Lfm Class Signal Doa Estimation Algorithm Based On Fractional Fourier Transform

Direction of arrival (DOA) estimation for non-stationary linear frequency modulation (LFM) signal has been a significant research point in the modern array signal processing field, which is widely used in radar, sonar, communication systems. For a newly developed time-frequency analysis tool, the fractional Fourier transform (FRFT) has more properties which are not be possessed by any other time-frequency analysis tools in the processing of LFM signal. Therefore, combining the FRFT with array signal processing, the dissertation is focused on the DOA estimation of LFM signal based on FRFT. The main contributions and innovations of the dissertation are:1. The energy-concentrated DOA estimation method ~[49-50] is introduced, using the energy concentration property of LFM signal in a certain fractional Fourier (FRF) domain to get the time-invariant direction matrix in that FRF domain, and signal direction can be estimated by the traditional MUSIC algorithm. However, this algorithm is not fit for coherent LFM signal whose time-frequency distributions is similar, combining with the forward/backward spatial smoothing technique in that FRF domain, DOA estimation of coherent LFM signal based on the FRFT is proposed. Theory deduction and computer simulation verify the algorithm can exactly estimate the DOA of coherent LFM signal, cross-terms is avoided in processing the multi-component signals. Combined with the traditional DOA matrix method, the energy-concentrated method is extended to realize the two dimension DOA estimation from solid interspace, which is fit for the practice application. Simulation result the method to be effective.2. A new de-chirp method based on the FRFT for estimating DOA of the LFM signal is proposed by using the property that LFM signal can be de-chirped into the single frequency signal in a certain FRF domain. The time-invariant direction vector is presented in the corresponding FRF domain, the DOA of LFM signal can be estimated by the traditional MUSIC method. Additionally, the theory deduction and Cramer-Rao bound are also provided and verified by the simulation results thus makes this method more reliable in theory and in practice. Compared with the DOA estimation algorithms based on the Wigner-Ville distribution (WVD), this method avoids focusing and interpolation, and needs no initial DOA estimation. So this approach has good estimate performance with little computation complexity, and for multi-source, there are no cross-stems.3. In allusion to the uniform circular array (UCA) which is widely used in the third mobile communication system, combing with the de-chirp method, an algorithm for DOA estimation based on the FRFT using UCA is proposed. The mode excitation -based beamforming is introduced in corresponding FRF domain, which can transform the UCA into the uniform linear array (ULA) in the mode space, and two-dimension DOA can be estimated by the traditional searching method. The method is verified to be effective by the computer simulations, meanwhile extend the application range of traditional method and make our method to be extensive practical value.4. The de-chirped method is extended into the unknown colored noise model and near-field source model. For the colored noise environment, the whiting-filter is estimated by the covariance matrix of the observed signals in the de-chirped FRF domian, and covariance matrix is transformed into white noise covariance one by per-whiting processing, the DOA of LFM signal in the colored noise environment can be estimated by the eigenvalue decomposed method. For the near-field sources, the non-linear peoperty and Fresnel approximation of the near-field spherical wave are analyzed in the same domain and the de-chirp method can be extended into the near-field mode, therefore the two-dimension joint estimations for DOA and distance of LFM signals can be accoplished. The theory deduction and computer simulation above the two extended algorithm are provided to verify the validity, meanwhile the application range of de-chirped method is enriched.