The SIMO Block Rayleigh Fading Channel Capacity Scaling with Number of Antennas, Bandwidth and Coherence Length
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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 Θ(min(B,√(NL),N)). This is achievable using Pilot-Assisted signaling. Energy Modulation signaling rate scales as Θ(min(B,√(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 Θ(min(B,N)). The coherent channel capacity scaling can be fully achieved in non-coherent channels when L≥Θ(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≪Θ(√(N))), Energy Modulation is effective in non-coherent channels.
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