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The paper outlines a new approach to the signal reconstruction process in multivariable wireless communications tasks. A new solution is proposed using the so-called Smith factorization, which is efficiently used in the synthesis of control systems described by polynomial matrix notation. In particular, the so-called polynomial S-inverse is used, which, together with the applied degrees of freedom, creates a potential for the improvement of the operation of wireless data communications systems comprising different numbers of inputs/antennas and outputs/antennas. Simulations performed in the Matlab environment indicate the practical applicability of the proposed solution.

Perfect reconstruction of signal—a new polynomial matrix inverse approach