Capacity Scaling of Single-source Wireless Networks: Effect of Multiple Antennas

We consider a wireless network in which a single source node located at the center of a unit area having $m$ antennas transmits messages to $n$ randomly located destination nodes in the same area having a single antenna each. To achieve the sum-rate proportional to $m$ by transmit beamforming, channel state information (CSI) is essentially required at the transmitter (CSIT), which is hard to obtain in practice because of the time-varying nature of the channels and feedback overhead. We show that, even without CSIT, the achievable sum-rate scales as $\Theta(m\log m)$ if a cooperation between receivers is allowed. By deriving the cut-set upper bound, we also show that $\Theta(m\log m)$ scaling is optimal. Specifically, for $n=\omega(m^2)$, the simple TDMA-based quantize-and-forward is enough to achieve the capacity scaling. For $n=\omega(m)$ and $n=\operatorname{O}(m^2)$, on the other hand, we apply the hierarchical cooperation to achieve the capacity scaling.