Dimension of channel matrix elements in MIMO systems
Sorry, I'm starting again.
$\mathbf{H(t,\tau)}=(h_{ij}(t,\tau))$. 

If I have $\mathbf{H}(t,\tau)=\mathbf{H(\tau)}$ and $N_t=1$ then $\mathbf{H}(\tau) \in \mathbb{C}^{N_r \times 1}$