Power Efficient Ultra-Reliable Communication for Rayleigh faded IR-HARQ systems

In this paper, we derive closed-form expressions for the retransmit powers to achieve ultra-reliable communication for a communication system that utilizes the IR-HARQ protocol. The Transmitter-Receiver system under consideration is situated within a cell which is considered to be a Rayleigh fading channel. We formulate the power allocation problem for the case of two retransmissions as a minimization of the average retransmit power under the constraint of a given target outage probability. We use the Karush-Kuhn-Tucker method to solve the optimization problem and obtain closed-form solutions for the two retransmissions. We show through simulations that the power values from the closed-form expressions for a given outage probability in the ultra-reliable region are much lesser compared to the open-loop power values. Further, we perform a throughput analysis and show that the overall throughput reduces when the number of retransmissions increases.