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 influence of concurrent disturbances on plant community dynamics in northern hemlock-hardwood forests

Throughout the Upper Great Lakes region, alterations to historic disturbance regimes have influenced plant community dynamics in hemlock-hardwood forests. Several important mesic forest species, eastern hemlock (Tsuga canadensis), yellow birch (Betula alleghaniensis), eastern white pine (Pinus strobus), and Canada yew (Taxus canadensis), are in decline due to exploitive logging practices used at the turn of the 20th century and the wave of intense fires that followed. Continued regeneration and recruitment failure is attributed to contemporary forest management practices and overbrowsing by white-tailed deer (Odocoileus virginianus). Therefore, I examined the influence of two concurrent disturbances, overstory removal and herbivory, on plant community dynamics in two hemlock-hardwood forests. I measured the post-disturbance regeneration response (herbaceous and woody species) inside and outside of deer exclosures in 20 artificial canopy gaps (50 – 450 m2) and monitored survival and growth for hundreds of planted seedlings. The results of this research show that interacting disturbances can play a large role in shaping plant community composition and structure in hemlock-hardwood forests. White-tailed deer herbivory homogenized the post-disturbance plant communities across the experimental gradient of gap areas, essentially making species compositions in small gaps “look like” those in large gaps. Deer browsing also influenced probability of survival for planted Canada yew cuttings; all else being equal an individual was nearly seven times more likely to survive if protected from herbivory (P < 0.001). In contrast, the ability of sugar maple (Acer saccharum) to persist under high levels of herbivory and respond rapidly to overstory release appears to be related to the presence of stem layering(i.e., portions of below-ground prostrate stem). Layering occurred in 52% of excavated saplings (n = 100) and was significantly associated with increased post-disturbance height growth. Understory light was also important to planted seedling establishment and height growth. Higher levels of direct under-canopy light negatively impacted survival for shade-tolerant hemlock and Canada yew, while an increase in diffuse light was linked to a higher probability of survival for yellow birch and height growth for hemlock and Canada yew. Increases in white pine height growth were also significantly associated with a decrease in canopy cover.