  This paper studies the capacity scaling of non-coherent Single-Input
Multiple-Output (SIMO) independent and identically distributed (i.i.d.)
Rayleigh block fading channels versus bandwidth ($B$), number of receive
antennas ($N$) and coherence block length ($L$). In non-coherent channels
(without Channel State Information --CSI) capacity scales as
$\Theta\left(\min(B,\sqrt{NL},N)\right)$. This is achievable using
Pilot-Assisted signaling. Energy Modulation signaling rate scales as
$\Theta\left(\min(B,\sqrt{N})\right)$. If $L$ is fixed while $B$ and $N$ grow,
the two expressions grow equally and Energy Modulation achieves the capacity
scaling. However, Energy Modulation rate does not scale as the capacity with
the variable $L$. The coherent channel capacity with a priori CSI, in turn,
scales as $\Theta\left(\min(B,N)\right)$. The coherent channel capacity scaling
can be fully achieved in non-coherent channels when $L\geq\Theta(N)$. In
summary, the channel coherence block length plays a pivotal role in modulation
selection and the capacity gap between coherent and non-coherent channels.
Pilot-Assisted signaling outperforms Energy Modulation's rate scaling versus
coherence block length. Only in high mobility scenarios where $L$ is much
smaller than the number of antennas ($L\ll\Theta(\sqrt{N})$), Energy Modulation
is effective in non-coherent channels.
