Hard Delay Constrained Communications over Parallel Fading Channels

Hard delay constrained communications have attracted considerable recent attention because of their potential applications in the emerging field of deterministic networking (DetNet). However, developing techniques to satisfy both hard delay constraints and average power constraints simultaneously has long been a challenge. In this paper, we consider hard delay constrained transmissions over frequency selective wireless channels or parallel fading channels, in which the instantaneous transmission power can be adapted. A time domain power allocation scheme, also referred to as the generalized channel inversion policy is proposed. We find that the hard delay constraint can be met when the number of parallel channels with independent channel gains is greater than or equal to two. Furthermore, given a target rate, the required average power can be obtained based on the explicit outage probability as a function of the instantaneous signal-to-noise ratio (SNR). To provide further insight, we present two approximate formulas of the average power based on our derived closed-form approximations for the outage probability in the high SNR regime, and also derive upper and lower bounds on the required average power.