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

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.