MIMO SINR and area spectral efficiency scaling conjecture

Equivalent formulations 1

Other statements of this same problem, merged from separate entries. Each is equivalent to the statement above — proving any one settles them all.

1. MIMO SINR and area spectral efficiency scaling conjecture

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

   $$\lim\limits_{\lambda \rightarrow \infty}\frac{N_r(\lambda)}{N_t(\lambda)}=y\in [0,1].$$

   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 $\frac{N_t(\lambda)}{\lambda}$ and the average ASE scales as $\lambda\log\left(1+\frac{N_t(\lambda)}{\lambda}\right)$. 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).