPS can be estimated. The proposed algorithm obtains a good estimation performancefor the lowest phase coefficient as compared with other nonlinear algorithms.