Stochastic Cramer-Rao bound for DOA estimation with a mixture of circular and noncircular signals

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.