  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.
