Sparse array extension for non-circular signals with subspace and compressive sensing based DOA estimation methods

The virtual array generation process based on typical sparse arrays is studied for a mixture of circular and non-circular impinging signals. It consists of two sub-arrays: one is the traditional difference co-array and the other one is the new sum co-array. The number of consecutive virtual array sensors is analysed for the nested array case, but it is difficult to give a closed-form result for a general sparse array. Based on the extended covariance matrix of the physical array, two classes of direction of arrival (DOA) estimation algorithms are then developed, with one based on the subspace method and one based on sparse representation or the compressive sensing (CS) concept. Both the consecutive and non-consecutive parts of the virtual array can be exploited by the CS-based method, while only the consecutive part can be exploited by the subspace-based one. As a result, the CS-based solution can have a better performance than the subspace-based one, though at the cost of significantly increased computational complexity. The two classes of algorithms can also deal with the special case when all the signals are noncircular. Simulation results are provided to verify the performance of the proposed algorithms.