Adaptive signal-subspace processing based on first-order perturbation analysis

An approach to adaptive signal-subspace processing of narrowband array data is presented. It is based on the application of first-order perturbation analysis. In the proposed approach, the correction term in the recursive estimate of the array covariance matrix at time k is viewed as a perturbation of the estimate at time k-1. Following this interpretation, the theory of perturbation of Hermitian matrices is applied in order to obtain a new recursion expressing the eigenstructure estimate of R_x(k), the true array covariance matrix at time k, in terms of the eigenstructure estimate of R_x(k-1). This algorithm can be realized by means of L linear combiners with nonlinear weight-vector adaptation equations, where L is the signal-subspace dimensionality. These nonlinear adaptation equations appear to be substitutes for the orthonormal weight constraints found in other algorithms. The results of preliminary simulations are discussed