Timely-Throughput Optimal Scheduling With Delayed CSIT for Chase Combining HARQ

Abstract

We consider a cross-layer packet scheduling problem with hybrid ARQ (HARQ) in fading channels in which the channel state information at the transmitter (CSIT) is known only after one slot delay. Packets arrive according to a Bernoulli process at the transmitter, and each packet is required to be timely-delivered at the receiver, within a delay of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$d$</tex-math></inline-formula> time-slots, and is dropped, if the delay deadline is not met. Since the transmitter has only a delayed CSIT, a HARQ with Chase combining is employed for error recovery. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">The problem is to decide the transmit-energy in each time-slot such that the timely-throughput is maximum for a given average transmit-energy constraint.</i> We pose this problem as a constrained Markov decision process, and provide an optimum policy based on Lagrangian relaxation. The optimum Lagrangian multiplier is obtained using a subgradient method. We obtain the structure of the optimum policy, based on which we propose a computationally simple policy READER that requires no CSIT. We show that for large Doppler spread (or mobility), the timely-throughput of READER is close to the optimum policy. We also provide two more policies: an optimum policy assuming perfect CSIT with zero delay, and a naive randomization policy, and compare the throughput performance of the proposed policies.