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Escaping the Densification Plateau in Cellular Networks Through mmWave Beamforming

We study how dense multi-antenna millimeter wave (mmWave) cellular network performance scales in terms of the base station (BS) spatial density $λ$, by studying the signal-to-interference-plus-noise ratio (SINR) and the area spectral efficiency (ASE). If the number of antennas at each BS scales at least linearly with $λ$, which increases the number of possible beam configurations and their main-lobe gain, and decreases their side-lobe gain, we prove that the SINR approaches a finite random variable that is independent of $λ$ and the ASE scales at least linearly with $λ$. In contrast, if the number of antennas scales sub-linearly with $λ$, then the SINR decays to zero and the ASE saturates to a constant. Thus, by moving to higher carrier frequencies with successively smaller antennas, and exploiting the correspondingly increased directionality, cellular operators can in principle avoid the densification plateau (or collapse) in cellular networks and instead continue to harvest linear sum throughput gains through BS densification.