Optimal power allocation over fading channels with stringent delay constraints

We study the optimal power allocation scheme for i.i.d. block-fading channels with a strict transmission delay constraint. In particular, we consider the maximization of the total throughput within a finite interval under a short-term average power constraint. When all the channel gains are known a priori, we demonstrate the mapping between the delay-constrained channel and the corresponding parallel channel for which both the single-user and multi-user channel results are well-known. The maximization problem becomes more complicated when only causal channel side information (CSI) is available. We show that under this assumption, constant power transmission is optimal in the limit of high signal-to-noise ratio (SNR). We also examine the optimal power policy and show that a simple linear power control scheme has near optimal performance. We next consider a two-user broadcast channel with a stringent delay constraint and causal feedback. We solve the optimal power control problem for this channel via dynamic programming. We discuss the solutions in the limit of both low and high SNR. Numerical results show the optimal scheme is approximately piecewise linear for general SNRs.