# How do we find the capacity of MIMO wideband point to point system?

This question is in the context of digital communication .

In many text books (wireless communication), when people derive the capacity of point to point communication system (one transmit one receive end) with multiple transmit and multiple receive antennas, people consider the narrow band flat fading channel. Below I write down the output equation of system with $N$ transmit antennas and $M$ receive antennas

$${\bf Y_{M\times 1} = H_{M\times N}X_{ N\times 1}+ Z_{M\times 1}}$$

The solution to find the maximum capacity is to do Singular Value Decomposition (SVD) of the channel as follows

$${\bf H = U D V^H}$$

The transmitter uses matrix ${\bf V}$ that is the transmit signal is $${\bf X'= VX}$$ while the receiver uses matrix ${\bf U}$ as follows

$${\bf Y'= U^HY}$$

My question is what about wideband channels, time varying frequency selective channels that is systems with channel such as

$${\bf H_{M\times N}(t)} \,\,\,\,\,\, t =0... T_{Delay}$$

How do we find the MIMO capacity of such channels. In one case, I think once can assume multicarrier (OFDM) system and divide the wideband channel into smaller narrow band and apply the algorithm I mentioned above. But what if its not multicarrier system? What is the optimal scheme, what should the transmitter and receiver do?