A Different Approach to Finding the Capacity of a Gaussian Vector Channel

The paper considers a Gaussian multiple-input multiple-output (MIMO) discretetime vector channel with memory. The problem is to find the capacity of such a channel. It is known that the capacity of Gaussian vector channels with memory was given in [1]. In the present paper, we show a different approach, which uses another definition of the capacity. For a channel with $n=2$ inputs and outputs, this approach gives an expression for the capacity which is different from that in [1]. The paper shows what the dependence of input signal components should be to give this capacity. A multidimensional water-filling interpretation works for the optimum vector input signal power distribution but cannot work for the description of the input component dependences. For the case of $n\geqslant3$ inputs and outputs, we give a lower bound on the channel capacity.