Abstract
The Cramer-Rao bound (CRB) offers insights into the inherent performance benchmark of any unbiased estimator developed for a specific parametric model, which is an important tool to evaluate the performance of direction-of-arrival (DOA) estimation algorithms. In this paper, a closed-form stochastic CRB for a mixture of circular and noncircular uncorrelated Gaussian signals is derived. As a general one, it can be transformed into some existing representative results. The existence condition of the CRB is also analysed based on sparse arrays, which allows the number of signals to be more than the number of physical sensors. Finally, numerical comparisons are conducted in various scenarios to demonstrate the validity of the derived CRB.
Highlights
Direction of arrival (DOA) estimation based on sensor arrays has been of great interest in many applications, such as radar, sonar, and wireless communications
The Cramer-Rao bound (CRB) especially applied to sparse arrays has been derived [3]– [6], and the existence conditions of these CRBs imply that more sources than the number of physical sensors can be identified by using sparse arrays
Symbols C, Ns and Nn are used in the rest of this section to represent circular signals, strictly noncircular signals, and nonstrictly noncircular signals, separately, and the number in front of the signal-type symbol represents the number of signals
Summary
Direction of arrival (DOA) estimation based on sensor arrays has been of great interest in many applications, such as radar, sonar, and wireless communications. We are only interested in the CRB for DOA estimation, and a closed-form CRB for DOA estimation avoids calculation of the nuisance parameters, and provides analytical insights into the dependence of the array performance on different parameters [1]–[20]. Many methods have been proposed for DOA estimation based on such arrays, which can estimate more sources than the number of physical sensors by exploiting the difference coarrays [21], [22], [26]–[32]. The CRB especially applied to sparse arrays has been derived [3]– [6], and the existence conditions of these CRBs imply that more sources than the number of physical sensors can be identified by using sparse arrays
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