MIMO-ISI channel equalization - Which price we have to pay for causality

In the investigation of equalizers and precoders for multiple-input multiple-output systems with intersymbol interference, completely new phenomena appear if the causality of theses filters is required. Both, for transmit as well as for receive filters, the stability norm is an important performance measure which is connected to several performance criteria in communications. The paper shows that the optimal causal precoder with minimal stability norm is linear but time variant, in general. It is time invariant only if the channel is flat fading. Moreover, it is discussed that there exist causal precoders or equalizers for which the stability norm grows exponential with the minimum number of transmit and receive antennas of the MIMO system, whereas the stability norm of the optimal non-causal inverse is always independent from the dimensions of the MIMO system.