Vector Time-Frequency AR Models for Nonstationary Multivariate Random Processes

We introduce the vector time-frequency autoregressive (VTFAR) model for a parsimonious parametric description of nonstationary vector random processes. The VTFAR model generalizes the recently proposed scalar TFAR model to the multivariate case. It is physically meaningful because nonstationarity and spectral correlation are represented in terms of frequency shifts, and it is parsimonious for the practically relevant class of underspread vector processes (i.e., nonstationary vector processes with rapidly decaying correlation in time and frequency). For vector processes with decaying correlation across the signals, we introduce a variant of the VTFAR model with banded parameter matrices. Furthermore, we present a VTFAR parameter estimator that is based on a system of linear equations with two-level block-Toeplitz structure, and we develop an efficient order-recursive algorithm for solving these equations. We also present information criteria for estimating the VTFAR model order and the matrix bandwidth of the banded VTFAR model. The performance of the proposed VTFAR parameter and order estimators is assessed through numerical simulations. Finally, an application to nonstationary multivariate spectral analysis is presented.