Research On Theories And Methods For Polynomial Phase Array Signal Processing Based On LPFT

Polynomial phase signals will be encountered in the applications of array signal processing, e.g., radar, sonar, communications, geological exploration, medical imaging and so on. The research on array signal processing with polynomial phase signal models is of more significance in array signal processing theory and its practical applications.In recent years, many novel and efficient approaches for non-stationary array signal analysis have been proposed. However, most of existing non-stationary array signal parameter estimation methods are restricted by the assumption of known signal sources instantaneous frequency, the applicability only for LFM signals, the disturbance of cross-term interference. To improve these methods, array signal processing methods with polynomial phase signal models are studied. In this dissertation, spatially narrowband polynomial phase signal model, spatially broadband polynomial phase signal model and polynomial phase signal model with mutual coupling effect are considered. The corresponding solutions are proposed.The main contributions of this dissertation can be generalized as:1. The key issue (eq. cross terms) of local polynomial Fourier transform (LPFT) application is studied.Over the years, the polynomial phase signal parameter estimation problem has more wider applications, which has attracted more attentions [24-48] and has been greatly developed. But, for multi-component PPS signals, the non-linear-type analysis methods [19,31,115] will be interfered by cross-terms. Up to now, this type has not obtained particularly encouraging results.In this paper, the LPFT is studied. As a generalization of linear transforms, e.g. short-time Fourier transform (STFT), S-transform analysis, LPFT has attracted more attentions [47-62] and has been applied to radar signal processing [54,56] and communication system of non-stationary interference suppression[51-53]. Although the linear-type transform has no cross-terms, the transform spectrogram is always defined as the square of the transform. It is also bilinear. Hence, it is necessary to study the cross-terms in linear transform spectrogram. The cross-terms of local polynomial periodogram (LPP) are derived and quantitatively analyzed by the definition of cross local polynomial periodogram (CLPP) and time-frequency correlative coefficients (TFCC). The relations between the signal contents and processing parameters with the cross-terms are identified. The reasons for ignoring the cross-terms in many references [54-56,117] are interpreted. It provides a theoretical basis for the application of LPFT. Meanwhile, the conclusion is applicable for linear-type transformation methods.2. The DOA estimation methods with spatially narrowband multi-source polynomial phase signals are studied by LPFT.The conventional array signal processing methods are limited with the stationary signal sources assumption. In practice, there are many non-stationary signals (e.g. polynomial phase signals) in the radar system, sonar system, and communications system. Hence, the study on narrow-band multi-source polynomial phase signals DOA estimation has more practical significance. In this context, four different DOA estimation methods are proposed.(1) The advantages and characteristics of time-frequency MUSIC are analyzed. Combined with the characteristics of LPFT, the LPFT-MUSIC method is proposed, which can deal with not only LFM signals, but also polynomial phase signals. The enhance factor of LPFT-DOA signal to noise ratio (SNR) is theoretically derived. It is also found that for the subspace methods, the LPFT-based array analysis can amplify the large eigenvalues which is closely related to signal sources, while the small eigenvalues corresponding to noise components do not change. Therefore, the LPFT-MUSIC can enlarge the analytical capacity of the spatial parameters. The simulations show that the performance of this method is better than time-frequency MUSIC and traditional MUSIC methods.(2) Time-frequency MUSIC which needs known IF information is not practical because the bias of IF estimation is difficult to be avoided particularly when the signal is corrupted by heavy noise. By analysis of the LPFT computing process, the characteristics of narrow-band array are used in LPFT calculations. Based on APFT, the modified LPFT-MUSIC is proposed. The unascertained problem of time-frequency characteristics and the performance degradation problem with unknown time-frequency characteristics by traditional time-frequency are solved. Compared with time-frequency MUSIC and original LPFT-MUSIC, this method can be extended with lower SNR and more noise types. The time-frequency property and DOA are estimated simultaneously.(3) A new rotation-invariant structure based on APFT-LPFT and the LPFT-ESPRIT for 1-D DOA estimation is proposed with uniform linear array. The time-frequency characteristics and DOA online estimation can also be achieved. Compared with LPFT-MUSIC, the computation is reduced (without searching over parameter space). Simulation results show that in the case of low SNR environment, especially when SNR<0dB, the performance advantage of LPFT-ESPRIT method is evident.(4) In array applications, the impinging direction of sources is not necessarily located in one plane. In the three-dimensional coordinate space, the sources can be identified by 2-D angle. With a parallel linear array model, a rotation-invariant structure is constructed with LPFT. The 2-D DOA estimation algorithm for polynomial phase signals is derived. A new two-dimensional parameter matching solution is proposed. Simulations show that the estimation success rate and accuracy of proposed method is better than those of traditional 2D-ESPRIT.3. The DOA estimation methods with spatially wideband polynomial phase signals are studied by LPFT.In communication systems[9,15], the quality of transmission channel can be improved with wideband models. In radar systems[14], more information can be achieved from target echo signals by increasing the signal bandwidth. Hence, there are more application prospects of wideband non-stationary array signals analysis. In this paper, two methods are proposed for wideband polynomial phase signals DOA estimation.(1) The existing time-frequency coherent signal subspace methods [96,119] which are based on Wigner-Ville distribution, are only suit for LFM signals and general noise assumption. A new wideband non-stationary array signal model is derived. With specificity of time-frequency structure and the mind of coherent subspace focusing transform, a broadband non-stationary LPFT coherent array signal subspace method is proposed. This method is efficient with the unknown correlated noise and other additive noise.(2) In array signal processing, the hoped direction information is described as a component of array output signal phase. In particular, for the wideband array model assumptions, the phase difference between the array elements is a function of azimuth angle and instantaneous frequency. So the element output model is more complicated. In this paper, a polynomial phase model is used to represent the noise-free output of the array element. Based on the polynomial phase characteristics of wideband array outputs, a wideband polynomial phase array signals DOA estimation method is proposed. This method considers the most extensive broadband array model assumptions and can reduce the computation and estimation error which comes from CSSM method with focusing transformation and initial direction estimation.4. The DOA estimation methods with array mutual coupling calibration are studied.In many array compact devices, the antenna elements must be closely spaced, and the resulting antenna mutual coupling effect is inevitable. High-frequency disturbance is another influence aspect of mutual coupling. Mutual coupling will directly affect the performance of system [17,18,103]. In this paper, two methods are proposed to solve the problem.(1) Based on fourth-order cumulant and the special mutual coupling transform model of the uniform linear arrays, a novel efficient mutual coupling compensation algorithm with DOA estimation is presented. Calibration sources are not required. And it's an on-line calibration method. Although fourth-order cumulant is more complex than traditional second-order method, more spatial information it can been get and the number of mutual coupling coefficients is not expanded with the increasing virtual arrays. Simulations show the effectiveness of proposed technique and illustrate that the estimation resolution of the algorithm is higher than second-order mutual coupling calibration method and the fourth-order method without mutual coupling consideration, in the case of Guassian color noise.(2) For a wider range of noise environments, such as unknown spatial correlated noise[128], Gaussian color noise[129] and Gaussian white noise with very low SNR, etc., a narrowband spatial signal mutual coupling calibration and DOA estimation method is proposed based on RARE-LPFT. The polynomial phase signal sources are also considered, so the method is more practical. The simulation results validate the robustness of this method.Summarily, the approaches proposed here for array signal processing with non-ideal models have many prominent virtues such as strong noise suppression ability, high estimation accuracy and a wide range of applications. Both theoretical analysis and simulation results validate the effectiveness of the new methods.