Esprit-type algorithms for a received mixture of circular and strictly non-circular signals

Recently, ESPRIT-based parameter estimation algorithms have been developed to exploit the structure of signals from strictly second-order (SO) non-circular (NC) sources. They achieve a higher estimation accuracy and can resolve up to twice as many sources. However, these NC methods assume that all the received signals are strictly non-circular. In this paper, we present the C-NC Standard ESPRIT and the C-NC Unitary ESPRIT algorithms designed for the more practical scenario of a received mixture of circular and strictly non-circular signals. Assuming that the number of circular and strictly non-circular signals is known, the two proposed methods yield closed-form estimates and C-NC Unitary ESPRIT also enables an entirely real-valued implementation. As a main result, it is shown that the estimation accuracy of the presented algorithms improves with an increasing number of strictly non-circular signals among a fixed number of sources. Thereby, not only the estimation accuracy of the strictly non-circular signals themselves is improved, but also the estimation accuracy of the circular signals. These results are validated by simulations.