Binary Power Optimality for Two Link Full-Duplex Network

In this paper, we analyse the optimality of binary power allocation in a network that includes full-duplex communication links. Considering a network with four communicating nodes, two of them operating in half-duplex mode and the other two in full-duplex mode, we prove that binary power allocation is optimum for the full-duplex nodes when maximizing the sum rate. We also prove that, for half-duplex nodes binary power allocation is not optimum in general. However, for the two special cases, 1) the low signal-to-noise-plus-interference (SINR) regime and, 2) the approximation by the arithmetic mean-geometric mean inequality, binary power allocation is optimum for the approximated sum rate even for the half-duplex nodes. We further analyse a third special case using a symmetric network for which the optimum power allocation is binary, under a sufficient condition. Numerical examples are included to illustrate the accuracy of the results.