Polarimetric Phased Antenna Arrays (PPAA) are widely used in many applications ranging from cellular and satellite communications to automotive and weather radars. To operate the phased array adaptively for the generation of multiple polarization states, the gain and phase of each antenna element (or each port in case of multiport antennas), so called the beamforming weights, have to be optimized. The optimization is performed based on the defined pattern goals and constraints such as the co- and cross- polarization gains and maximum side-lobe levels. By all means, the optimization of complex beamforming weights depends on the architecture of the phased array. Since a PPAA might consist of thousands of antennas, low-cost architectures, requiring a lower number of RF chains, are studied by the researchers through element polarization optimization techniques. Although low-cost solutions considerably lower the cost and complexity of a PPAA, they deteriorate the polarimetric performance of the array due to the lack of optimization studies considering polarimetry.

In this thesis, optimization strategies for low-cost PPAAs are discussed. It is found that the state of the art optimization algorithms limit the operation of a low-cost PPAA to two polarization states, and the polarimetric performance of the array deteriorates substantially for any other polarization state. However, the synthesis of more polarization states from a single array may be demanded for performance enhancement. A new optimization algorithm, mainly using convex optimization, is proposed to extend the capabilities of a low-cost PPAA to three polarizations with a minimal trade-off in the remaining two polarizations. It is shown that for a 16 by 16 ideal planar low-cost PPAA, the EIRP of an arbitrary third polarization (in addition to H and V) can be improved by $3$ dB with a negligible loss in H and V, compared to the state of the art algorithms. Moreover, the low-cost PPAA is simplified even further through subarraying. A new subarrayed architecture, built on the low-cost topology, is proposed along with a novel optimization strategy to further lower the cost of a PPAA. It is shown that with only a $1$ dB loss of EIRP in H and V, a low-cost PPAA can be subarrayed. Lastly, the pattern synthesis problem for low-cost PPAAs is discussed. To maintain polarization purity and the overall pattern shape, the cross-polarized field is also subjected to shaping constraints. The joint pattern and polarization synthesis are explained for the dual-polarized and low-cost architecture, full-wave simulations are integrated into the optimization, and effectiveness of the proposed algorithms are verified. It is shown that for a 13 by 13 array, the co-polarized field can be shaped with a maximum ripple size of $\pm1$ dB, and the cross-polarized field can be suppressed more than $40$ dB with respect to the mask shape.