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Thesis Title

Performance Analysis of Subspace based methods for Direction of Arrival Estimation

Thesis Abstract

In this dissertation, the performance analysis of eigen decomposition based subspace methods for Direction Of Arrival (DOA) estimation of signals impinging on an array of sensors is presented. The performance of the subspace methods depends upon the quality of the subspaces (obtained from the covariance matrix of the received data) and the analysis quantifies the sensitivity of the method's solution to perturbations in the covariance matrix. The procedure for a rigorous, theoretical, asymptotic analysis of subspace methods consists of two stages. First, a relationship between the perturbation in the covariance matrix and the error in the subspaces, using a first-order perturbation of the covariance matrix is obtained. Next, the error in the DOA is related to the error in the subspaces, based on the subspace method used. Combining the two stages, the error in the DOA is related directly to the error in the covariance matrix and the statistics are obtained from the statistics of the covariance matrix.

This systematic procedure of analysis can be used to analyse the methods due to various sources of error in the covariance matrix. In this dissertation, attention is focussed on a Uniform Linear Array (ULA), with the perturbations in the covariance matrix due to finite number of snapshots and sensor noise. Based on the asymptotic analysis, a comparative performance study of the noise subspace methods - MUSIC (and Root-MUSIC), Minimum-Norm method and signal subspace methods- ESPRIT, TAM using various covariance estimators like the Forward smoothing, Forward-Backward smoothing estimators is carried out. Various properties of the estimates of the DOA (and the corresponding signal zero), obtained from the subspace methods, are derived, which give a better insight into the methods' working mechanism. In general, the Forward-Backward smoothing covariance matrix is shown to be better conditioned than the Forward smoothing covariance matrix and is therefore preferred. it is shown that amongst the subspace methods, MUSIC performs the best when the Forward covariance estimate is used. In general rooting is preferable to spectral forms. For MUSIC, in particular Root-MUSIC, is preferable to spectral MUSIC, since the flatness (or sharpness) of the peaks of the spectrum could be misleading about the accuracy of the estimates. The DOA estimates obained from ESPRIT and Minimum-Norm method, using the smoothed covariance matrices, show a significant improvement and match the performance of MUSIC, when an optimal choice of sub-arrays is made. In contrast, smoothing deteriorates the performance of MUSIC.

Year of Graduation: 1994