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Sufficient condition for invertibility of square FIR MIMO systems

: Wahls, S.; Boche, H.


Douglas, S.C. ; IEEE Signal Processing Society:
IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2010. Proceedings. Vol.5 : 14-19 March 2010, Dallas, Texas, USA
Piscataway/NJ: IEEE, 2010
ISBN: 978-1-4244-4295-9
ISBN: 978-1-4244-4296-6
International Conference on Acoustics, Speech and Signal Processing (ICASSP) <35, 2010, Dallas/Tex.>
Conference Paper
Fraunhofer HHI ()

We derive a sufficient condition for a square FIR MIMO system to have a causal and stable IIR inverse. The condition requires that the spectral norm of the normalized channel impulse response (i.e., the first tap is the identity matrix) is below a certain bound. Intuitively, this means that the system has a strong first tap. This condition often is easier to check than the usual minimum-phaseness, where the roots of the systems determinant have to be computed. Simple approximations of the bound are found. Furthermore, we also give a negative result: the Wiener Filter, which approximates the inverse under low noise conditions, nevertheless always is non-causal. We apply our results to two inversion problems with causality and stability constraint. These problems arise in oversampled noise-shaping subband coding and residual interference cancellation in precoded systems, respectively.