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

• Published in: IEEE journal on selected areas in information theory 2022-03, Vol.3 (1), p.54-68
• Main Author: Gomez-Cuba, Felipe
• Format: Article
• Language: English
• Subjects: Antennas; Bandwidth; Bandwidths; Channel capacity; Channel estimation; Channels; Coherence; Coherence length; energy modulation; Fading; Massive MIMO; Modulation; non-coherent channel; Receiving antennas; Scaling; Signaling; Wideband; wideband communications
• ISSN: 2641-8770; 2641-8770
• DOI: 10.1109/JSAIT.2022.3157519

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.