Angular Parameters Estimation of Multiple Incoherently Distributed Sources Generating Noncircular Signals

In this paper, we introduce for the first time a new method for the estimation of the angular parameters [i.e., central directions of arrival (DOAs) and angular spreads] of multiple non-circular and incoherently-distributed (ID) sources. The new method is derived by going through three different stages to finally obtain a robust solution that allows decoupling the estimation of each central DOA from its associated angular spread by means of two consecutive 1-D searches. By doing so, we reduce significantly the complexity of the proposed technique as compared to the brute-force 2D grid search solution. This new technique is also oblivious to the sources' angular distribution or any mismatch thereof. By analyzing its performance, we show that our new estimator outperforms most well-known state-of-the-art techniques in terms of estimation accuracy and robustness, especially for small DOA separations and/or low SNR levels. We also derive an explicit expression for the stochastic Cramér-Rao lower bounds (CRLBs) of the underlying estimation problem. These CRLBs are compared to those for circular ID signals. It will be shown that the noncircularity of the signals is more informative about the angular parameters when the sources have different angular distributions and/or when the angular spreads increase. Besides, the noncircular CRLBs depend on the noncircularity rate, the noncircularity phase separation, and the DOA separation.