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

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.