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.

Adaptive Sampling with Mobile Sensor Networks

Mobile sensor networks have unique advantages compared with wireless sensor networks. The mobility enables mobile sensors to flexibly reconfigure themselves to meet sensing requirements. In this dissertation, an adaptive sampling method for mobile sensor networks is presented. Based on the consideration of sensing resource constraints, computing abilities, and onboard energy limitations, the adaptive sampling method follows a down sampling scheme, which could reduce the total number of measurements, and lower sampling cost. Compressive sensing is a recently developed down sampling method, using a small number of randomly distributed measurements for signal reconstruction. However, original signals cannot be reconstructed using condensed measurements, as addressed by Shannon Sampling Theory. Measurements have to be processed under a sparse domain, and convex optimization methods should be applied to reconstruct original signals. Restricted isometry property would guarantee signals can be recovered with little information loss. While compressive sensing could effectively lower sampling cost, signal reconstruction is still a great research challenge. Compressive sensing always collects random measurements, whose information amount cannot be determined in prior. If each measurement is optimized as the most informative measurement, the reconstruction performance can perform much better. Based on the above consideration, this dissertation is focusing on an adaptive sampling approach, which could find the most informative measurements in unknown environments and reconstruct original signals. With mobile sensors, measurements are collect sequentially, giving the chance to uniquely optimize each of them. When mobile sensors are about to collect a new measurement from the surrounding environments, existing information is shared among networked sensors so that each sensor would have a global view of the entire environment. Shared information is analyzed under Haar Wavelet domain, under which most nature signals appear sparse, to infer a model of the environments. The most informative measurements can be determined by optimizing model parameters. As a result, all the measurements collected by the mobile sensor network are the most informative measurements given existing information, and a perfect reconstruction would be expected. To present the adaptive sampling method, a series of research issues will be addressed, including measurement evaluation and collection, mobile network establishment, data fusion, sensor motion, signal reconstruction, etc. Two dimensional scalar field will be reconstructed using the method proposed. Both single mobile sensors and mobile sensor networks will be deployed in the environment, and reconstruction performance of both will be compared.In addition, a particular mobile sensor, a quadrotor UAV is developed, so that the adaptive sampling method can be used in three dimensional scenarios.