Computationally efficient direction of arrival estimation with unknown number of signals

In this paper, we investigate the problem of direction of arrival (DOA) estimation with unknown number of signals in the framework of beamforming. We show that the real part of the array output covariance matrix (R-AOCM) can be reformulated as an entire AOCM of a virtual array with available signal model for fast DOA estimate. By introducing an optimization problem to minimize the variance of the weighted output of this virtual array, DOA can be found by a novel real-valued real part Capon (R-Capon) estimator accordingly. Moreover, we prove that the rank of the R-AOCM is always no less than that of the entire AOCM, which suggests that R-Capon outperforms the standard Capon in scenarios with small numbers of snapshots. We also prove that the inverse of the R-AOCM can be equivalently jointed by those of two sub-matrices of about half sizes, and hence R-Capon has a significantly reduced computational complexity. These advantages as well as the theoretical analysis are finally verified by numerical simulations over a wide range of scenarios.