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Design optimality plays a central role in the area of statistical experimental design. In general, problems in design optimality are composed of two vital, but separable, components. One of these is determining conditions under which a design is optimal (such as criterion bounds, values of design parameters, or special structure in the information matrix). The other is construction of designs satisfying those conditions. Most papers deal with either optimality conditions, or design construction in accordance with desired combinatorial properties, but not both. This dissertation determines optimal designs for three treatments in the one-way and multi-way heterogeneity settings, first proving optimality through a series of bounding arguments, then applying combinatorial techniques for their construction. Among the results established are optimality with respect to the well known E and A criteria. A- and E-optimal block designs and row-column designs with three treatments are found, for any parameter set. E-optimal hyperrectangles with three treatments are also found, for any parameter set. Systems of distinct representatives theory is used for the construction of optimal designs. Efficiencies relative to optimal criterion values are used to determine robustness of block designs against loss of a small number of blocks. Nonisomorphic bal anced incomplete block designs are ranked based on their robustness. A complete list of most robust BIBDs for v ≤ 10, r ≤ 15 is compiled. / Ph. D.

在行列設計(row-column design)的架構下，當行總和與列總和皆為總試驗處理數的倍數時，我們考慮行效果與列效果的相互比較之最適性。延續Shah和Sinha(1993)的結果，在給定行總和及列總和的情況下，我們導出達成齊一最適設計(uniformly optimal design)的充分條件。此外，當總實驗單位固定時，達成全域最適設計(universally optimal design)的充分條件亦被求出。我們同時列舉許多相關的設計排列法。 / We consider the problem of comparing row effects and column effects in the row-column design setup when the row sizes and column sizes are all multiples of the number of treatments. Following the work of Shah and Sinha (1993), we derive a sufficient condition for uniformly optimal designs for given values of the row sizes and column sizes. We also derive a sufficient condition for universally optimal designs when the total number of experimental units is fixed. Several examples of designs with high efficiencies are provided.

The Electronically Steered Phased Array is one of the most versatile antennas used in radars applications. Some of the advantages of electronic steering are faster scan, no moving parts and higher reliability. However, the cost of phased arrays has always been prohibitive - in the order of $1M per square meter. The cost of a phased array is largely impacted by the cost of the high frequency electronics at each element and the cost of packaging. Advances in IC integration will allow incorporating multiple elements such as low noise amplifier, power amplifier, phase shifters and up/down-conversion into one or two ICs. Even though the cost for large quantities of ICs (both Silicon and GaAs) has lowered, the high cost of IC packaging and the array backplane still make the use of phase arrays for radar applications costly. The focus of this research is on techniques that reduce the packaging and the backplane cost of large electronically steered arrays. These techniques are based on simplified signal distributions schemes, reduction of layers in the backplane and use of inexpensive materials. Two architectures designed based on these techniques, as well as a novel BGA active antenna package for dual polarized phased arrays are presented. The first architecture, called the series fed row-column architecture, focuses on the reduction of phase shifters and control signals used in the backplane of the array. The second architecture, called the parallel plate feed architecture, is based on a simplified scheme for distribution of the local oscillator signal. A prototype making use of each one of these architectures is presented. Analysis of advantages and disadvantages of each of these architectures is described. The necessity of cost reduction is a factor that can possibly impact the polarization performance of the antenna. This factor is a motivation to study and develop calibration techniques that reduce the cross-polarization of electronically steered phased arrays. Advances on Interleaving Sparse Arrays, a beam forming technique for polarization improvement/correction in phased arrays, are also presented.

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