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.

Effects of Chemical Deicers on Amphibian Communites

Roads and highways present a unique challenge to wildlife as they exhibit substantial impacts on the surrounding ecosystem through the interruption of a number of ecological processes. With new roads added to the national highway system every year, an understanding of these impacts is required for effective mitigation of potential environmental impacts. A major contributor to these negative effects is the deposition of chemicals used in winter deicing activities to nearby surface waters. These chemicals often vary in composition and may affect freshwater species differently. The negative impacts of widespread deposition of sodium chloride (NaCl) have prompted a search for an `environmentally friendly' alternative. However, little research has investigated the potential environmental effects of widespread use of these alternatives. Herein, I detail the results of laboratory tests and field surveys designed to determine the impacts of road salt (NaCl) and other chemical deicers on amphibian communities in Michigan's Upper Peninsula. Using larval amphibians I demonstrate the lethal impacts of a suite of chemical deicers on this sensitive, freshwater species. Larval wood frogs (Lithobates sylvatica) were tolerant of short-term (96 hours) exposure to urea (CH4N2O), sodium chloride (NaCl), and magnesium chloride (MgCl2). However, these larvae were very sensitive to acetate products (C8H12CaMgO8, CH3COOK) and calcium chloride (CaCl2). These differences in tolerance suggest that certain deicers may be more harmful to amphibians than others. Secondly, I expanded this analysis to include an experiment designed to determine the sublethal effects of chronic exposure to environmentally realistic concentrations of NaCl on two unique amphibian species, L. sylvatica and green frogs (L. clamitans). L. sylvatica tend to breed in small, ephemeral wetlands and metamorphose within a single season. However, L. clamitans breed primarily in more permanent wetlands and often remain as tadpoles for one year or more. These species employ different life history strategies in this region which may influence their response to chronic NaCl exposure. Both species demonstrated potentially harmful effects on individual fitness. L. sylvatica larvae had a high incidence of edema suggesting the NaCl exposure was a significant physiologic stressor to these larvae. L. clamitans larvae reduced tail length during their exposure which may affect adult fitness of these individuals. In order to determine the risk local amphibians face when using these roadside pools, I conducted a survey of the spatial distribution of chloride in the three northernmost counties of Michigan. This area receives a relatively low amount of NaCl which is confined to state and federal highways. The chloride concentrations in this region were much lower than those in urban systems; however, amphibians breeding in the local area may encounter harmful chloride levels arising from temporal variations in hydroperiods. Spatial variation of chloride levels suggests the road-effect zone for amphibians may be as large as 1000 m from a salt-treated highway. Lastly, I performed an analysis of the use of specific conductance to predict chloride concentrations in natural surface water bodies. A number of studies have used this regression to predict chloride concentrations from measurements of specific conductance. This method is often chosen in the place of ion chromatography due to budget and time constraints. However, using a regression method to characterize this relationship does not result in accurate chloride ion concentration estimates.