New direction finding and beamforming algorithms for sensor arrays with uncertainties

Abstract

Sensor arrays have been successfully applied to many engineering fields and the theoretical as well as applied aspects of senor array processing have received intensive research interest. Practically, sensor array systems usually suffer from uncertainties such as unknown gains and phases, mutual coupling, and look direction mismatch. In this thesis, problems of direction finding and beamforming in the presence of array uncertainties are addressed, and new algorithms to tackle these problems are developed.

In certain applications, senor arrays are only partly calibrated. Hence, the exact responses of some sensors are unknown, which degrades the performance of traditional direction finding techniques. To tackle this problem, a new method for direction finding with partly calibrated uniform linear arrays (ULAs) is proposed. It generalizes the estimation of signal parameters via rotational invariance techniques (ESPRIT) by modeling the imperfection of the ULA as gain and phase uncertainties. For a fully calibrated array, it reduces to the standard ESPRIT algorithm. In this method, the direction-of-arrivals (DOAs), unknown gains and phases of the uncalibrated sensors can be estimated in closed-form without performing spectral grid search. Moreover, it can be further improved by a refining scheme proposed. Its superiority over existing methods is demonstrated by simulation results.

Apart from unknown gains and phases, the mutual coupling caused by interactions among sensors also seriously deteriorate the performance of array processing techniques. In ULAs, the mutual coupling matrix (MCM) can be approximated as a banded symmetric Toeplitz matrix. Using this specific property, a new parameterization of the steering vector is proposed and the corresponding method for joint estimation of DOAs and MCM is derived. Compared with the conventional subarray-based method, the proposed one makes use of the whole array and achieves better performance especially for weak signals. On the other hand, the specific property is further employed to develop a new approach to calibrate the steering vector. By incorporating the calibrated steering vector with a diagonally loaded robust beamformer, a new adaptive beamformer for ULAs with mutual coupling is obtained. It is found that the resultant steering vector estimate considerably improves the robustness of the beamformer against mutual coupling.

Another common uncertainty in sensor array systems is the look direction mismatch. Though numerous robust beamformers have been developed accordingly, most of them cannot offer sufficient robustness against large look direction errors. To this end, a new robust beamforming method which can flexibly control the magnitude response in the look direction is proposed. By linearizing the nonconvex constraints in the original problem, the resultant problem is convex and can be solved using second-order cone programming (SOCP). Moreover, to further improve the robustness against array covariance uncertainties, this method is extended by optimizing its worst-case performance. Unlike some conventional methods restricted to specific arrays, the proposed method is applicable to arbitrary array geometries. Simulation results show that the proposed method offers comparable performance to the optimal solution for uniform linear arrays, and also achieves good results under different array specifications and geometries.