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MIMO SINR and area spectral efficiency scaling conjecture

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Let Nt(λ)N_t(\lambda) and Nr(λ)N_r(\lambda) be the numbers of transmit and receive antennas, respectively, with

lim⁡λ→∞Nr(λ)Nt(λ)=y∈[0,1].\lim\limits_{\lambda \rightarrow \infty}\frac{N_r(\lambda)}{N_t(\lambda)}=y\in [0,1].

Consider eigenbeamforming with a single data stream and a physically feasible path loss model satisfying the requirements in Assumption 1. MIMO scaling conjecture. The average SINR scales as

Nt(λ)λ,\frac{N_t(\lambda)}{\lambda},

and the average area spectral efficiency scales as

λlog⁡(1+Nt(λ)λ).\lambda\log\left(1+\frac{N_t(\lambda)}{\lambda}\right).

The preceding bounds establish only that the average SINR lies between the corresponding MISO scaling laws with Nt(λ)N_t(\lambda) and Nt(λ)Nr(λ)N_t(\lambda)N_r(\lambda) antennas, and similarly bound the average area spectral efficiency. Simulations in the stated setting suggest that the lower-bound scaling is the exact one, but the parser provides no evidence that this claim has been proved or resolved.

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  1. MIMO SINR and area spectral efficiency scaling conjecture

    Let Nt(λ)N_t(\lambda) and Nr(λ)N_r(\lambda) denote the numbers of transmit and receive antennas, respectively, and suppose

    lim⁡λ→∞Nr(λ)Nt(λ)=y∈[0,1].\lim\limits_{\lambda \rightarrow \infty}\frac{N_r(\lambda)}{N_t(\lambda)}=y\in [0,1].

    Consider eigenbeamforming with a single data stream and a physically feasible path loss model satisfying the requirements in Assumption 1. MIMO SINR and ASE scaling conjecture. The average SINR scales as Nt(λ)λ\frac{N_t(\lambda)}{\lambda} and the average ASE scales as λlog⁡(1+Nt(λ)λ)\lambda\log\left(1+\frac{N_t(\lambda)}{\lambda}\right). This conjecture is motivated by the reported simulation results, which show the average SINR following the lower-bound scaling and the average ASE growing linearly with the BS density in the examined setting; no resolution is supplied.

    source: Ahmad AlAmmouri, Jeffrey G. Andrews and Francois Baccelli, “Area Spectral Efficiency and SINR Scaling Laws in Multi-Antenna Cellular Networks”, arXiv:2002.04118 (2020).

References

Primary source

Ahmad AlAmmouri, Jeffrey G. Andrews and Francois Baccelli, “Scaling Laws of Dense Multi-Antenna Cellular Networks”, arXiv:2001.05083 (2020).

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