Impact of dimension on causal equalization of the MIMO two-tap channel

We consider equalization of multiple-input multiple-output (MIMO) two-tap channels under a causality constraint. Due to the work of Treil it is well known, that for causal equalizers of N + 1 times N channels the stability norm can grow exponentially fast with N, while it is upper bounded independently of N for the pseudoinverse. In this paper we give a illustrative example for a two-tap channel which exhibits this effect. Monte-Carlo simulations indicate, that this behavior is exemplary for two-tap channels with a strong second tap. Based on further simulations, we observe a rule of thumb on how much antenna diversity is necessary for causal equalization in the general N + K times N case.