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.

ALTERNATING CURRENT DIELECTROPHORETIC MANIPULATION OF ERYTHROCYTES IN MEDICAL MICRODEVICE TECHNOLOGY

Medical microdevices have gained popularity in the past few decades because they allow the medical laboratory to be taken out into the field and for disease diagnostics to happen with a smaller sample volume, at a lower cost and much faster. Blood is the human body's most readily available and informative diagnostic fluid because of the wealth of information it provides about the body's general health including enzymatic, proteomic and immunological states. The purpose of this project is to optimize operating conditions and study ABO-Rh erythrocytes dielectrophoretic responses to alternating current electric signals. The end goal of this project is the creation of a relatively inexpensive microfluidic device, which can be used for the ABO-Rh typing of a blood sample. This dissertation presents results showing how blood samples of a known ABO- Rh blood type exhibit differing behavior to the same electrical stimulus based on their blood type. The first panel of donors and experiments, presented in Chapter 4 occurred when a sample of known blood type was injected into a microdevice with a T-shaped electrode configuration and the erythorcytes were found to rupture at a rate specific to their ABO-Rh blood type. The second set of experiments, presented in Chapter 5, were originally published in Electrophoresis in 20111. Novel in this work was the discovery that treatment of human erythrocytes with β-galactosidase successfully removed ABO surface antigens such that native A and B blood no longer agglutinated with the proper antibodies. This work was performed in a medium of conductivity 0.9S/m which is close to the measured conductivity of pooled plasma (~1.1S/m). The ability to perform dielectrophoresis experiments at physiological conductivities conditions is advantageous for future portable devices because the device/instrument would not need to store dilution buffers. The final results of this project, presented in Chapter 6, explore the entire dielectrophoretic spectra of the ABO-Rh erythrocytes including the cross-over frequency and the magnitudes of the positive or negative dielectrophoretic response. These were completed at lower medium conductivities of 0.1S/m and 0.01-0.04S/m. These results show that by using the sweep function built into the Agilent alternating current generator it is possible to explore how a single group of blood cells will react to rapid changes in frequency and will provide the user with curve that can be matched the theoretical dielectrophoretic response curves. As a whole this project shows that it is possible to distinguish human erythrocytes by their ABO-Rh blood type via three different dielectrophoretic methods. This work builds on the foundation of that it is possible to distinguish healthy from infected cells2-7, similar cell types1,7-14 and other work regarding the dielectrophoresis of human erythrocytes1,10,11. This work has implications in both medical diagnostics and future dielectrophoretic work because it has shown that ABO-Rh blood type is now a factor, which must be identified when working with a human blood sample. It also shows that the creation of a microfluidic device that subjects human erythrocytes to a dielectrophoretic impulse and then exports an ABO-Rh blood type is a near future possibility.