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Statistical Performance Analysis of DOA Estimation Methods

Haddadi, Farzan | 2010

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  1. Type of Document: Ph.D. Dissertation
  2. Language: Farsi
  3. Document No: 40413 (05)
  4. University: Sharif University of Technology
  5. Department: Electrical Engineering
  6. Advisor(s): Nayebi, Mohammad Mahdi; Aref, Mohammad Reza
  7. Abstract:
  8. In this thesis, we investigate the statistical performance of the array processing algorithms. Theoretical performance analysis leads to better methods that outperform the existing algorithms. Besides, analytical performance analysis, results in a more profound understanding of the nature of the considered problem. First of all, problem of covariance matrix estimation, in the non-Gaussian signal case will be investigated. We will focus on a nonparametric estimator which relies on the sign of the data to estimate the covariance matrix on an element-by-element basis. It was known that, sign estimator may give invalid covariance estimates in higher dimensions of the data. We prove this fact in this thesis. Next, signal direction of arrival estimation, under the assumption of temporal correlation of the signals will be studied. A number of existing theoretical results on the statistical performance of this signal model will be extended. In particular, new characteristics of the Cramer-Rao bound will be developed. An important inequality will be proved that complements an existing inequality. This inequality will demonstrate new aspects of the array processing problem. Theoretical performance analysis will be used to improve existing methods in this problem. In the last section, the popular method of source enumeration, MDL, will be investigated. After two decades of unsuccessful attempts, we will calculate the error probability of MDL. Using this performance analysis, we gain a view of the reason of high probability of miss in this method and will propose new ways to mitigate this weakness which are still in progress.
  9. Keywords:
  10. Error Probability ; Array Signal Processing ; Statistical Performance Analysis ; Cramer-Rao Bound ; Non-Parametric Estimation ; Temporal Correlation ; Minimum Description Length Method

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