Study On Robust Beamforming And Sparse Spatial Spectrum Estimation

Array signal processing techniques are widely applied to the fields of Radar, Sonarwireless communication, medical imaging, etc. It can be divided into two main parts in thearray signal processing: adaptive beamforming and spatial spectrum estimation techniques.Corresponding to each part, this dissertationion focuses on the issue of robust beamformingdesign and sparse-signal-reconstruction-based spatial spectrum estimation. Based on a deepstudy on the related theory and existing algorithms, the dissertation has developed some newmethods on the robust beamforming and high resolution spatial spectrum estimation. Themain contributions are as follows.1) The problem of steering vector mismatch for the robust beamformer design isconsidered and a steering vector calibration method is proposed. The proposed technique canobtain the SV directly and efficiently by iterating second-order cone programming. Moreover,the feasibility and convergence of the proposed algorithms can be guaranteed. The proposedbeamformer avoids the equality constraints in the conventional method, thus more degrees offreedom are saved.2) A wideband beamformer with mainlobe control is proposed. To make the beamformerrobust against direction of arrival (DOA) mismatch, inequality rather than equality constraintsare used to restrict the mainlobe response, thus more degrees of freedom are saved. Theconstraints involved are nonconvex, therefore are linearly approximated so that thebeamformer can be obtained efficiently by iterating a second-order cone program and can beapplied to arbitrary types of arrays. Moreover, the response variance element is introduced toachieve a frequency invariant beamwidth. The simulation results demonstrate theeffectiveness of the proposed method.3) A robust beamformer is proposed by modifying the generalized sidelobe canceler(GSC) and using the concept of worst-case performance optimization. With the GSC-likestructure, convex constraints can be directly applied to make the beamformer robust againstDOA mismatch. Then, the beamformer is improved to be robust against arbitrary systemimperfections by applying the worst-case optimization method. The DOA mismatch and othergeneral imperfections can be treated separately in the beamformer, thus an over-conservativerobustness design may be avoided.4）By introducing the sparse iterative covariance-based estimation (SPICE) approach, a robust beamformer with joint robustness against the desired signal mismatch and theinterference coherence is proposed. With the SPICE, we firstly calibrate the look directionmismatch, and then reconstruct the interference-plus-noise covariance matrix (INCM) toreplace the conventional sample covariance matrix. This is shown to greatly improve therobustness of adaptive beamformers since a quasi signal-free environment is provided.Moreover, since the SPICE is robust to signal coherence, the proposed beamformer cansuppress the coherent interferences.5) An INCM reconstruction method is proposed by exploiting the cyclostationarity ofinterference signals. In contrast to the existing INCM reconstruction methods, the proposedtechnique is based on the knowledge of the interferences’ cycle frequencies and needs noinformation of the array structure, thus it can deal with unknown perturbations in the array.Moreover, the proposed technique is suitable to the case when the locations of theinterferences and desired signal are close. The numerical simulations show that the proposedmethod improves the robustness of adaptive beamformers and has superior performance to theexisting INCM reconstruction methods especially for strong interferences.6) A DOA estimation technique is proposed by jointly exploiting the signalcyclostationarity and spatial sparsity. Based on the cyclic conjugate correlation matrix, theproposed estimator exhibits the signal selectivity at a desired cycle frequency, thus thenumber and characteristics of the interference can be arbitrary and unknown. Moreover, byusing the sparse representation framework with the weighted l1-norm minimization, theresolution and accuracy of DOA estimation can be greatly improved. The effectiveness of theproposed method is examined by numerical examples.