  This work investigates the energy-efficient resource allocation for
layered-division multiplexing (LDM) based non-orthogonal multicast and unicast
transmission in cell-free massive multiple-input multiple-output (MIMO)
systems, where each user equipment (UE) performs wireless information and power
transfer simultaneously. To begin with, the achievable data rates for multicast
and unicast services are derived in closed form, as well as the received radio
frequency (RF) power at each UE. Based on the analytical results, a nonsmooth
and nonconvex optimization problem for energy efficiency (EE) maximization is
formulated, which is however a challenging fractional programming problem with
complex constraints. To suit the massive access setting, a first-order
algorithm is developed to find both initial feasible point and the nearly
optimal solution. Moreover, an accelerated algorithm is designed to improve the
convergence speed. Numerical results demonstrate that the proposed first-order
algorithms can achieve almost the same EE as that of second-order approaches
yet with much lower computational complexity, which provides insight into the
superiority of the proposed algorithms for massive access in cell-free massive
MIMO systems.
