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

Estimation and Minimization of the Cramer-Rao lower bound for radio direction-finding on the azimuth and elevation of planar antenna arrays

In this paper an approach of obtaining optimal planar antenna arrays consisting of omnidirectional sensors is proposed. The novelty of the proposed approach is to apply an exact expression of the Cramer-Rao lower bound for an arbitrary planar antenna array consisting of a number of omnidirectional elements which has been presented in the further chapters of the paper. The obtained formula describes the influence of antenna elements locations on the direction-of-arrival estimation accuracy. It has been shown that the direction-of-arrival accuracy via planar antenna arrays is determined as the sum of squares of differences between all omnidirectional elements coordinates along x- and y-axis. Thus knowing an expected area or sector of signal source it is very easy to calculate optimal arrangement of antenna elements in order to reduce direction-finding errors, because obtained by that way positions gives the best match according to the maximum likelihood criterion. It is worth nothing that such antenna arrays are useful in the way that they allow estimating the coordinates of radio emission sources in the three-dimensional coordinate space, i.e. in azimuth and elevation. In order to confirm the proposed methodology optimal antenna arrays constructed after minimization of the new formulas are researched. It is found out that the new shapes of antenna arrays based on the analytical expressions have better direction-of-arrival accuracy in comparison with the circular ones