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Traditionally uniform arrays are used to implement beamformers. However, in order to avoid grating lobes the maximum adjacent sensor separation is half of the operating wavelength. For large aperture sizes this can be problematic due to the cost associated with the number of sensors required. Instead sparse arrays become a desirable alternative, as they allow separations greater than half a wavelength while still avoiding grating lobes due to the non-uniform nature of the sensor locations. However, the tradeoff is their unpredictable sidelobe behaviour which means some degree of optimisation is required. This thesis looks at methods to optimise the sensor locations to give a desirable array response. Firstly, this is done using genetic algorithms, where a size constraint can be applied on the optimisation process with the response designed to be robust against norm-bounded steering vector errors. Compressive sensing based design methods are also considered as a more efficient alternative, with methods of enforcing the size constraint and ensuring robustness again considered. Design examples show that a comparable performance to genetic algorithms can be achieved in a much shorter computation time. The original formulation of the compressive sensing problem can be converted to a modified l1 norm minimisation for the design of wideband and vector-sensor arrays. For the wideband case the design method is also extended to consider frequency invariant beamformers and temporal sparsity. |
