Problem with Convolution in MIMO System
I think it should be:

$$ \boldsymbol{y}_{i} = {H}_{i} \boldsymbol{x} + \boldsymbol{n}_{i} $$

For the $ i $ -th antenna and $ {H}_{i} $ being the convolution matrix of this specific channel.
You could write this in a Matrix Form where $ H $ becomes a tensor.
In case $ \forall i, j, \; {H}_{i} = {H}_{j} $ then it can be made simpler.

You could also work on the samples:

$$ \boldsymbol{y} \left[ m \right] = H \left[ m \right] \boldsymbol{x} \left[ m \right] + n $$ 

Where in this case $ {y}_{i} \left[ n \right] $ is the $ i $ -th antenna at time sample $ m $ and the $ i $ -th row of $ H \left[ m \right] $ is the response of the channel $ i $ at time $ m $.
This model allows time variant channels.