Reduced-control antenna arrays reduce the number of controls required for beamforming while maintaining a given array aperture. A reduced-control array for direction finding (DF), inspired by the concept of compressive sensing (CS), was recently proposed which uses random compression weights for combining antenna-element signals into fewer measurements. However, this compressive array had not been studied in terms of traditional characteristics such as directivity, sidelobe level (SLL) or beamwidth. In this work, random compression weights are shown to be suboptimal and a need for the optimisation of compressive arrays is expressed. Existing codebook optimisation algorithms prove to be the best starting point for the optimisation of compressive arrays, but are computationally complex. A computationally efficient codebook optimisation algorithm is proposed to address this problem, which inspires the compressive-array optimisation algorithm to follow. Compressive antenna arrays are formulated as a generalisation of reduced-control arrays and a framework is presented for their optimisation in terms of SLL. By allowing arbitrary compression weights, compressive arrays are shown to improve on existing reduced-control techniques. A feed network consisting of interconnected couplers and fixed phase shifters is proposed, enabling the implementation of compressive arrays in microwave hardware. The practical feasibility of compressive arrays is illustrated by successfully manufacturing a 3-GHz prototype compressive array with integrated antenna elements. / Thesis (PhD)--University of Pretoria, 2020. / Electrical, Electronic and Computer Engineering / PhD / Unrestricted