A Low-Complexity DOA Estimation Algorithm for Distributed Sources Under the Coexistence of Circular and Non-circular Sources

‍ ‍Traditionally， researchers use the ideal point source model when designing Direction-of-Arrival （DOA） estimation algorithms. With the development of modern society， the demand for source localization in dense urban areas is growing. Applications such as the direction-finding of low-altitude unmanned aerial vehicles （UAVs） are becoming increasingly important. Signals from the source are reflected and scattered by surrounding objects before they reach the sensor array. The traditional point source model is no longer capable of accurately describing such a complex environment. Methods based on the ideal mathematical model may suffer from severe performance deterioration and need to be reconsidered under the distributed source model. Moreover， many studies focus on either circular or non-circular signals independently， without considering the coexistence of both signal types in real-world scenarios. Given the limitations of current approaches， we propose a low-complexity DOA estimation algorithm to address the challenges associated with estimating the DOAs of sources in complex urban areas with a mixture of circular and non-circular signals. First， we choose to employ the coherently distributed source model in this study. We derive the received signal model for a mixture of both circular and strictly non-circular signals. Then， we use the observed signal vector and its complex conjugate counterpart to construct an extended signal vector， leveraging the additional information provided by the non-circular phases. This approach enhances the accuracy and robustness of DOA estimation in the presence of both circular and non-circular signals. Next， we analyze the Generalized Estimation of Signal Parameters via Rotational Invariance Techniques （GESPRIT） algorithm and derive the cost function for our proposed algorithm. Through a one-dimensional peak searching procedure， we obtain the nominal DOAs of the sources. Several numerical simulations are conducted to illustrate the proposed algorithm in detail. Comparisons with several competing methods demonstrate the reliability and advantages of our approach. Results show that MIX-GESPRIT not only achieves an optimal balance between computational cost and direction-finding accuracy but also exhibits strong robustness and practicality.