Array signal processing is an interesting field that uses sensors placed in particular geometric arrangements for the detection and processing of signals. One of the most significant features is that the array is able to perform spatial discrimination besides the well known frequency filtering approach. The spatial filtering process is referred to as beamforming. The objective of beamforming is to enhance a desired signal meanwhile canceling interferences coming from other directions and suppressing the background noise. The arrangement of the sensing elements is essential in determining the performance of source localization and beamforming.;Among different geometry arrangements, the ring array is preferable for 3-D beamforming because provides full azimuth coverage and reduces the cone of uncertainty present in the uniform linear array (ULA) to just two direction of arrivals (DOAs) while maintaining an azimuthal uniform beampattern. The concentric ring array (CRA) has additional flexibility in adaptive beamforming. Furthermore, it can utilize nested array design and achieves frequency invariant characteristics. The spherical array (SA) has all the advantages of the ring array plus maintaining a uniform beampattern in all directions and eliminating the DOA uncertainty.;This thesis introduces new methods for the partial adaptive beamforming using CRA and SA for acoustic signals on a partially known interference environment. This work is originally based on the element space partial adaptive beamformers of D. Abraham and H. Cox. More recently, Y. Li employs a CRA where the whole array is decomposed into sub-arrays that perform element space individual beamforming using intra-ring weights. Then, the sub-array outputs are combined together with adaptive inter-ring weights to form the overall beamformer output.;The first contribution of this thesis resides in novel methods to choose the intra-ring and inter-ring weights. They are designed to take advantage of the prior knowledge about the characteristics of some of the interferences present in the acoustic field without reducing the beamformer's degrees of freedom (DOFs). The appropriate amount of prior knowledge included in the design of the intra-ring weights is in the form of a fixed penalty factor value. The intra-ring weights are designed to cancel the interferences with prior knowledge. The inter-ring weights are adaptively obtained to cancel the unknown interferences.;The second contribution of this thesis lies on the optimization of the penalty factor that is automatically obtained to minimize the amount of residual error in the beamformer output at any time.;The third contribution of this thesis is the idea of combining the element space along with the beamspace beamforming, where the prior knowledge is added in form of beamspace beams pointing towards the interferences with known characteristics, meanwhile keeping the sub-arrays that use element space beamforming to handle the interferences with unknown characteristics. The combined beamspace element space (CBSES) is found to be robust against interference uncertainties and presents a consistent behavior for different scenarios.;The fourth contribution extends the CRA element space partial adaptive beamformer to the SA. We analyze several sensor arrangements and we suggest two novel sensor arrangements for beamforming with the SA that uses parallel ring sub-arrays. The partial adaptive beamformer design achieves huge computational savings, faster convergence and similar performance than that of the fully adaptive beamformer. Finally, the design of a broadband beamformer using nesting on an SA is also presented. Array nesting will increase the frequency range of the array and will reuse elements from different nests. Thus, reducing the total number of sensor elements needed.;The last contribution of this thesis is the implementation of two robust algorithms against the SA sensor misplacement. The proposed algorithms use a better distortionless constraint that includes the sensor position errors, contrary to the constraint used in the diagonal loading robust method, which does not include the errors.
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