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

TL;DR

This paper analyzes how the capacity of non-coherent SIMO Rayleigh fading channels scales with bandwidth, antennas, and coherence length, revealing the importance of coherence length in modulation choice and capacity limits.

Contribution

It provides a detailed capacity scaling analysis for non-coherent SIMO Rayleigh channels, highlighting the role of coherence length and comparing Pilot-Assisted and Energy Modulation strategies.

Findings

Capacity scales as min(B, sqrt(NL), N) in non-coherent channels.

Energy Modulation scales as min(B, sqrt(N)), but does not match capacity scaling with L.

Coherent capacity scales as min(B, N), achievable in non-coherent channels when L ≥ Θ(N).

Abstract

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.