**6. Conclusions**

In this chapter, we have presented a decomposition-based approach for dealing with the identification of high-dimension MISO systems. Unlike the conventional method, which is based on the identification of the global system impulse response, our solution focuses on regarding the system as an *N*-order tensor and thus estimating *N* shorter filters. At the end, the solutions are combined ("tensorized" together) into the original high-dimension tensor. Based on the tensor decomposition technique, an iterative Wiener filter was proposed, along with a family of LMS-based algorithms suitable for the identification of such systems, also called multilinear systems. In addition to the lower computational complexity, the proposed solutions achieve superior performance as compared to their conventional counterparts from the point of view of convergence rate, tracking capability, and steady-state misadjustment. Experiments have also shown the performance improvement of the proposed adaptive algorithms for multilinear forms in long-length system identification in different scenarios, even for highly correlated input signals.
