On the Energy Delay Tradeoff of HARQ-IR in Wireless Multiuser Systems

Energy delay tradeoff (EDT) is a fundamental tradeoff that plays a crucial role in understanding the energy efficiency of various transmission schemes. In particular, for hybrid automatic repeat request (HARQ) protocols, the EDT can be well defined. In this paper, in order to understand the EDT for a wireless multiuser system, we consider various downlink transmission schemes where the HARQ with incremental redundancy (HARQ-IR) protocol is employed for reliable transmissions to users. For a given total power, the impact of different transmission schemes in conjunction with power allocation on EDT is extensively studied. Among the transmission schemes, it is shown that the threshold-based transmission (TBT) scheme efficiently lowers the minimum energy per bit (EB) in spite of limited prior channel state information (CSI) feedback. The study is further extended to a more plausible scenario where users have different channel statistics. In doing so, we consider a proportional fairness scheduling based on relative channel gain that can be easily accommodated in the proposed TBT scheme, and study its EDT behaviors. Performance evaluations show that the schemes incorporating proportional fairness achieve good EDT performances while guaranteeing the fairness among users.