Approximate closed-form power allocation scheme for multiple-input–multiple-output hybrid automatic repeat request protocols over Rayleigh block fading channels

In this study, the outage-limited optimal power allocation problem for hybrid automatic repeat request (HARQ) protocol over multiple-input-multiple-output (MIMO) block Rayleigh fading channels is addressed. Considering three typical HARQ protocols, the authors first derive the approximate outage probabilities of the MIMO HARQ protocols at the high signal-to-noise ratio region. On the basis of the approximations, they then formulate an optimisation problem of minimising the average total power usage with the constraints of the targeted outage probability and the maximum number of transmission rounds. A closed-form optimal power sequence is obtained by solving the outage-limited optimisation problem. Applying the solutions, the monotonicity of the optimal power sequence is further investigated. It is found that the optimal power sequence is monotonically increasing when the targeted outage probability is smaller than a threshold. They also study the impacts of the system parameters on the optimal power sequence and the power allocation gain under various conditions. Finally, the numerical and simulation results are presented to verify the theoretical derivation.