Aperture-Varying Autoregressive Modeling of Multiple Spread Sources

Parametric models introduced for the covariance matrix of a mixture of spread sources in M-element antenna arrays allow for a significant reduction of training sample support required for accurate (adaptive) estimation, if properly chosen. Depending on the spreading mechanism, these models may vary dramatically, and therefore in non-homogeneous scenarios with both spread and non-spread sources, selection of a signal parametric model for the covariance matrix of the entire mixture is problematic. Autoregressive models AR(m) have been long ago introduced for arbitrary Toeplitz covariance matrix approximations, with corresponding maximum-entropy spatial spectrum estimates provided for spectral analysis of the underlying scenario. Unfortunately, these models are not applicable for non plane-wave ("wrinkled") sources that are observed in some multipath conditions. As a natural generalization of stationary AR(m) models, we therefore suggest aperture-varying autoregressive models AVAR(m), with reasonably low order m required for sufficiently accurate covariance matrix approximation in most cases. In addition, the associated maximum entropy aperture-varying spectrum (sensor-angle distribution) may be used for accurate "wrinkled" sources identification. An AVAR(m) order estimation procedure is introduced that allows for the selection of an AVAR(m) model that statistically is as likely as the unknown true covariance matrix.