Blind MIMO system identification using constrained factor decomposition of output generating function derivatives

Abstract

This work addresses the blind identification of complex MIMO systems driven by complex input signals using a new tensor decomposition approach. We show that a collection of successive second-order derivatives of the second generating function of the system outputs can be stored in a higher-order tensor following a constrained factor (CONFAC) decomposition. The proposed decomposition captures the repeated linear combinations involving real and imaginary components of the MIMO system matrix arising from the successive differentiation of output’s generating function derivatives. By exploiting different derivative forms computed at multiple points of the observation space, an “extended” CONFAC decomposition enjoying essential uniqueness is obtained. Thanks to this uniqueness property, a blind estimation of the MIMO system response matrix is possible.