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This paper studies the capacity scaling of non-coherent Single-InputMultiple-Output (SIMO) independent and identically distributed (i.i.d.)Rayleigh block fading channels versus bandwidth ($B$), number of receiveantennas ($N$) 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 usingPilot-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 capacityscaling. However, Energy Modulation rate does not scale as the capacity withthe variable $L$. The coherent channel capacity with a priori CSI, in turn,scales as $\Theta\left(\min(B,N)\right)$. The coherent channel capacity scalingcan be fully achieved in non-coherent channels when $L\geq\Theta(N)$. Insummary, the channel coherence block length plays a pivotal role in modulationselection and the capacity gap between coherent and non-coherent channels.Pilot-Assisted signaling outperforms Energy Modulation's rate scaling versuscoherence block length. Only in high mobility scenarios where $L$ is muchsmaller than the number of antennas ($L\ll\Theta(\sqrt{N})$), Energy Modulationis effective in non-coherent channels.

The SIMO Block Rayleigh Fading Channel Capacity Scaling with Number of Antennas, Bandwidth and Coherence Length