Study On Spectral Spectrum Estimation Algorithm Under Non-ideal Array Gain/Phase Response

Estimating direction of arrival (DOA) and range of one or more interesting signals which are located in some spatial field simultaneously is one of the most important research area of array signal processing. It is widely used in various military and economic fields such as radar, sonar, communications, seismology and medical imaging.Most high-resolution spatial spectrum estimation algorithms require precise knowledge about the receiving array manifold. However, in reality the array manifold errors are inevitable, the high-resolution spatial spectrum estimation algorithms wil suffer form severe performance degradation. Hence it is very necessary to calibrate the array manifold errors before spatial spectrum estimation. This dissertation has made deep research on the spatial spectrum estimation algorithms of different array manifold when the array exists gain and phase response errors.This dissertation has made improvements on the existing source localization algorithms, and made deep research on the problem of array calibration when the array exists gain and phase response errors. Several new algorithms are proposed.1) The author proposes a self-calibrated algorithm of array gain and phase response errors for uniform linear array. Considering the special manifold of uniform linear array, we discuss the ambiguities of the estimations of DOA and sensor gain and phase response errors. Based on the ambiguous relations, we propose an iterative algorithm for the estimation of DOA and sensor gain and phase response errors. The step of removing the phase ambiguities is included. We also show that the phase ambiguities can be removed if we assume one sensor phase response of the array has been calibrated. Compared with the existing algorithms, the iterative algorithm is robust and doesn't need good initial value. It has high estimateion precision and fast convergent speed even when the array exists large gain and phase response errors.2) The author proposes a2-D DOAs estimated algorithm for uniform rectangular array. Considering the large computational complexity of the classical2-D MUSIC algorithm, we make an improvement. Based on the property of the steering vector of uniform rectangular array, it can be transformed two matrices multiplication form. Then the proposed algorithm can avoid2-D searching by transforming2-D searching into two1-D searchings. The computation load of the proposed algorithm is relieved effectively. The estimated parameters are paired automatically. Simulation results show that the proposed algorithm can achieve accurate and stable estimated results. 3) A self-calibrated algorithm for unique planar equispaced array is proposed. Considering the special manifold of unique planar equispaced array, we discuss the ambiguities of the estimations of2-D DO As and sensor gain and phase response errors. Based on the ambiguous relations, we propose an iterative algorithm for the estimation of2-D DOAs and sensor gain and phase response errors. The step of removing the phase ambiguities is included. We also show that the phase ambiguities can be removed if we assume two sensor phase responses of the array have been calibrated.4) A new near-field source localization algorithm based on a uniform linear array was proposed. The proposed algorithm estimates each parameter separately but does not need pairing parameters. It can be divided into two important steps. The first step is bearing-related electric angle estimation based on the ESPRIT algorithm by constructing a special cumulant matrix. The second step is the other electric angle estimation based on the1-D MUSIC spectrum. It offers much lower computational complexity than the traditional near-field2-D MUSIC algorithm and has better performance than the high-order ESPRIT algorithm. Simulation results demonstrate that the performance of the proposed algorithm is close to the Cramer-Rao Bound (CRB).5) Based on the new near-field localization algorithm, a method for joint estimation of near-field source parameters and array gain/phase response is proposed. Considering the special uniform linear array manifold for near-field source, we discuss the ambiguities of the estimations of near-field source parameters and sensor gain and phase response. Based on the ambiguous relations, we propose an iterative algorithm for the estimation of near-field source parameters and sensor gain and phase response. The step of removing the phase ambiguities is included. We also show that the phase ambiguities can be removed if we assume two sensor phase responses of the array have been calibrated.6) Closed-form expressions of the CRB for the estimation of near-field source location under unknown array gain/phase responses are derived. The expressions do not involve complicated matrix operations such as matrix inverse. Hence they can be efficiently calculated. Various affecting factors on the behaviour of the bounds are analyzed. From the CRB analysis, we conclude that any priori unknown gain uncertainty will not affect the CRB, but unknown phase response will lead to worse CRB.