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 $\Theta (\min (B,\sqrt {NL},N))$ . This is achievable using Pilot-Assisted signaling. Energy Modulation signaling rate scales as $\Theta (\min (B,\sqrt {N}))$ . 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 $\Theta (\min (B,N))$ . 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.
