New iterative algorithm for the computation of the rank-deficient Capon filter in spectral estimation

In nonparametric complex spectral estimation, higher resolution is achieved when the covariance matrix is allowed to be rank-deficient. Several approaches are applied to remedy matrix singularity, such as diagonal loading, rank reduction and additional constraints. Conventional solution of the optimal Capon filter is derived from the gradient functions of the constraint minimization problem, and calculated via the input covariance matrix inversion. In this paper, the gradient functions are reformulated as a single one with the same solution, which is solved by an adaptive-step algorithm based on conjugate gradient method. The optimal Capon filter is iteratively calculated without any matrix inversion. The proposed algorithm is also directly applied to the computation of the optimal Capon filter with rank-deficient input covariance matrix. In simulations, performances of the proposed algorithm are compared with the existing methods. Higher convergence speed is achieved. The iteration number is selected to offset the frequency resolution and the signal mismatch problem.