Power Adaptive HARQ for Ultrareliability via a Novel Outage Probability Bound

Hybrid automatic repeat request (HARQ) is a key enabler for the extremely strict reliability requirements as imposed in future networks. This paper studies power control for HARQ in order to minimize the expected energy consumption of wireless transmission given the outage probability constraint and the maximum average number of retransmissions. The main difficulty in solving the above power control problem is due to the fact that the outage probability cannot be expressed analytically in terms of the power variables. Prior works have suggested using a classic upper bound on the outage probability by assuming unbounded transmit powers throughout HARQ, thus approximating the power control problem in a geometric programming (GP) form. In contrast, this work proposes a novel and much tighter upper bound by taking practical power constraints into account. Numerical examples show that the GP method with the new upper bound outperforms one with the classic upper bound significantly. Analytical insights are also gained into the proposed GP method. Moreover, the paper extends the above results to the multi-antenna channels in which antenna diversity is harnessed to further enhance reliability.