Energy Minimization of a QAM System

In this paper, an energy minimization problem for a quadrature amplitude modulation (QAM) system with automatic repeat request (ARQ) is considered. We formulate an optimization problem with constellation size and transmit power as the variables. We give an efficient and accurate geometric programming (GP) approximation to the problem and illustrate the solution using a numerical example. We learn that the transmit power or equivalently bit error rate (BER) should be carefully chosen for minimal energy. Our analysis provides guidelines for setting the BER in an energy optimal way for various packet lengths.