HIGH PERFORMANCE, LOW COST SUBSPACE DECOMPOSITION AND POLYNOMIAL ROOTING FOR REAL TIME DIRECTION OF ARRIVAL ESTIMATION: ANALYSIS AND IMPLEMENTATION

This thesis develops high performance real-time signal processing modules for direction of arrival (DOA) estimation for localization systems. It proposes highly parallel algorithms for performing subspace decomposition and polynomial rooting, which are otherwise traditionally implemented using sequential algorithms. The proposed algorithms address the emerging need for real-time localization for a wide range of applications. As the antenna array size increases, the complexity of signal processing algorithms increases, making it increasingly difficult to satisfy the real-time constraints. This thesis addresses real-time implementation by proposing parallel algorithms, that maintain considerable improvement over traditional algorithms, especially for systems with larger number of antenna array elements. Singular value decomposition (SVD) and polynomial rooting are two computationally complex steps and act as the bottleneck to achieving real-time performance. The proposed algorithms are suitable for implementation on field programmable gated arrays (FPGAs), single instruction multiple data (SIMD) hardware or application specific integrated chips (ASICs), which offer large number of processing elements that can be exploited for parallel processing. The designs proposed in this thesis are modular, easily expandable and easy to implement. Firstly, this thesis proposes a fast converging SVD algorithm. The proposed method reduces the number of iterations it takes to converge to correct singular values, thus achieving closer to real-time performance. A general algorithm and a modular system design are provided making it easy for designers to replicate and extend the design to larger matrix sizes. Moreover, the method is highly parallel, which can be exploited in various hardware platforms mentioned earlier. A fixed point implementation of proposed SVD algorithm is presented. The FPGA design is pipelined to the maximum extent to increase the maximum achievable frequency of operation. The system was developed with the objective of achieving high throughput. Various modern cores available in FPGAs were used to maximize the performance and details of these modules are presented in detail. Finally, a parallel polynomial rooting technique based on Newton’s method applicable exclusively to root-MUSIC polynomials is proposed. Unique characteristics of root-MUSIC polynomial’s complex dynamics were exploited to derive this polynomial rooting method. The technique exhibits parallelism and converges to the desired root within fixed number of iterations, making this suitable for polynomial rooting of large degree polynomials. We believe this is the first time that complex dynamics of root-MUSIC polynomial were analyzed to propose an algorithm. In all, the thesis addresses two major bottlenecks in a direction of arrival estimation system, by providing simple, high throughput, parallel algorithms.

The Processing of Aluminum Gasarites via Thermal Decomposition of Interstitial Hydrides

Gasarite structures are a unique type of metallic foam containing tubular pores. The original methods for their production limited them to laboratory study despite appealing foam properties. Thermal decomposition processing of gasarites holds the potential to increase the application of gasarite foams in engineering design by removing several barriers to their industrial scale production. The following study characterized thermal decomposition gasarite processing both experimentally and theoretically. It was found that significant variation was inherent to this process therefore several modifications were necessary to produce gasarites using this method. Conventional means to increase porosity and enhance pore morphology were studied. Pore morphology was determined to be more easily replicated if pores were stabilized by alumina additions and powders were dispersed evenly. In order to better characterize processing, high temperature and high ramp rate thermal decomposition data were gathered. It was found that the high ramp rate thermal decomposition behavior of several hydrides was more rapid than hydride kinetics at low ramp rates. This data was then used to estimate the contribution of several pore formation mechanisms to the development of pore structure. It was found that gas-metal eutectic growth can only be a viable pore formation mode if non-equilibrium conditions persist. Bubble capture cannot be a dominant pore growth mode due to high bubble terminal velocities. Direct gas evolution appears to be the most likely pore formation mode due to high gas evolution rate from the decomposing particulate and microstructural pore growth trends. The overall process was evaluated for its economic viability. It was found that thermal decomposition has potential for industrialization, but further refinements are necessary in order for the process to be viable.