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.

EXPLORING CHANGES IN DETRITAL FLOCCULENT LAYER DYNAMICS DUE TO SHIFTS IN MACROPHYTE COMMUNITIES IN THE NORTHERN EVERGLADES

A shift in plant communities of the Water Conservation Areas (WCAs) within the Everglades has been linked to changes in hydrology and high levels of nutrient loading from surrounding agicultural areas. This has resulted in the encroachment of dense cattail stands (Typha domingensis) into areas that had previously been a ridge and slough landscape populated primarily by native sawgrass (Cladium jamaicense). In order to study ecological management solutions in this area, WCA-2A was broken into study plots; several of which became open water areas through the application of herbicide and burning regimens. The open water areas allowed for Chara spp (a submersed algal species) to replace Typha domingensis as the dominant macrophyte. This study investigated the polymer and ionic profiles of Chara spp, Typha domingensis and Cladium jamaicense and their contributions to detrital flocculent (floc) in the study plots where they are the dominant macrophytes. Floc is not only an important food source for aquatic species; it also supports many algal, fungal and bacterial communities. Data gathered in this study indicated that the floc sample from a phosphorus enriched open water study plot (EO1) where Chara spp was the dominant macrophyte may contain cell wall polymers from sources other than Chara spp (most likely Typha domingensis), while the chemical and polymeric profile of the floc of the study plot where Typha domingensis is the dominant macrophyte (EC1) suggests that the floc layer has contributions from algal sources as well as Typha domingensis. Additionally, monoclonal antibodies to Arabinoglalactan protein (AGP) and (1,4)-β-D galactan were identified as possible biomarkers for distinguishing algal dominated floc layers from layers dominated by emergent vegetation. Calcium labeling could be a useful tool for this as well because of the high amount of Ca2+ associated with Chara spp cell walls. When looking into the soluble phosphorus content of the macrophytes and paired floc samples of WCA-2A, it was found that Chara spp may be contributing a greater amount of Ca-bound phosphorus to floc layers where it is the dominant macrophyte when compared to floc layers from study plots dominated by emergent macrophytes. Floc layers also appear to be acting as a nutrient sink for soluble phosphorus. The findings of this study support the overall hypothesis that the shift from native emergent macrophyte communities to submersed macrophyte communities in study sites of the northern Everglades is affecting the polymeric/chemical profile and ionic content of detrital floc layers. The effects of this shift may contribute to changes in complex flocculent community dynamics.