Tensor/Quaternion-valued Robust Adaptive Beamform-ing With Electromagnetic Vector-sensor Arrays

The tensor/quaternion-valued robust adaptive beamforming problems are investigatedbased on electromagnetic vector-sensor arrays in this dissertation, whose main contribu-tions are summarized as the following three aspects.Based on electromagnetic vector-sensor arrays, the problem of robust adaptive beam-forming is first studied within the tensor algebra framework. By exploiting the inherentmultidimensional smoothing processes involved in the matrix contractions of the co-variance tensor and adopting the well-known worst-cast constraint, a tensorial robustadaptive beamforming is presented to tackle the steering vector mismatch problem inthe presence of coherent interferences. In addition, the two-stage structure of the pro-posed scheme effectively combines the Bartlett and minimum variance distortionlessresponse beamformers together, and is therefore capable of suppressing coherent inter-ferences with improved robustness in a compact manner. Simulation results demon-strate a favorable performance of our proposed method.To cope with the performance degradation of recently proposed quaternion-valuedadaptive beamformers in terms of both mismatched steering vectors and sample covar-iance matrices’ finite sample size errors, a robust adaptive beamforming algorithmbased on two-component electromagnetic vector-sensor arrays is presented by extend-ing the well-known worst-case constraint into the quaternion domain. We then refor-mulate the corresponding quaternion-valued non-convex optimization problem into areal-valued convex quadratic form, which can be easily solved via second-order coneprogramming method. After the solution of a quaternion-valued Lagrange problem, it isalso demonstrated that the proposed algorithm can be classified as a specific type of thediagonal loading scheme. Theoretical derivations and numerical simulations both indi-cate a superior performance of our new method in dealing with the model mismatcherrors.A novel quaternionic signal model is firstly presented based on the spatial subarray di-vision using spatially stretched tripole arrays. Afterwards, a principal eigenspace pro-jection based method is studied in the quaternion domain. Since the proposed scheme is free of solving the convex optimization problem that has high computational com-plexity, it is preferable to the aforementioned quaternion-valued worst-case constrainedbeamformer for practical scenarios. Furthermore, the widely linear processing modelwhich can further exploit the second-order information of quaternion output vectors isapplied to yield a better performance for the quaternion-valued principal eigenspaceprojection scheme. Numerical simulations show that the proposed algorithm canachieve an excellent performance with reduced computational complexity, and outper-forms the other schemes simulated especially in the case of low signal-to-noise ratiosand large sample sizes.