MIMO Volterra filter equalization using pth-order inverse approach

The equalization of nonlinear systems is an important application of Volterra filters. The pth-order inverse is one of the important approaches of Volterra equalization, but up to the present it has only been applied to the single-input multiple-output (SISO) case. The convergence of the Volterra filter equalization and the error bound using the pth-order approximation equalizer instead of the Volterra equalizer have not yet been reported. In this paper, we generalize this method to the multi-input and multi-output (MIMO) Volterra filter case, and discuss the convergence of Volterra filter equalization and the error bound using the pth-order approximation equalizer instead of the Volterra equalizer. The concept of local I₂ stability for the MIMO Volterra filter is first introduced, and then the algorithmic formula of the pth-order inverse is presented by using the multi-dimensional z-transform. In the end, the convergence of the MIMO Volterra filter equalization and the error bound using the pth-order approximation equalizer instead of the Volterra equalizer are discussed. The proposed algorithms are corroborated with a simulation example