  Massive multiple-input multiple-output (MIMO) precoders are typically
designed by minimizing the transmit power subject to a quality-of-service (QoS)
constraint. However, current sustainability goals incentivize more
energy-efficient solutions and thus it is of paramount importance to minimize
the consumed power directly. Minimizing the consumed power of the power
amplifier (PA), one of the most consuming components, gives rise to a convex,
non-differentiable optimization problem, which has been solved in the past
using conventional convex solvers. Additionally, this problem can be solved
using a proximal gradient descent (PGD) algorithm, which suffers from slow
convergence. In this work, to overcome the slow convergence, a deep unfolded
version of the algorithm is proposed, which can achieve close-to-optimal
solutions in only 20 iterations compared to the 3500 plus iterations needed by
the PGD algorithm. Results indicate that the deep unfolding algorithm is three
orders of magnitude faster than a conventional convex solver and four orders of
magnitude faster than the PGD.
