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.

Fixed block configuration GDDs with block size 6 and (3, r)-regular graphs

Chapter 1 is used to introduce the basic tools and mechanics used within this thesis. Most of the definitions used in the thesis will be defined, and we provide a basic survey of topics in graph theory and design theory pertinent to the topics studied in this thesis. In Chapter 2, we are concerned with the study of fixed block configuration group divisible designs, GDD(n; m; k; λ1; λ2). We study those GDDs in which each block has configuration (s; t), that is, GDDs in which each block has exactly s points from one of the two groups and t points from the other. Chapter 2 begins with an overview of previous results and constructions for small group size and block sizes 3, 4 and 5. Chapter 2 is largely devoted to presenting constructions and results about GDDs with two groups and block size 6. We show the necessary conditions are sufficient for the existence of GDD(n, 2, 6; λ1, λ2) with fixed block configuration (3; 3). For configuration (1; 5), we give minimal or nearminimal index constructions for all group sizes n ≥ 5 except n = 10, 15, 160, or 190. For configuration (2, 4), we provide constructions for several families ofGDD(n, 2, 6; λ1, λ2)s. Chapter 3 addresses characterizing (3, r)-regular graphs. We begin with providing previous results on the well studied class of (2, r)-regular graphs and some results on the structure of large (t; r)-regular graphs. In Chapter 3, we completely characterize all (3, 1)-regular and (3, 2)-regular graphs, as well has sharpen existing bounds on the order of large (3, r)- regular graphs of a certain form for r ≥ 3. Finally, the appendix gives computational data resulting from Sage and C programs used to generate (3, 3)-regular graphs on less than 10 vertices.

AN EXPERIMENTAL STUDY OF PARTIAL LOW RISK DEPLOYMENT IN A FIXED VEHICLE ENVIRONMENT

This study will look at the passenger air bag (PAB) performance in a fix vehicle environment using Partial Low Risk Deployment (PLRD) as a strategy. This development will follow test methods against actual baseline vehicle data and Federal Motor Vehicle Safety Standards 208 (FMVSS 208). FMVSS 208 states that PAB compliance in vehicle crash testing can be met using one of three deployment methods. The primary method suppresses PAB deployment, with the use of a seat weight sensor or occupant classification sensor (OCS), for three-year old and six-year old occupants including the presence of a child seat. A second method, PLRD allows deployment on all size occupants suppressing only for the presents of a child seat. A third method is Low Risk Deployment (LRD) which allows PAB deployment in all conditions, all statures including any/all child seats. This study outlines a PLRD development solution for achieving FMVSS 208 performance. The results of this study should provide an option for system implementation including opportunities for system efficiency and other considerations. The objective is to achieve performance levels similar too or incrementally better than the baseline vehicles National Crash Assessment Program (NCAP) Star rating. In addition, to define systemic flexibility where restraint features can be added or removed while improving occupant performance consistency to the baseline. A certified vehicles’ air bag system will typically remain in production until the vehicle platform is redesigned. The strategy to enable the PLRD hypothesis will be to first match the baseline out of position occupant performance (OOP) for the three and six-year old requirements. Second, improve the 35mph belted 5th percentile female NCAP star rating over the baseline vehicle. Third establish an equivalent FMVSS 208 certification for the 25mph unbelted 50th percentile male. FMVSS 208 high-speed requirement defines the federal minimum crash performance required for meeting frontal vehicle crash-test compliance. The intent of NCAP 5-Star rating is to provide the consumer with information about crash protection, beyond what is required by federal law. In this study, two vehicles segments were used for testing to compare and contrast to their baseline vehicles performance. Case Study 1 (CS1) used a cross over vehicle platform and Case Study 2 (CS2) used a small vehicle segment platform as their baselines. In each case study, the restraints systems were from different restraint supplier manufactures and each case contained that suppliers approach to PLRD. CS1 incorporated a downsized twins shaped bag, a carryover inflator, standard vents, and a strategic positioned bag diffuser to help disperse the flow of gas to improve OOP. The twin shaped bag with two segregated sections (lobes) to enabled high-speed baseline performance correlation on the HYGE Sled. CS2 used an A-Symmetric (square shape) PAB with standard size vents, including a passive vent, to obtain OOP similar to the baseline. The A-Symmetric shape bag also helped to enabled high-speed baseline performance improvements in HYGE Sled testing in CS2. The anticipated CS1 baseline vehicle-pulse-index (VPI) target was in the range of 65-67. However, actual dynamic vehicle (barrier) testing was overshadowed with the highest crash pulse from the previous tested vehicles with a VPI of 71. The result from the 35mph NCAP Barrier test was a solid 4-Star (4.7 Star) respectfully. In CS2, the vehicle HYGE Sled development VPI range, from the baseline was 61-62 respectively. Actual NCAP test produced a chest deflection result of 26mm versus the anticipated baseline target of 12mm. The initial assessment of this condition was thought to be due to the vehicles significant VPI increase to 67. A subsequent root cause investigation confirmed a data integrity issue due to the instrumentation. In an effort to establish a true vehicle test data point a second NCAP test was performed but faced similar instrumentation issues. As a result, the chest deflect hit the target of 12.1mm; however a femur load spike, similar to the baseline, now skewed the results. With noted level of performance improvement in chest deflection, the NCAP star was assessed as directional for 5-Star capable performance. With an actual rating of 3-Star due to instrumentation, using data extrapolation raised the ratings to 5-Star. In both cases, no structural changes were made to the surrogate vehicle and the results in each case matched their perspective baseline vehicle platforms. These results proved the PLRD is viable for further development and production implementation.

ALTERNATING CURRENT DIELECTROPHORESIS OF CORE-SHELL NANOPARTICLES: EXPERIMENTS AND COMPARISON WITH THEORY

Nanoparticles are fascinating where physical and optical properties are related to size. Highly controllable synthesis methods and nanoparticle assembly are essential [6] for highly innovative technological applications. Among nanoparticles, nonhomogeneous core-shell nanoparticles (CSnp) have new properties that arise when varying the relative dimensions of the core and the shell. This CSnp structure enables various optical resonances, and engineered energy barriers, in addition to the high charge to surface ratio. Assembly of homogeneous nanoparticles into functional structures has become ubiquitous in biosensors (i.e. optical labeling) [7, 8], nanocoatings [9-13], and electrical circuits [14, 15]. Limited nonhomogenous nanoparticle assembly has only been explored. Many conventional nanoparticle assembly methods exist, but this work explores dielectrophoresis (DEP) as a new method. DEP is particle polarization via non-uniform electric fields while suspended in conductive fluids. Most prior DEP efforts involve microscale particles. Prior work on core-shell nanoparticle assemblies and separately, nanoparticle characterizations with dielectrophoresis and electrorotation [2-5], did not systematically explore particle size, dielectric properties (permittivity and electrical conductivity), shell thickness, particle concentration, medium conductivity, and frequency. This work is the first, to the best of our knowledge, to systematically examine these dielectrophoretic properties for core-shell nanoparticles. Further, we conduct a parametric fitting to traditional core-shell models. These biocompatible core-shell nanoparticles were studied to fill a knowledge gap in the DEP field. Experimental results (chapter 5) first examine medium conductivity, size and shell material dependencies of dielectrophoretic behaviors of spherical CSnp into 2D and 3D particle-assemblies. Chitosan (amino sugar) and poly-L-lysine (amino acid, PLL) CSnp shell materials were custom synthesized around a hollow (gas) core by utilizing a phospholipid micelle around a volatile fluid templating for the shell material; this approach proves to be novel and distinct from conventional core-shell models wherein a conductive core is coated with an insulative shell. Experiments were conducted within a 100 nl chamber housing 100 um wide Ti/Au quadrapole electrodes spaced 25 um apart. Frequencies from 100kHz to 80MHz at fixed local field of 5Vpp were tested with 10-5 and 10-3 S/m medium conductivities for 25 seconds. Dielectrophoretic responses of ~220 and 340(or ~400) nm chitosan or PLL CSnp were compiled as a function of medium conductivity, size and shell material.