Enforcing symmetry in tensor network MIMO Volterra identification

The estimation of an exponential number of model parameters in a truncated Volterra model can be circumvented by using a low-rank tensor decomposition approach. This low-rank property of the tensor decomposition can be interpreted as the assumption that all Volterra parameters are structured. In this article, we investigate whether it is possible to explicitly enforce symmetry of the Volterra kernels to the low-rank tensor decomposition. We show that low-rank symmetric Volterra identification is an ill-conditioned problem as the low-rank property of the exact symmetric kernels cannot be upheld in the presence of measurement noise. Furthermore, an algorithm is derived to compute the symmetric Volterra kernels directly in tensor network form.