  We consider the allocation of spectral and power resources to the mobiles
(i.e., user equipment (UE)) in a cell every subframe (1 ms) for the Long Term
Evolution (LTE) orthogonal frequency division multiple access (OFDMA) cellular
network. To enable scheduling based on packet delays, we design a novel
mechanism for inferring the packet delays approximately from the buffer status
reports (BSR) transmitted by the UEs; the BSR reports only contain queue length
information. We then consider a constrained optimization problem with a concave
objective function - schedulers such as those based on utility maximization,
maximum weight scheduling, and recent results on iterative scheduling for small
queue/delay follow as special cases. In particular, the construction of the
non-differentiable objective function based on packet delays is novel. We model
constraints on bandwidth, peak transmit power at the UE, and the transmit power
spectral density (PSD) at the UE due to fractional power control. When
frequency diversity doesn't exist or is not exploited at a fast time-scale, we
use subgradient analysis to construct an O(N log L) (per iteration with small
number of iterations) algorithm to compute the optimal resource allocation for
N users and L points of non-differentiability in the objective function. For a
frequency diversity scheduler with M sub-bands, the corre- sponding complexity
per iteration is essentially O(N(M^2+L^2)). Unlike previous iterative policies
based on delay/queue, in our approach the complexity of scheduling can be
reduced when the coherence bandwidth is larger. Through detailed system
simulations (based on NGMN and 3GPP evaluation methodology) which model H-ARQ,
finite resource grants per sub-frame, deployment, realistic traffic, power
limitations, interference, and channel fading, we demonstrate the effectiveness
of our schemes for LTE.
