Latency-Optimal Uplink Scheduling Policy in Training-based Large-Scale Antenna Systems

In this paper, an uplink scheduling policy problem to minimize the network latency, defined as the air-time to serve all of users with a quality-of-service (QoS), under an energy constraint is considered in a training-based large-scale antenna systems (LSAS) employing a simple linear receiver. An optimal algorithm providing the exact latency-optimal uplink scheduling policy is proposed with a polynomial-time complexity. Via numerical simulations, it is shown that the proposed scheduling policy can provide several times lower network latency over the conventional ones in realistic environments. In addition, the proposed scheduling policy and its network latency are analyzed asymptotically to provide better insights on the system behavior. Four operating regimes are classified according to the average received signal quality, $\rho$, and the number of BS antennas, $M$. It turns out that orthogonal pilots are optimal only in the regime $\rho\gg1$ and $M\ll \log^2\rho$. In other regimes ($\rho\ll 1$ or $M\gg \log^2\rho$), it turns out that non-orthogonal pilots become optimal. More rigorously, the use of non-orthogonal pilots can reduce the network latency by a factor of $\Theta(M)$ when $\rho\ll 1$ or by a factor of $\Theta(\sqrt{M}/\log M)$ when $\rho\gg 1$ and $M\gg \log\rho$, which would be a critical guideline for designing 5G future cellular systems.