PhD Thesis: Efficient Methods for Unambiguous Direction of Arrival Estimation with Co-Prime Linear Arrays

Thesis Title: Efficient Methods for Unambiguous Direction of Arrival Estimation with Co-Prime Linear Arrays
Author: Dr. Ashok Chandrasekaran
Author Affiliation: School of Computing and Data Science, Sai University, Chennai, India
Ph.D. Granting Institution: Anna University, Chennai, India

Abstract:

In the array signal processing research, estimation of the direction-of-arrival (DOA) of the transmitted source signal has long been of great interest and plays an important role in both civilian and military applications such as radar, sonar, geophysics, acoustics, bioengineering, seismology, multimedia, radio astronomy and wireless communication. Non-uniform linear array (NULA) design, also known as the sparse linear array (SLA) design has been developed for DOA estimation considering the limitations seen in the uniform linear array (ULA) design. The SLA design can attain a large effective array aperture with fewer array elements and also mitigates the influence of mutual coupling effects between array elements. Recently, the co-prime linear array (CLA) design has gained considerable research interest among several SLA designs such as minimal redundant array (MRA), minimum-hole array (MHA) and nested linear array (NLA). However, CLA designs such as general co-prime linear array (GCLA) and unfolded co-prime linear array (UCLA) face the critical problem of ambiguity resulting in an ambiguous estimate of true DOAs. Specifically, GCLA suffers from the problem of pair-matching ambiguity in subarray domain processing but both GCLA and UCLA suffer from the problem of grating-angle ambiguity. 

This thesis focuses on the key objectives as follows (i) To resolve the ambiguity problem such as pair-matching and grating-angle ambiguity in estimating the DOA of the incoming source signals using the GCLA and UCLA (ii) To achieve a reliable estimation of true DOAs with superior estimation performances in terms of accuracy, angular resolution and degrees-of-freedom (DOF) compared to the existing methods (ii) To offer good generalization and robustness in estimation performance with less computational complexity and execution time compared to the existing methods.

In the first proposed solution, the true DOAs are distinguished from ambiguous estimates obtained from UCLA-MUSIC using the estimated power of the transmitted source signals. Here, the source power function derived is based on the signal subspace eigenvalues and its associated eigenvectors to estimate the power of the transmitted source signals. In the second proposed solution, an improved polynomial rooting-based method for high-resolution unambiguous DOA estimation is performed. A polynomial function is derived based on the orthogonality between the noise subspace eigenvectors and array directional vectors. A maximum signal power function is proposed based on the spatial filtering and second-order differential counterparts for the selection of the signal roots associated with the true DOAs over the ambiguous roots. In the third proposed solution, a computationally efficient DOA estimation method based on support vector regression (SVR) is proposed. The ambiguity problem is resolved by treating DOA estimation as approximating the unknown regression function that maps the signal subspace eigenvectors with the DOA of the incoming source signals.

The effectiveness and superiority of the aforementioned proposed solutions are supported by several standard simulation studies in terms of estimation reliability, estimation accuracy, angular resolution, computational complexity, execution time and DOF.